Modular group algebras of finite representation type

Counting the groups of finite representation type of order 2 = [ 2 ]

Counting the groups of finite representation type of order 3 = [ 3 ]

Counting the groups of finite representation type of order 4 = [ 2, 2 ]
Checking it in characteristic 2
  C4
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 5 = [ 5 ]

Counting the groups of finite representation type of order 6 = [ 2, 3 ]

Counting the groups of finite representation type of order 7 = [ 7 ]

Counting the groups of finite representation type of order 8 = [ 2, 2, 2 ]
Checking it in characteristic 2
  C8
  Of finite representation type:   1
  Of infinite representation type: 4

Counting the groups of finite representation type of order 9 = [ 3, 3 ]
Checking it in characteristic 3
  C9
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 10 = [ 2, 5 ]

Counting the groups of finite representation type of order 11 = [ 11 ]

Counting the groups of finite representation type of order 12 = [ 2, 2, 3 ]
Checking it in characteristic 2
  C3 : C4  C12
  Of finite representation type:   2
  Of infinite representation type: 3

Counting the groups of finite representation type of order 13 = [ 13 ]

Counting the groups of finite representation type of order 14 = [ 2, 7 ]

Counting the groups of finite representation type of order 15 = [ 3, 5 ]

Counting the groups of finite representation type of order 16 = [ 2, 2, 2, 2 ]
Checking it in characteristic 2
  C16
  Of finite representation type:   1
  Of infinite representation type: 13

Counting the groups of finite representation type of order 17 = [ 17 ]

Counting the groups of finite representation type of order 18 = [ 2, 3, 3 ]
Checking it in characteristic 3
  D18  C18
  Of finite representation type:   2
  Of infinite representation type: 3

Counting the groups of finite representation type of order 19 = [ 19 ]

Counting the groups of finite representation type of order 20 = [ 2, 2, 5 ]
Checking it in characteristic 2
  C5 : C4  C20  C5 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 21 = [ 3, 7 ]

Counting the groups of finite representation type of order 22 = [ 2, 11 ]

Counting the groups of finite representation type of order 23 = [ 23 ]

Counting the groups of finite representation type of order 24 = [ 2, 2, 2, 3 ]
Checking it in characteristic 2
  C3 : C8  C24
  Of finite representation type:   2
  Of infinite representation type: 13

Counting the groups of finite representation type of order 25 = [ 5, 5 ]
Checking it in characteristic 5
  C25
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 26 = [ 2, 13 ]

Counting the groups of finite representation type of order 27 = [ 3, 3, 3 ]
Checking it in characteristic 3
  C27
  Of finite representation type:   1
  Of infinite representation type: 4

Counting the groups of finite representation type of order 28 = [ 2, 2, 7 ]
Checking it in characteristic 2
  C7 : C4  C28
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 29 = [ 29 ]

Counting the groups of finite representation type of order 30 = [ 2, 3, 5 ]

Counting the groups of finite representation type of order 31 = [ 31 ]

Counting the groups of finite representation type of order 32 = [ 2, 2, 2, 2, 2 ]
Checking it in characteristic 2
  C32
  Of finite representation type:   1
  Of infinite representation type: 50

Counting the groups of finite representation type of order 33 = [ 3, 11 ]

Counting the groups of finite representation type of order 34 = [ 2, 17 ]

Counting the groups of finite representation type of order 35 = [ 5, 7 ]

Counting the groups of finite representation type of order 36 = [ 2, 2, 3, 3 ]
Checking it in characteristic 2
  C9 : C4  C36  C3 x (C3 : C4)  (C3 x C3) : C4  C12 x C3  (C3 x C3) : C4
  Of finite representation type:   6
  Of infinite representation type: 8
Checking it in characteristic 3
  C9 : C4  C36  (C2 x C2) : C9  D36  C18 x C2
  Of finite representation type:   5
  Of infinite representation type: 9

Counting the groups of finite representation type of order 37 = [ 37 ]

Counting the groups of finite representation type of order 38 = [ 2, 19 ]

Counting the groups of finite representation type of order 39 = [ 3, 13 ]

Counting the groups of finite representation type of order 40 = [ 2, 2, 2, 5 ]
Checking it in characteristic 2
  C5 : C8  C40  C5 : C8
  Of finite representation type:   3
  Of infinite representation type: 11

Counting the groups of finite representation type of order 41 = [ 41 ]

Counting the groups of finite representation type of order 42 = [ 2, 3, 7 ]

Counting the groups of finite representation type of order 43 = [ 43 ]

Counting the groups of finite representation type of order 44 = [ 2, 2, 11 ]
Checking it in characteristic 2
  C11 : C4  C44
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 45 = [ 3, 3, 5 ]
Checking it in characteristic 3
  C45
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 46 = [ 2, 23 ]

