Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
7490 conjugacy classes of subgroups.
The subgroup lattice has 931 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10576183 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #7622885 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #6353352 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #512867 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #512864 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #512860 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #512857 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #512616 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #512566 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #63092 | — | 2 | 2 | no | — |
| 11 | #63022 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #62001 | — | 2 | 1 | no | — |
| 13 | #61111 | — | 2 | 3 | no | — |
| 14 | #61110 | C22 | 1 | 6 | yes | — |
| 15 | #61107 | — | 2 | 12 | no | — |
| 16 | #61105 | C22 | 1 | 6 | yes | — |
| 17 | C2×#3291 | — | 2 | 3 | no | — |
| 18 | #60646 | C22 | 1 | 1 | yes | characteristic |
| 19 | #60470 | — | 2 | 2 | no | — |
| 20 | #60402 | — | 2 | 2 | no | — |
| 21 | #60391 | C22 | 1 | 2 | yes | — |
| 22 | #60388 | — | 2 | 1 | no | — |
| 23 | #60183 | — | 2 | 1 | no | — |
| 24 | #33559 | C22 | 1 | 12 | yes | complemented |
| 25 | #33555 | — | 2 | 12 | no | — |
| 26 | #33546 | C22 | 1 | 12 | yes | complemented |
| 27 | #33360 | C22 | 1 | 2 | yes | complemented |
| 28 | #33351 | — | 2 | 2 | no | — |
| 29 | #18714 | C22 | 1 | 3 | yes | complemented |
| 30 | #18686 | C22 | 1 | 3 | yes | complemented |
| 31 | #18626 | — | 2 | 3 | no | — |
| 32 | #18569 | — | 2 | 3 | no | — |
| 33 | #18527 | C22 | 1 | 3 | yes | complemented |
| 34 | #18480 | C22 | 1 | 3 | yes | complemented |
| 35 | #17773 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #17520 | — | 2 | 1 | no | — |
| 37 | #13676 | C22 | 1 | 4 | yes | complemented |
| 38 | #13675 | C22 | 1 | 12 | yes | complemented |
| 39 | #13674 | C22 | 1 | 12 | yes | complemented |
| 40 | #13673 | C22 | 1 | 12 | yes | complemented |
| 41 | #13673 | C22 | 1 | 24 | yes | complemented |
| 42 | #13585 | C22 | 1 | 6 | yes | complemented |
| 43 | #13583 | C22 | 1 | 6 | yes | complemented |
| 44 | #13562 | C22 | 1 | 12 | yes | complemented |
| 45 | #13560 | C22 | 1 | 12 | yes | complemented |
| 46 | 2−1+6 | D4 | 1 | 2 | yes | complemented |
| 47 | H(7,𝔽2) | — | 2 | 1 | no | — |
| 48 | #3586 | — | 2 | 2 | no | — |
| 49 | #3586 | — | 2 | 12 | no | — |
| 50 | #3586 | — | 4 | 8 | no | — |
| 51 | #3585 | — | 2 | 2 | no | — |
| 52 | #3585 | — | 2 | 12 | no | — |
| 53 | #3585 | — | 4 | 8 | no | — |
| 54 | #3584 | — | 2 | 1 | no | — |
| 55 | #3584 | — | 2 | 12 | no | — |
| 56 | #3584 | — | 4 | 8 | no | — |
| 57 | C2×#577 | — | 2 | 2 | no | — |
| 58 | C2×#577 | — | 2 | 12 | no | — |
| 59 | C2×#577 | — | 4 | 8 | no | — |
| 60 | #3573 | — | 2 | 2 | no | — |
| 61 | #3549 | C23 | 1 | 3 | yes | complemented |
| 62 | #3546 | — | 4 | 3 | no | — |
| 63 | #3540 | — | 2 | 6 | no | — |
| 64 | #3518 | — | 4 | 1 | no | — |
| 65 | #3511 | — | 2 | 3 | no | — |
| 66 | #3506 | — | 4 | 3 | no | — |
| 67 | #3499 | C23 | 1 | 1 | yes | characteristic |
| 68 | #3498 | D4 | 1 | 1 | yes | characteristic, complemented |
| 69 | #3487 | — | 2 | 2 | no | — |
| 70 | #3487 | — | 4 | 2 | no | — |
| 71 | #3483 | — | 2 | 1 | no | — |
| 72 | #3481 | C23 | 1 | 3 | yes | complemented |
| 73 | D4×#41 | — | 4 | 1 | no | — |
| 74 | #3391 | — | 4 | 1 | no | — |
| 75 | #3362 | — | 4 | 1 | no | — |
| 76 | #3325 | — | 4 | 3 | no | — |
| 77 | #3293 | — | 2 | 6 | no | — |
| 78 | #3292 | C23 | 1 | 12 | yes | — |
| 79 | #3291 | — | 2 | 24 | no | — |
| 80 | #3291 | — | 2 | 6 | no | — |
| 81 | #3291 | — | 2 | 12 | no | — |
| 82 | #3291 | C23 | 1 | 4 | yes | — |
| 83 | #3290 | — | 2 | 24 | no | — |
| 84 | #3289 | — | 2 | 24 | no | — |
| 85 | #3288 | — | 2 | 24 | no | — |
| 86 | #3274 | — | 4 | 3 | no | — |
| 87 | #3253 | — | 2 | 3 | no | — |
| 88 | #3205 | — | 2 | 3 | no | — |
| 89 | #3154 | — | 2 | 6 | no | — |
| 90 | #3152 | D4 | 1 | 3 | yes | complemented |
| 91 | #3151 | C23 | 1 | 3 | yes | — |
| 92 | #3147 | C23 | 1 | 3 | yes | — |
| 93 | C2×#492 | D4 | 1 | 3 | yes | complemented |
| 94 | #3106 | — | 2 | 3 | no | — |
| 95 | #3069 | — | 2 | 12 | no | — |
| 96 | #3068 | — | 2 | 12 | no | — |
| 97 | #3067 | — | 2 | 12 | no | — |
| 98 | C2×#471 | — | 2 | 12 | no | — |
| 99 | #3038 | — | 2 | 3 | no | — |
| 100 | #3027 | — | 2 | 12 | no | — |
| 101 | #3027 | — | 4 | 6 | no | — |
| 102 | #3025 | — | 2 | 12 | no | — |
| 103 | #3025 | — | 4 | 6 | no | — |
| 104 | #3022 | D4 | 1 | 12 | yes | complemented |
| 105 | #3021 | — | 2 | 6 | no | — |
| 106 | #3020 | — | 2 | 6 | no | — |
| 107 | #3019 | — | 2 | 6 | no | — |
| 108 | #3018 | — | 2 | 6 | no | — |
