Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
2060 conjugacy classes of subgroups.
The subgroup lattice has 1021 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61329 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61089 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60817 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60622 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #30938 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #30551 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #30258 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #29858 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #28763 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #28632 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #25924 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #25875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #25747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #25588 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #25180 | C2 | 1 | 4 | yes | maximal, complemented |
| 17 | #24456 | C2 | 1 | 4 | yes | maximal, complemented |
| 18 | #22234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #21137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | C2×#576 | C22 | 1 | 2 | yes | — |
| 21 | #3508 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #3503 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #3498 | C22 | 1 | 1 | yes | characteristic |
| 24 | #3498 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3375 | — | 2 | 1 | no | — |
| 26 | #3373 | — | 2 | 1 | no | — |
| 27 | #3368 | — | 2 | 1 | no | — |
| 28 | #3366 | — | 2 | 1 | no | — |
| 29 | #3365 | — | 2 | 1 | no | — |
| 30 | #3362 | — | 2 | 1 | no | — |
| 31 | #3361 | — | 2 | 1 | no | — |
| 32 | #3358 | — | 2 | 1 | no | — |
| 33 | #3287 | — | 2 | 1 | no | — |
| 34 | #3287 | — | 2 | 1 | no | — |
| 35 | D4×D8 | — | 2 | 1 | no | — |
| 36 | D4×D8 | — | 2 | 1 | no | — |
| 37 | #3274 | — | 2 | 1 | no | — |
| 38 | #3274 | — | 2 | 1 | no | — |
| 39 | #3274 | — | 2 | 1 | no | — |
| 40 | #3274 | — | 2 | 1 | no | — |
| 41 | #3220 | — | 2 | 4 | no | — |
| 42 | #3207 | — | 2 | 1 | no | — |
| 43 | #3207 | — | 2 | 1 | no | — |
| 44 | #3205 | — | 2 | 1 | no | — |
| 45 | #3205 | — | 2 | 1 | no | — |
| 46 | #3151 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #3141 | — | 2 | 1 | no | — |
| 50 | #3141 | C22 | 1 | 1 | yes | characteristic |
| 51 | #3138 | — | 2 | 1 | no | — |
| 52 | #3138 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #3138 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #3136 | — | 2 | 4 | no | — |
| 55 | #3136 | C22 | 1 | 2 | yes | complemented |
| 56 | #3136 | C22 | 1 | 4 | yes | complemented |
| 57 | #3131 | — | 2 | 1 | no | — |
| 58 | #3131 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×#486 | — | 2 | 1 | no | — |
| 60 | C2×#486 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×#486 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #3081 | C22 | 1 | 2 | yes | complemented |
| 63 | #3079 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C2×#472 | C22 | 1 | 4 | yes | complemented |
| 65 | #3058 | C22 | 1 | 2 | yes | — |
| 66 | #3045 | C22 | 1 | 2 | yes | — |
| 67 | #3041 | C22 | 1 | 4 | yes | complemented |
| 68 | #3038 | C22 | 1 | 1 | yes | characteristic |
| 69 | #3038 | C22 | 1 | 1 | yes | characteristic |
| 70 | #3038 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | C2×#453 | C22 | 1 | 4 | yes | complemented |
| 72 | #3008 | C22 | 1 | 2 | yes | — |
| 73 | #3008 | C22 | 1 | 2 | yes | — |
| 74 | #3008 | C22 | 1 | 4 | yes | complemented |
| 75 | #2960 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #2946 | C22 | 1 | 2 | yes | complemented |
| 77 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 78 | #2931 | C22 | 1 | 1 | yes | characteristic |
| 79 | #2922 | C22 | 1 | 1 | yes | characteristic, complemented |
| 80 | #2897 | C22 | 1 | 4 | yes | complemented |
| 81 | C4×#131 | C22 | 1 | 1 | yes | characteristic, complemented |
| 82 | #2867 | C22 | 1 | 1 | yes | characteristic, complemented |
| 83 | #2858 | C22 | 1 | 1 | yes | characteristic, complemented |
| 84 | #2063 | C22 | 1 | 4 | yes | complemented |
| 85 | #2051 | C22 | 1 | 4 | yes | complemented |
| 86 | #2051 | C22 | 1 | 4 | yes | complemented |
| 87 | #2045 | C22 | 1 | 4 | yes | complemented |
| 88 | #2037 | C22 | 1 | 4 | yes | complemented |
| 89 | #2027 | C22 | 1 | 4 | yes | complemented |
| 90 | #2011 | C22 | 1 | 4 | yes | complemented |
| 91 | #2011 | C22 | 1 | 4 | yes | complemented |
| 92 | #2002 | C22 | 1 | 4 | yes | complemented |
| 93 | #2002 | C22 | 1 | 4 | yes | complemented |
| 94 | #1997 | C22 | 1 | 1 | yes | characteristic, complemented |
| 95 | #1994 | C22 | 1 | 1 | yes | characteristic, complemented |
| 96 | #1978 | C22 | 1 | 4 | yes | complemented |
| 97 | #1978 | C22 | 1 | 4 | yes | complemented |
| 98 | #1965 | C22 | 1 | 1 | yes | characteristic, complemented |
| 99 | #1965 | C22 | 1 | 1 | yes | characteristic, complemented |
| 100 | #1965 | C22 | 1 | 1 | yes | characteristic, complemented |
| 101 | #1962 | C22 | 1 | 1 | yes | characteristic |
| 102 | #1929 | C22 | 1 | 2 | yes | complemented |
| 103 | #1929 | C22 | 1 | 4 | yes | complemented |
| 104 | #1922 | C22 | 1 | 2 | yes | complemented |
| 105 | #1907 | C22 | 1 | 4 | yes | complemented |
| 106 | #1887 | C22 | 1 | 4 | yes | complemented |
| 107 | #1883 | C22 | 1 | 4 | yes | complemented |
| 108 | #1876 | C22 | 1 | 2 | yes | — |
| 109 | #1866 | C22 | 1 | 2 | yes | complemented |
| 110 | #1866 | C22 | 1 | 4 | yes | complemented |
| 111 | #1848 | C22 | 1 | 1 | yes | characteristic, complemented |
