← #72231234
Subgroups — #72231234
Order 14400.
1514 conjugacy classes of subgroups.
The subgroup lattice has 782 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #72231206 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×#72229770 | C2 | 1 | 2 | yes | maximal |
| 3 | C3×#11925546 | C4 | 1 | 2 | yes | complemented |
| 4 | C3×#11925377 | C4 | 1 | 4 | yes | complemented |
| 5 | C3×C5×#6762 | C4 | 1 | 2 | yes | complemented |
| 6 | #72231171 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C3×#11925375 | C22 | 1 | 4 | yes | — |
| 8 | C2×#72229304 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #72231083 | — | 3 | 2 | no | maximal |
| 10 | C22×C3⋊(C3⋊#1044) | C4 | 1 | 1 | yes | characteristic |
| 11 | #72229770 | D3 | 1 | 2 | yes | — |
| 12 | #72229759 | — | 3 | 4 | no | — |
| 13 | C3×#11717347 | — | 3 | 2 | no | — |
| 14 | #72229728 | — | 3 | 4 | no | — |
| 15 | C2×#11925349 | — | 3 | 2 | no | — |
| 16 | C2×#11925349 | — | 6 | 1 | no | — |
| 17 | #72229548 | — | 5 | 2 | no | maximal |
| 18 | C2×C32×#6036 | C22 | 1 | 1 | yes | characteristic |
| 19 | #72229304 | C4 | 1 | 1 | yes | characteristic |
| 20 | #72229304 | C4 | 1 | 1 | yes | characteristic |
| 21 | #72229304 | C22 | 1 | 1 | yes | characteristic |
| 22 | #72229304 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×C3⋊(C3⋊#1043) | C4 | 1 | 1 | yes | characteristic |
| 24 | C22×C32×C5⋊D5 | C2×C4 | 1 | 1 | yes | characteristic |
| 25 | C2×C3⋊(C3⋊#1044) | — | 2 | 2 | no | — |
| 26 | C2×C3⋊(C3⋊#1044) | C2×C4 | 1 | 1 | yes | characteristic |
| 27 | C2×C3⋊(C3⋊#1044) | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | C2×C3⋊(C3⋊#1043) | — | 2 | 2 | no | — |
| 29 | C2×C3⋊(C3⋊#1043) | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C3⋊(C3⋊#1043) | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C2×C32×C5×Dic5 | C2×C4 | 1 | 2 | yes | — |
| 32 | C32×#6036 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C32×#6036 | C2×C4 | 1 | 2 | yes | — |
| 34 | C32×#6036 | C23 | 1 | 1 | yes | characteristic |
| 35 | C3×C3⋊#6032 | C2×C4 | 1 | 4 | yes | complemented |
| 36 | C3×C5×C3⋊#170 | C2×C4 | 1 | 4 | yes | complemented |
| 37 | #13107464 | — | 9 | 1 | no | Hall |
| 38 | C2×C4×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 39 | C3×D5⋊#208 | — | 5 | 2 | no | — |
| 40 | C3×D5×#208 | — | 5 | 2 | no | — |
| 41 | #13085445 | — | 5 | 4 | no | — |
| 42 | #13085443 | — | 5 | 4 | no | — |
| 43 | C22×C3⋊#1044 | — | 3 | 2 | no | — |
| 44 | C22×C3⋊#1044 | — | 6 | 1 | no | — |
| 45 | C22×C3⋊#1043 | — | 3 | 2 | no | — |
| 46 | C22×C3⋊#1043 | — | 6 | 1 | no | — |
| 47 | C2×C3×#6036 | — | 2 | 1 | no | — |
| 48 | C2×C3×#6036 | C2×D3 | 1 | 2 | yes | — |
| 49 | #11925546 | Dic3 | 1 | 2 | yes | complemented |
| 50 | C5×#6762 | Dic3 | 1 | 2 | yes | complemented |
| 51 | C3×#87853 | — | 3 | 2 | no | — |
| 52 | C3×C5×#704 | — | 3 | 2 | no | — |
| 53 | #11925377 | Dic3 | 1 | 4 | yes | complemented |
| 54 | #11925375 | C2×D3 | 1 | 4 | yes | — |
| 55 | #11925349 | — | 3 | 2 | no | — |
| 56 | #11925349 | — | 3 | 2 | no | — |
| 57 | #11925349 | — | 3 | 2 | no | — |
| 58 | #11925349 | — | 3 | 2 | no | — |
| 59 | #11925349 | — | 6 | 1 | no | — |
| 60 | #11925349 | — | 6 | 1 | no | — |
| 61 | #11925349 | — | 6 | 1 | no | — |
| 62 | #11925349 | — | 6 | 1 | no | — |
| 63 | C3×#87829 | — | 3 | 4 | no | — |
| 64 | C3×#87827 | — | 3 | 4 | no | — |
| 65 | M16×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 66 | #11751698 | — | 15 | 2 | no | — |
| 67 | C22×C32×C52 | C42 | 1 | 1 | yes | characteristic |
| 68 | C2×C32×C5⋊D5 | — | 2 | 1 | no | — |
| 69 | C2×C32×C5⋊D5 | — | 2 | 1 | no | — |
| 70 | C2×C32×C5⋊D5 | C42 | 1 | 1 | yes | characteristic |
| 71 | C2×C32×C5⋊D5 | C22×C4 | 1 | 1 | yes | characteristic |
| 72 | C3⋊(C3⋊#1044) | — | 2 | 1 | no | — |
| 73 | C3⋊(C3⋊#1044) | M16 | 1 | 2 | yes | complemented |
| 74 | C3⋊(C3⋊#1043) | — | 2 | 1 | no | — |
| 75 | C3⋊(C3⋊#1043) | M16 | 1 | 2 | yes | complemented |
| 76 | C32×C5×Dic5 | C42 | 1 | 2 | yes | — |
| 77 | C32×C5×Dic5 | C22×C4 | 1 | 2 | yes | — |
| 78 | C2×#87830 | — | 9 | 1 | no | — |
| 79 | #11717347 | — | 3 | 2 | no | — |
| 80 | #11717302 | — | 9 | 2 | no | — |
| 81 | #11717300 | — | 9 | 2 | no | — |
| 82 | C22×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 83 | C22×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 84 | C22×C3⋊ΓL(1,𝔽16) | — | 20 | 1 | no | — |
| 85 | C2×C32×C4×D5 | — | 5 | 2 | no | — |