| 109 | #3018 | C23 | 1 | 12 | yes | — |
| 110 | C2×#456 | — | 2 | 6 | no | — |
| 111 | C2×#453 | — | 2 | 6 | no | — |
| 112 | #2991 | — | 2 | 1 | no | — |
| 113 | #2957 | — | 2 | 6 | no | — |
| 114 | #2956 | — | 2 | 6 | no | — |
| 115 | #2955 | — | 2 | 6 | no | — |
| 116 | C2×#443 | — | 2 | 6 | no | — |
| 117 | #2916 | — | 2 | 1 | no | — |
| 118 | #2901 | — | 2 | 2 | no | — |
| 119 | #2889 | D4 | 1 | 2 | yes | complemented |
| 120 | #2888 | — | 2 | 1 | no | — |
| 121 | #2884 | — | 2 | 2 | no | — |
| 122 | #2884 | — | 4 | 2 | no | — |
| 123 | C4×#131 | D4 | 1 | 1 | yes | characteristic, complemented |
| 124 | #2199 | — | 2 | 24 | no | — |
| 125 | #2198 | C23 | 1 | 8 | yes | complemented |
| 126 | #2197 | — | 2 | 24 | no | — |
| 127 | #2196 | C23 | 1 | 24 | yes | complemented |
| 128 | #2129 | — | 2 | 6 | no | — |
| 129 | #2126 | C23 | 1 | 12 | yes | complemented |
| 130 | #2122 | — | 2 | 12 | no | — |
| 131 | #2120 | — | 2 | 12 | no | — |
| 132 | #1634 | — | 2 | 3 | no | — |
| 133 | #1632 | — | 2 | 3 | no | — |
| 134 | #1630 | C23 | 1 | 1 | yes | characteristic, complemented |
| 135 | #1629 | C23 | 1 | 3 | yes | complemented |
| 136 | #1624 | — | 2 | 6 | no | — |
| 137 | #1624 | — | 2 | 3 | no | — |
| 138 | #1622 | — | 2 | 3 | no | — |
| 139 | #1622 | — | 2 | 6 | no | — |
| 140 | #1620 | C23 | 1 | 3 | yes | complemented |
| 141 | #1619 | C23 | 1 | 3 | yes | complemented |
| 142 | #1619 | C23 | 1 | 6 | yes | complemented |
| 143 | #1560 | C23 | 1 | 3 | yes | complemented |
| 144 | #1548 | — | 2 | 3 | no | — |
| 145 | #1543 | C23 | 1 | 3 | yes | complemented |
| 146 | #1492 | — | 2 | 3 | no | — |
| 147 | #1489 | — | 2 | 3 | no | — |
| 148 | #1484 | — | 2 | 3 | no | — |
| 149 | #1476 | — | 2 | 3 | no | — |
| 150 | #1409 | C23 | 1 | 4 | yes | complemented |
| 151 | #1408 | C23 | 1 | 12 | yes | complemented |
| 152 | #1402 | C23 | 1 | 8 | yes | complemented |
| 153 | #1402 | C23 | 1 | 24 | yes | complemented |
| 154 | #585 | — | 2 | 2 | no | — |
| 155 | #585 | — | 2 | 6 | no | — |
| 156 | #585 | — | 4 | 6 | no | — |
| 157 | #585 | — | 4 | 8 | no | — |
| 158 | #585 | — | 4 | 8 | no | — |
| 159 | #585 | — | 8 | 1 | no | — |
| 160 | #585 | C2×D4 | 1 | 12 | yes | — |
| 161 | C2×2−1+4 | — | 2 | 6 | no | — |
| 162 | C2×2−1+4 | — | 4 | 2 | no | — |
| 163 | C2×2−1+4 | — | 4 | 8 | no | — |
| 164 | C2×2−1+4 | C2×D4 | 1 | 2 | yes | — |
| 165 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 166 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 167 | C2×H(5,𝔽2) | — | 4 | 8 | no | — |
| 168 | C2×H(5,𝔽2) | — | 8 | 3 | no | — |
| 169 | C22×#41 | — | 2 | 2 | no | — |
| 170 | #578 | — | 2 | 4 | no | — |
| 171 | #578 | — | 2 | 24 | no | — |
| 172 | #578 | — | 4 | 12 | no | — |
| 173 | #578 | — | 4 | 24 | no | — |
| 174 | #578 | — | 4 | 8 | no | — |
| 175 | #577 | — | 2 | 8 | no | — |
| 176 | #577 | — | 2 | 24 | no | — |
| 177 | #577 | — | 2 | 48 | no | — |
| 178 | #577 | — | 2 | 8 | no | — |
| 179 | #577 | — | 4 | 8 | no | — |
| 180 | #577 | — | 4 | 8 | no | — |
| 181 | #577 | — | 4 | 12 | no | — |
| 182 | #577 | — | 4 | 12 | no | — |
| 183 | #577 | — | 4 | 24 | no | — |
| 184 | #577 | — | 4 | 24 | no | — |
| 185 | #577 | — | 4 | 24 | no | — |
| 186 | #577 | — | 4 | 24 | no | — |
| 187 | #577 | — | 4 | 8 | no | — |
| 188 | #577 | — | 4 | 8 | no | — |
| 189 | #576 | — | 2 | 4 | no | — |
| 190 | #576 | — | 2 | 24 | no | — |
| 191 | #576 | — | 4 | 12 | no | — |
| 192 | #576 | — | 4 | 24 | no | — |
| 193 | #576 | — | 4 | 8 | no | — |
| 194 | #575 | — | 2 | 6 | no | — |
| 195 | #575 | — | 2 | 12 | no | — |
| 196 | #575 | — | 2 | 12 | no | — |
| 197 | #575 | — | 4 | 24 | no | — |
| 198 | #575 | — | 4 | 24 | no | — |
| 199 | #575 | — | 4 | 24 | no | — |
| 200 | C2×#137 | — | 2 | 6 | no | — |
| 201 | C2×#137 | — | 2 | 12 | no | — |
| 202 | C2×#137 | — | 4 | 12 | no | — |
| 203 | C2×#137 | — | 4 | 24 | no | — |
| 204 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 205 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 206 | C2×AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 207 | C2×AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 208 | C2×AGL(1,ℤ/8) | — | 4 | 3 | no | — |
| 209 | C2×#135 | — | 2 | 6 | no | — |
| 210 | C2×#135 | — | 2 | 6 | no | — |
| 211 | C2×#135 | — | 4 | 12 | no | — |
| 212 | C2×#135 | — | 4 | 24 | no | — |
| 213 | C22×SD16 | — | 2 | 6 | no | — |
| 214 | C22×SD16 | — | 4 | 12 | no | — |
| 215 | #568 | — | 2 | 2 | no | — |
| 216 | #568 | — | 2 | 12 | no | — |
| 217 | #568 | — | 4 | 8 | no | — |
| 218 | C2×#131 | — | 2 | 1 | no | — |
| 219 | C2×#131 | — | 2 | 12 | no | — |
| 220 | C2×#131 | — | 4 | 8 | no | — |
| 221 | H(3,𝔽4) | — | 2 | 6 | no | — |
| 222 | #560 | — | 4 | 6 | no | — |
| 223 | #559 | — | 4 | 6 | no | — |
| 224 | #559 | C24 | 1 | 1 | yes | characteristic |
| 225 | Q82 | — | 2 | 1 | no | — |