| 112 | #1792 | C22 | 1 | 4 | yes | complemented |
| 113 | C4×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 114 | C4×#104 | C22 | 1 | 1 | yes | characteristic, complemented |
| 115 | C4×#104 | C22 | 1 | 1 | yes | characteristic, complemented |
| 116 | #1744 | C22 | 1 | 1 | yes | characteristic, complemented |
| 117 | C2×H(5,𝔽2) | C23 | 1 | 2 | yes | — |
| 118 | C2×H(5,𝔽2) | C23 | 1 | 2 | yes | — |
| 119 | #576 | — | 4 | 8 | no | — |
| 120 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 121 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 122 | C2×AGL(1,ℤ/8) | C23 | 1 | 2 | yes | — |
| 123 | C2×AGL(1,ℤ/8) | C23 | 1 | 2 | yes | — |
| 124 | C2×AGL(1,ℤ/8) | C23 | 1 | 2 | yes | — |
| 125 | C2×AGL(1,ℤ/8) | C23 | 1 | 4 | yes | — |
| 126 | C2×#135 | — | 2 | 2 | no | — |
| 127 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 128 | C22×D8 | — | 2 | 2 | no | — |
| 129 | C22×D8 | C23 | 1 | 2 | yes | — |
| 130 | C22×D8 | C23 | 1 | 2 | yes | — |
| 131 | C22×D8 | C23 | 1 | 4 | yes | — |
| 132 | C2×#131 | C23 | 1 | 2 | yes | — |
| 133 | C2×#131 | C23 | 1 | 2 | yes | — |
| 134 | #559 | — | 2 | 1 | no | — |
| 135 | #559 | — | 2 | 1 | no | — |
| 136 | Q82 | — | 2 | 1 | no | — |
| 137 | #557 | — | 2 | 1 | no | — |
| 138 | #554 | — | 2 | 1 | no | — |
| 139 | #554 | — | 4 | 1 | no | — |
| 140 | #550 | — | 2 | 1 | no | — |
| 141 | #550 | — | 2 | 1 | no | — |
| 142 | #550 | — | 2 | 1 | no | — |
| 143 | #550 | — | 2 | 1 | no | — |
| 144 | #550 | — | 2 | 1 | no | — |
| 145 | #550 | — | 2 | 1 | no | — |
| 146 | D4×Q8 | — | 2 | 1 | no | — |
| 147 | D4×Q8 | — | 4 | 1 | no | — |
| 148 | #546 | — | 4 | 1 | no | — |
| 149 | #546 | — | 4 | 1 | no | — |
| 150 | D42 | — | 2 | 1 | no | — |
| 151 | D42 | — | 2 | 1 | no | — |
| 152 | D42 | — | 2 | 1 | no | — |
| 153 | D42 | — | 2 | 1 | no | — |
| 154 | D42 | — | 4 | 1 | no | — |
| 155 | D42 | — | 4 | 1 | no | — |
| 156 | D42 | — | 4 | 1 | no | — |
| 157 | D42 | — | 4 | 1 | no | — |
| 158 | #544 | — | 2 | 2 | no | — |
| 159 | #544 | C23 | 1 | 2 | yes | — |
| 160 | #540 | — | 2 | 2 | no | — |
| 161 | #535 | — | 2 | 2 | no | — |
| 162 | #535 | — | 2 | 2 | no | — |
| 163 | #535 | C23 | 1 | 2 | yes | — |
| 164 | #535 | C23 | 1 | 2 | yes | — |
| 165 | #535 | C23 | 1 | 2 | yes | — |
| 166 | #533 | — | 2 | 1 | no | — |
| 167 | #533 | C23 | 1 | 1 | yes | characteristic |
| 168 | #532 | — | 2 | 1 | no | — |
| 169 | #532 | — | 2 | 1 | no | — |
| 170 | #532 | — | 2 | 1 | no | — |
| 171 | #532 | — | 2 | 1 | no | — |
| 172 | #532 | C23 | 1 | 1 | yes | characteristic |
| 173 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 174 | C2×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 175 | C2×#127 | — | 2 | 1 | no | — |
| 176 | C2×#127 | — | 2 | 1 | no | — |
| 177 | C2×#127 | — | 4 | 1 | no | — |
| 178 | C2×#127 | — | 4 | 1 | no | — |
| 179 | C2×#127 | C23 | 1 | 4 | yes | — |
| 180 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 181 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 182 | C2×#127 | C23 | 1 | 1 | yes | characteristic |
| 183 | C2×#124 | — | 4 | 1 | no | — |
| 184 | #520 | C23 | 1 | 2 | yes | — |
| 185 | #518 | C23 | 1 | 2 | yes | — |
| 186 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 187 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 188 | #496 | — | 2 | 2 | no | — |
| 189 | #493 | — | 2 | 1 | no | — |
| 190 | #493 | — | 2 | 1 | no | — |
| 191 | #493 | — | 2 | 1 | no | — |
| 192 | #493 | — | 2 | 1 | no | — |
| 193 | #493 | — | 2 | 1 | no | — |
| 194 | #493 | — | 2 | 1 | no | — |
| 195 | #493 | — | 2 | 1 | no | — |
| 196 | #493 | — | 2 | 2 | no | — |
| 197 | #492 | — | 2 | 1 | no | — |
| 198 | #490 | — | 2 | 2 | no | — |
| 199 | #490 | — | 2 | 2 | no | — |
| 200 | #490 | — | 2 | 2 | no | — |
| 201 | #490 | — | 2 | 4 | no | — |
| 202 | #489 | — | 2 | 2 | no | — |
| 203 | #489 | — | 2 | 2 | no | — |
| 204 | #489 | — | 2 | 4 | no | — |
| 205 | #488 | — | 2 | 2 | no | — |
| 206 | #488 | — | 2 | 4 | no | — |
| 207 | #488 | D4 | 1 | 4 | yes | complemented |
| 208 | #487 | — | 2 | 1 | no | — |
| 209 | #487 | D4 | 1 | 1 | yes | characteristic, complemented |
| 210 | #487 | D4 | 1 | 1 | yes | characteristic, complemented |
| 211 | #486 | — | 2 | 1 | no | — |
| 212 | #486 | — | 2 | 1 | no | — |
| 213 | #486 | — | 2 | 1 | no | — |
| 214 | #486 | — | 2 | 1 | no | — |
| 215 | #486 | — | 2 | 1 | no | — |
| 216 | #486 | — | 2 | 2 | no | — |
| 217 | #486 | — | 2 | 4 | no | — |
| 218 | #486 | — | 2 | 1 | no | — |
| 219 | #486 | — | 2 | 1 | no | — |
| 220 | #486 | — | 2 | 1 | no | — |
| 221 | #486 | — | 2 | 1 | no | — |
| 222 | #486 | — | 2 | 1 | no | — |
| 223 | #486 | — | 2 | 2 | no | — |
| 224 | #486 | — | 2 | 1 | no | — |
| 225 | #486 | D4 | 1 | 1 | yes | characteristic, complemented |
| 226 | #486 | D4 | 1 | 1 | yes | characteristic, complemented |
| 227 | #478 | — | 2 | 2 | no | — |
| 228 | #478 | — | 2 | 2 | no | — |
| 229 | #477 | — | 2 | 1 | no | — |
| 230 | #476 | — | 2 | 1 | no | — |
| 231 | #476 | — | 2 | 2 | no | — |
| 232 | #475 | — | 2 | 1 | no | — |
| 233 | #474 | — | 2 | 1 | no | — |
| 234 | #474 | — | 2 | 2 | no | — |
| 235 | #472 | — | 4 | 8 | no | — |
| 236 | #469 | — | 2 | 2 | no | — |
| 237 | #469 | — | 2 | 2 | no | — |
| 238 | #466 | — | 2 | 2 | no | — |
| 239 | #466 | — | 2 | 2 | no | — |
| 240 | #464 | — | 2 | 2 | no | — |
| 241 | #463 | — | 2 | 2 | no | — |
| 242 | #463 | — | 2 | 4 | no | — |
| 243 | #463 | — | 2 | 4 | no | — |
| 244 | #460 | — | 2 | 2 | no | — |
| 245 | #460 | — | 2 | 1 | no | — |
| 246 | #460 | — | 2 | 1 | no | — |
| 247 | #460 | — | 2 | 1 | no | — |
| 248 | #460 | — | 2 | 1 | no | — |
| 249 | #460 | — | 2 | 1 | no | — |
| 250 | #460 | — | 2 | 1 | no | — |