| 86 | C4×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 87 | C4×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 88 | C4×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 89 | C4×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 90 | C3×#6762 | — | 5 | 2 | no | — |
| 91 | C3×#6762 | AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 92 | C3×#6758 | — | 5 | 4 | no | — |
| 93 | C3×D5⋊(C3⋊C8) | — | 5 | 4 | no | — |
| 94 | C3×#6710 | — | 5 | 2 | no | — |
| 95 | C3×C5×#208 | — | 5 | 2 | no | — |
| 96 | C3×#6649 | — | 5 | 4 | no | — |
| 97 | C3×D5×C3⋊C8 | — | 5 | 4 | no | — |
| 98 | C22×C3×C5⋊D5 | — | 2 | 1 | no | — |
| 99 | C22×C3×C5⋊D5 | C4×D3 | 1 | 2 | yes | — |
| 100 | C2×C3⋊#1044 | — | 3 | 2 | no | — |
| 101 | C2×C3⋊#1044 | — | 3 | 2 | no | — |
| 102 | C2×C3⋊#1044 | — | 6 | 1 | no | — |
| 103 | C2×C3⋊#1044 | — | 6 | 1 | no | — |
| 104 | C2×C3⋊#1044 | — | 6 | 4 | no | — |
| 105 | C2×C3⋊#1044 | — | 6 | 2 | no | — |
| 106 | C2×C3⋊#1044 | — | 6 | 2 | no | — |
| 107 | C2×C3⋊#1043 | — | 3 | 2 | no | — |
| 108 | C2×C3⋊#1043 | — | 3 | 2 | no | — |
| 109 | C2×C3⋊#1043 | — | 6 | 1 | no | — |
| 110 | C2×C3⋊#1043 | — | 6 | 1 | no | — |
| 111 | C2×C3⋊#1043 | — | 6 | 4 | no | — |
| 112 | C2×C3⋊#1043 | — | 6 | 2 | no | — |
| 113 | C2×C3⋊#1043 | — | 6 | 2 | no | — |
| 114 | C2×C3×C5×Dic5 | — | 2 | 2 | no | — |
| 115 | C2×C3×C5×Dic5 | C4×D3 | 1 | 2 | yes | — |
| 116 | C2×C3×C5×Dic5 | C2×Dic3 | 1 | 2 | yes | — |
| 117 | C3×#6036 | — | 2 | 2 | no | — |
| 118 | C3×#6036 | — | 2 | 1 | no | — |
| 119 | C3×#6036 | — | 2 | 1 | no | — |
| 120 | C3×#6036 | C4×D3 | 1 | 2 | yes | — |
| 121 | C3×#6036 | C4×D3 | 1 | 2 | yes | — |
| 122 | C3×#6036 | C2×Dic3 | 1 | 2 | yes | — |
| 123 | C3×#6036 | C22×D3 | 1 | 2 | yes | — |
| 124 | C3⋊#6032 | C2×Dic3 | 1 | 4 | yes | complemented |
| 125 | C5×C3⋊#170 | C2×Dic3 | 1 | 4 | yes | complemented |
| 126 | C3×#6032 | — | 3 | 4 | no | — |
| 127 | C3×C5×#170 | — | 3 | 4 | no | — |
| 128 | #10591060 | — | 25 | 1 | no | Hall |
| 129 | C2×C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 130 | C2×C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 131 | C2×C4×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 132 | D5⋊#208 | — | 5 | 2 | no | — |
| 133 | C3×D5⋊M16 | — | 15 | 2 | no | — |
| 134 | C3×D5×M16 | — | 15 | 2 | no | — |
| 135 | D5×#208 | — | 5 | 2 | no | — |
| 136 | #91221 | — | 15 | 4 | no | — |
| 137 | C8×ΓL(1,𝔽16) | — | 15 | 4 | no | — |
| 138 | #91150 | — | 15 | 4 | no | — |
| 139 | ΓL(1,𝔽16)⋊C8 | — | 15 | 4 | no | — |
| 140 | C2×C32×C52 | — | 2 | 1 | no | — |
| 141 | C2×C32×C52 | C2×C42 | 1 | 1 | yes | characteristic |
| 142 | C32×C5⋊D5 | — | 2 | 1 | no | — |
| 143 | C32×C5⋊D5 | C2×M16 | 1 | 1 | yes | characteristic |
| 144 | C32×C5⋊D5 | C2×M16 | 1 | 1 | yes | characteristic |
| 145 | C22×#1044 | — | 9 | 1 | no | — |
| 146 | C22×#1043 | — | 9 | 1 | no | — |
| 147 | C2×#6036 | D32 | 1 | 1 | yes | characteristic |
| 148 | #87853 | — | 3 | 2 | no | — |
| 149 | C5×#704 | — | 3 | 2 | no | — |
| 150 | #87830 | — | 9 | 1 | no | — |
| 151 | #87830 | — | 9 | 1 | no | — |
| 152 | #87830 | — | 9 | 1 | no | — |
| 153 | #87830 | — | 9 | 1 | no | — |
| 154 | #87829 | — | 3 | 4 | no | — |
| 155 | #87827 | — | 3 | 4 | no | — |
| 156 | C22×C32×D5 | — | 5 | 2 | no | — |
| 157 | C22×C32×D5 | — | 20 | 1 | no | — |
| 158 | C2×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 159 | C2×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 160 | C2×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 161 | C2×C3⋊ΓL(1,𝔽16) | — | 5 | 2 | no | — |
| 162 | C2×C3⋊ΓL(1,𝔽16) | — | 10 | 4 | no | — |
| 163 | C2×C3⋊ΓL(1,𝔽16) | — | 10 | 4 | no | — |
| 164 | C2×C3⋊ΓL(1,𝔽16) | — | 20 | 1 | no | — |
| 165 | C2×C3⋊ΓL(1,𝔽16) | — | 20 | 2 | no | — |
| 166 | C2×C3⋊ΓL(1,𝔽16) | — | 20 | 2 | no | — |
| 167 | C2×C3⋊ΓL(1,𝔽16) | — | 20 | 1 | no | — |
| 168 | C2×C32×C4×C5 | — | 5 | 2 | no | — |
| 169 | C2×C32×Dic5 | C2×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 170 | C32×C4×D5 | — | 5 | 2 | no | — |
| 171 | C32×C4×D5 | — | 5 | 2 | no | — |
| 172 | C32×C4×D5 | — | 5 | 2 | no | — |
| 173 | C32×C4×D5 | — | 5 | 2 | no | — |
| 174 | C3×C3⋊#170 | — | 5 | 4 | no | — |
| 175 | C3×C3⋊#170 | C2×AGL(1,𝔽5) | 1 | 4 | yes | complemented |
| 176 | C3×C3⋊#168 | — | 5 | 4 | no | — |
| 177 | C3×C5×C3⋊C8 | — | 5 | 4 | no | — |
| 178 | M16×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 179 | C22×C3×C52 | — | 2 | 1 | no | — |
| 180 | C22×C3×C52 | C4×Dic3 | 1 | 2 | yes | — |
| 181 | C2×C3×C5⋊D5 | — | 2 | 1 | no | — |