| 226 | #556 | — | 4 | 6 | no | — |
| 227 | #556 | — | 4 | 3 | no | — |
| 228 | #555 | — | 2 | 3 | no | — |
| 229 | #555 | — | 2 | 3 | no | — |
| 230 | #555 | — | 4 | 3 | no | — |
| 231 | #555 | — | 4 | 3 | no | — |
| 232 | #554 | — | 2 | 3 | no | — |
| 233 | #553 | — | 4 | 3 | no | — |
| 234 | #553 | — | 4 | 6 | no | — |
| 235 | #551 | — | 2 | 6 | no | — |
| 236 | #550 | — | 2 | 1 | no | — |
| 237 | #550 | — | 2 | 3 | no | — |
| 238 | #550 | — | 4 | 1 | no | — |
| 239 | #550 | — | 4 | 6 | no | — |
| 240 | #550 | — | 4 | 1 | no | — |
| 241 | #550 | — | 8 | 8 | no | — |
| 242 | D4×Q8 | — | 4 | 1 | no | — |
| 243 | #548 | — | 4 | 2 | no | — |
| 244 | #548 | — | 4 | 6 | no | — |
| 245 | #548 | — | 8 | 8 | no | — |
| 246 | #547 | — | 4 | 3 | no | — |
| 247 | #547 | — | 4 | 3 | no | — |
| 248 | #546 | — | 4 | 3 | no | — |
| 249 | #546 | — | 4 | 6 | no | — |
| 250 | D42 | — | 4 | 3 | no | — |
| 251 | D42 | — | 4 | 3 | no | — |
| 252 | D42 | C24 | 1 | 3 | yes | — |
| 253 | #542 | — | 4 | 6 | no | — |
| 254 | #542 | — | 4 | 6 | no | — |
| 255 | #538 | — | 4 | 12 | no | — |
| 256 | #537 | — | 4 | 3 | no | — |
| 257 | #536 | C2×D4 | 1 | 6 | yes | — |
| 258 | #535 | — | 2 | 6 | no | — |
| 259 | #535 | — | 2 | 6 | no | — |
| 260 | #535 | — | 2 | 3 | no | — |
| 261 | #535 | — | 4 | 6 | no | — |
| 262 | #535 | — | 4 | 12 | no | — |
| 263 | #533 | — | 4 | 3 | no | — |
| 264 | #532 | — | 2 | 3 | no | — |
| 265 | #532 | — | 4 | 3 | no | — |
| 266 | #532 | — | 4 | 3 | no | — |
| 267 | #532 | C2×D4 | 1 | 3 | yes | — |
| 268 | #532 | C24 | 1 | 3 | yes | — |
| 269 | C2×C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 270 | C2×#127 | C2×D4 | 1 | 3 | yes | — |
| 271 | #529 | — | 4 | 3 | no | — |
| 272 | #525 | — | 2 | 6 | no | — |
| 273 | #525 | — | 2 | 6 | no | — |
| 274 | #525 | — | 4 | 6 | no | — |
| 275 | #525 | — | 4 | 12 | no | — |
| 276 | #520 | — | 4 | 3 | no | — |
| 277 | #519 | — | 2 | 2 | no | — |
| 278 | #519 | — | 4 | 2 | no | — |
| 279 | C4×#41 | — | 2 | 3 | no | — |
| 280 | C4×#41 | — | 4 | 1 | no | — |
| 281 | C4×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C2×C4×D4 | — | 4 | 3 | no | — |
| 283 | #497 | — | 2 | 6 | no | — |
| 284 | #496 | — | 2 | 6 | no | — |
| 285 | #495 | — | 2 | 6 | no | — |
| 286 | #494 | C2×D4 | 1 | 3 | yes | — |
| 287 | #493 | — | 4 | 3 | no | — |
| 288 | #493 | C24 | 1 | 3 | yes | — |
| 289 | #492 | — | 2 | 6 | no | — |
| 290 | #492 | C2×D4 | 1 | 3 | yes | — |
| 291 | #492 | C2×D4 | 1 | 6 | yes | — |
| 292 | #492 | C24 | 1 | 1 | yes | characteristic |
| 293 | #486 | — | 4 | 3 | no | — |
| 294 | #482 | — | 4 | 3 | no | — |
| 295 | #477 | — | 2 | 1 | no | — |
| 296 | #476 | — | 2 | 3 | no | — |
| 297 | #476 | — | 4 | 3 | no | — |
| 298 | #473 | — | 2 | 24 | no | — |
| 299 | #472 | — | 2 | 24 | no | — |
| 300 | #471 | — | 2 | 48 | no | — |
| 301 | #471 | — | 2 | 24 | no | — |
| 302 | #471 | — | 2 | 8 | no | — |
| 303 | #469 | — | 4 | 6 | no | — |
| 304 | #460 | — | 2 | 3 | no | — |
| 305 | #460 | — | 4 | 3 | no | — |
| 306 | #459 | — | 2 | 3 | no | — |
| 307 | #459 | — | 2 | 6 | no | — |
| 308 | #459 | — | 4 | 3 | no | — |
| 309 | #459 | — | 4 | 3 | no | — |
| 310 | #458 | — | 2 | 8 | no | — |
| 311 | #458 | — | 4 | 12 | no | — |
| 312 | B(4,𝔽2) | — | 2 | 24 | no | — |
| 313 | B(4,𝔽2) | — | 4 | 12 | no | — |
| 314 | B(4,𝔽2) | — | 4 | 24 | no | — |
| 315 | #456 | — | 2 | 24 | no | — |
| 316 | #456 | — | 2 | 12 | no | — |
| 317 | #456 | — | 2 | 4 | no | — |
| 318 | #455 | — | 2 | 12 | no | — |
| 319 | #455 | C2×D4 | 1 | 24 | yes | — |
| 320 | #454 | — | 2 | 12 | no | — |
| 321 | #454 | — | 2 | 12 | no | — |
| 322 | #453 | — | 2 | 24 | no | — |
| 323 | #453 | — | 2 | 12 | no | — |
| 324 | #453 | C24 | 1 | 8 | yes | — |
| 325 | #449 | — | 4 | 3 | no | — |
| 326 | #447 | — | 4 | 6 | no | — |
| 327 | C8×Q8 | — | 4 | 1 | no | — |
| 328 | #444 | — | 2 | 24 | no | — |
| 329 | #443 | — | 2 | 12 | no | — |
| 330 | #443 | — | 2 | 12 | no | — |
| 331 | #443 | — | 2 | 4 | no | — |
| 332 | #443 | — | 2 | 12 | no | — |
| 333 | C4×SD16 | — | 4 | 3 | no | — |
| 334 | C4×D8 | — | 4 | 3 | no | — |
| 335 | #436 | — | 4 | 3 | no | — |
| 336 | #431 | — | 2 | 3 | no | — |
| 337 | #430 | — | 2 | 6 | no | — |
| 338 | C2×#108 | — | 2 | 6 | no | — |
| 339 | #423 | — | 2 | 3 | no | — |
| 340 | #421 | — | 2 | 12 | no | — |
| 341 | C2×#104 | — | 2 | 12 | no | — |
| 342 | #418 | — | 4 | 3 | no | — |
| 343 | #413 | — | 2 | 6 | no | — |
| 344 | #413 | C2×D4 | 1 | 12 | yes | — |
| 345 | C2×#101 | — | 2 | 6 | no | — |
| 346 | C2×#100 | — | 2 | 6 | no | — |
| 347 | #410 | — | 2 | 12 | no | — |
| 348 | #410 | — | 4 | 12 | no | — |
| 349 | #410 | — | 4 | 12 | no | — |
| 350 | #410 | — | 4 | 6 | no | — |
| 351 | #405 | — | 2 | 3 | no | — |
| 352 | C4×M16 | C2×D4 | 1 | 3 | yes | — |
| 353 | C2×C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 354 | #354 | — | 2 | 12 | no | — |