| 251 | #459 | — | 2 | 2 | no | — |
| 252 | #459 | — | 2 | 1 | no | — |
| 253 | #459 | — | 2 | 1 | no | — |
| 254 | #459 | — | 2 | 1 | no | — |
| 255 | #459 | — | 2 | 1 | no | — |
| 256 | #459 | — | 2 | 1 | no | — |
| 257 | #459 | — | 2 | 1 | no | — |
| 258 | #459 | — | 2 | 4 | no | — |
| 259 | #459 | — | 2 | 4 | no | — |
| 260 | #453 | — | 4 | 8 | no | — |
| 261 | #449 | — | 2 | 4 | no | — |
| 262 | #449 | — | 2 | 4 | no | — |
| 263 | #449 | — | 2 | 2 | no | — |
| 264 | #449 | — | 2 | 2 | no | — |
| 265 | #449 | — | 2 | 2 | no | — |
| 266 | #449 | — | 2 | 2 | no | — |
| 267 | #447 | — | 2 | 4 | no | — |
| 268 | #447 | — | 2 | 4 | no | — |
| 269 | #447 | — | 2 | 2 | no | — |
| 270 | #447 | — | 2 | 2 | no | — |
| 271 | #447 | — | 2 | 2 | no | — |
| 272 | #447 | — | 2 | 2 | no | — |
| 273 | #446 | — | 2 | 1 | no | — |
| 274 | #446 | — | 2 | 1 | no | — |
| 275 | C8×Q8 | — | 2 | 1 | no | — |
| 276 | C8×Q8 | — | 2 | 1 | no | — |
| 277 | #442 | — | 2 | 2 | no | — |
| 278 | #440 | — | 2 | 2 | no | — |
| 279 | C4×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 280 | C4×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 281 | C4×SD16 | — | 2 | 2 | no | — |
| 282 | C4×SD16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 283 | C4×SD16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 284 | C4×SD16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 285 | C4×SD16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 286 | C4×D8 | — | 2 | 2 | no | — |
| 287 | C4×D8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 288 | C4×D8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 289 | #436 | — | 2 | 1 | no | — |
| 290 | #436 | — | 2 | 1 | no | — |
| 291 | C8×D4 | — | 2 | 1 | no | — |
| 292 | C8×D4 | — | 2 | 1 | no | — |
| 293 | #433 | — | 2 | 2 | no | — |
| 294 | #431 | — | 2 | 1 | no | — |
| 295 | #431 | — | 2 | 1 | no | — |
| 296 | C2×#108 | C23 | 1 | 2 | yes | — |
| 297 | C2×#108 | C23 | 1 | 4 | yes | — |
| 298 | #428 | C23 | 1 | 2 | yes | — |
| 299 | #427 | C23 | 1 | 1 | yes | characteristic |
| 300 | #424 | C23 | 1 | 2 | yes | — |
| 301 | #424 | C23 | 1 | 2 | yes | — |
| 302 | #423 | C23 | 1 | 1 | yes | characteristic |
| 303 | #423 | C23 | 1 | 1 | yes | characteristic |
| 304 | C2×#104 | C23 | 1 | 2 | yes | — |
| 305 | C2×#104 | C23 | 1 | 2 | yes | — |
| 306 | C2×#104 | C23 | 1 | 4 | yes | — |
| 307 | #418 | — | 2 | 4 | no | — |
| 308 | #418 | C23 | 1 | 2 | yes | — |
| 309 | #418 | C23 | 1 | 2 | yes | — |
| 310 | #418 | C23 | 1 | 4 | yes | — |
| 311 | #418 | C23 | 1 | 4 | yes | — |
| 312 | #418 | C23 | 1 | 2 | yes | — |
| 313 | #417 | — | 2 | 4 | no | — |
| 314 | #417 | C23 | 1 | 2 | yes | — |
| 315 | #417 | C23 | 1 | 4 | yes | — |
| 316 | #416 | — | 2 | 4 | no | — |
| 317 | #416 | C23 | 1 | 4 | yes | — |
| 318 | #416 | C23 | 1 | 1 | yes | characteristic |
| 319 | #416 | C23 | 1 | 1 | yes | characteristic |
| 320 | C2×#102 | — | 2 | 4 | no | — |
| 321 | C2×#102 | C23 | 1 | 2 | yes | — |
| 322 | C2×#102 | C23 | 1 | 4 | yes | — |
| 323 | C2×#102 | C23 | 1 | 2 | yes | — |
| 324 | C2×#100 | C23 | 1 | 4 | yes | — |
| 325 | C2×#100 | C23 | 1 | 4 | yes | — |
| 326 | C2×#100 | C23 | 1 | 4 | yes | — |
| 327 | #408 | C23 | 1 | 2 | yes | — |
| 328 | #408 | C23 | 1 | 2 | yes | — |
| 329 | #405 | — | 2 | 2 | no | — |
| 330 | #405 | C23 | 1 | 2 | yes | — |
| 331 | #405 | C23 | 1 | 2 | yes | — |
| 332 | C4×M16 | — | 2 | 1 | no | — |
| 333 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 334 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 335 | C2×C4×C8 | — | 2 | 1 | no | — |
| 336 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 337 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 338 | #390 | — | 4 | 1 | no | — |
| 339 | #390 | C23 | 1 | 4 | yes | — |
| 340 | C43 | C23 | 1 | 1 | yes | characteristic |
| 341 | #343 | C23 | 1 | 4 | yes | — |
| 342 | #341 | C23 | 1 | 2 | yes | — |
| 343 | #339 | C23 | 1 | 4 | yes | — |
| 344 | #339 | C23 | 1 | 2 | yes | — |
| 345 | #339 | C23 | 1 | 2 | yes | — |
| 346 | #336 | C23 | 1 | 2 | yes | — |
| 347 | #336 | C23 | 1 | 2 | yes | — |
| 348 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 349 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 350 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 351 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 352 | C2×#41 | — | 2 | 2 | no | — |
| 353 | C2×#41 | — | 2 | 2 | no | — |
| 354 | C2×#41 | — | 2 | 2 | no | — |
| 355 | C2×#41 | — | 2 | 2 | no | — |
| 356 | C2×#41 | — | 4 | 1 | no | — |
| 357 | C2×#41 | — | 4 | 1 | no | — |
| 358 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 359 | C2×#41 | C24 | 1 | 2 | yes | — |
| 360 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 361 | C22×Q8 | — | 2 | 1 | no | — |
| 362 | C22×Q8 | — | 4 | 1 | no | — |
| 363 | C22×D4 | — | 2 | 2 | no | — |
| 364 | C22×D4 | — | 2 | 2 | no | — |
| 365 | C22×D4 | — | 2 | 2 | no | — |
| 366 | C22×D4 | — | 2 | 2 | no | — |
| 367 | C22×D4 | — | 2 | 1 | no | — |
| 368 | C22×D4 | — | 2 | 1 | no | — |
| 369 | C22×D4 | — | 2 | 1 | no | — |
| 370 | C22×D4 | — | 2 | 1 | no | — |
| 371 | C22×D4 | — | 2 | 1 | no | — |
| 372 | C22×D4 | — | 2 | 1 | no | — |
| 373 | C22×D4 | — | 4 | 1 | no | — |
| 374 | C22×D4 | — | 4 | 1 | no | — |
| 375 | C22×D4 | — | 4 | 1 | no | — |
| 376 | C22×D4 | — | 4 | 1 | no | — |
| 377 | C22×D4 | — | 4 | 4 | no | — |
| 378 | C22×D4 | — | 4 | 2 | no | — |
| 379 | C22×D4 | — | 4 | 2 | no | — |
| 380 | C22×D4 | C24 | 1 | 2 | yes | — |
| 381 | C22×D4 | C24 | 1 | 2 | yes | — |
| 382 | C22×D4 | C24 | 1 | 2 | yes | — |