| 182 | C2×C3×C5⋊D5 | — | 2 | 1 | no | — |
| 183 | C2×C3×C5⋊D5 | — | 2 | 1 | no | — |
| 184 | C2×C3×C5⋊D5 | — | 2 | 1 | no | — |
| 185 | C2×C3×C5⋊D5 | — | 2 | 2 | no | — |
| 186 | C2×C3×C5⋊D5 | — | 2 | 2 | no | — |
| 187 | C2×C3×C5⋊D5 | — | 2 | 1 | no | — |
| 188 | C2×C3×C5⋊D5 | — | 2 | 1 | no | — |
| 189 | C2×C3×C5⋊D5 | C4×Dic3 | 1 | 2 | yes | — |
| 190 | C2×C3×C5⋊D5 | C2×C4×D3 | 1 | 2 | yes | — |
| 191 | C3⋊#1044 | — | 3 | 4 | no | — |
| 192 | C3⋊#1044 | — | 6 | 2 | no | — |
| 193 | C3⋊#1044 | — | 6 | 1 | no | — |
| 194 | C3⋊#1044 | — | 6 | 1 | no | — |
| 195 | C3⋊#1044 | — | 6 | 2 | no | — |
| 196 | C3⋊#1043 | — | 3 | 4 | no | — |
| 197 | C3⋊#1043 | — | 6 | 2 | no | — |
| 198 | C3⋊#1043 | — | 6 | 1 | no | — |
| 199 | C3⋊#1043 | — | 6 | 1 | no | — |
| 200 | C3⋊#1043 | — | 6 | 2 | no | — |
| 201 | C3×C5×Dic5 | — | 2 | 2 | no | — |
| 202 | C3×C5×Dic5 | — | 2 | 2 | no | — |
| 203 | C3×C5×Dic5 | C4×Dic3 | 1 | 2 | yes | — |
| 204 | C3×C5×Dic5 | C4×Dic3 | 1 | 2 | yes | — |
| 205 | C3×C5×Dic5 | C2×C4×D3 | 1 | 2 | yes | — |
| 206 | C3×C5×Dic5 | C22×Dic3 | 1 | 2 | yes | — |
| 207 | C2×C4×C3⋊Dic3 | — | 25 | 1 | no | — |
| 208 | C2×C3×#208 | — | 25 | 2 | no | — |
| 209 | #63555 | — | 25 | 2 | no | — |
| 210 | #63553 | — | 25 | 2 | no | — |
| 211 | C22×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 212 | C22×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 213 | C22×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 214 | C22×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 215 | C22×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 216 | C22×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 217 | C22×ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 218 | C22×ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 219 | C22×ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 220 | C2×C3×C4×D5 | — | 5 | 2 | no | — |
| 221 | C2×C3×C4×D5 | — | 5 | 2 | no | — |
| 222 | C2×C3×C4×D5 | — | 10 | 2 | no | — |
| 223 | #6762 | — | 5 | 2 | no | — |
| 224 | #6762 | ΓL(1,𝔽16) | 1 | 2 | yes | complemented |
| 225 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 226 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 227 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 228 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 229 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 230 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 231 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 232 | C4×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 233 | C4×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 234 | C4×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 235 | C4×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 236 | C4×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 237 | #6758 | — | 5 | 4 | no | — |
| 238 | D5⋊(C3⋊C8) | — | 5 | 4 | no | — |
| 239 | C3×#704 | — | 3 | 2 | no | — |
| 240 | C3×#704 | — | 15 | 2 | no | — |
| 241 | C3×#700 | — | 15 | 4 | no | — |
| 242 | C3×D5⋊C8 | — | 15 | 4 | no | — |
| 243 | C3×C5×M16 | — | 15 | 2 | no | — |
| 244 | #6710 | — | 5 | 2 | no | — |
| 245 | C5×#208 | — | 5 | 2 | no | — |
| 246 | C3×#681 | — | 15 | 2 | no | — |
| 247 | C3×#676 | — | 15 | 4 | no | — |
| 248 | C3×C8×D5 | — | 15 | 4 | no | — |
| 249 | #6649 | — | 5 | 4 | no | — |
| 250 | D5×C3⋊C8 | — | 5 | 4 | no | — |
| 251 | C32×C52 | C4×M16 | 1 | 1 | yes | characteristic, complemented, Hall |
| 252 | C22×C5⋊D5 | #624 | 1 | 1 | yes | characteristic |
| 253 | C2×#1044 | — | 9 | 1 | no | — |
| 254 | C2×#1044 | — | 9 | 1 | no | — |
| 255 | C2×#1044 | — | 18 | 2 | no | — |
| 256 | C2×#1043 | — | 9 | 1 | no | — |
| 257 | C2×#1043 | — | 9 | 1 | no | — |
| 258 | C2×#1043 | — | 18 | 2 | no | — |
| 259 | C2×C5×Dic5 | D3×Dic3 | 1 | 2 | yes | — |
| 260 | #6036 | D3×Dic3 | 1 | 2 | yes | — |
| 261 | #6036 | #624 | 1 | 1 | yes | characteristic |
| 262 | #6036 | C2×D32 | 1 | 1 | yes | characteristic |
| 263 | #6032 | — | 3 | 4 | no | — |
| 264 | C5×#170 | — | 3 | 4 | no | — |
| 265 | Dic3×M16 | — | 75 | 2 | no | — |
| 266 | C22×C32×C5 | — | 4 | 1 | no | — |
| 267 | C22×C32×C5 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 268 | C2×C32×D5 | — | 5 | 2 | no | — |
| 269 | C2×C32×D5 | — | 5 | 2 | no | — |
| 270 | C2×C32×D5 | — | 10 | 2 | no | — |
| 271 | C2×C32×D5 | — | 10 | 2 | no | — |
| 272 | C2×C32×D5 | — | 20 | 1 | no | — |
| 273 | C2×C32×D5 | — | 20 | 1 | no | — |
| 274 | C2×C32×D5 | — | 20 | 1 | no | — |
| 275 | C2×C32×D5 | — | 20 | 1 | no | — |