| 355 | #353 | C24 | 1 | 8 | yes | — |
| 356 | #352 | — | 2 | 8 | no | — |
| 357 | AΣL(1,𝔽16) | — | 2 | 24 | no | — |
| 358 | #333 | — | 2 | 3 | no | — |
| 359 | #333 | — | 2 | 3 | no | — |
| 360 | #331 | C24 | 1 | 1 | yes | characteristic |
| 361 | #331 | C24 | 1 | 3 | yes | — |
| 362 | Q8⋊C8 | — | 2 | 3 | no | — |
| 363 | Q8⋊C8 | — | 2 | 1 | no | — |
| 364 | D4⋊C8 | — | 2 | 6 | no | — |
| 365 | D4⋊C8 | — | 2 | 3 | no | — |
| 366 | D4⋊C8 | — | 2 | 3 | no | — |
| 367 | 2−1+4 | — | 2 | 8 | no | — |
| 368 | 2−1+4 | — | 2 | 4 | no | — |
| 369 | 2−1+4 | — | 2 | 12 | no | — |
| 370 | 2−1+4 | — | 4 | 12 | no | — |
| 371 | 2−1+4 | — | 4 | 12 | no | — |
| 372 | 2−1+4 | — | 4 | 2 | no | — |
| 373 | 2−1+4 | — | 4 | 8 | no | — |
| 374 | 2−1+4 | — | 4 | 24 | no | — |
| 375 | 2−1+4 | — | 8 | 6 | no | — |
| 376 | 2−1+4 | — | 8 | 8 | no | — |
| 377 | 2−1+4 | — | 8 | 4 | no | — |
| 378 | 2−1+4 | — | 8 | 12 | no | — |
| 379 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 380 | H(5,𝔽2) | — | 2 | 12 | no | — |
| 381 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 382 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 383 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 384 | H(5,𝔽2) | — | 4 | 6 | no | — |
| 385 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 386 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 387 | H(5,𝔽2) | — | 8 | 6 | no | — |
| 388 | H(5,𝔽2) | — | 8 | 12 | no | — |
| 389 | H(5,𝔽2) | — | 8 | 6 | no | — |
| 390 | H(5,𝔽2) | — | 8 | 24 | no | — |
| 391 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 392 | H(5,𝔽2) | C22×D4 | 1 | 8 | yes | — |
| 393 | C2×#41 | — | 2 | 6 | no | — |
| 394 | C2×#41 | — | 2 | 3 | no | — |
| 395 | C2×#41 | — | 2 | 12 | no | — |
| 396 | C2×#41 | — | 2 | 3 | no | — |
| 397 | C2×#41 | — | 4 | 12 | no | — |
| 398 | C2×#41 | — | 4 | 3 | no | — |
| 399 | C2×#41 | — | 4 | 6 | no | — |
| 400 | C2×#41 | — | 4 | 8 | no | — |
| 401 | C2×#41 | — | 4 | 8 | no | — |
| 402 | C2×#41 | — | 4 | 1 | no | — |
| 403 | C2×#41 | — | 4 | 1 | no | — |
| 404 | C2×#41 | — | 4 | 24 | no | — |
| 405 | C2×#41 | — | 4 | 12 | no | — |
| 406 | C2×#41 | — | 4 | 12 | no | — |
| 407 | C2×#41 | — | 4 | 24 | no | — |
| 408 | C2×#41 | — | 8 | 6 | no | — |
| 409 | C2×#41 | — | 8 | 24 | no | — |
| 410 | C2×#41 | — | 8 | 6 | no | — |
| 411 | C2×#41 | — | 8 | 8 | no | — |
| 412 | C2×#41 | — | 8 | 8 | no | — |
| 413 | C2×#41 | — | 8 | 12 | no | — |
| 414 | C2×#41 | #120 | 1 | 1 | yes | characteristic |
| 415 | C2×#41 | C22×D4 | 1 | 6 | yes | — |
| 416 | C22×Q8 | — | 2 | 2 | no | — |
| 417 | C22×Q8 | — | 4 | 8 | no | — |
| 418 | C22×Q8 | — | 4 | 12 | no | — |
| 419 | C22×Q8 | #120 | 1 | 6 | yes | — |
| 420 | C22×D4 | — | 2 | 6 | no | — |
| 421 | C22×D4 | — | 2 | 3 | no | — |
| 422 | C22×D4 | — | 4 | 3 | no | — |
| 423 | C22×D4 | — | 4 | 12 | no | — |
| 424 | C22×D4 | — | 4 | 3 | no | — |
| 425 | C22×D4 | — | 4 | 3 | no | — |
| 426 | C22×D4 | — | 8 | 6 | no | — |
| 427 | C22×D4 | — | 8 | 12 | no | — |
| 428 | C23×C4 | — | 2 | 6 | no | — |
| 429 | #137 | — | 2 | 24 | no | — |
| 430 | #137 | — | 2 | 8 | no | — |
| 431 | #137 | — | 2 | 24 | no | — |
| 432 | #137 | — | 4 | 24 | no | — |
| 433 | #137 | — | 4 | 24 | no | — |
| 434 | #137 | — | 4 | 24 | no | — |
| 435 | #137 | — | 4 | 24 | no | — |
| 436 | #137 | — | 4 | 48 | no | — |
| 437 | #137 | — | 4 | 8 | no | — |
| 438 | #137 | — | 4 | 12 | no | — |
| 439 | #137 | — | 4 | 12 | no | — |
| 440 | #137 | — | 4 | 24 | no | — |
| 441 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 442 | AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 443 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 444 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 445 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 446 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 447 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 448 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 449 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 450 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 451 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 452 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 453 | AGL(1,ℤ/8) | — | 16 | 6 | no | — |
| 454 | #135 | — | 2 | 4 | no | — |
| 455 | #135 | — | 2 | 12 | no | — |
| 456 | #135 | — | 2 | 12 | no | — |
| 457 | #135 | — | 2 | 12 | no | — |
| 458 | #135 | — | 4 | 12 | no | — |
| 459 | #135 | — | 4 | 12 | no | — |
| 460 | #135 | — | 4 | 24 | no | — |
| 461 | #135 | — | 4 | 24 | no | — |
| 462 | #135 | — | 4 | 8 | no | — |
| 463 | #135 | — | 4 | 48 | no | — |
| 464 | #135 | — | 4 | 24 | no | — |
| 465 | #135 | — | 4 | 24 | no | — |
| 466 | #135 | — | 4 | 24 | no | — |
| 467 | C2×Q16 | — | 2 | 6 | no | — |
| 468 | C2×Q16 | — | 2 | 6 | no | — |