| 383 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 384 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 385 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 386 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 387 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 388 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 389 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 390 | #135 | — | 2 | 4 | no | — |
| 391 | #135 | — | 4 | 8 | no | — |
| 392 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×SD16 | — | 2 | 2 | no | — |
| 394 | C2×SD16 | — | 2 | 2 | no | — |
| 395 | C2×SD16 | — | 2 | 2 | no | — |
| 396 | C2×SD16 | — | 2 | 4 | no | — |
| 397 | C2×SD16 | C2×D4 | 1 | 1 | yes | characteristic |
| 398 | C2×SD16 | C2×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×D8 | — | 2 | 2 | no | — |
| 400 | C2×D8 | — | 2 | 2 | no | — |
| 401 | C2×D8 | — | 2 | 2 | no | — |
| 402 | C2×D8 | — | 2 | 4 | no | — |
| 403 | C2×D8 | — | 2 | 2 | no | — |
| 404 | C2×D8 | — | 2 | 2 | no | — |
| 405 | C2×D8 | — | 2 | 2 | no | — |
| 406 | C2×D8 | — | 2 | 2 | no | — |
| 407 | C2×D8 | — | 2 | 4 | no | — |
| 408 | C2×D8 | — | 2 | 4 | no | — |
| 409 | C2×D8 | — | 4 | 4 | no | — |
| 410 | C2×D8 | — | 4 | 4 | no | — |
| 411 | C2×D8 | — | 4 | 4 | no | — |
| 412 | C2×D8 | — | 4 | 4 | no | — |
| 413 | C2×D8 | — | 4 | 8 | no | — |
| 414 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 415 | #131 | — | 2 | 4 | no | — |
| 416 | #131 | — | 4 | 2 | no | — |
| 417 | #131 | — | 4 | 4 | no | — |
| 418 | C2×M16 | — | 2 | 2 | no | — |
| 419 | C2×M16 | — | 2 | 2 | no | — |
| 420 | C2×M16 | C24 | 1 | 2 | yes | — |
| 421 | C2×M16 | C24 | 1 | 2 | yes | — |
| 422 | C2×M16 | C24 | 1 | 2 | yes | — |
| 423 | C2×M16 | C24 | 1 | 2 | yes | — |
| 424 | C22×C8 | — | 2 | 2 | no | — |
| 425 | C22×C8 | — | 2 | 2 | no | — |
| 426 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 427 | C22×C8 | C24 | 1 | 2 | yes | — |
| 428 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 429 | C4⋊Q8 | — | 2 | 2 | no | — |
| 430 | C4⋊Q8 | — | 2 | 2 | no | — |
| 431 | C4⋊Q8 | — | 2 | 1 | no | — |
| 432 | C4⋊Q8 | — | 2 | 1 | no | — |
| 433 | C4⋊Q8 | — | 2 | 1 | no | — |
| 434 | C4⋊Q8 | — | 2 | 1 | no | — |
| 435 | C4⋊Q8 | — | 4 | 1 | no | — |
| 436 | C4⋊Q8 | — | 4 | 1 | no | — |
| 437 | C4⋊Q8 | — | 4 | 2 | no | — |
| 438 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 439 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 440 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 441 | #127 | — | 2 | 2 | no | — |
| 442 | #127 | — | 2 | 2 | no | — |
| 443 | #127 | — | 2 | 2 | no | — |
| 444 | #127 | — | 2 | 1 | no | — |
| 445 | #127 | — | 2 | 1 | no | — |
| 446 | #127 | — | 2 | 1 | no | — |
| 447 | #127 | — | 2 | 1 | no | — |
| 448 | #127 | — | 2 | 1 | no | — |
| 449 | #127 | — | 2 | 1 | no | — |
| 450 | #127 | — | 2 | 1 | no | — |
| 451 | #127 | — | 2 | 1 | no | — |
| 452 | #127 | — | 2 | 1 | no | — |
| 453 | #127 | — | 2 | 1 | no | — |
| 454 | #127 | — | 2 | 1 | no | — |
| 455 | #127 | — | 2 | 1 | no | — |
| 456 | #127 | — | 4 | 4 | no | — |
| 457 | #127 | — | 4 | 4 | no | — |
| 458 | #127 | — | 4 | 1 | no | — |
| 459 | #127 | — | 4 | 1 | no | — |
| 460 | #127 | — | 4 | 1 | no | — |
| 461 | #127 | — | 4 | 1 | no | — |
| 462 | #127 | — | 8 | 4 | no | — |
| 463 | #127 | — | 8 | 4 | no | — |
| 464 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 465 | #125 | — | 2 | 2 | no | — |
| 466 | #125 | — | 2 | 2 | no | — |
| 467 | #125 | — | 4 | 2 | no | — |
| 468 | #125 | C2×D4 | 1 | 2 | yes | — |
| 469 | #124 | — | 2 | 2 | no | — |
| 470 | #124 | — | 2 | 2 | no | — |
| 471 | #124 | — | 2 | 2 | no | — |
| 472 | #124 | — | 4 | 1 | no | — |
| 473 | #124 | — | 4 | 1 | no | — |
| 474 | #124 | — | 8 | 4 | no | — |
| 475 | #124 | C2×D4 | 1 | 2 | yes | — |
| 476 | #123 | — | 4 | 2 | no | — |
| 477 | #123 | — | 4 | 2 | no | — |
| 478 | C22⋊Q8 | — | 2 | 1 | no | — |
| 479 | C22⋊Q8 | — | 2 | 1 | no | — |
| 480 | C22⋊Q8 | — | 4 | 2 | no | — |
| 481 | C22⋊Q8 | — | 4 | 2 | no | — |
| 482 | C22⋊Q8 | — | 4 | 2 | no | — |
| 483 | C22⋊Q8 | — | 4 | 1 | no | — |
| 484 | C22⋊Q8 | — | 4 | 1 | no | — |
| 485 | #121 | — | 2 | 1 | no | — |
| 486 | #121 | — | 2 | 1 | no | — |
| 487 | #121 | — | 2 | 2 | no | — |
| 488 | #121 | — | 2 | 2 | no | — |
| 489 | #121 | — | 2 | 2 | no | — |
| 490 | #121 | — | 2 | 2 | no | — |
| 491 | #121 | — | 2 | 2 | no | — |
| 492 | #121 | — | 2 | 2 | no | — |
| 493 | #121 | — | 4 | 2 | no | — |
| 494 | #121 | — | 4 | 2 | no | — |
| 495 | #121 | — | 4 | 2 | no | — |
| 496 | #121 | — | 4 | 2 | no | — |
| 497 | #121 | — | 4 | 2 | no | — |
| 498 | #121 | — | 4 | 2 | no | — |
| 499 | #121 | — | 4 | 1 | no | — |
| 500 | #121 | — | 4 | 1 | no | — |
| 501 | #121 | — | 4 | 1 | no | — |
| 502 | #121 | — | 4 | 1 | no | — |
| 503 | #121 | — | 4 | 1 | no | — |
| 504 | #121 | — | 4 | 1 | no | — |
| 505 | #120 | — | 4 | 2 | no | — |
| 506 | #120 | — | 4 | 2 | no | — |
| 507 | #120 | — | 4 | 2 | no | — |
| 508 | #120 | — | 4 | 2 | no | — |
| 509 | #120 | — | 4 | 2 | no | — |
| 510 | #120 | — | 4 | 2 | no | — |
| 511 | #120 | — | 4 | 2 | no | — |
| 512 | C4×Q8 | — | 2 | 1 | no | — |
| 513 | C4×Q8 | — | 2 | 1 | no | — |
| 514 | C4×Q8 | — | 2 | 2 | no | — |
| 515 | C4×Q8 | — | 4 | 1 | no | — |
| 516 | C4×Q8 | — | 4 | 1 | no | — |
| 517 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 518 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 519 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 520 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 521 | C4×D4 | — | 2 | 1 | no | — |
| 522 | C4×D4 | — | 2 | 1 | no | — |
| 523 | C4×D4 | — | 2 | 1 | no | — |
| 524 | C4×D4 | — | 2 | 1 | no | — |
| 525 | C4×D4 | — | 2 | 2 | no | — |
| 526 | C4×D4 | — | 2 | 2 | no | — |