| 276 | C2×C32×D5 | — | 20 | 1 | no | — |
| 277 | C2×C32×D5 | — | 20 | 1 | no | — |
| 278 | C3⋊ΓL(1,𝔽16) | — | 5 | 4 | no | — |
| 279 | C3⋊ΓL(1,𝔽16) | — | 5 | 4 | no | — |
| 280 | C3⋊ΓL(1,𝔽16) | — | 10 | 2 | no | — |
| 281 | C3⋊ΓL(1,𝔽16) | — | 10 | 2 | no | — |
| 282 | C3⋊ΓL(1,𝔽16) | — | 20 | 2 | no | — |
| 283 | C3⋊ΓL(1,𝔽16) | — | 20 | 1 | no | — |
| 284 | C3⋊ΓL(1,𝔽16) | — | 20 | 1 | no | — |
| 285 | C32×C4×C5 | — | 5 | 2 | no | — |
| 286 | C32×C4×C5 | — | 5 | 2 | no | — |
| 287 | C32×Dic5 | C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 288 | C32×Dic5 | C22×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 289 | C2×C4×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 290 | D5⋊M16 | — | 15 | 2 | no | — |
| 291 | D5×M16 | — | 15 | 2 | no | — |
| 292 | #3992 | — | 45 | 4 | no | — |
| 293 | C8×AGL(1,𝔽5) | — | 45 | 4 | no | — |
| 294 | C2×C3×C52 | — | 2 | 1 | no | — |
| 295 | C2×C3×C52 | — | 2 | 1 | no | — |
| 296 | C2×C3×C52 | — | 2 | 2 | no | — |
| 297 | C2×C3×C52 | — | 2 | 1 | no | — |
| 298 | C2×C3×C52 | C2×C4×Dic3 | 1 | 2 | yes | — |
| 299 | C3×C5⋊D5 | — | 2 | 1 | no | — |
| 300 | C3×C5⋊D5 | — | 2 | 1 | no | — |
| 301 | C3×C5⋊D5 | — | 2 | 2 | no | — |
| 302 | C3×C5⋊D5 | — | 2 | 1 | no | — |
| 303 | C3×C5⋊D5 | — | 2 | 1 | no | — |
| 304 | C3×C5⋊D5 | D3×M16 | 1 | 2 | yes | — |
| 305 | C3×C5⋊D5 | D3×M16 | 1 | 2 | yes | — |
| 306 | C22×C32×C4 | — | 25 | 1 | no | — |
| 307 | C22×C3⋊Dic3 | — | 25 | 1 | no | — |
| 308 | C22×C3⋊Dic3 | — | 25 | 1 | no | — |
| 309 | C4×C3⋊Dic3 | — | 25 | 1 | no | — |
| 310 | C4×C3⋊Dic3 | — | 25 | 1 | no | — |
| 311 | C4×C3⋊Dic3 | — | 25 | 1 | no | — |
| 312 | C4×C3⋊Dic3 | — | 25 | 1 | no | — |
| 313 | C3×#208 | — | 5 | 2 | no | — |
| 314 | C3×#208 | — | 25 | 4 | no | — |
| 315 | C3×#208 | — | 25 | 2 | no | — |
| 316 | C2×C3×C3⋊C8 | — | 25 | 4 | no | — |
| 317 | C22×C3×D5 | — | 5 | 2 | no | — |
| 318 | C22×C3×D5 | — | 5 | 2 | no | — |
| 319 | C22×C3×D5 | — | 10 | 2 | no | — |
| 320 | C22×C3×D5 | — | 20 | 2 | no | — |
| 321 | C22×C3×D5 | — | 20 | 1 | no | — |
| 322 | C22×C3×D5 | — | 20 | 1 | no | — |
| 323 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 324 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 325 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 326 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 327 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 328 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 329 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 330 | C2×ΓL(1,𝔽16) | — | 15 | 2 | no | — |
| 331 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 332 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 333 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 334 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 335 | C2×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 336 | C2×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 337 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 338 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 339 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 340 | C2×ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 341 | C2×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 342 | C2×ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 343 | C2×ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 344 | C2×ΓL(1,𝔽16) | — | 60 | 4 | no | — |
| 345 | C2×ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 346 | C2×ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 347 | C2×ΓL(1,𝔽16) | — | 60 | 4 | no | — |
| 348 | C2×ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 349 | C2×ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 350 | C2×ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 351 | C2×ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 352 | C2×ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 353 | C2×ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 354 | C2×ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 355 | C2×C3×C4×C5 | — | 5 | 2 | no | — |
| 356 | C2×C3×C4×C5 | — | 5 | 2 | no | — |
| 357 | C2×C3×C4×C5 | — | 10 | 2 | no | — |
| 358 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 359 | C2×C3×Dic5 | D3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 360 | C2×C3×Dic5 | C2×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 361 | C3×C4×D5 | — | 5 | 2 | no | — |
| 362 | C3×C4×D5 | — | 5 | 2 | no | — |
| 363 | C3×C4×D5 | — | 5 | 2 | no | — |
| 364 | C3×C4×D5 | — | 5 | 2 | no | — |