| 469 | C2×Q16 | — | 4 | 24 | no | — |
| 470 | C2×Q16 | — | 4 | 12 | no | — |
| 471 | C2×SD16 | — | 2 | 12 | no | — |
| 472 | C2×SD16 | — | 2 | 6 | no | — |
| 473 | C2×SD16 | — | 2 | 12 | no | — |
| 474 | C2×SD16 | — | 2 | 2 | no | — |
| 475 | C2×SD16 | — | 4 | 12 | no | — |
| 476 | C2×SD16 | — | 4 | 12 | no | — |
| 477 | C2×SD16 | — | 4 | 24 | no | — |
| 478 | C2×SD16 | — | 4 | 48 | no | — |
| 479 | C2×SD16 | — | 4 | 8 | no | — |
| 480 | C2×SD16 | — | 4 | 12 | no | — |
| 481 | C2×SD16 | — | 4 | 12 | no | — |
| 482 | C2×SD16 | — | 4 | 3 | no | — |
| 483 | C2×D8 | — | 2 | 6 | no | — |
| 484 | C2×D8 | — | 2 | 6 | no | — |
| 485 | C2×D8 | — | 4 | 24 | no | — |
| 486 | C2×D8 | — | 4 | 12 | no | — |
| 487 | C2×D8 | — | 4 | 6 | no | — |
| 488 | C2×D8 | — | 4 | 3 | no | — |
| 489 | #131 | — | 2 | 4 | no | — |
| 490 | #131 | — | 2 | 4 | no | — |
| 491 | #131 | — | 2 | 8 | no | — |
| 492 | #131 | — | 2 | 24 | no | — |
| 493 | #131 | — | 4 | 12 | no | — |
| 494 | #131 | — | 4 | 12 | no | — |
| 495 | #131 | — | 4 | 24 | no | — |
| 496 | #131 | — | 4 | 8 | no | — |
| 497 | C2×M16 | — | 2 | 3 | no | — |
| 498 | C2×M16 | — | 2 | 12 | no | — |
| 499 | C2×M16 | — | 4 | 12 | no | — |
| 500 | C2×M16 | — | 4 | 24 | no | — |
| 501 | C2×M16 | — | 4 | 3 | no | — |
| 502 | C22×C8 | — | 2 | 3 | no | — |
| 503 | C22×C8 | — | 4 | 12 | no | — |
| 504 | C4⋊Q8 | — | 2 | 3 | no | — |
| 505 | C4⋊Q8 | — | 4 | 3 | no | — |
| 506 | C4⋊Q8 | — | 4 | 3 | no | — |
| 507 | C4⋊Q8 | #120 | 1 | 6 | yes | — |
| 508 | C4⋊Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 509 | C4⋊Q8 | C22×D4 | 1 | 3 | yes | — |
| 510 | #127 | — | 2 | 3 | no | — |
| 511 | #127 | — | 2 | 3 | no | — |
| 512 | #127 | — | 4 | 3 | no | — |
| 513 | #127 | — | 4 | 6 | no | — |
| 514 | #127 | — | 4 | 3 | no | — |
| 515 | #127 | — | 8 | 12 | no | — |
| 516 | #127 | C22×D4 | 1 | 3 | yes | — |
| 517 | #127 | C25 | 1 | 1 | yes | characteristic |
| 518 | #126 | — | 4 | 6 | no | — |
| 519 | #126 | — | 4 | 12 | no | — |
| 520 | #125 | — | 4 | 3 | no | — |
| 521 | #124 | — | 2 | 3 | no | — |
| 522 | #124 | — | 4 | 1 | no | — |
| 523 | #124 | — | 4 | 6 | no | — |
| 524 | #124 | — | 4 | 12 | no | — |
| 525 | #124 | — | 4 | 6 | no | — |
| 526 | #124 | — | 4 | 6 | no | — |
| 527 | #124 | — | 4 | 3 | no | — |
| 528 | #124 | — | 8 | 12 | no | — |
| 529 | #124 | C22×D4 | 1 | 6 | yes | — |
| 530 | #123 | — | 2 | 6 | no | — |
| 531 | #123 | — | 2 | 2 | no | — |
| 532 | #123 | — | 4 | 6 | no | — |
| 533 | #123 | — | 4 | 6 | no | — |
| 534 | #123 | — | 4 | 12 | no | — |
| 535 | #123 | — | 4 | 8 | no | — |
| 536 | C22⋊Q8 | — | 4 | 6 | no | — |
| 537 | C22⋊Q8 | — | 4 | 6 | no | — |
| 538 | C22⋊Q8 | — | 4 | 3 | no | — |
| 539 | C22⋊Q8 | — | 4 | 6 | no | — |
| 540 | C22⋊Q8 | — | 4 | 6 | no | — |
| 541 | C22⋊Q8 | — | 8 | 12 | no | — |
| 542 | #121 | — | 2 | 6 | no | — |
| 543 | #121 | — | 4 | 3 | no | — |
| 544 | #121 | — | 4 | 6 | no | — |
| 545 | #121 | — | 4 | 3 | no | — |
| 546 | #121 | — | 4 | 3 | no | — |
| 547 | #121 | — | 4 | 6 | no | — |
| 548 | #121 | — | 4 | 12 | no | — |
| 549 | #121 | — | 4 | 6 | no | — |
| 550 | #121 | — | 4 | 6 | no | — |
| 551 | #121 | — | 4 | 6 | no | — |
| 552 | #121 | — | 4 | 3 | no | — |
| 553 | #121 | — | 4 | 3 | no | — |
| 554 | #121 | — | 4 | 3 | no | — |
| 555 | #121 | — | 8 | 3 | no | — |
| 556 | #121 | — | 8 | 24 | no | — |
| 557 | #121 | — | 8 | 12 | no | — |
| 558 | #120 | — | 2 | 12 | no | — |
| 559 | #120 | — | 2 | 6 | no | — |
| 560 | #120 | — | 2 | 6 | no | — |
| 561 | #120 | — | 4 | 12 | no | — |
| 562 | #120 | — | 4 | 24 | no | — |
| 563 | #120 | — | 8 | 3 | no | — |
| 564 | C4×Q8 | — | 2 | 1 | no | — |
| 565 | C4×Q8 | — | 2 | 3 | no | — |
| 566 | C4×Q8 | — | 2 | 1 | no | — |
| 567 | C4×Q8 | — | 4 | 6 | no | — |
| 568 | C4×Q8 | — | 4 | 6 | no | — |
| 569 | C4×Q8 | — | 4 | 1 | no | — |
| 570 | C4×Q8 | — | 8 | 8 | no | — |
| 571 | C4×D4 | — | 2 | 3 | no | — |
| 572 | C4×D4 | — | 2 | 3 | no | — |
| 573 | C4×D4 | — | 2 | 3 | no | — |
| 574 | C4×D4 | — | 4 | 3 | no | — |
| 575 | C4×D4 | — | 4 | 3 | no | — |
| 576 | C4×D4 | — | 4 | 3 | no | — |
| 577 | C4×D4 | — | 4 | 1 | no | — |
| 578 | C4×D4 | — | 4 | 3 | no | — |
| 579 | C4×D4 | — | 4 | 6 | no | — |
| 580 | C4×D4 | — | 4 | 6 | no | — |
| 581 | C4×D4 | — | 4 | 3 | no | — |
| 582 | C4×D4 | — | 4 | 12 | no | — |
| 583 | C4×D4 | — | 4 | 3 | no | — |
| 584 | C4×D4 | — | 4 | 6 | no | — |
| 585 | C4×D4 | — | 4 | 3 | no | — |
| 586 | C4×D4 | — | 8 | 24 | no | — |
| 587 | #117 | — | 2 | 6 | no | — |
| 588 | #117 | — | 2 | 6 | no | — |
| 589 | #117 | — | 2 | 3 | no | — |
| 590 | #117 | — | 4 | 3 | no | — |
| 591 | #117 | — | 4 | 6 | no | — |
| 592 | #117 | — | 4 | 3 | no | — |
| 593 | #117 | — | 4 | 12 | no | — |
| 594 | #117 | #120 | 1 | 3 | yes | — |