| 527 | C4×D4 | — | 2 | 2 | no | — |
| 528 | C4×D4 | — | 2 | 2 | no | — |
| 529 | C4×D4 | — | 2 | 2 | no | — |
| 530 | C4×D4 | — | 2 | 1 | no | — |
| 531 | C4×D4 | — | 2 | 1 | no | — |
| 532 | C4×D4 | — | 4 | 1 | no | — |
| 533 | C4×D4 | — | 4 | 1 | no | — |
| 534 | C4×D4 | — | 4 | 1 | no | — |
| 535 | C4×D4 | — | 4 | 1 | no | — |
| 536 | C4×D4 | — | 4 | 1 | no | — |
| 537 | C4×D4 | — | 4 | 1 | no | — |
| 538 | C4×D4 | — | 4 | 2 | no | — |
| 539 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 540 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 541 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 542 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 543 | #117 | — | 2 | 1 | no | — |
| 544 | #117 | — | 2 | 1 | no | — |
| 545 | #117 | — | 2 | 2 | no | — |
| 546 | #117 | C24 | 1 | 1 | yes | characteristic |
| 547 | #117 | C24 | 1 | 1 | yes | characteristic |
| 548 | #117 | C24 | 1 | 2 | yes | — |
| 549 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 550 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 551 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 552 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 553 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 554 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 555 | C2×C42 | — | 2 | 1 | no | — |
| 556 | C2×C42 | — | 2 | 1 | no | — |
| 557 | C2×C42 | — | 2 | 1 | no | — |
| 558 | C2×C42 | — | 2 | 1 | no | — |
| 559 | C2×C42 | C24 | 1 | 2 | yes | — |
| 560 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 561 | #108 | — | 4 | 2 | no | — |
| 562 | #108 | — | 4 | 4 | no | — |
| 563 | #107 | — | 2 | 2 | no | — |
| 564 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 565 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 566 | #106 | — | 2 | 2 | no | — |
| 567 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 568 | #106 | C2×D4 | 1 | 1 | yes | characteristic |
| 569 | C4⋊C8 | — | 2 | 2 | no | — |
| 570 | C4⋊C8 | — | 2 | 2 | no | — |
| 571 | C4⋊C8 | — | 2 | 2 | no | — |
| 572 | C4⋊C8 | — | 2 | 2 | no | — |
| 573 | C4⋊C8 | — | 2 | 1 | no | — |
| 574 | C4⋊C8 | — | 2 | 1 | no | — |
| 575 | C4⋊C8 | — | 2 | 1 | no | — |
| 576 | C4⋊C8 | — | 2 | 1 | no | — |
| 577 | #104 | — | 2 | 4 | no | — |
| 578 | #104 | — | 4 | 2 | no | — |
| 579 | #104 | — | 4 | 4 | no | — |
| 580 | #103 | — | 2 | 4 | no | — |
| 581 | #103 | — | 2 | 2 | no | — |
| 582 | #103 | C2×D4 | 1 | 4 | yes | — |
| 583 | #103 | C2×D4 | 1 | 4 | yes | — |
| 584 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 585 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 586 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 587 | #103 | C2×D4 | 1 | 1 | yes | characteristic |
| 588 | #102 | — | 2 | 4 | no | — |
| 589 | #102 | — | 2 | 2 | no | — |
| 590 | #102 | — | 2 | 4 | no | — |
| 591 | #102 | — | 2 | 4 | no | — |
| 592 | #102 | — | 2 | 2 | no | — |
| 593 | #102 | — | 2 | 2 | no | — |
| 594 | #102 | — | 2 | 2 | no | — |
| 595 | #102 | — | 2 | 2 | no | — |
| 596 | #102 | — | 2 | 4 | no | — |
| 597 | #102 | — | 2 | 4 | no | — |
| 598 | #102 | — | 2 | 2 | no | — |
| 599 | #102 | — | 2 | 2 | no | — |
| 600 | #102 | — | 2 | 2 | no | — |
| 601 | #102 | — | 2 | 2 | no | — |
| 602 | #102 | — | 2 | 4 | no | — |
| 603 | #102 | — | 2 | 4 | no | — |
| 604 | #102 | — | 2 | 2 | no | — |
| 605 | #102 | — | 2 | 2 | no | — |
| 606 | #102 | C2×D4 | 1 | 4 | yes | — |
| 607 | #102 | C2×D4 | 1 | 4 | yes | — |
| 608 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 609 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 610 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 611 | #102 | C2×D4 | 1 | 1 | yes | characteristic |
| 612 | #100 | — | 4 | 4 | no | — |
| 613 | #100 | — | 4 | 4 | no | — |
| 614 | #100 | — | 4 | 4 | no | — |
| 615 | C22⋊C8 | — | 2 | 2 | no | — |
| 616 | C22⋊C8 | — | 2 | 2 | no | — |
| 617 | C22⋊C8 | — | 2 | 2 | no | — |
| 618 | C22⋊C8 | — | 2 | 2 | no | — |
| 619 | #97 | — | 2 | 2 | no | — |
| 620 | #97 | — | 2 | 2 | no | — |
| 621 | #97 | — | 2 | 1 | no | — |
| 622 | #97 | — | 2 | 1 | no | — |
| 623 | C4×C8 | — | 2 | 2 | no | — |
| 624 | C4×C8 | — | 2 | 2 | no | — |
| 625 | C4×C8 | — | 2 | 1 | no | — |
| 626 | C4×C8 | — | 2 | 1 | no | — |
| 627 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 628 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 629 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 630 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 631 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 632 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 633 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 634 | C24 | — | 2 | 2 | no | — |
| 635 | C24 | — | 2 | 2 | no | — |
| 636 | C24 | — | 2 | 2 | no | — |
| 637 | C24 | — | 4 | 2 | no | — |
| 638 | C24 | — | 4 | 2 | no | — |
| 639 | #41 | — | 2 | 2 | no | — |
| 640 | #41 | — | 2 | 4 | no | — |
| 641 | #41 | — | 2 | 2 | no | — |
| 642 | #41 | — | 2 | 2 | no | — |
| 643 | #41 | — | 2 | 4 | no | — |
| 644 | #41 | — | 4 | 8 | no | — |
| 645 | #41 | — | 4 | 4 | no | — |
| 646 | #41 | — | 4 | 4 | no | — |
| 647 | #41 | — | 8 | 4 | no | — |
| 648 | #41 | — | 8 | 2 | no | — |
| 649 | #41 | — | 8 | 2 | no | — |
| 650 | #41 | — | 16 | 2 | no | — |
| 651 | #41 | — | 16 | 2 | no | — |
| 652 | #41 | H(5,𝔽2) | 1 | 4 | yes | — |
| 653 | C2×Q8 | — | 2 | 1 | no | — |
| 654 | C2×Q8 | — | 2 | 1 | no | — |
| 655 | C2×Q8 | — | 4 | 2 | no | — |
| 656 | C2×Q8 | — | 4 | 1 | no | — |
| 657 | C2×Q8 | — | 4 | 1 | no | — |
| 658 | C2×Q8 | — | 8 | 2 | no | — |
| 659 | C2×Q8 | — | 16 | 2 | no | — |