| 365 | C3×C4×D5 | — | 5 | 2 | no | — |
| 366 | C3×C4×D5 | — | 5 | 2 | no | — |
| 367 | C3×C4×D5 | — | 5 | 2 | no | — |
| 368 | C3×C4×D5 | — | 5 | 2 | no | — |
| 369 | C3×C4×D5 | — | 10 | 2 | no | — |
| 370 | C3×C4×D5 | — | 10 | 2 | no | — |
| 371 | C3×C4×D5 | — | 10 | 2 | no | — |
| 372 | C3×C4×D5 | — | 10 | 2 | no | — |
| 373 | C3⋊#170 | — | 5 | 4 | no | — |
| 374 | C3⋊#170 | C2×ΓL(1,𝔽16) | 1 | 4 | yes | complemented |
| 375 | C3×#170 | — | 3 | 4 | no | — |
| 376 | C3×#170 | — | 15 | 4 | no | — |
| 377 | C3×C5×C8 | — | 15 | 4 | no | — |
| 378 | C3⋊#168 | — | 5 | 4 | no | — |
| 379 | C3×#168 | — | 15 | 4 | no | — |
| 380 | C5×C3⋊C8 | — | 5 | 4 | no | — |
| 381 | C22×C52 | Dic32 | 1 | 1 | yes | characteristic |
| 382 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 383 | C2×C5⋊D5 | — | 2 | 1 | no | — |
| 384 | C2×C5⋊D5 | Dic32 | 1 | 1 | yes | characteristic |
| 385 | C2×C5⋊D5 | C2×#624 | 1 | 1 | yes | characteristic |
| 386 | #1044 | — | 9 | 2 | no | — |
| 387 | #1044 | — | 18 | 1 | no | — |
| 388 | #1043 | — | 9 | 2 | no | — |
| 389 | #1043 | — | 18 | 1 | no | — |
| 390 | C5×Dic5 | Dic32 | 1 | 2 | yes | — |
| 391 | C5×Dic5 | C2×D3×Dic3 | 1 | 2 | yes | — |
| 392 | C2×C3×M16 | — | 75 | 2 | no | — |
| 393 | C2×C4×Dic3 | — | 75 | 2 | no | — |
| 394 | C2×C4×Dic3 | — | 150 | 1 | no | — |
| 395 | C2×#208 | — | 25 | 2 | no | — |
| 396 | #815 | — | 75 | 4 | no | — |
| 397 | C8×Dic3 | — | 75 | 4 | no | — |
| 398 | C2×C32×C5 | — | 2 | 2 | no | — |
| 399 | C2×C32×C5 | — | 4 | 1 | no | — |
| 400 | C2×C32×C5 | — | 4 | 1 | no | — |
| 401 | C2×C32×C5 | — | 4 | 1 | no | — |
| 402 | C2×C32×C5 | C2×C4×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 403 | C32×D5 | — | 5 | 2 | no | — |
| 404 | C32×D5 | — | 5 | 2 | no | — |
| 405 | C32×D5 | — | 10 | 2 | no | — |
| 406 | C32×D5 | — | 20 | 1 | no | — |
| 407 | C32×D5 | — | 20 | 1 | no | — |
| 408 | C32×D5 | — | 20 | 1 | no | — |
| 409 | C32×D5 | — | 20 | 1 | no | — |
| 410 | C22×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 411 | C22×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 412 | C22×AGL(1,𝔽5) | — | 180 | 1 | no | — |
| 413 | C2×C4×D5 | — | 5 | 2 | no | — |
| 414 | #704 | — | 3 | 2 | no | — |
| 415 | #704 | — | 15 | 2 | no | — |
| 416 | C4×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 417 | C4×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 418 | C4×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 419 | C4×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 420 | #700 | — | 15 | 4 | no | — |
| 421 | D5⋊C8 | — | 15 | 4 | no | — |
| 422 | C5×M16 | — | 15 | 2 | no | — |
| 423 | #681 | — | 15 | 2 | no | — |
| 424 | #676 | — | 15 | 4 | no | — |
| 425 | C8×D5 | — | 15 | 4 | no | — |
| 426 | C3×C52 | — | 2 | 1 | no | — |
| 427 | C3×C52 | Dic3×M16 | 1 | 2 | yes | complemented |
| 428 | C23×C32 | — | 25 | 1 | no | — |
| 429 | C2×C32×C4 | — | 5 | 2 | no | — |
| 430 | C2×C32×C4 | — | 25 | 1 | no | — |
| 431 | C2×C32×C4 | — | 25 | 2 | no | — |
| 432 | C2×C32×C4 | — | 25 | 1 | no | — |
| 433 | C2×C3⋊Dic3 | — | 25 | 1 | no | — |
| 434 | C2×C3⋊Dic3 | — | 25 | 1 | no | — |
| 435 | C2×C3⋊Dic3 | — | 25 | 1 | no | — |
| 436 | C2×C3⋊Dic3 | — | 25 | 1 | no | — |
| 437 | C2×C3⋊Dic3 | — | 50 | 2 | no | — |
| 438 | C2×C3⋊Dic3 | — | 50 | 2 | no | — |
| 439 | C3×C3⋊C8 | — | 5 | 4 | no | — |
| 440 | C3×C3⋊C8 | — | 25 | 4 | no | — |
| 441 | C4×M16 | — | 225 | 1 | no | Sylow |
| 442 | C22×C3×C5 | — | 2 | 2 | no | — |
| 443 | C22×C3×C5 | — | 4 | 1 | no | — |
| 444 | C22×C3×C5 | — | 4 | 1 | no | — |
| 445 | C22×C3×C5 | — | 4 | 2 | no | — |
| 446 | C22×C3×C5 | Dic3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 447 | C22×C3×C5 | C4×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 448 | C2×C3×D5 | — | 5 | 2 | no | — |
| 449 | C2×C3×D5 | — | 5 | 2 | no | — |
| 450 | C2×C3×D5 | — | 5 | 2 | no | — |
| 451 | C2×C3×D5 | — | 5 | 2 | no | — |
| 452 | C2×C3×D5 | — | 10 | 2 | no | — |
| 453 | C2×C3×D5 | — | 10 | 2 | no | — |
| 454 | C2×C3×D5 | — | 10 | 2 | no | — |
| 455 | C2×C3×D5 | — | 10 | 2 | no | — |
| 456 | C2×C3×D5 | — | 10 | 2 | no | — |
| 457 | C2×C3×D5 | — | 10 | 2 | no | — |
| 458 | C2×C3×D5 | — | 10 | 2 | no | — |
| 459 | C2×C3×D5 | — | 10 | 2 | no | — |
| 460 | C2×C3×D5 | — | 10 | 2 | no | — |
| 461 | C2×C3×D5 | — | 10 | 2 | no | — |
| 462 | C2×C3×D5 | — | 20 | 2 | no | — |
| 463 | C2×C3×D5 | — | 20 | 2 | no | — |
| 464 | C2×C3×D5 | — | 20 | 1 | no | — |
| 465 | C2×C3×D5 | — | 20 | 1 | no | — |