Counting the groups of finite representation type of order 47 = [ 47 ]

Counting the groups of finite representation type of order 48 = [ 2, 2, 2, 2, 3 ]
Checking it in characteristic 2
  C3 : C16  C48
  Of finite representation type:   2
  Of infinite representation type: 50

Counting the groups of finite representation type of order 49 = [ 7, 7 ]
Checking it in characteristic 7
  C49
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 50 = [ 2, 5, 5 ]
Checking it in characteristic 5
  D50  C50
  Of finite representation type:   2
  Of infinite representation type: 3

Counting the groups of finite representation type of order 51 = [ 3, 17 ]

Counting the groups of finite representation type of order 52 = [ 2, 2, 13 ]
Checking it in characteristic 2
  C13 : C4  C52  C13 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 53 = [ 53 ]

Counting the groups of finite representation type of order 54 = [ 2, 3, 3, 3 ]
Checking it in characteristic 3
  D54  C54
  Of finite representation type:   2
  Of infinite representation type: 13

Counting the groups of finite representation type of order 55 = [ 5, 11 ]

Counting the groups of finite representation type of order 56 = [ 2, 2, 2, 7 ]
Checking it in characteristic 2
  C7 : C8  C56
  Of finite representation type:   2
  Of infinite representation type: 11

Counting the groups of finite representation type of order 57 = [ 3, 19 ]

Counting the groups of finite representation type of order 58 = [ 2, 29 ]

Counting the groups of finite representation type of order 59 = [ 59 ]

Counting the groups of finite representation type of order 60 = [ 2, 2, 3, 5 ]
Checking it in characteristic 2
  C5 x (C3 : C4)  C3 x (C5 : C4)  C15 : C4  C60  C3 x (C5 : C4)  C15 : C4
  Of finite representation type:   6
  Of infinite representation type: 7

Counting the groups of finite representation type of order 61 = [ 61 ]

Counting the groups of finite representation type of order 62 = [ 2, 31 ]

Counting the groups of finite representation type of order 63 = [ 3, 3, 7 ]
Checking it in characteristic 3
  C7 : C9  C63
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 64 = [ 2, 2, 2, 2, 2, 2 ]
Checking it in characteristic 2
  C64
  Of finite representation type:   1
  Of infinite representation type: 266

Counting the groups of finite representation type of order 65 = [ 5, 13 ]

Counting the groups of finite representation type of order 66 = [ 2, 3, 11 ]

Counting the groups of finite representation type of order 67 = [ 67 ]

Counting the groups of finite representation type of order 68 = [ 2, 2, 17 ]
Checking it in characteristic 2
  C17 : C4  C68  C17 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 69 = [ 3, 23 ]

Counting the groups of finite representation type of order 70 = [ 2, 5, 7 ]

Counting the groups of finite representation type of order 71 = [ 71 ]

Counting the groups of finite representation type of order 72 = [ 2, 2, 2, 3, 3 ]
Checking it in characteristic 2
  C9 : C8  C72  C3 x (C3 : C8)  (C3 x C3) : C8  C24 x C3  (C3 x C3) : C8  (C3 x C3) : C8
  Of finite representation type:   7
  Of infinite representation type: 43
Checking it in characteristic 3
  C9 : C8  C72  Q8 : C9  C9 : Q8  C4 x D18  D72  C2 x (C9 : C4)  (C18 x C2) : C2  C36 x C2  C9 x D8  C9 x Q8  ((C2 x C2) : C9) : C2  C2 x ((C2 x C2) : C9)  C2 x C2 x D18  C18 x C2 x C2
  Of finite representation type:   15
  Of infinite representation type: 35

Counting the groups of finite representation type of order 73 = [ 73 ]

Counting the groups of finite representation type of order 74 = [ 2, 37 ]

Counting the groups of finite representation type of order 75 = [ 3, 5, 5 ]
Checking it in characteristic 5
  C75
  Of finite representation type:   1
  Of infinite representation type: 2

Counting the groups of finite representation type of order 76 = [ 2, 2, 19 ]
Checking it in characteristic 2
  C19 : C4  C76
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 77 = [ 7, 11 ]

Counting the groups of finite representation type of order 78 = [ 2, 3, 13 ]

Counting the groups of finite representation type of order 79 = [ 79 ]

Counting the groups of finite representation type of order 80 = [ 2, 2, 2, 2, 5 ]
Checking it in characteristic 2
  C5 : C16  C80  C5 : C16
  Of finite representation type:   3
  Of infinite representation type: 49

Counting the groups of finite representation type of order 81 = [ 3, 3, 3, 3 ]
Checking it in characteristic 3
  C81
  Of finite representation type:   1
  Of infinite representation type: 14

Counting the groups of finite representation type of order 82 = [ 2, 41 ]

Counting the groups of finite representation type of order 83 = [ 83 ]

Counting the groups of finite representation type of order 84 = [ 2, 2, 3, 7 ]
Checking it in characteristic 2
  (C7 : C4) : C3  C4 x (C7 : C3)  C7 x (C3 : C4)  C3 x (C7 : C4)  C21 : C4  C84
  Of finite representation type:   6
  Of infinite representation type: 9

Counting the groups of finite representation type of order 85 = [ 5, 17 ]

Counting the groups of finite representation type of order 86 = [ 2, 43 ]

Counting the groups of finite representation type of order 87 = [ 3, 29 ]

Counting the groups of finite representation type of order 88 = [ 2, 2, 2, 11 ]
Checking it in characteristic 2
  C11 : C8  C88
  Of finite representation type:   2
  Of infinite representation type: 10

Counting the groups of finite representation type of order 89 = [ 89 ]

Counting the groups of finite representation type of order 90 = [ 2, 3, 3, 5 ]
Checking it in characteristic 3
  C5 x D18  C9 x D10  D90  C90
  Of finite representation type:   4
  Of infinite representation type: 6

Counting the groups of finite representation type of order 91 = [ 7, 13 ]

Counting the groups of finite representation type of order 92 = [ 2, 2, 23 ]
Checking it in characteristic 2
  C23 : C4  C92
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 93 = [ 3, 31 ]

Counting the groups of finite representation type of order 94 = [ 2, 47 ]

Counting the groups of finite representation type of order 95 = [ 5, 19 ]

Counting the groups of finite representation type of order 96 = [ 2, 2, 2, 2, 2, 3 ]
Checking it in characteristic 2
  C3 : C32  C96
  Of finite representation type:   2
  Of infinite representation type: 229

Counting the groups of finite representation type of order 97 = [ 97 ]

Counting the groups of finite representation type of order 98 = [ 2, 7, 7 ]
Checking it in characteristic 7
  D98  C98
  Of finite representation type:   2
  Of infinite representation type: 3

Counting the groups of finite representation type of order 99 = [ 3, 3, 11 ]
Checking it in characteristic 3
  C99
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 100 = [ 2, 2, 5, 5 ]
Checking it in characteristic 2
  C25 : C4  C100  C25 : C4  C5 x (C5 : C4)  (C5 x C5) : C4  C20 x C5  C5 x (C5 : C4)  (C5 x C5) : C4  (C5 x C5) : C4  (C5 x C5) : C4
  Of finite representation type:   10
  Of infinite representation type: 6
Checking it in characteristic 5
  C25 : C4  C100  C25 : C4  D100  C50 x C2
  Of finite representation type:   5
  Of infinite representation type: 11

Counting the groups of finite representation type of order 101 = [ 101 ]

Counting the groups of finite representation type of order 102 = [ 2, 3, 17 ]

Counting the groups of finite representation type of order 103 = [ 103 ]

Counting the groups of finite representation type of order 104 = [ 2, 2, 2, 13 ]
Checking it in characteristic 2
  C13 : C8  C104  C13 : C8
  Of finite representation type:   3
  Of infinite representation type: 11

Counting the groups of finite representation type of order 105 = [ 3, 5, 7 ]

Counting the groups of finite representation type of order 106 = [ 2, 53 ]

Counting the groups of finite representation type of order 107 = [ 107 ]

Counting the groups of finite representation type of order 108 = [ 2, 2, 3, 3, 3 ]
Checking it in characteristic 2
  C27 : C4  C108  C3 x (C9 : C4)  C9 x (C3 : C4)  ((C3 x C3) : C4) : C3  (C9 : C4) : C3  (C9 x C3) : C4  ((C3 x C3) : C3) : C4  C36 x C3  C4 x ((C3 x C3) : C3)  C4 x (C9 : C3)  ((C3 x C3) : C3) : C4  C3 x \
C3 x (C3 : C4)  C3 x ((C3 x C3) : C4)  (C3 x C3 x C3) : C4  C12 x C3 x C3  C3 x ((C3 x C3) : C4)  (C3 x C3 x C3) : C4
  Of finite representation type:   18
  Of infinite representation type: 27
Checking it in characteristic 3
  C27 : C4  C108  (C2 x C2) : C27  D108  C54 x C2
  Of finite representation type:   5
  Of infinite representation type: 40

Counting the groups of finite representation type of order 109 = [ 109 ]

Counting the groups of finite representation type of order 110 = [ 2, 5, 11 ]

Counting the groups of finite representation type of order 111 = [ 3, 37 ]

Counting the groups of finite representation type of order 112 = [ 2, 2, 2, 2, 7 ]
Checking it in characteristic 2
  C7 : C16  C112
  Of finite representation type:   2
  Of infinite representation type: 41

Counting the groups of finite representation type of order 113 = [ 113 ]

Counting the groups of finite representation type of order 114 = [ 2, 3, 19 ]

Counting the groups of finite representation type of order 115 = [ 5, 23 ]

Counting the groups of finite representation type of order 116 = [ 2, 2, 29 ]
Checking it in characteristic 2
  C29 : C4  C116  C29 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 117 = [ 3, 3, 13 ]
Checking it in characteristic 3
  C13 : C9  C117
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 118 = [ 2, 59 ]

Counting the groups of finite representation type of order 119 = [ 7, 17 ]

Counting the groups of finite representation type of order 120 = [ 2, 2, 2, 3, 5 ]
Checking it in characteristic 2
  C5 x (C3 : C8)  C3 x (C5 : C8)  C15 : C8  C120  C3 x (C5 : C8)  C15 : C8
  Of finite representation type:   6
  Of infinite representation type: 41

Counting the groups of finite representation type of order 121 = [ 11, 11 ]
Checking it in characteristic 11
  C121
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 122 = [ 2, 61 ]

Counting the groups of finite representation type of order 123 = [ 3, 41 ]

Counting the groups of finite representation type of order 124 = [ 2, 2, 31 ]
Checking it in characteristic 2
  C31 : C4  C124
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 125 = [ 5, 5, 5 ]
Checking it in characteristic 5
  C125
  Of finite representation type:   1
  Of infinite representation type: 4

Counting the groups of finite representation type of order 126 = [ 2, 3, 3, 7 ]
Checking it in characteristic 3
  (C7 : C9) : C2  C2 x (C7 : C9)  C7 x D18  C9 x D14  D126  C126
  Of finite representation type:   6
  Of infinite representation type: 10

Counting the groups of finite representation type of order 127 = [ 127 ]

Counting the groups of finite representation type of order 128 = [ 2, 2, 2, 2, 2, 2, 2 ]
Checking it in characteristic 2
  C128
  Of finite representation type:   1
  Of infinite representation type: 2327

Counting the groups of finite representation type of order 129 = [ 3, 43 ]

Counting the groups of finite representation type of order 130 = [ 2, 5, 13 ]

Counting the groups of finite representation type of order 131 = [ 131 ]

Counting the groups of finite representation type of order 132 = [ 2, 2, 3, 11 ]
Checking it in characteristic 2
  C11 x (C3 : C4)  C3 x (C11 : C4)  C33 : C4  C132
  Of finite representation type:   4
  Of infinite representation type: 6

Counting the groups of finite representation type of order 133 = [ 7, 19 ]

Counting the groups of finite representation type of order 134 = [ 2, 67 ]

Counting the groups of finite representation type of order 135 = [ 3, 3, 3, 5 ]
Checking it in characteristic 3
  C135
  Of finite representation type:   1
  Of infinite representation type: 4

Counting the groups of finite representation type of order 136 = [ 2, 2, 2, 17 ]
Checking it in characteristic 2
  C17 : C8  C136  C17 : C8  C17 : C8
  Of finite representation type:   4
  Of infinite representation type: 11

Counting the groups of finite representation type of order 137 = [ 137 ]

Counting the groups of finite representation type of order 138 = [ 2, 3, 23 ]

Counting the groups of finite representation type of order 139 = [ 139 ]

Counting the groups of finite representation type of order 140 = [ 2, 2, 5, 7 ]
Checking it in characteristic 2
  C7 x (C5 : C4)  C5 x (C7 : C4)  C35 : C4  C140  C7 x (C5 : C4)  C35 : C4
  Of finite representation type:   6
  Of infinite representation type: 5

Counting the groups of finite representation type of order 141 = [ 3, 47 ]

Counting the groups of finite representation type of order 142 = [ 2, 71 ]

Counting the groups of finite representation type of order 143 = [ 11, 13 ]