| 660 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 661 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 662 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 663 | C2×D4 | — | 2 | 1 | no | — |
| 664 | C2×D4 | — | 2 | 1 | no | — |
| 665 | C2×D4 | — | 2 | 2 | no | — |
| 666 | C2×D4 | — | 2 | 1 | no | — |
| 667 | C2×D4 | — | 2 | 1 | no | — |
| 668 | C2×D4 | — | 2 | 2 | no | — |
| 669 | C2×D4 | — | 2 | 2 | no | — |
| 670 | C2×D4 | — | 2 | 2 | no | — |
| 671 | C2×D4 | — | 2 | 2 | no | — |
| 672 | C2×D4 | — | 2 | 2 | no | — |
| 673 | C2×D4 | — | 2 | 2 | no | — |
| 674 | C2×D4 | — | 2 | 4 | no | — |
| 675 | C2×D4 | — | 2 | 4 | no | — |
| 676 | C2×D4 | — | 2 | 4 | no | — |
| 677 | C2×D4 | — | 2 | 4 | no | — |
| 678 | C2×D4 | — | 2 | 4 | no | — |
| 679 | C2×D4 | — | 2 | 4 | no | — |
| 680 | C2×D4 | — | 4 | 8 | no | — |
| 681 | C2×D4 | — | 4 | 2 | no | — |
| 682 | C2×D4 | — | 4 | 2 | no | — |
| 683 | C2×D4 | — | 4 | 2 | no | — |
| 684 | C2×D4 | — | 4 | 2 | no | — |
| 685 | C2×D4 | — | 4 | 2 | no | — |
| 686 | C2×D4 | — | 4 | 2 | no | — |
| 687 | C2×D4 | — | 4 | 2 | no | — |
| 688 | C2×D4 | — | 4 | 2 | no | — |
| 689 | C2×D4 | — | 4 | 2 | no | — |
| 690 | C2×D4 | — | 4 | 2 | no | — |
| 691 | C2×D4 | — | 4 | 4 | no | — |
| 692 | C2×D4 | — | 4 | 4 | no | — |
| 693 | C2×D4 | — | 4 | 1 | no | — |
| 694 | C2×D4 | — | 4 | 1 | no | — |
| 695 | C2×D4 | — | 4 | 1 | no | — |
| 696 | C2×D4 | — | 4 | 1 | no | — |
| 697 | C2×D4 | — | 4 | 1 | no | — |
| 698 | C2×D4 | — | 4 | 1 | no | — |
| 699 | C2×D4 | — | 4 | 1 | no | — |
| 700 | C2×D4 | — | 4 | 1 | no | — |
| 701 | C2×D4 | — | 4 | 1 | no | — |
| 702 | C2×D4 | — | 4 | 1 | no | — |
| 703 | C2×D4 | — | 4 | 1 | no | — |
| 704 | C2×D4 | — | 4 | 1 | no | — |
| 705 | C2×D4 | — | 8 | 2 | no | — |
| 706 | C2×D4 | — | 8 | 2 | no | — |
| 707 | C2×D4 | — | 8 | 2 | no | — |
| 708 | C2×D4 | — | 8 | 2 | no | — |
| 709 | C2×D4 | — | 8 | 2 | no | — |
| 710 | C2×D4 | — | 8 | 2 | no | — |
| 711 | C2×D4 | — | 8 | 8 | no | — |
| 712 | C2×D4 | — | 8 | 4 | no | — |
| 713 | C2×D4 | — | 8 | 2 | no | — |
| 714 | C2×D4 | — | 8 | 2 | no | — |
| 715 | C2×D4 | — | 8 | 8 | no | — |
| 716 | C2×D4 | — | 8 | 8 | no | — |
| 717 | C2×D4 | — | 8 | 8 | no | — |
| 718 | C2×D4 | — | 8 | 8 | no | — |
| 719 | C2×D4 | — | 16 | 2 | no | — |
| 720 | C2×D4 | — | 16 | 2 | no | — |
| 721 | C2×D4 | — | 16 | 2 | no | — |
| 722 | C2×D4 | — | 16 | 2 | no | — |
| 723 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 724 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 725 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 726 | C22×C4 | — | 2 | 1 | no | — |
| 727 | C22×C4 | — | 2 | 2 | no | — |
| 728 | C22×C4 | — | 2 | 1 | no | — |
| 729 | C22×C4 | — | 2 | 1 | no | — |
| 730 | C22×C4 | — | 2 | 1 | no | — |
| 731 | C22×C4 | — | 2 | 1 | no | — |
| 732 | C22×C4 | — | 2 | 1 | no | — |
| 733 | C22×C4 | — | 2 | 2 | no | — |
| 734 | C22×C4 | — | 2 | 2 | no | — |
| 735 | C22×C4 | — | 4 | 2 | no | — |
| 736 | C22×C4 | — | 4 | 2 | no | — |
| 737 | C22×C4 | — | 4 | 2 | no | — |
| 738 | C22×C4 | — | 4 | 2 | no | — |
| 739 | C22×C4 | — | 4 | 2 | no | — |
| 740 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 741 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 742 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 743 | Q16 | — | 2 | 2 | no | — |
| 744 | SD16 | — | 2 | 2 | no | — |
| 745 | SD16 | — | 2 | 2 | no | — |
| 746 | SD16 | — | 4 | 4 | no | — |
| 747 | SD16 | — | 4 | 4 | no | — |
| 748 | SD16 | — | 4 | 4 | no | — |
| 749 | SD16 | — | 8 | 4 | no | — |
| 750 | D8 | — | 2 | 2 | no | — |
| 751 | D8 | — | 4 | 4 | no | — |
| 752 | D8 | — | 4 | 4 | no | — |
| 753 | D8 | — | 4 | 4 | no | — |
| 754 | D8 | — | 4 | 4 | no | — |
| 755 | D8 | — | 4 | 4 | no | — |
| 756 | D8 | — | 8 | 4 | no | — |
| 757 | D8 | — | 8 | 4 | no | — |
| 758 | D8 | — | 8 | 2 | no | — |
| 759 | D8 | — | 8 | 2 | no | — |
| 760 | D8 | — | 8 | 4 | no | — |
| 761 | M16 | — | 2 | 2 | no | — |
| 762 | M16 | — | 2 | 2 | no | — |
| 763 | M16 | — | 2 | 4 | no | — |
| 764 | M16 | — | 2 | 4 | no | — |
| 765 | M16 | — | 2 | 2 | no | — |
| 766 | M16 | — | 2 | 2 | no | — |
| 767 | M16 | — | 4 | 4 | no | — |
| 768 | M16 | — | 4 | 4 | no | — |
| 769 | C2×C8 | — | 2 | 2 | no | — |
| 770 | C2×C8 | — | 2 | 2 | no | — |
| 771 | C2×C8 | — | 2 | 2 | no | — |
| 772 | C2×C8 | — | 2 | 2 | no | — |
| 773 | C2×C8 | — | 2 | 2 | no | — |
| 774 | C2×C8 | — | 2 | 2 | no | — |
| 775 | C2×C8 | — | 2 | 2 | no | — |
| 776 | C2×C8 | — | 2 | 2 | no | — |
| 777 | C2×C8 | — | 4 | 4 | no | — |
| 778 | C2×C8 | — | 4 | 4 | no | — |
| 779 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 780 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 781 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 782 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 783 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 784 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 785 | C4⋊C4 | — | 2 | 1 | no | — |
| 786 | C4⋊C4 | — | 2 | 1 | no | — |
| 787 | C4⋊C4 | — | 2 | 1 | no | — |
| 788 | C4⋊C4 | — | 2 | 1 | no | — |
| 789 | C4⋊C4 | — | 2 | 1 | no | — |
| 790 | C4⋊C4 | — | 2 | 1 | no | — |
| 791 | C4⋊C4 | — | 2 | 1 | no | — |
| 792 | C4⋊C4 | — | 2 | 1 | no | — |
| 793 | C4⋊C4 | — | 2 | 2 | no | — |
| 794 | C4⋊C4 | — | 2 | 2 | no | — |
| 795 | C4⋊C4 | — | 2 | 2 | no | — |
| 796 | C4⋊C4 | — | 2 | 2 | no | — |
| 797 | C4⋊C4 | — | 4 | 2 | no | — |
| 798 | C4⋊C4 | — | 4 | 2 | no | — |
| 799 | C4⋊C4 | — | 4 | 2 | no | — |
| 800 | C4⋊C4 | — | 4 | 2 | no | — |
| 801 | C4⋊C4 | — | 4 | 1 | no | — |
| 802 | C4⋊C4 | — | 4 | 1 | no | — |