| 595 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 596 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 597 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 598 | C2×C42 | — | 4 | 3 | no | — |
| 599 | C2×C42 | C22×D4 | 1 | 3 | yes | — |
| 600 | #108 | — | 2 | 4 | no | — |
| 601 | #108 | — | 2 | 12 | no | — |
| 602 | #107 | — | 4 | 1 | no | — |
| 603 | #106 | — | 4 | 3 | no | — |
| 604 | C4⋊C8 | — | 2 | 3 | no | — |
| 605 | C4⋊C8 | — | 2 | 1 | no | — |
| 606 | C4⋊C8 | — | 4 | 3 | no | — |
| 607 | #104 | — | 2 | 24 | no | — |
| 608 | #104 | — | 2 | 8 | no | — |
| 609 | #103 | — | 4 | 1 | no | — |
| 610 | #102 | — | 4 | 3 | no | — |
| 611 | #102 | — | 4 | 6 | no | — |
| 612 | #102 | — | 4 | 3 | no | — |
| 613 | #102 | — | 4 | 3 | no | — |
| 614 | #101 | — | 2 | 4 | no | — |
| 615 | #101 | — | 2 | 12 | no | — |
| 616 | #100 | — | 2 | 12 | no | — |
| 617 | #100 | C22×D4 | 1 | 8 | yes | — |
| 618 | #99 | — | 2 | 8 | no | — |
| 619 | #99 | — | 4 | 24 | no | — |
| 620 | #99 | — | 4 | 8 | no | — |
| 621 | #99 | — | 4 | 12 | no | — |
| 622 | C22⋊C8 | — | 4 | 3 | no | — |
| 623 | #97 | — | 2 | 3 | no | — |
| 624 | C4×C8 | — | 2 | 3 | no | — |
| 625 | C4×C8 | — | 4 | 3 | no | — |
| 626 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 627 | C4×C8 | C22×D4 | 1 | 3 | yes | — |
| 628 | C24 | — | 2 | 6 | no | — |
| 629 | C24 | — | 4 | 3 | no | — |
| 630 | C24 | — | 8 | 6 | no | — |
| 631 | #41 | — | 2 | 4 | no | — |
| 632 | #41 | — | 2 | 24 | no | — |
| 633 | #41 | — | 2 | 8 | no | — |
| 634 | #41 | — | 4 | 12 | no | — |
| 635 | #41 | — | 4 | 12 | no | — |
| 636 | #41 | — | 4 | 12 | no | — |
| 637 | #41 | — | 4 | 24 | no | — |
| 638 | #41 | — | 4 | 8 | no | — |
| 639 | #41 | — | 4 | 12 | no | — |
| 640 | #41 | — | 4 | 8 | no | — |
| 641 | #41 | — | 4 | 24 | no | — |
| 642 | #41 | — | 4 | 8 | no | — |
| 643 | #41 | — | 4 | 24 | no | — |
| 644 | #41 | — | 8 | 12 | no | — |
| 645 | #41 | — | 8 | 12 | no | — |
| 646 | #41 | — | 8 | 24 | no | — |
| 647 | #41 | — | 8 | 12 | no | — |
| 648 | #41 | — | 8 | 12 | no | — |
| 649 | #41 | — | 8 | 4 | no | — |
| 650 | #41 | — | 8 | 24 | no | — |
| 651 | #41 | — | 8 | 12 | no | — |
| 652 | #41 | — | 8 | 24 | no | — |
| 653 | #41 | — | 8 | 24 | no | — |
| 654 | #41 | — | 8 | 3 | no | — |
| 655 | #41 | — | 8 | 3 | no | — |
| 656 | #41 | — | 8 | 24 | no | — |
| 657 | #41 | — | 8 | 12 | no | — |
| 658 | #41 | — | 8 | 4 | no | — |
| 659 | #41 | — | 8 | 4 | no | — |
| 660 | #41 | — | 16 | 3 | no | — |
| 661 | #41 | — | 16 | 3 | no | — |
| 662 | #41 | — | 16 | 12 | no | — |
| 663 | C2×Q8 | — | 2 | 6 | no | — |
| 664 | C2×Q8 | — | 2 | 12 | no | — |
| 665 | C2×Q8 | — | 2 | 1 | no | — |
| 666 | C2×Q8 | — | 2 | 1 | no | — |
| 667 | C2×Q8 | — | 4 | 3 | no | — |
| 668 | C2×Q8 | — | 4 | 12 | no | — |
| 669 | C2×Q8 | — | 4 | 8 | no | — |
| 670 | C2×Q8 | — | 4 | 8 | no | — |
| 671 | C2×Q8 | — | 4 | 12 | no | — |
| 672 | C2×Q8 | — | 4 | 24 | no | — |
| 673 | C2×Q8 | — | 4 | 8 | no | — |
| 674 | C2×Q8 | — | 8 | 6 | no | — |
| 675 | C2×Q8 | — | 8 | 24 | no | — |
| 676 | C2×Q8 | — | 8 | 6 | no | — |
| 677 | C2×Q8 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 678 | C2×Q8 | C2×#120 | 1 | 6 | yes | — |
| 679 | C2×D4 | — | 2 | 12 | no | — |
| 680 | C2×D4 | — | 2 | 3 | no | — |
| 681 | C2×D4 | — | 2 | 6 | no | — |
| 682 | C2×D4 | — | 2 | 3 | no | — |
| 683 | C2×D4 | — | 4 | 12 | no | — |
| 684 | C2×D4 | — | 4 | 1 | no | — |
| 685 | C2×D4 | — | 4 | 3 | no | — |
| 686 | C2×D4 | — | 4 | 3 | no | — |
| 687 | C2×D4 | — | 4 | 6 | no | — |
| 688 | C2×D4 | — | 4 | 24 | no | — |
| 689 | C2×D4 | — | 4 | 8 | no | — |
| 690 | C2×D4 | — | 4 | 24 | no | — |
| 691 | C2×D4 | — | 4 | 12 | no | — |
| 692 | C2×D4 | — | 4 | 8 | no | — |
| 693 | C2×D4 | — | 4 | 12 | no | — |
| 694 | C2×D4 | — | 4 | 3 | no | — |
| 695 | C2×D4 | — | 4 | 6 | no | — |
| 696 | C2×D4 | — | 4 | 6 | no | — |
| 697 | C2×D4 | — | 4 | 3 | no | — |
| 698 | C2×D4 | — | 4 | 3 | no | — |
| 699 | C2×D4 | — | 4 | 3 | no | — |
| 700 | C2×D4 | — | 8 | 3 | no | — |
| 701 | C2×D4 | — | 8 | 24 | no | — |
| 702 | C2×D4 | — | 8 | 12 | no | — |
| 703 | C2×D4 | — | 8 | 12 | no | — |
| 704 | C2×D4 | — | 8 | 12 | no | — |
| 705 | C2×D4 | — | 8 | 12 | no | — |
| 706 | C2×D4 | — | 8 | 24 | no | — |
| 707 | C2×D4 | — | 8 | 6 | no | — |
| 708 | C2×D4 | — | 8 | 24 | no | — |
| 709 | C2×D4 | — | 8 | 24 | no | — |
| 710 | C2×D4 | — | 8 | 6 | no | — |
| 711 | C2×D4 | — | 8 | 24 | no | — |
| 712 | C2×D4 | — | 16 | 3 | no | — |
| 713 | C2×D4 | — | 16 | 3 | no | — |
| 714 | C2×D4 | — | 16 | 3 | no | — |
| 715 | C2×D4 | — | 16 | 3 | no | — |
| 716 | C2×D4 | B(4,𝔽2) | 1 | 3 | yes | — |
| 717 | C2×D4 | C23×D4 | 1 | 2 | yes | — |
| 718 | C22×C4 | — | 2 | 3 | no | — |
| 719 | C22×C4 | — | 2 | 6 | no | — |
| 720 | C22×C4 | — | 2 | 6 | no | — |
| 721 | C22×C4 | — | 2 | 2 | no | — |
| 722 | C22×C4 | — | 4 | 12 | no | — |
| 723 | C22×C4 | — | 4 | 3 | no | — |