| 466 | C2×C3×D5 | — | 20 | 2 | no | — |
| 467 | C2×C3×D5 | — | 20 | 1 | no | — |
| 468 | C2×C3×D5 | — | 20 | 1 | no | — |
| 469 | C2×C3×D5 | — | 20 | 2 | no | — |
| 470 | C2×C3×D5 | — | 20 | 1 | no | — |
| 471 | C2×C3×D5 | — | 20 | 1 | no | — |
| 472 | C2×C3×D5 | — | 20 | 2 | no | — |
| 473 | C2×C3×D5 | — | 20 | 1 | no | — |
| 474 | C2×C3×D5 | — | 20 | 1 | no | — |
| 475 | C2×C3×D5 | — | 20 | 2 | no | — |
| 476 | C2×C3×D5 | — | 20 | 1 | no | — |
| 477 | C2×C3×D5 | — | 20 | 1 | no | — |
| 478 | C2×C3×D5 | — | 20 | 1 | no | — |
| 479 | C2×C3×D5 | — | 20 | 1 | no | — |
| 480 | ΓL(1,𝔽16) | — | 15 | 4 | no | — |
| 481 | ΓL(1,𝔽16) | — | 15 | 4 | no | — |
| 482 | ΓL(1,𝔽16) | — | 15 | 4 | no | — |
| 483 | ΓL(1,𝔽16) | — | 15 | 4 | no | — |
| 484 | ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 485 | ΓL(1,𝔽16) | — | 30 | 4 | no | — |
| 486 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 487 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 488 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 489 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 490 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 491 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 492 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 493 | ΓL(1,𝔽16) | — | 30 | 2 | no | — |
| 494 | ΓL(1,𝔽16) | — | 60 | 4 | no | — |
| 495 | ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 496 | ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 497 | ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 498 | ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 499 | ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 500 | ΓL(1,𝔽16) | — | 60 | 2 | no | — |
| 501 | ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 502 | ΓL(1,𝔽16) | — | 60 | 1 | no | — |
| 503 | C3×C4×C5 | — | 5 | 2 | no | — |
| 504 | C3×C4×C5 | — | 5 | 2 | no | — |
| 505 | C3×C4×C5 | — | 5 | 2 | no | — |
| 506 | C3×C4×C5 | — | 5 | 2 | no | — |
| 507 | C3×C4×C5 | — | 10 | 2 | no | — |
| 508 | C3×C4×C5 | — | 10 | 2 | no | — |
| 509 | C3×Dic5 | — | 2 | 2 | no | — |
| 510 | C3×Dic5 | — | 2 | 2 | no | — |
| 511 | C3×Dic5 | Dic3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 512 | C3×Dic5 | C4×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 513 | C3×Dic5 | C2×D3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 514 | C3×Dic5 | C22×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 515 | C2×C52 | — | 2 | 1 | no | — |
| 516 | C2×C52 | C2×Dic32 | 1 | 1 | yes | characteristic |
| 517 | C5⋊D5 | — | 2 | 1 | no | — |
| 518 | C5⋊D5 | #63818 | 1 | 1 | yes | characteristic |
| 519 | C5⋊D5 | #63818 | 1 | 1 | yes | characteristic |
| 520 | C22×C3×C4 | — | 25 | 2 | no | — |
| 521 | C22×C3×C4 | — | 50 | 1 | no | — |
| 522 | C22×Dic3 | — | 75 | 2 | no | — |
| 523 | C22×Dic3 | — | 75 | 2 | no | — |
| 524 | C22×Dic3 | — | 150 | 1 | no | — |
| 525 | C22×Dic3 | — | 150 | 1 | no | — |
| 526 | C3×M16 | — | 15 | 2 | no | — |
| 527 | C3×M16 | — | 75 | 4 | no | — |
| 528 | C3×M16 | — | 75 | 2 | no | — |
| 529 | C2×C3×C8 | — | 75 | 4 | no | — |
| 530 | C4×Dic3 | — | 75 | 2 | no | — |
| 531 | C4×Dic3 | — | 75 | 2 | no | — |
| 532 | C4×Dic3 | — | 75 | 2 | no | — |
| 533 | C4×Dic3 | — | 75 | 2 | no | — |
| 534 | C4×Dic3 | — | 150 | 1 | no | — |
| 535 | C4×Dic3 | — | 150 | 1 | no | — |
| 536 | C4×Dic3 | — | 150 | 1 | no | — |
| 537 | C4×Dic3 | — | 150 | 1 | no | — |
| 538 | #208 | — | 5 | 2 | no | — |
| 539 | #208 | — | 25 | 4 | no | — |
| 540 | #208 | — | 25 | 2 | no | — |
| 541 | C2×C3⋊C8 | — | 25 | 4 | no | — |
| 542 | C32×C5 | — | 4 | 1 | no | — |
| 543 | C32×C5 | M16×AGL(1,𝔽5) | 1 | 2 | yes | complemented |
| 544 | C22×D5 | — | 5 | 2 | no | — |
| 545 | C22×D5 | — | 20 | 1 | no | — |
| 546 | C2×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 547 | C2×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 548 | C2×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 549 | C2×AGL(1,𝔽5) | — | 45 | 2 | no | — |
| 550 | C2×AGL(1,𝔽5) | — | 90 | 4 | no | — |
| 551 | C2×AGL(1,𝔽5) | — | 90 | 4 | no | — |
| 552 | C2×AGL(1,𝔽5) | — | 180 | 2 | no | — |
| 553 | C2×AGL(1,𝔽5) | — | 180 | 2 | no | — |
| 554 | C2×AGL(1,𝔽5) | — | 180 | 1 | no | — |
| 555 | C2×AGL(1,𝔽5) | — | 180 | 1 | no | — |
| 556 | C2×C4×C5 | — | 5 | 2 | no | — |
| 557 | C2×Dic5 | D3×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 558 | C4×D5 | — | 5 | 2 | no | — |
| 559 | C4×D5 | — | 5 | 2 | no | — |
| 560 | C4×D5 | — | 5 | 2 | no | — |
| 561 | C4×D5 | — | 5 | 2 | no | — |