Counting the groups of finite representation type of order 144 = [ 2, 2, 2, 2, 3, 3 ]
Checking it in characteristic 2
  C9 : C16  C144  C3 x (C3 : C16)  (C3 x C3) : C16  C48 x C3  (C3 x C3) : C16  (C3 x C3) : C16
  Of finite representation type:   7
  Of infinite representation type: 190
Checking it in characteristic 3
  C9 : C16  C144  (C4 x C4) : C9  C9 : Q16  C8 x D18  C72 : C2  C72 : C2  D144  C2 x (C9 : C8)  (C9 : C8) : C2  C4 x (C9 : C4)  (C9 : C4) : C4  C36 : C4  (C36 x C2) : C2  (C9 : Q8) : C2  (C9 x D8) : C2  C9\
 : Q16  (C9 x Q8) : C2  (C2 x (C9 : C4)) : C2  C36 x C4  C9 x ((C4 x C2) : C2)  C9 x (C4 : C4)  C72 x C2  C9 x (C8 : C2)  C9 x D16  C9 x QD16  C9 x Q16  C2 . (((C2 x C2) : C9) : C2) = (Q8 : C9) . C2  (Q8 :\
 C9) : C2  ((C2 x C2) : C9) : C4  C4 x ((C2 x C2) : C9)  C2 x (Q8 : C9)  (Q8 : C9) : C2  C2 x (C9 : Q8)  C2 x C4 x D18  C2 x D72  (C36 x C2) : C2  D8 x D18  (C2 x (C9 : C4)) : C2  Q8 x D18  (C4 x D18) : C2\
  C2 x C2 x (C9 : C4)  C2 x ((C18 x C2) : C2)  C36 x C2 x C2  C18 x D8  C18 x Q8  C9 x ((C4 x C2) : C2)  C2 x (((C2 x C2) : C9) : C2)  C2 x C2 x ((C2 x C2) : C9)  (C2 x C2 x C2 x C2) : C9  C2 x C2 x C2 x D\
18  C18 x C2 x C2 x C2
  Of finite representation type:   52
  Of infinite representation type: 145

Counting the groups of finite representation type of order 145 = [ 5, 29 ]

Counting the groups of finite representation type of order 146 = [ 2, 73 ]

Counting the groups of finite representation type of order 147 = [ 3, 7, 7 ]
Checking it in characteristic 7
  C49 : C3  C147
  Of finite representation type:   2
  Of infinite representation type: 4

Counting the groups of finite representation type of order 148 = [ 2, 2, 37 ]
Checking it in characteristic 2
  C37 : C4  C148  C37 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 149 = [ 149 ]

Counting the groups of finite representation type of order 150 = [ 2, 3, 5, 5 ]
Checking it in characteristic 5
  C25 x S3  C3 x D50  D150  C150
  Of finite representation type:   4
  Of infinite representation type: 9

Counting the groups of finite representation type of order 151 = [ 151 ]

Counting the groups of finite representation type of order 152 = [ 2, 2, 2, 19 ]
Checking it in characteristic 2
  C19 : C8  C152
  Of finite representation type:   2
  Of infinite representation type: 10

Counting the groups of finite representation type of order 153 = [ 3, 3, 17 ]
Checking it in characteristic 3
  C153
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 154 = [ 2, 7, 11 ]

Counting the groups of finite representation type of order 155 = [ 5, 31 ]

Counting the groups of finite representation type of order 156 = [ 2, 2, 3, 13 ]
Checking it in characteristic 2
  (C13 : C4) : C3  C4 x (C13 : C3)  C13 x (C3 : C4)  C3 x (C13 : C4)  C39 : C4  C156  (C13 : C4) : C3  C3 x (C13 : C4)  C39 : C4
  Of finite representation type:   9
  Of infinite representation type: 9

Counting the groups of finite representation type of order 157 = [ 157 ]

Counting the groups of finite representation type of order 158 = [ 2, 79 ]

Counting the groups of finite representation type of order 159 = [ 3, 53 ]

Counting the groups of finite representation type of order 160 = [ 2, 2, 2, 2, 2, 5 ]
Checking it in characteristic 2
  C5 : C32  C160  C5 : C32
  Of finite representation type:   3
  Of infinite representation type: 235

Counting the groups of finite representation type of order 161 = [ 7, 23 ]

Counting the groups of finite representation type of order 162 = [ 2, 3, 3, 3, 3 ]
Checking it in characteristic 3
  D162  C162
  Of finite representation type:   2
  Of infinite representation type: 53

Counting the groups of finite representation type of order 163 = [ 163 ]

Counting the groups of finite representation type of order 164 = [ 2, 2, 41 ]
Checking it in characteristic 2
  C41 : C4  C164  C41 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 165 = [ 3, 5, 11 ]

Counting the groups of finite representation type of order 166 = [ 2, 83 ]

Counting the groups of finite representation type of order 167 = [ 167 ]

Counting the groups of finite representation type of order 168 = [ 2, 2, 2, 3, 7 ]
Checking it in characteristic 2
  (C7 : C8) : C3  C8 x (C7 : C3)  C7 x (C3 : C8)  C3 x (C7 : C8)  C21 : C8  C168
  Of finite representation type:   6
  Of infinite representation type: 51

Counting the groups of finite representation type of order 169 = [ 13, 13 ]
Checking it in characteristic 13
  C169
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 170 = [ 2, 5, 17 ]

Counting the groups of finite representation type of order 171 = [ 3, 3, 19 ]
Checking it in characteristic 3
  C19 : C9  C171  C19 : C9
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 172 = [ 2, 2, 43 ]
Checking it in characteristic 2
  C43 : C4  C172
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 173 = [ 173 ]

Counting the groups of finite representation type of order 174 = [ 2, 3, 29 ]

Counting the groups of finite representation type of order 175 = [ 5, 5, 7 ]
Checking it in characteristic 5
  C175
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 176 = [ 2, 2, 2, 2, 11 ]
Checking it in characteristic 2
  C11 : C16  C176
  Of finite representation type:   2
  Of infinite representation type: 40

Counting the groups of finite representation type of order 177 = [ 3, 59 ]

Counting the groups of finite representation type of order 178 = [ 2, 89 ]

Counting the groups of finite representation type of order 179 = [ 179 ]

Counting the groups of finite representation type of order 180 = [ 2, 2, 3, 3, 5 ]
Checking it in characteristic 2
  C5 x (C9 : C4)  C9 x (C5 : C4)  C45 : C4  C180  C9 x (C5 : C4)  C45 : C4  C3 x C3 x (C5 : C4)  C15 x (C3 : C4)  C3 x (C15 : C4)  C5 x ((C3 x C3) : C4)  (C15 x C3) : C4  C60 x C3  C3 x C3 x (C5 : C4)  C3 \
x (C15 : C4)  (C15 x C3) : C4  C5 x ((C3 x C3) : C4)  (C15 x C3) : C4  (C15 x C3) : C4
  Of finite representation type:   18
  Of infinite representation type: 19
Checking it in characteristic 3
  C5 x (C9 : C4)  C9 x (C5 : C4)  C45 : C4  C180  C9 x (C5 : C4)  C45 : C4  D10 x D18  C5 x ((C2 x C2) : C9)  C18 x D10  C10 x D18  D180  C90 x C2
  Of finite representation type:   12
  Of infinite representation type: 25

Counting the groups of finite representation type of order 181 = [ 181 ]

Counting the groups of finite representation type of order 182 = [ 2, 7, 13 ]

Counting the groups of finite representation type of order 183 = [ 3, 61 ]

Counting the groups of finite representation type of order 184 = [ 2, 2, 2, 23 ]
Checking it in characteristic 2
  C23 : C8  C184
  Of finite representation type:   2
  Of infinite representation type: 10

Counting the groups of finite representation type of order 185 = [ 5, 37 ]

Counting the groups of finite representation type of order 186 = [ 2, 3, 31 ]

Counting the groups of finite representation type of order 187 = [ 11, 17 ]

Counting the groups of finite representation type of order 188 = [ 2, 2, 47 ]
Checking it in characteristic 2
  C47 : C4  C188
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 189 = [ 3, 3, 3, 7 ]
Checking it in characteristic 3
  C7 : C27  C189
  Of finite representation type:   2
  Of infinite representation type: 11

Counting the groups of finite representation type of order 190 = [ 2, 5, 19 ]

Counting the groups of finite representation type of order 191 = [ 191 ]

Counting the groups of finite representation type of order 192 = [ 2, 2, 2, 2, 2, 2, 3 ]
Checking it in characteristic 2
  C3 : C64  C192
  Of finite representation type:   2
  Of infinite representation type: 1541

Counting the groups of finite representation type of order 193 = [ 193 ]

Counting the groups of finite representation type of order 194 = [ 2, 97 ]

Counting the groups of finite representation type of order 195 = [ 3, 5, 13 ]

Counting the groups of finite representation type of order 196 = [ 2, 2, 7, 7 ]
Checking it in characteristic 2
  C49 : C4  C196  C7 x (C7 : C4)  (C7 x C7) : C4  C28 x C7  (C7 x C7) : C4
  Of finite representation type:   6
  Of infinite representation type: 6
Checking it in characteristic 7
  C49 : C4  C196  D196  C98 x C2
  Of finite representation type:   4
  Of infinite representation type: 8

Counting the groups of finite representation type of order 197 = [ 197 ]

Counting the groups of finite representation type of order 198 = [ 2, 3, 3, 11 ]
Checking it in characteristic 3
  C11 x D18  C9 x D22  D198  C198
  Of finite representation type:   4
  Of infinite representation type: 6

Counting the groups of finite representation type of order 199 = [ 199 ]

Counting the groups of finite representation type of order 200 = [ 2, 2, 2, 5, 5 ]
Checking it in characteristic 2
  C25 : C8  C200  C25 : C8  C5 x (C5 : C8)  (C5 x C5) : C8  C40 x C5  C5 x (C5 : C8)  (C5 x C5) : C8  (C5 x C5) : C8  (C5 x C5) : C8  (C5 x C5) : C8
  Of finite representation type:   11
  Of infinite representation type: 41
Checking it in characteristic 5
  C25 : C8  C200  C25 : C8  C25 : Q8  C4 x D50  D200  C2 x (C25 : C4)  (C50 x C2) : C2  C100 x C2  C25 x D8  C25 x Q8  C2 x (C25 : C4)  C2 x C2 x D50  C50 x C2 x C2
  Of finite representation type:   14
  Of infinite representation type: 38

Counting the groups of finite representation type of order 201 = [ 3, 67 ]

Counting the groups of finite representation type of order 202 = [ 2, 101 ]

Counting the groups of finite representation type of order 203 = [ 7, 29 ]

Counting the groups of finite representation type of order 204 = [ 2, 2, 3, 17 ]
Checking it in characteristic 2
  C17 x (C3 : C4)  C3 x (C17 : C4)  C51 : C4  C204  C3 x (C17 : C4)  C51 : C4
  Of finite representation type:   6
  Of infinite representation type: 6

Counting the groups of finite representation type of order 205 = [ 5, 41 ]

Counting the groups of finite representation type of order 206 = [ 2, 103 ]

Counting the groups of finite representation type of order 207 = [ 3, 3, 23 ]
Checking it in characteristic 3
  C207
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 208 = [ 2, 2, 2, 2, 13 ]
Checking it in characteristic 2
  C13 : C16  C208  C13 : C16
  Of finite representation type:   3
  Of infinite representation type: 48

Counting the groups of finite representation type of order 209 = [ 11, 19 ]

Counting the groups of finite representation type of order 210 = [ 2, 3, 5, 7 ]

Counting the groups of finite representation type of order 211 = [ 211 ]

Counting the groups of finite representation type of order 212 = [ 2, 2, 53 ]
Checking it in characteristic 2
  C53 : C4  C212  C53 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 213 = [ 3, 71 ]

Counting the groups of finite representation type of order 214 = [ 2, 107 ]

Counting the groups of finite representation type of order 215 = [ 5, 43 ]

Counting the groups of finite representation type of order 216 = [ 2, 2, 2, 3, 3, 3 ]
Checking it in characteristic 2
  C27 : C8  C216  C3 x (C9 : C8)  C9 x (C3 : C8)  ((C3 x C3) : C8) : C3  (C9 : C8) : C3  (C9 x C3) : C8  ((C3 x C3) : C3) : C8  C72 x C3  C8 x ((C3 x C3) : C3)  C8 x (C9 : C3)  ((C3 x C3) : C3) : C8  C3 x \
C3 x (C3 : C8)  C3 x ((C3 x C3) : C8)  (C3 x C3 x C3) : C8  C24 x C3 x C3  ((C3 x C3) : C3) : C8  C3 x ((C3 x C3) : C8)  (C3 x C3 x C3) : C8  C3 x ((C3 x C3) : C8)  (C3 x C3 x C3) : C8
  Of finite representation type:   21
  Of infinite representation type: 156
Checking it in characteristic 3
  C27 : C8  C216  Q8 : C27  C27 : Q8  C4 x D54  D216  C2 x (C27 : C4)  (C54 x C2) : C2  C108 x C2  C27 x D8  C27 x Q8  ((C2 x C2) : C27) : C2  C2 x ((C2 x C2) : C27)  C2 x C2 x D54  C54 x C2 x C2
  Of finite representation type:   15
  Of infinite representation type: 162

Counting the groups of finite representation type of order 217 = [ 7, 31 ]

Counting the groups of finite representation type of order 218 = [ 2, 109 ]

Counting the groups of finite representation type of order 219 = [ 3, 73 ]

Counting the groups of finite representation type of order 220 = [ 2, 2, 5, 11 ]
Checking it in characteristic 2
  (C11 : C5) : C4  C4 x (C11 : C5)  C11 x (C5 : C4)  C5 x (C11 : C4)  C55 : C4  C220  C11 x (C5 : C4)  C55 : C4
  Of finite representation type:   8
  Of infinite representation type: 7

Counting the groups of finite representation type of order 221 = [ 13, 17 ]

Counting the groups of finite representation type of order 222 = [ 2, 3, 37 ]

Counting the groups of finite representation type of order 223 = [ 223 ]

Counting the groups of finite representation type of order 224 = [ 2, 2, 2, 2, 2, 7 ]
Checking it in characteristic 2
  C7 : C32  C224
  Of finite representation type:   2
  Of infinite representation type: 195

Counting the groups of finite representation type of order 225 = [ 3, 3, 5, 5 ]
Checking it in characteristic 3
  C225  (C5 x C5) : C9  C45 x C5
  Of finite representation type:   3
  Of infinite representation type: 3
Checking it in characteristic 5
  C225  C75 x C3
  Of finite representation type:   2
  Of infinite representation type: 4

Counting the groups of finite representation type of order 226 = [ 2, 113 ]

Counting the groups of finite representation type of order 227 = [ 227 ]

Counting the groups of finite representation type of order 228 = [ 2, 2, 3, 19 ]
Checking it in characteristic 2
  (C19 : C4) : C3  C4 x (C19 : C3)  C19 x (C3 : C4)  C3 x (C19 : C4)  C57 : C4  C228
  Of finite representation type:   6
  Of infinite representation type: 9

Counting the groups of finite representation type of order 229 = [ 229 ]

Counting the groups of finite representation type of order 230 = [ 2, 5, 23 ]

Counting the groups of finite representation type of order 231 = [ 3, 7, 11 ]

Counting the groups of finite representation type of order 232 = [ 2, 2, 2, 29 ]
Checking it in characteristic 2
  C29 : C8  C232  C29 : C8
  Of finite representation type:   3
  Of infinite representation type: 11

Counting the groups of finite representation type of order 233 = [ 233 ]

Counting the groups of finite representation type of order 234 = [ 2, 3, 3, 13 ]
Checking it in characteristic 3
  (C13 : C9) : C2  C2 x (C13 : C9)  C13 x D18  C9 x D26  D234  C234
  Of finite representation type:   6
  Of infinite representation type: 10

Counting the groups of finite representation type of order 235 = [ 5, 47 ]

Counting the groups of finite representation type of order 236 = [ 2, 2, 59 ]
Checking it in characteristic 2
  C59 : C4  C236
  Of finite representation type:   2
  Of infinite representation type: 2

Counting the groups of finite representation type of order 237 = [ 3, 79 ]

Counting the groups of finite representation type of order 238 = [ 2, 7, 17 ]

Counting the groups of finite representation type of order 239 = [ 239 ]

Counting the groups of finite representation type of order 240 = [ 2, 2, 2, 2, 3, 5 ]
Checking it in characteristic 2
  C5 x (C3 : C16)  C3 x (C5 : C16)  C15 : C16  C240  C3 x (C5 : C16)  C15 : C16
  Of finite representation type:   6
  Of infinite representation type: 202

Counting the groups of finite representation type of order 241 = [ 241 ]

Counting the groups of finite representation type of order 242 = [ 2, 11, 11 ]
Checking it in characteristic 11
  D242  C242
  Of finite representation type:   2
  Of infinite representation type: 3

Counting the groups of finite representation type of order 243 = [ 3, 3, 3, 3, 3 ]
Checking it in characteristic 3
  C243
  Of finite representation type:   1
  Of infinite representation type: 66

Counting the groups of finite representation type of order 244 = [ 2, 2, 61 ]
Checking it in characteristic 2
  C61 : C4  C244  C61 : C4
  Of finite representation type:   3
  Of infinite representation type: 2

Counting the groups of finite representation type of order 245 = [ 5, 7, 7 ]
Checking it in characteristic 7
  C245
  Of finite representation type:   1
  Of infinite representation type: 1

Counting the groups of finite representation type of order 246 = [ 2, 3, 41 ]

Counting the groups of finite representation type of order 247 = [ 13, 19 ]

Counting the groups of finite representation type of order 248 = [ 2, 2, 2, 31 ]
Checking it in characteristic 2
  C31 : C8  C248
  Of finite representation type:   2
  Of infinite representation type: 10

Counting the groups of finite representation type of order 249 = [ 3, 83 ]

Counting the groups of finite representation type of order 250 = [ 2, 5, 5, 5 ]
Checking it in characteristic 5
  D250  C250
  Of finite representation type:   2
  Of infinite representation type: 13

Counting the groups of finite representation type of order 251 = [ 251 ]

Counting the groups of finite representation type of order 252 = [ 2, 2, 3, 3, 7 ]
Checking it in characteristic 2
  (C7 : C9) : C4  C4 x (C7 : C9)  C7 x (C9 : C4)  C9 x (C7 : C4)  C63 : C4  C252  C3 x ((C7 : C4) : C3)  (C3 : C4) x (C7 : C3)  (C21 : C4) : C3  C12 x (C7 : C3)  C3 x C3 x (C7 : C4)  C21 x (C3 : C4)  C3 x \
(C21 : C4)  C7 x ((C3 x C3) : C4)  (C21 x C3) : C4  C84 x C3  C7 x ((C3 x C3) : C4)  (C21 x C3) : C4
  Of finite representation type:   18
  Of infinite representation type: 28
Checking it in characteristic 3
  (C7 : C9) : C4  C4 x (C7 : C9)  C7 x (C9 : C4)  C9 x (C7 : C4)  C63 : C4  C252  C2 x ((C7 : C9) : C2)  D14 x D18  C2 x C2 x (C7 : C9)  C7 x ((C2 x C2) : C9)  (C14 x C2) : C9  C18 x D14  C14 x D18  D252  \
C126 x C2
  Of finite representation type:   15
  Of infinite representation type: 31

Counting the groups of finite representation type of order 253 = [ 11, 23 ]

Counting the groups of finite representation type of order 254 = [ 2, 127 ]

Counting the groups of finite representation type of order 255 = [ 3, 5, 17 ]