| 724 | C22×C4 | — | 4 | 3 | no | — |
| 725 | C22×C4 | — | 4 | 6 | no | — |
| 726 | C22×C4 | — | 4 | 24 | no | — |
| 727 | C22×C4 | — | 4 | 3 | no | — |
| 728 | C22×C4 | — | 4 | 3 | no | — |
| 729 | C22×C4 | — | 8 | 6 | no | — |
| 730 | C22×C4 | — | 8 | 12 | no | — |
| 731 | C22×C4 | — | 8 | 12 | no | — |
| 732 | C22×C4 | — | 8 | 12 | no | — |
| 733 | C22×C4 | C2×#120 | 1 | 3 | yes | — |
| 734 | Q16 | — | 2 | 4 | no | — |
| 735 | Q16 | — | 2 | 12 | no | — |
| 736 | Q16 | — | 4 | 12 | no | — |
| 737 | Q16 | — | 4 | 24 | no | — |
| 738 | Q16 | — | 4 | 8 | no | — |
| 739 | SD16 | — | 2 | 8 | no | — |
| 740 | SD16 | — | 2 | 24 | no | — |
| 741 | SD16 | — | 4 | 6 | no | — |
| 742 | SD16 | — | 4 | 2 | no | — |
| 743 | SD16 | — | 4 | 6 | no | — |
| 744 | SD16 | — | 4 | 24 | no | — |
| 745 | SD16 | — | 4 | 2 | no | — |
| 746 | SD16 | — | 4 | 24 | no | — |
| 747 | SD16 | — | 4 | 8 | no | — |
| 748 | SD16 | — | 4 | 24 | no | — |
| 749 | SD16 | — | 4 | 8 | no | — |
| 750 | SD16 | — | 8 | 6 | no | — |
| 751 | D8 | — | 2 | 4 | no | — |
| 752 | D8 | — | 2 | 12 | no | — |
| 753 | D8 | — | 4 | 12 | no | — |
| 754 | D8 | — | 4 | 8 | no | — |
| 755 | D8 | — | 4 | 24 | no | — |
| 756 | D8 | — | 16 | 3 | no | — |
| 757 | D8 | — | 16 | 6 | no | — |
| 758 | M16 | — | 2 | 12 | no | — |
| 759 | M16 | — | 2 | 8 | no | — |
| 760 | M16 | — | 4 | 8 | no | — |
| 761 | M16 | — | 4 | 24 | no | — |
| 762 | M16 | — | 4 | 12 | no | — |
| 763 | M16 | — | 16 | 3 | no | — |
| 764 | C2×C8 | — | 2 | 6 | no | — |
| 765 | C2×C8 | — | 2 | 6 | no | — |
| 766 | C2×C8 | — | 2 | 1 | no | — |
| 767 | C2×C8 | — | 2 | 3 | no | — |
| 768 | C2×C8 | — | 4 | 8 | no | — |
| 769 | C2×C8 | — | 4 | 24 | no | — |
| 770 | C2×C8 | — | 4 | 12 | no | — |
| 771 | C2×C8 | — | 4 | 1 | no | — |
| 772 | C2×C8 | — | 4 | 3 | no | — |
| 773 | C4⋊C4 | — | 2 | 3 | no | — |
| 774 | C4⋊C4 | — | 2 | 3 | no | — |
| 775 | C4⋊C4 | — | 2 | 1 | no | — |
| 776 | C4⋊C4 | — | 4 | 3 | no | — |
| 777 | C4⋊C4 | — | 4 | 6 | no | — |
| 778 | C4⋊C4 | — | 4 | 1 | no | — |
| 779 | C4⋊C4 | — | 4 | 6 | no | — |
| 780 | C4⋊C4 | — | 4 | 6 | no | — |
| 781 | C4⋊C4 | — | 4 | 3 | no | — |
| 782 | C4⋊C4 | — | 4 | 1 | no | — |
| 783 | C4⋊C4 | — | 4 | 3 | no | — |
| 784 | C4⋊C4 | — | 8 | 12 | no | — |
| 785 | C4⋊C4 | — | 8 | 8 | no | — |
| 786 | C22⋊C4 | — | 2 | 3 | no | — |
| 787 | C22⋊C4 | — | 2 | 6 | no | — |
| 788 | C22⋊C4 | — | 2 | 2 | no | — |
| 789 | C22⋊C4 | — | 4 | 6 | no | — |
| 790 | C22⋊C4 | — | 4 | 3 | no | — |
| 791 | C22⋊C4 | — | 4 | 6 | no | — |
| 792 | C22⋊C4 | — | 4 | 12 | no | — |
| 793 | C22⋊C4 | — | 4 | 6 | no | — |
| 794 | C22⋊C4 | — | 4 | 2 | no | — |
| 795 | C22⋊C4 | — | 4 | 3 | no | — |
| 796 | C22⋊C4 | — | 4 | 3 | no | — |
| 797 | C22⋊C4 | — | 4 | 8 | no | — |
| 798 | C22⋊C4 | — | 8 | 3 | no | — |
| 799 | C22⋊C4 | — | 8 | 24 | no | — |
| 800 | C22⋊C4 | — | 8 | 8 | no | — |
| 801 | C42 | — | 2 | 3 | no | — |
| 802 | C42 | — | 4 | 1 | no | — |
| 803 | C42 | — | 4 | 3 | no | — |
| 804 | C42 | — | 4 | 6 | no | — |
| 805 | C42 | — | 4 | 3 | no | — |
| 806 | C42 | — | 8 | 12 | no | — |
| 807 | C42 | C2×#120 | 1 | 3 | yes | — |
| 808 | C42 | C23×D4 | 1 | 1 | yes | characteristic |
| 809 | C23 | — | 2 | 2 | no | — |
| 810 | C23 | — | 4 | 12 | no | — |
| 811 | C23 | — | 4 | 8 | no | — |
| 812 | C23 | — | 4 | 3 | no | — |
| 813 | C23 | — | 4 | 3 | no | — |
| 814 | C23 | — | 8 | 6 | no | — |
| 815 | C23 | — | 8 | 12 | no | — |
| 816 | C23 | — | 8 | 6 | no | — |
| 817 | C23 | — | 16 | 6 | no | — |
| 818 | C23 | — | 32 | 3 | no | — |
| 819 | C23 | — | 64 | 6 | no | — |
| 820 | C23 | C2×B(4,𝔽2) | 1 | 3 | yes | — |
| 821 | Q8 | — | 2 | 8 | no | — |
| 822 | Q8 | — | 4 | 6 | no | — |
| 823 | Q8 | — | 4 | 2 | no | — |
| 824 | Q8 | — | 4 | 1 | no | — |
| 825 | Q8 | — | 4 | 1 | no | — |
| 826 | Q8 | — | 4 | 12 | no | — |
| 827 | Q8 | — | 4 | 12 | no | — |
| 828 | Q8 | — | 8 | 12 | no | — |
| 829 | Q8 | — | 8 | 4 | no | — |
| 830 | Q8 | — | 16 | 3 | no | — |
| 831 | Q8 | #2196 | 1 | 4 | yes | — |
| 832 | D4 | — | 2 | 8 | no | — |
| 833 | D4 | — | 2 | 6 | no | — |
| 834 | D4 | — | 4 | 2 | no | — |
| 835 | D4 | — | 4 | 6 | no | — |
| 836 | D4 | — | 4 | 3 | no | — |
| 837 | D4 | — | 4 | 3 | no | — |
| 838 | D4 | — | 4 | 24 | no | — |
| 839 | D4 | — | 4 | 8 | no | — |
| 840 | D4 | — | 4 | 12 | no | — |
| 841 | D4 | — | 8 | 1 | no | — |
| 842 | D4 | — | 8 | 1 | no | — |
| 843 | D4 | — | 8 | 3 | no | — |
| 844 | D4 | — | 8 | 3 | no | — |
| 845 | D4 | — | 8 | 6 | no | — |
| 846 | D4 | — | 8 | 8 | no | — |
| 847 | D4 | — | 8 | 12 | no | — |
| 848 | D4 | — | 8 | 24 | no | — |
| 849 | D4 | — | 8 | 6 | no | — |
| 850 | D4 | — | 8 | 4 | no | — |
| 851 | D4 | — | 8 | 6 | no | — |
| 852 | D4 | — | 8 | 6 | no | — |
| 853 | D4 | — | 16 | 6 | no | — |
| 854 | D4 | — | 16 | 3 | no | — |
| 855 | D4 | — | 16 | 3 | no | — |