| 562 | #170 | — | 3 | 4 | no | — |
| 563 | #170 | — | 15 | 4 | no | — |
| 564 | C5×C8 | — | 15 | 4 | no | — |
| 565 | #168 | — | 15 | 4 | no | — |
| 566 | C22×C32 | — | 25 | 1 | no | — |
| 567 | C22×C32 | — | 25 | 1 | no | — |
| 568 | C22×C32 | — | 50 | 1 | no | — |
| 569 | C22×C32 | — | 50 | 1 | no | — |
| 570 | C22×C32 | AGL(1,𝔽5)2 | 1 | 1 | yes | characteristic |
| 571 | C32×C4 | — | 5 | 2 | no | — |
| 572 | C32×C4 | — | 5 | 2 | no | — |
| 573 | C3⋊Dic3 | — | 25 | 2 | no | — |
| 574 | C3⋊Dic3 | — | 25 | 2 | no | — |
| 575 | C3⋊Dic3 | — | 50 | 1 | no | — |
| 576 | C3⋊Dic3 | — | 50 | 1 | no | — |
| 577 | C2×M16 | — | 75 | 2 | no | — |
| 578 | C2×C42 | — | 225 | 1 | no | — |
| 579 | #97 | — | 225 | 2 | no | — |
| 580 | C4×C8 | — | 225 | 2 | no | — |
| 581 | C2×C3×C5 | — | 2 | 2 | no | — |
| 582 | C2×C3×C5 | — | 2 | 2 | no | — |
| 583 | C2×C3×C5 | — | 2 | 2 | no | — |
| 584 | C2×C3×C5 | — | 2 | 2 | no | — |
| 585 | C2×C3×C5 | — | 2 | 2 | no | — |
| 586 | C2×C3×C5 | — | 4 | 1 | no | — |
| 587 | C2×C3×C5 | — | 4 | 1 | no | — |
| 588 | C2×C3×C5 | — | 4 | 2 | no | — |
| 589 | C2×C3×C5 | — | 4 | 1 | no | — |
| 590 | C2×C3×C5 | — | 4 | 1 | no | — |
| 591 | C2×C3×C5 | — | 4 | 2 | no | — |
| 592 | C2×C3×C5 | — | 4 | 1 | no | — |
| 593 | C2×C3×C5 | — | 4 | 1 | no | — |
| 594 | C2×C3×C5 | — | 4 | 2 | no | — |
| 595 | C2×C3×C5 | C2×Dic3×AGL(1,𝔽5) | 1 | 2 | yes | — |
| 596 | C2×C3×C5 | C2×C4×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 597 | C3×D5 | — | 5 | 2 | no | — |
| 598 | C3×D5 | — | 5 | 2 | no | — |
| 599 | C3×D5 | — | 5 | 2 | no | — |
| 600 | C3×D5 | — | 5 | 2 | no | — |
| 601 | C3×D5 | — | 10 | 2 | no | — |
| 602 | C3×D5 | — | 10 | 2 | no | — |
| 603 | C3×D5 | — | 10 | 2 | no | — |
| 604 | C3×D5 | — | 10 | 2 | no | — |
| 605 | C3×D5 | — | 10 | 2 | no | — |
| 606 | C3×D5 | — | 10 | 2 | no | — |
| 607 | C3×D5 | — | 20 | 2 | no | — |
| 608 | C3×D5 | — | 20 | 2 | no | — |
| 609 | C3×D5 | — | 20 | 1 | no | — |
| 610 | C3×D5 | — | 20 | 1 | no | — |
| 611 | C3×D5 | — | 20 | 1 | no | — |
| 612 | C3×D5 | — | 20 | 1 | no | — |
| 613 | C3×D5 | — | 20 | 2 | no | — |
| 614 | C3×D5 | — | 20 | 1 | no | — |
| 615 | C3×D5 | — | 20 | 1 | no | — |
| 616 | C3×D5 | — | 20 | 1 | no | — |
| 617 | C3×D5 | — | 20 | 1 | no | — |
| 618 | C3×D5 | — | 20 | 2 | no | — |
| 619 | C52 | #10591060 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 620 | C23×C3 | — | 25 | 2 | no | — |
| 621 | C23×C3 | — | 50 | 1 | no | — |
| 622 | C2×C3×C4 | — | 5 | 2 | no | — |
| 623 | C2×C3×C4 | — | 5 | 2 | no | — |
| 624 | C2×C3×C4 | — | 10 | 2 | no | — |
| 625 | C2×C3×C4 | — | 25 | 2 | no | — |
| 626 | C2×C3×C4 | — | 25 | 2 | no | — |
| 627 | C2×C3×C4 | — | 25 | 2 | no | — |
| 628 | C2×C3×C4 | — | 25 | 2 | no | — |
| 629 | C2×C3×C4 | — | 50 | 1 | no | — |
| 630 | C2×C3×C4 | — | 50 | 1 | no | — |
| 631 | C2×C3×C4 | — | 50 | 2 | no | — |
| 632 | C2×Dic3 | — | 75 | 2 | no | — |
| 633 | C2×Dic3 | — | 75 | 2 | no | — |
| 634 | C2×Dic3 | — | 75 | 2 | no | — |
| 635 | C2×Dic3 | — | 75 | 2 | no | — |
| 636 | C2×Dic3 | — | 150 | 4 | no | — |
| 637 | C2×Dic3 | — | 150 | 4 | no | — |
| 638 | C2×Dic3 | — | 150 | 2 | no | — |
| 639 | C2×Dic3 | — | 150 | 2 | no | — |
| 640 | C2×Dic3 | — | 150 | 2 | no | — |
| 641 | C2×Dic3 | — | 150 | 2 | no | — |
| 642 | C2×Dic3 | — | 150 | 1 | no | — |
| 643 | C2×Dic3 | — | 150 | 1 | no | — |
| 644 | C2×Dic3 | — | 150 | 1 | no | — |
| 645 | C2×Dic3 | — | 150 | 1 | no | — |
| 646 | C3×C8 | — | 15 | 4 | no | — |
| 647 | C3×C8 | — | 75 | 4 | no | — |
| 648 | C3⋊C8 | — | 5 | 4 | no | — |
| 649 | C3⋊C8 | — | 25 | 4 | no | — |
| 650 | C22×C5 | — | 4 | 1 | no | — |
| 651 | C22×C5 | Dic3×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 652 | C2×D5 | — | 5 | 2 | no | — |
| 653 | C2×D5 | — | 5 | 2 | no | — |
| 654 | C2×D5 | — | 10 | 2 | no | — |
| 655 | C2×D5 | — | 10 | 2 | no | — |
| 656 | C2×D5 | — | 20 | 1 | no | — |
| 657 | C2×D5 | — | 20 | 1 | no | — |
| 658 | C2×D5 | — | 20 | 1 | no | — |
| 659 | C2×D5 | — | 20 | 1 | no | — |
| 660 | C2×D5 | — | 20 | 1 | no | — |
| 661 | C2×D5 | — | 20 | 1 | no | — |
| 662 | AGL(1,𝔽5) | — | 45 | 4 | no | — |
| 663 | AGL(1,𝔽5) | — | 45 | 4 | no | — |
| 664 | AGL(1,𝔽5) | — | 90 | 2 | no | — |
| 665 | AGL(1,𝔽5) | — | 90 | 2 | no | — |
| 666 | AGL(1,𝔽5) | — | 180 | 1 | no | — |
| 667 | AGL(1,𝔽5) | — | 180 | 1 | no | — |
| 668 | AGL(1,𝔽5) | — | 180 | 2 | no | — |
| 669 | C4×C5 | — | 5 | 2 | no | — |
| 670 | C4×C5 | — | 5 | 2 | no | — |