| 803 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 804 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 805 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 806 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 807 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 808 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 809 | C22⋊C4 | — | 2 | 1 | no | — |
| 810 | C22⋊C4 | — | 2 | 2 | no | — |
| 811 | C22⋊C4 | — | 2 | 1 | no | — |
| 812 | C22⋊C4 | — | 2 | 1 | no | — |
| 813 | C22⋊C4 | — | 2 | 1 | no | — |
| 814 | C22⋊C4 | — | 2 | 1 | no | — |
| 815 | C22⋊C4 | — | 2 | 1 | no | — |
| 816 | C22⋊C4 | — | 2 | 2 | no | — |
| 817 | C22⋊C4 | — | 2 | 2 | no | — |
| 818 | C22⋊C4 | — | 4 | 2 | no | — |
| 819 | C22⋊C4 | — | 4 | 2 | no | — |
| 820 | C22⋊C4 | — | 4 | 2 | no | — |
| 821 | C22⋊C4 | — | 4 | 2 | no | — |
| 822 | C22⋊C4 | — | 4 | 2 | no | — |
| 823 | C22⋊C4 | — | 4 | 2 | no | — |
| 824 | C22⋊C4 | — | 4 | 2 | no | — |
| 825 | C22⋊C4 | — | 4 | 2 | no | — |
| 826 | C22⋊C4 | — | 4 | 2 | no | — |
| 827 | C22⋊C4 | — | 8 | 8 | no | — |
| 828 | C42 | — | 2 | 4 | no | — |
| 829 | C42 | — | 2 | 1 | no | — |
| 830 | C42 | — | 2 | 1 | no | — |
| 831 | C42 | — | 2 | 1 | no | — |
| 832 | C42 | — | 2 | 1 | no | — |
| 833 | C42 | — | 2 | 1 | no | — |
| 834 | C42 | — | 2 | 2 | no | — |
| 835 | C42 | — | 2 | 1 | no | — |
| 836 | C42 | — | 2 | 2 | no | — |
| 837 | C42 | — | 2 | 2 | no | — |
| 838 | C42 | — | 4 | 2 | no | — |
| 839 | C42 | — | 4 | 2 | no | — |
| 840 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 841 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 842 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 843 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 844 | C23 | — | 2 | 1 | no | — |
| 845 | C23 | — | 2 | 1 | no | — |
| 846 | C23 | — | 2 | 2 | no | — |
| 847 | C23 | — | 4 | 2 | no | — |
| 848 | C23 | — | 4 | 2 | no | — |
| 849 | C23 | — | 4 | 2 | no | — |
| 850 | C23 | — | 4 | 4 | no | — |
| 851 | C23 | — | 4 | 4 | no | — |
| 852 | C23 | — | 4 | 4 | no | — |
| 853 | C23 | — | 8 | 4 | no | — |
| 854 | C23 | — | 8 | 2 | no | — |
| 855 | C23 | — | 8 | 2 | no | — |
| 856 | C23 | — | 8 | 2 | no | — |
| 857 | C23 | — | 8 | 2 | no | — |
| 858 | C23 | — | 8 | 2 | no | — |
| 859 | C23 | — | 8 | 2 | no | — |
| 860 | C23 | — | 8 | 4 | no | — |
| 861 | C23 | — | 16 | 2 | no | — |
| 862 | C23 | — | 16 | 2 | no | — |
| 863 | C23 | — | 16 | 2 | no | — |
| 864 | C23 | — | 16 | 2 | no | — |
| 865 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 866 | Q8 | — | 2 | 1 | no | — |
| 867 | Q8 | — | 2 | 1 | no | — |
| 868 | Q8 | — | 2 | 4 | no | — |
| 869 | Q8 | — | 2 | 1 | no | — |
| 870 | Q8 | — | 4 | 2 | no | — |
| 871 | Q8 | — | 4 | 2 | no | — |
| 872 | Q8 | — | 8 | 2 | no | — |
| 873 | Q8 | — | 16 | 1 | no | — |
| 874 | Q8 | — | 16 | 2 | no | — |
| 875 | Q8 | #535 | 1 | 2 | yes | — |
| 876 | D4 | — | 2 | 4 | no | — |
| 877 | D4 | — | 2 | 1 | no | — |
| 878 | D4 | — | 2 | 4 | no | — |
| 879 | D4 | — | 2 | 1 | no | — |
| 880 | D4 | — | 2 | 1 | no | — |
| 881 | D4 | — | 4 | 2 | no | — |
| 882 | D4 | — | 4 | 4 | no | — |
| 883 | D4 | — | 4 | 2 | no | — |
| 884 | D4 | — | 4 | 2 | no | — |
| 885 | D4 | — | 4 | 2 | no | — |
| 886 | D4 | — | 4 | 4 | no | — |
| 887 | D4 | — | 4 | 4 | no | — |
| 888 | D4 | — | 4 | 4 | no | — |
| 889 | D4 | — | 4 | 2 | no | — |
| 890 | D4 | — | 4 | 2 | no | — |
| 891 | D4 | — | 4 | 2 | no | — |
| 892 | D4 | — | 4 | 2 | no | — |
| 893 | D4 | — | 4 | 2 | no | — |
| 894 | D4 | — | 8 | 4 | no | — |
| 895 | D4 | — | 8 | 4 | no | — |
| 896 | D4 | — | 8 | 4 | no | — |
| 897 | D4 | — | 8 | 4 | no | — |
| 898 | D4 | — | 8 | 2 | no | — |
| 899 | D4 | — | 8 | 2 | no | — |
| 900 | D4 | — | 8 | 2 | no | — |
| 901 | D4 | — | 8 | 2 | no | — |
| 902 | D4 | — | 8 | 2 | no | — |
| 903 | D4 | — | 8 | 2 | no | — |
| 904 | D4 | — | 16 | 1 | no | — |
| 905 | D4 | — | 16 | 1 | no | — |
| 906 | D4 | — | 16 | 1 | no | — |
| 907 | D4 | — | 16 | 1 | no | — |
| 908 | D4 | — | 16 | 1 | no | — |
| 909 | D4 | — | 16 | 1 | no | — |
| 910 | D4 | — | 16 | 2 | no | — |
| 911 | D4 | — | 16 | 2 | no | — |
| 912 | D4 | — | 16 | 2 | no | — |
| 913 | D4 | — | 16 | 2 | no | — |
| 914 | D4 | — | 16 | 2 | no | — |
| 915 | D4 | — | 16 | 2 | no | — |
| 916 | D4 | — | 16 | 16 | no | — |
| 917 | D4 | #535 | 1 | 2 | yes | — |
| 918 | C2×C4 | — | 2 | 1 | no | — |
| 919 | C2×C4 | — | 2 | 4 | no | — |
| 920 | C2×C4 | — | 2 | 2 | no | — |
| 921 | C2×C4 | — | 2 | 2 | no | — |
| 922 | C2×C4 | — | 2 | 4 | no | — |
| 923 | C2×C4 | — | 2 | 1 | no | — |
| 924 | C2×C4 | — | 2 | 1 | no | — |
| 925 | C2×C4 | — | 2 | 1 | no | — |
| 926 | C2×C4 | — | 2 | 1 | no | — |
| 927 | C2×C4 | — | 2 | 1 | no | — |
| 928 | C2×C4 | — | 2 | 2 | no | — |
| 929 | C2×C4 | — | 2 | 2 | no | — |
| 930 | C2×C4 | — | 2 | 2 | no | — |
| 931 | C2×C4 | — | 4 | 2 | no | — |
| 932 | C2×C4 | — | 4 | 2 | no | — |
| 933 | C2×C4 | — | 4 | 2 | no | — |
| 934 | C2×C4 | — | 4 | 2 | no | — |
| 935 | C2×C4 | — | 4 | 2 | no | — |
| 936 | C2×C4 | — | 4 | 2 | no | — |
| 937 | C2×C4 | — | 4 | 2 | no | — |
| 938 | C2×C4 | — | 4 | 2 | no | — |
| 939 | C2×C4 | — | 4 | 2 | no | — |
| 940 | C2×C4 | — | 4 | 2 | no | — |
| 941 | C2×C4 | — | 8 | 4 | no | — |
| 942 | C2×C4 | — | 8 | 4 | no | — |
| 943 | C2×C4 | — | 8 | 2 | no | — |
| 944 | C2×C4 | — | 16 | 2 | no | — |
| 945 | C2×C4 | — | 16 | 2 | no | — |
| 946 | C2×C4 | — | 16 | 2 | no | — |
| 947 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 948 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 949 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 950 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 951 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 952 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 953 | C2×C4 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 954 | C2×C4 | #585 | 1 | 2 | yes | — |
| 955 | C8 | — | 2 | 1 | no | — |
| 956 | C8 | — | 2 | 1 | no | — |
| 957 | C8 | — | 2 | 2 | no | — |
| 958 | C8 | — | 2 | 2 | no | — |
| 959 | C8 | — | 2 | 1 | no | — |
| 960 | C8 | — | 2 | 1 | no | — |
| 961 | C8 | — | 4 | 2 | no | — |
| 962 | C8 | — | 4 | 2 | no | — |
| 963 | C8 | — | 4 | 2 | no | — |
| 964 | C8 | — | 4 | 2 | no | — |
| 965 | C22 | — | 2 | 1 | no | — |
| 966 | C22 | — | 2 | 1 | no | — |
| 967 | C22 | — | 2 | 2 | no | — |
| 968 | C22 | — | 4 | 1 | no | — |
| 969 | C22 | — | 4 | 1 | no | — |
| 970 | C22 | — | 4 | 2 | no | — |
| 971 | C22 | — | 4 | 1 | no | — |
| 972 | C22 | — | 4 | 1 | no | — |
| 973 | C22 | — | 4 | 2 | no | — |
| 974 | C22 | — | 4 | 1 | no | — |
| 975 | C22 | — | 4 | 2 | no | — |
| 976 | C22 | — | 8 | 2 | no | — |
| 977 | C22 | — | 8 | 2 | no | — |
| 978 | C22 | — | 8 | 2 | no | — |
| 979 | C22 | — | 8 | 2 | no | — |
| 980 | C22 | — | 8 | 2 | no | — |
| 981 | C22 | — | 8 | 2 | no | — |
| 982 | C22 | — | 8 | 2 | no | — |
| 983 | C22 | — | 8 | 2 | no | — |
| 984 | C22 | — | 8 | 2 | no | — |
| 985 | C22 | — | 16 | 4 | no | — |
| 986 | C22 | — | 16 | 4 | no | — |
| 987 | C22 | — | 16 | 4 | no | — |
| 988 | C22 | — | 32 | 4 | no | — |
| 989 | C22 | — | 32 | 4 | no | — |
| 990 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 991 | C22 | #3558 | 1 | 2 | yes | — |
| 992 | C4 | — | 2 | 2 | no | — |
| 993 | C4 | — | 2 | 1 | no | — |
| 994 | C4 | — | 2 | 1 | no | — |
| 995 | C4 | — | 4 | 4 | no | — |
| 996 | C4 | — | 4 | 1 | no | — |
| 997 | C4 | — | 4 | 2 | no | — |
| 998 | C4 | — | 4 | 1 | no | — |
| 999 | C4 | — | 4 | 1 | no | — |
| 1000 | C4 | — | 4 | 2 | no | — |
| 1001 | C4 | — | 4 | 1 | no | — |
| 1002 | C4 | — | 4 | 1 | no | — |
| 1003 | C4 | — | 4 | 2 | no | — |
| 1004 | C4 | — | 8 | 2 | no | — |
| 1005 | C4 | #3288 | 1 | 2 | yes | — |
| 1006 | C4 | #3292 | 1 | 2 | yes | — |
| 1007 | C4 | C2×#535 | 1 | 1 | yes | characteristic |
| 1008 | C4 | #3488 | 1 | 2 | yes | — |
| 1009 | C4 | #3500 | 1 | 1 | yes | characteristic |
| 1010 | C2 | — | 2 | 2 | no | — |
| 1011 | C2 | — | 4 | 2 | no | — |
| 1012 | C2 | — | 8 | 1 | no | — |
| 1013 | C2 | — | 8 | 2 | no | — |
| 1014 | C2 | — | 16 | 2 | no | — |
| 1015 | C2 | — | 16 | 2 | no | — |
| 1016 | C2 | — | 16 | 2 | no | — |
| 1017 | C2 | #37677 | 1 | 1 | yes | characteristic |
| 1018 | C2 | C2×#3288 | 1 | 1 | yes | characteristic |
| 1019 | C2 | C2×#3292 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61329 | C2 | semidirect |
| 2. #61089 | C2 | semidirect |
| 3. #60817 | C2 | semidirect |
| 4. #60622 | C2 | semidirect |
| 5. #33190 | C2 | semidirect |
| 6. #30938 | C2 | semidirect |
| 7. #30551 | C2 | semidirect |
| 8. #30258 | C2 | semidirect |
| 9. #29858 | C2 | semidirect |
| 10. #28763 | C2 | semidirect |
| 11. #28632 | C2 | semidirect |
| 12. #25924 | C2 | semidirect |
| 13. #25875 | C2 | semidirect |
| 14. #25747 | C2 | semidirect |
| 15. #25588 | C2 | semidirect |
| 16. #25180 | C2 | semidirect |
| 17. #24456 | C2 | semidirect |
| 18. #22234 | C2 | semidirect |
| 19. #21137 | C2 | semidirect |
| 21. #3508 | C22 | semidirect |
| 22. #3503 | C22 | semidirect |
| 48. C2×#493 | C22 | semidirect |
| 52. #3138 | C22 | semidirect |
| 53. #3138 | C22 | semidirect |
| 55. #3136 | C22 | semidirect |
| 56. #3136 | C22 | semidirect |
| 60. C2×#486 | C22 | semidirect |
| 61. C2×#486 | C22 | semidirect |
| 62. #3081 | C22 | semidirect |
| 63. #3079 | C22 | semidirect |
| 64. C2×#472 | C22 | semidirect |
| 67. #3041 | C22 | semidirect |
| 70. #3038 | C22 | semidirect |
| 71. C2×#453 | C22 | semidirect |
| 74. #3008 | C22 | semidirect |
| 75. #2960 | C22 | semidirect |
| 76. #2946 | C22 | semidirect |
| 79. #2922 | C22 | semidirect |
| 80. #2897 | C22 | semidirect |
| 81. C4×#131 | C22 | semidirect |
| 82. #2867 | C22 | semidirect |
| 83. #2858 | C22 | semidirect |
| 84. #2063 | C22 | semidirect |
| 85. #2051 | C22 | semidirect |
| 86. #2051 | C22 | semidirect |
| 87. #2045 | C22 | semidirect |
| 88. #2037 | C22 | semidirect |
| 89. #2027 | C22 | semidirect |
| 90. #2011 | C22 | semidirect |
| 91. #2011 | C22 | semidirect |
| 92. #2002 | C22 | semidirect |
| 93. #2002 | C22 | semidirect |
| 94. #1997 | C22 | semidirect |
| 95. #1994 | C22 | semidirect |
| 96. #1978 | C22 | semidirect |
| 97. #1978 | C22 | semidirect |
| 98. #1965 | C22 | semidirect |
| 99. #1965 | C22 | semidirect |
| 100. #1965 | C22 | semidirect |
| 102. #1929 | C22 | semidirect |
| 103. #1929 | C22 | semidirect |
| 104. #1922 | C22 | semidirect |
| 105. #1907 | C22 | semidirect |
| 106. #1887 | C22 | semidirect |
| 107. #1883 | C22 | semidirect |
| 109. #1866 | C22 | semidirect |
| 110. #1866 | C22 | semidirect |
| 111. #1848 | C22 | semidirect |
| 112. #1792 | C22 | semidirect |
| 113. C4×#108 | C22 | semidirect |
| 114. C4×#104 | C22 | semidirect |
| 115. C4×#104 | C22 | semidirect |
| 116. #1744 | C22 | semidirect |
| 207. #488 | D4 | semidirect |
| 209. #487 | D4 | semidirect |
| 210. #487 | D4 | semidirect |
| 225. #486 | D4 | semidirect |
| 226. #486 | D4 | semidirect |
| 279. C4×Q16 | D4 | semidirect |
| 280. C4×Q16 | D4 | semidirect |
| 282. C4×SD16 | D4 | semidirect |
| 283. C4×SD16 | D4 | semidirect |
| 284. C4×SD16 | D4 | semidirect |
| 285. C4×SD16 | D4 | semidirect |
| 287. C4×D8 | D4 | semidirect |
| 288. C4×D8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61329 | 2 |
| #61089 | 2 |
| #60817 | 2 |
| #60622 | 2 |
| #33190 | 2 |
| #30938 | 2 |
| #30551 | 2 |
| #30258 | 2 |
| #29858 | 2 |
| #28763 | 2 |
| #28632 | 2 |
| #25924 | 2 |
| #25875 | 2 |
| #25747 | 2 |
| #25588 | 2 |
| #25180 | 2 |
| #24456 | 2 |
| #22234 | 2 |
| #21137 | 2 |