| 856 | D4 | — | 16 | 6 | no | — |
| 857 | D4 | — | 16 | 6 | no | — |
| 858 | D4 | — | 32 | 3 | no | — |
| 859 | D4 | — | 32 | 24 | no | — |
| 860 | C2×C4 | — | 2 | 1 | no | — |
| 861 | C2×C4 | — | 2 | 6 | no | — |
| 862 | C2×C4 | — | 2 | 3 | no | — |
| 863 | C2×C4 | — | 2 | 6 | no | — |
| 864 | C2×C4 | — | 4 | 8 | no | — |
| 865 | C2×C4 | — | 4 | 3 | no | — |
| 866 | C2×C4 | — | 4 | 3 | no | — |
| 867 | C2×C4 | — | 4 | 12 | no | — |
| 868 | C2×C4 | — | 4 | 12 | no | — |
| 869 | C2×C4 | — | 4 | 24 | no | — |
| 870 | C2×C4 | — | 4 | 8 | no | — |
| 871 | C2×C4 | — | 4 | 3 | no | — |
| 872 | C2×C4 | — | 4 | 1 | no | — |
| 873 | C2×C4 | — | 4 | 1 | no | — |
| 874 | C2×C4 | — | 4 | 1 | no | — |
| 875 | C2×C4 | — | 8 | 3 | no | — |
| 876 | C2×C4 | — | 8 | 3 | no | — |
| 877 | C2×C4 | — | 8 | 6 | no | — |
| 878 | C2×C4 | — | 8 | 24 | no | — |
| 879 | C2×C4 | — | 8 | 12 | no | — |
| 880 | C2×C4 | — | 8 | 8 | no | — |
| 881 | C2×C4 | — | 8 | 6 | no | — |
| 882 | C2×C4 | — | 8 | 6 | no | — |
| 883 | C2×C4 | — | 8 | 2 | no | — |
| 884 | C2×C4 | — | 8 | 8 | no | — |
| 885 | C2×C4 | — | 16 | 6 | no | — |
| 886 | C2×C4 | — | 16 | 3 | no | — |
| 887 | C2×C4 | C2×B(4,𝔽2) | 1 | 3 | yes | — |
| 888 | C2×C4 | C22×#120 | 1 | 1 | yes | characteristic |
| 889 | C8 | — | 2 | 1 | no | — |
| 890 | C8 | — | 2 | 1 | no | — |
| 891 | C8 | — | 2 | 6 | no | — |
| 892 | C8 | — | 4 | 8 | no | — |
| 893 | C8 | — | 8 | 3 | no | — |
| 894 | C8 | — | 8 | 1 | no | — |
| 895 | C22 | — | 2 | 3 | no | — |
| 896 | C22 | — | 4 | 3 | no | — |
| 897 | C22 | — | 4 | 2 | no | — |
| 898 | C22 | — | 4 | 8 | no | — |
| 899 | C22 | — | 8 | 2 | no | — |
| 900 | C22 | — | 8 | 3 | no | — |
| 901 | C22 | — | 8 | 3 | no | — |
| 902 | C22 | — | 8 | 3 | no | — |
| 903 | C22 | — | 8 | 3 | no | — |
| 904 | C22 | — | 16 | 3 | no | — |
| 905 | C22 | — | 16 | 12 | no | — |
| 906 | C22 | — | 16 | 8 | no | — |
| 907 | C22 | — | 16 | 12 | no | — |
| 908 | C22 | — | 32 | 6 | no | — |
| 909 | C22 | — | 32 | 12 | no | — |
| 910 | C22 | C22×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 911 | C4 | — | 2 | 1 | no | — |
| 912 | C4 | — | 2 | 1 | no | — |
| 913 | C4 | — | 2 | 1 | no | — |
| 914 | C4 | — | 4 | 3 | no | — |
| 915 | C4 | — | 4 | 6 | no | — |
| 916 | C4 | — | 4 | 8 | no | — |
| 917 | C4 | — | 8 | 3 | no | — |
| 918 | C4 | — | 8 | 1 | no | — |
| 919 | C4 | — | 8 | 1 | no | — |
| 920 | C4 | — | 8 | 1 | no | — |
| 921 | C4 | — | 16 | 8 | no | — |
| 922 | C4 | C2×#2196 | 1 | 6 | yes | — |
| 923 | C2 | — | 2 | 1 | no | — |
| 924 | C2 | — | 4 | 3 | no | — |
| 925 | C2 | — | 8 | 2 | no | — |
| 926 | C2 | — | 8 | 8 | no | — |
| 927 | C2 | — | 16 | 3 | no | — |
| 928 | C2 | — | 16 | 3 | no | — |
| 929 | C2 | C22×#2196 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C22×#2196 |
| commutator, Frattini, cosocle | #127 | C25 |
| LCS | G ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 ◁ C2×#41 ◁ #3499 ◁ G | |
| LECS | G ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10576183 | C2 | semidirect |
| 2. #7622885 | C2 | semidirect |
| 3. #6353352 | C2 | semidirect |
| 4. #512867 | C2 | semidirect |
| 5. #512864 | C2 | semidirect |
| 6. #512860 | C2 | semidirect |
| 7. #512857 | C2 | semidirect |
| 8. #512616 | C2 | semidirect |
| 9. #512566 | C2 | semidirect |
| 11. #63022 | C22 | semidirect |
| 24. #33559 | C22 | semidirect |
| 26. #33546 | C22 | semidirect |
| 27. #33360 | C22 | semidirect |
| 29. #18714 | C22 | semidirect |
| 30. #18686 | C22 | semidirect |
| 33. #18527 | C22 | semidirect |
| 34. #18480 | C22 | semidirect |
| 35. #17773 | C22 | semidirect |
| 37. #13676 | C22 | semidirect |
| 38. #13675 | C22 | semidirect |
| 39. #13674 | C22 | semidirect |
| 40. #13673 | C22 | semidirect |
| 41. #13673 | C22 | semidirect |
| 42. #13585 | C22 | semidirect |
| 43. #13583 | C22 | semidirect |
| 44. #13562 | C22 | semidirect |
| 45. #13560 | C22 | semidirect |
| 46. 2−1+6 | D4 | semidirect |
| 61. #3549 | C23 | semidirect |
| 68. #3498 | D4 | semidirect |
| 72. #3481 | C23 | semidirect |
| 90. #3152 | D4 | semidirect |
| 93. C2×#492 | D4 | semidirect |
| 104. #3022 | D4 | semidirect |
| 119. #2889 | D4 | semidirect |
| 123. C4×#131 | D4 | semidirect |
| 125. #2198 | C23 | semidirect |
| 127. #2196 | C23 | semidirect |
| 129. #2126 | C23 | semidirect |
| 134. #1630 | C23 | semidirect |
| 135. #1629 | C23 | semidirect |
| 140. #1620 | C23 | semidirect |
| 141. #1619 | C23 | semidirect |
| 142. #1619 | C23 | semidirect |
| 143. #1560 | C23 | semidirect |
| 145. #1543 | C23 | semidirect |
| 150. #1409 | C23 | semidirect |
| 151. #1408 | C23 | semidirect |
| 152. #1402 | C23 | semidirect |
| 153. #1402 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10576183 | 2 |
| #7622885 | 2 |
| #6353352 | 2 |
| #512867 | 2 |
| #512864 | 2 |
| #512860 | 2 |
| #512857 | 2 |
| #512616 | 2 |
| #512566 | 2 |