| 671 | Dic5 | Dic3×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 672 | Dic5 | C2×D3×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 673 | C2×C32 | — | 2 | 1 | no | — |
| 674 | C2×C32 | — | 25 | 1 | no | — |
| 675 | C2×C32 | — | 25 | 1 | no | — |
| 676 | C2×C32 | — | 50 | 1 | no | — |
| 677 | C2×C32 | C2×AGL(1,𝔽5)2 | 1 | 1 | yes | characteristic |
| 678 | C22×C4 | — | 25 | 1 | no | — |
| 679 | C22×C4 | — | 225 | 1 | no | — |
| 680 | C22×C4 | — | 225 | 1 | no | — |
| 681 | M16 | — | 15 | 2 | no | — |
| 682 | M16 | — | 75 | 4 | no | — |
| 683 | M16 | — | 75 | 2 | no | — |
| 684 | C2×C8 | — | 75 | 4 | no | — |
| 685 | C42 | — | 225 | 1 | no | — |
| 686 | C42 | — | 225 | 1 | no | — |
| 687 | C42 | — | 225 | 1 | no | — |
| 688 | C42 | — | 225 | 1 | no | — |
| 689 | C3×C5 | — | 2 | 2 | no | — |
| 690 | C3×C5 | — | 4 | 1 | no | — |
| 691 | C3×C5 | — | 4 | 1 | no | — |
| 692 | C3×C5 | — | 4 | 2 | no | — |
| 693 | C3×C5 | #11751698 | 1 | 2 | yes | complemented |
| 694 | C3×C5 | M16×ΓL(1,𝔽16) | 1 | 2 | yes | complemented |
| 695 | C22×C3 | — | 2 | 1 | no | — |
| 696 | C22×C3 | — | 25 | 2 | no | — |
| 697 | C22×C3 | — | 25 | 2 | no | — |
| 698 | C22×C3 | — | 50 | 1 | no | — |
| 699 | C22×C3 | — | 50 | 1 | no | — |
| 700 | C22×C3 | — | 50 | 2 | no | — |
| 701 | C22×C3 | — | 50 | 2 | no | — |
| 702 | C22×C3 | — | 50 | 1 | no | — |
| 703 | C22×C3 | — | 50 | 1 | no | — |
| 704 | C22×C3 | — | 50 | 1 | no | — |
| 705 | C22×C3 | — | 50 | 1 | no | — |
| 706 | C22×C3 | AGL(1,𝔽5)×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 707 | C3×C4 | — | 5 | 2 | no | — |
| 708 | C3×C4 | — | 5 | 2 | no | — |
| 709 | C3×C4 | — | 5 | 2 | no | — |
| 710 | C3×C4 | — | 5 | 2 | no | — |
| 711 | C3×C4 | — | 10 | 2 | no | — |
| 712 | C3×C4 | — | 10 | 2 | no | — |
| 713 | Dic3 | — | 75 | 4 | no | — |
| 714 | Dic3 | — | 75 | 4 | no | — |
| 715 | Dic3 | — | 150 | 2 | no | — |
| 716 | Dic3 | — | 150 | 2 | no | — |
| 717 | Dic3 | — | 150 | 1 | no | — |
| 718 | Dic3 | — | 150 | 1 | no | — |
| 719 | Dic3 | — | 150 | 1 | no | — |
| 720 | Dic3 | — | 150 | 1 | no | — |
| 721 | Dic3 | — | 150 | 2 | no | — |
| 722 | Dic3 | — | 150 | 2 | no | — |
| 723 | C2×C5 | — | 2 | 2 | no | — |
| 724 | C2×C5 | — | 4 | 1 | no | — |
| 725 | C2×C5 | — | 4 | 1 | no | — |
| 726 | C2×C5 | — | 4 | 1 | no | — |
| 727 | C2×C5 | C2×Dic3×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 728 | D5 | — | 5 | 2 | no | — |
| 729 | D5 | — | 5 | 2 | no | — |
| 730 | D5 | — | 10 | 2 | no | — |
| 731 | D5 | — | 20 | 1 | no | — |
| 732 | D5 | — | 20 | 1 | no | — |
| 733 | D5 | — | 20 | 1 | no | — |
| 734 | D5 | — | 20 | 1 | no | — |
| 735 | C32 | #13107464 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 736 | C23 | — | 25 | 1 | no | — |
| 737 | C2×C4 | — | 5 | 2 | no | — |
| 738 | C2×C4 | — | 25 | 1 | no | — |
| 739 | C2×C4 | — | 25 | 1 | no | — |
| 740 | C2×C4 | — | 25 | 2 | no | — |
| 741 | C2×C4 | — | 450 | 2 | no | — |
| 742 | C2×C4 | — | 450 | 2 | no | — |
| 743 | C2×C4 | — | 225 | 1 | no | — |
| 744 | C2×C4 | — | 225 | 1 | no | — |
| 745 | C2×C4 | — | 225 | 1 | no | — |
| 746 | C2×C4 | — | 225 | 1 | no | — |
| 747 | C8 | — | 15 | 4 | no | — |
| 748 | C8 | — | 75 | 4 | no | — |
| 749 | C2×C3 | — | 2 | 1 | no | — |
| 750 | C2×C3 | — | 2 | 1 | no | — |
| 751 | C2×C3 | — | 2 | 2 | no | — |
| 752 | C2×C3 | — | 2 | 1 | no | — |
| 753 | C2×C3 | — | 25 | 2 | no | — |
| 754 | C2×C3 | — | 25 | 2 | no | — |
| 755 | C2×C3 | — | 50 | 1 | no | — |
| 756 | C2×C3 | — | 50 | 1 | no | — |
| 757 | C2×C3 | — | 50 | 1 | no | — |
| 758 | C2×C3 | — | 50 | 1 | no | — |
| 759 | C2×C3 | — | 50 | 2 | no | — |
| 760 | C2×C3 | C2×AGL(1,𝔽5)×ΓL(1,𝔽16) | 1 | 2 | yes | — |
| 761 | C5 | — | 4 | 1 | no | — |
| 762 | C5 | #72229548 | 1 | 2 | yes | complemented |
| 763 | C22 | — | 25 | 1 | no | — |
| 764 | C22 | — | 25 | 1 | no | — |
| 765 | C22 | — | 50 | 1 | no | — |
| 766 | C22 | — | 50 | 1 | no | — |
| 767 | C22 | ΓL(1,𝔽16)2 | 1 | 1 | yes | characteristic |
| 768 | C4 | — | 5 | 2 | no | — |
| 769 | C4 | — | 5 | 2 | no | — |
| 770 | C4 | — | 450 | 1 | no | — |
| 771 | C4 | — | 450 | 1 | no | — |
| 772 | C4 | — | 225 | 2 | no | — |
| 773 | C4 | — | 225 | 2 | no | — |
| 774 | C3 | — | 2 | 1 | no | — |
| 775 | C3 | #72231083 | 1 | 2 | yes | complemented |
| 776 | C2 | — | 2 | 1 | no | — |
| 777 | C2 | — | 25 | 1 | no | — |
| 778 | C2 | — | 25 | 1 | no | — |
| 779 | C2 | — | 50 | 1 | no | — |
| 780 | C2 | C2×ΓL(1,𝔽16)2 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta