Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
8172 conjugacy classes of subgroups.
The subgroup lattice has 944 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10575254 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #7622466 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #512616 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #512613 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | #512601 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#13585 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#3585 | — | 2 | 2 | no | — |
| 8 | #62812 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#3498 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #60650 | — | 2 | 2 | no | — |
| 11 | #60650 | — | 2 | 6 | no | — |
| 12 | #60647 | C4 | 1 | 2 | yes | complemented |
| 13 | #60647 | C22 | 1 | 6 | yes | — |
| 14 | #60646 | C4 | 1 | 6 | yes | complemented |
| 15 | #60646 | C22 | 1 | 2 | yes | — |
| 16 | #60644 | — | 2 | 6 | no | — |
| 17 | #60639 | C4 | 1 | 3 | yes | complemented |
| 18 | #60639 | C22 | 1 | 3 | yes | — |
| 19 | C2×#3151 | C4 | 1 | 3 | yes | complemented |
| 20 | C2×#3151 | C22 | 1 | 3 | yes | — |
| 21 | #60070 | — | 2 | 2 | no | — |
| 22 | C4×#568 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #33362 | — | 2 | 2 | no | — |
| 24 | #33361 | — | 2 | 6 | no | — |
| 25 | #33360 | C22 | 1 | 4 | yes | complemented |
| 26 | #33359 | C22 | 1 | 12 | yes | complemented |
| 27 | #33358 | — | 2 | 6 | no | — |
| 28 | C2×#2126 | C22 | 1 | 12 | yes | complemented |
| 29 | #13586 | C22 | 1 | 4 | yes | complemented |
| 30 | #13585 | C22 | 1 | 12 | yes | complemented |
| 31 | #13585 | C22 | 1 | 24 | yes | complemented |
| 32 | #13584 | C22 | 1 | 24 | yes | complemented |
| 33 | #13583 | C22 | 1 | 24 | yes | complemented |
| 34 | C2×#1408 | C22 | 1 | 24 | yes | complemented |
| 35 | C2×#585 | D4 | 1 | 2 | yes | — |
| 36 | C22×H(5,𝔽2) | — | 2 | 1 | no | — |
| 37 | #3585 | — | 4 | 16 | no | — |
| 38 | #3585 | — | 4 | 16 | no | — |
| 39 | C2×#577 | — | 2 | 12 | no | — |
| 40 | C2×#577 | — | 2 | 4 | no | — |
| 41 | C2×#576 | — | 2 | 4 | no | — |
| 42 | C2×#576 | — | 2 | 12 | no | — |
| 43 | C2×#575 | — | 2 | 6 | no | — |
| 44 | C2×#575 | — | 2 | 6 | no | — |
| 45 | C22×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 46 | C22×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 47 | C2×#568 | — | 2 | 1 | no | — |
| 48 | #3500 | D4 | 1 | 2 | yes | — |
| 49 | #3500 | D4 | 1 | 6 | yes | — |
| 50 | #3499 | C2×C4 | 1 | 3 | yes | — |
| 51 | #3499 | C23 | 1 | 1 | yes | characteristic |
| 52 | #3498 | — | 2 | 1 | no | — |
| 53 | #3498 | — | 2 | 3 | no | — |
| 54 | #3498 | — | 4 | 3 | no | — |
| 55 | #3498 | — | 4 | 1 | no | — |
| 56 | #3498 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | #3498 | C2×C4 | 1 | 6 | yes | complemented |
| 58 | #3498 | C2×C4 | 1 | 2 | yes | complemented |
| 59 | #3498 | C23 | 1 | 3 | yes | — |
| 60 | #3497 | — | 4 | 1 | no | — |
| 61 | #3496 | — | 4 | 3 | no | — |
| 62 | D4×#41 | — | 4 | 3 | no | — |
| 63 | D4×#41 | — | 4 | 1 | no | — |
| 64 | C2×#550 | — | 4 | 1 | no | — |
| 65 | C2×D42 | — | 4 | 3 | no | — |
| 66 | #3449 | D4 | 1 | 6 | yes | — |
| 67 | C2×#535 | — | 2 | 3 | no | — |
| 68 | C2×#532 | C2×C4 | 1 | 3 | yes | — |
| 69 | C2×#532 | C2×C4 | 1 | 3 | yes | complemented |
| 70 | C2×#532 | C23 | 1 | 3 | yes | — |
| 71 | C22×#127 | C2×C4 | 1 | 3 | yes | complemented |
| 72 | #3428 | — | 4 | 2 | no | — |
| 73 | C2×C4×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #3155 | — | 2 | 12 | no | — |
| 75 | #3155 | — | 2 | 12 | no | — |
| 76 | #3155 | — | 2 | 24 | no | — |
| 77 | #3154 | — | 2 | 12 | no | — |
| 78 | #3154 | — | 2 | 24 | no | — |
| 79 | #3154 | — | 2 | 12 | no | — |
| 80 | #3153 | — | 2 | 6 | no | — |
| 81 | #3153 | — | 2 | 6 | no | — |
| 82 | #3153 | — | 2 | 6 | no | — |
| 83 | #3153 | — | 2 | 6 | no | — |
| 84 | #3152 | C2×C4 | 1 | 3 | yes | complemented |
| 85 | #3152 | C2×C4 | 1 | 6 | yes | complemented |
| 86 | #3152 | C2×C4 | 1 | 6 | yes | complemented |
| 87 | #3152 | C23 | 1 | 1 | yes | characteristic |
| 88 | #3151 | — | 2 | 6 | no | — |
| 89 | #3151 | — | 2 | 6 | no | — |
| 90 | #3151 | — | 2 | 6 | no | — |
| 91 | #3151 | — | 2 | 6 | no | — |
| 92 | #3151 | C2×C4 | 1 | 3 | yes | complemented |
| 93 | #3151 | C2×C4 | 1 | 6 | yes | complemented |
| 94 | #3151 | C2×C4 | 1 | 12 | yes | complemented |
| 95 | #3151 | C2×C4 | 1 | 6 | yes | complemented |
| 96 | #3151 | C2×C4 | 1 | 6 | yes | complemented |
| 97 | #3151 | C23 | 1 | 3 | yes | — |
| 98 | #3151 | C23 | 1 | 6 | yes | — |
| 99 | #3151 | C23 | 1 | 6 | yes | — |
| 100 | #3150 | — | 2 | 6 | no | — |
| 101 | #3150 | — | 2 | 6 | no | — |
| 102 | C2×#496 | — | 2 | 6 | no | — |
| 103 | C2×#496 | — | 2 | 6 | no | — |
| 104 | #3147 | C2×C4 | 1 | 12 | yes | complemented |
| 105 | #3147 | C2×C4 | 1 | 6 | yes | complemented |
| 106 | #3147 | C23 | 1 | 6 | yes | — |
| 107 | C2×#493 | C2×C4 | 1 | 6 | yes | complemented |
| 108 | C2×#493 | C23 | 1 | 6 | yes | — |
| 109 | C2×#492 | C2×C4 | 1 | 6 | yes | complemented |
| 110 | C2×#492 | C2×C4 | 1 | 6 | yes | complemented |
| 111 | #2884 | — | 2 | 4 | no | — |
| 112 | #2884 | — | 4 | 2 | no | — |
| 113 | #2883 | — | 2 | 12 | no | — |
| 114 | #2883 | — | 4 | 6 | no | — |
| 115 | C2×#410 | — | 2 | 12 | no | — |
| 116 | C2×#410 | — | 4 | 6 | no | — |
| 117 | #2875 | — | 2 | 1 | no | — |
| 118 | #2875 | — | 2 | 3 | no | — |
| 119 | C4×#131 | C2×C4 | 1 | 6 | yes | complemented |
| 120 | C4×#131 | C2×C4 | 1 | 2 | yes | complemented |
| 121 | #2873 | — | 2 | 3 | no | — |
| 122 | C2×C4×M16 | C2×C4 | 1 | 3 | yes | complemented |
| 123 | C2×C4×M16 | C2×C4 | 1 | 3 | yes | complemented |
| 124 | #2129 | — | 2 | 12 | no | — |
| 125 | #2128 | — | 2 | 12 | no | — |
| 126 | #2127 | — | 2 | 24 | no | — |
| 127 | #2126 | — | 2 | 12 | no | — |
| 128 | #2126 | — | 2 | 12 | no | — |
| 129 | #2126 | C23 | 1 | 8 | yes | — |
| 130 | #2126 | C23 | 1 | 24 | yes | complemented |
| 131 | C2×#354 | — | 2 | 12 | no | — |
| 132 | C2×#353 | C23 | 1 | 24 | yes | complemented |
| 133 | #1409 | C23 | 1 | 16 | yes | complemented |
| 134 | #1408 | C23 | 1 | 48 | yes | complemented |
| 135 | #585 | — | 4 | 8 | no | — |
| 136 | #585 | — | 4 | 8 | no | — |
| 137 | C2×2−1+4 | — | 2 | 2 | no | — |
| 138 | C2×2−1+4 | C22⋊C4 | 1 | 6 | yes | — |
| 139 | C2×2−1+4 | C2×D4 | 1 | 2 | yes | — |
| 140 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 141 | C2×H(5,𝔽2) | — | 2 | 2 | no | — |
| 142 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 143 | C2×H(5,𝔽2) | — | 4 | 3 | no | — |
| 144 | C2×H(5,𝔽2) | — | 4 | 1 | no | — |
| 145 | C2×H(5,𝔽2) | — | 4 | 8 | no | — |
| 146 | C2×H(5,𝔽2) | — | 4 | 8 | no | — |
| 147 | C2×H(5,𝔽2) | C22⋊C4 | 1 | 2 | yes | — |
| 148 | C2×H(5,𝔽2) | C2×D4 | 1 | 6 | yes | — |
| 149 | C22×#41 | — | 2 | 2 | no | — |
| 150 | C22×#41 | — | 2 | 6 | no | — |
| 151 | C22×#41 | — | 2 | 3 | no | — |
| 152 | C22×#41 | — | 4 | 1 | no | — |
| 153 | C22×#41 | C22⋊C4 | 1 | 6 | yes | — |
| 154 | C22×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 155 | C22×#41 | C2×D4 | 1 | 6 | yes | — |
| 156 | C23×D4 | — | 2 | 3 | no | — |
| 157 | C23×D4 | — | 4 | 3 | no | — |
| 158 | C23×D4 | — | 4 | 3 | no | — |
| 159 | #577 | — | 4 | 32 | no | — |
| 160 | #577 | — | 4 | 96 | no | — |
| 161 | #576 | — | 4 | 96 | no | — |
| 162 | #576 | — | 4 | 32 | no | — |
| 163 | #575 | — | 4 | 24 | no | — |
| 164 | #575 | — | 4 | 24 | no | — |
| 165 | #575 | — | 4 | 24 | no | — |
| 166 | #575 | — | 4 | 24 | no | — |
| 167 | C2×#137 | — | 2 | 6 | no | — |
| 168 | C2×#137 | — | 2 | 2 | no | — |
| 169 | C2×#137 | — | 2 | 12 | no | — |
| 170 | C2×#137 | — | 2 | 12 | no | — |
| 171 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 172 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 173 | C2×AGL(1,ℤ/8) | — | 2 | 24 | no | — |
| 174 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 175 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 176 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 177 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 178 | C2×AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 179 | C2×AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 180 | C2×AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 181 | C2×AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 182 | C2×AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 183 | C2×#135 | — | 2 | 24 | no | — |
| 184 | C2×#135 | — | 2 | 12 | no | — |
| 185 | C2×#135 | — | 2 | 12 | no | — |
| 186 | C22×SD16 | — | 2 | 12 | no | — |
| 187 | C22×SD16 | — | 2 | 12 | no | — |
| 188 | C22×D8 | — | 2 | 12 | no | — |
| 189 | C22×D8 | — | 2 | 12 | no | — |
| 190 | #568 | — | 2 | 16 | no | — |
| 191 | C2×#131 | — | 2 | 2 | no | — |
| 192 | C2×#131 | — | 2 | 6 | no | — |
| 193 | C22×M16 | — | 2 | 3 | no | — |
| 194 | C22×M16 | — | 2 | 3 | no | — |
| 195 | #550 | — | 4 | 1 | no | — |
| 196 | #550 | — | 4 | 3 | no | — |
| 197 | #550 | — | 4 | 6 | no | — |
| 198 | #550 | — | 4 | 2 | no | — |
| 199 | #550 | — | 4 | 6 | no | — |
| 200 | #550 | — | 4 | 2 | no | — |
| 201 | D4×Q8 | — | 4 | 3 | no | — |
| 202 | D4×Q8 | — | 4 | 1 | no | — |
| 203 | #548 | — | 4 | 6 | no | — |
| 204 | #548 | — | 4 | 2 | no | — |
| 205 | #547 | — | 4 | 3 | no | — |
| 206 | #547 | — | 4 | 6 | no | — |
| 207 | #547 | — | 4 | 3 | no | — |
| 208 | #546 | — | 4 | 6 | no | — |
| 209 | #546 | — | 4 | 12 | no | — |
| 210 | #546 | — | 4 | 6 | no | — |
| 211 | D42 | — | 4 | 3 | no | — |
| 212 | D42 | — | 4 | 6 | no | — |
| 213 | D42 | — | 4 | 3 | no | — |
| 214 | D42 | — | 4 | 12 | no | — |
| 215 | D42 | — | 4 | 6 | no | — |
| 216 | D42 | — | 4 | 6 | no | — |
| 217 | D42 | — | 4 | 12 | no | — |
| 218 | D42 | — | 4 | 6 | no | — |
| 219 | D42 | — | 4 | 6 | no | — |
| 220 | #537 | — | 4 | 6 | no | — |
| 221 | #536 | C22⋊C4 | 1 | 6 | yes | — |
| 222 | #536 | C22⋊C4 | 1 | 12 | yes | — |
| 223 | #536 | C2×D4 | 1 | 6 | yes | — |
| 224 | #535 | — | 2 | 6 | no | — |
| 225 | #535 | — | 2 | 6 | no | — |
| 226 | #535 | — | 2 | 12 | no | — |
| 227 | #535 | — | 4 | 6 | no | — |
| 228 | #535 | — | 4 | 6 | no | — |
| 229 | #535 | C22⋊C4 | 1 | 6 | yes | — |
| 230 | #535 | C2×D4 | 1 | 6 | yes | — |
| 231 | #535 | C2×D4 | 1 | 12 | yes | — |
| 232 | #534 | — | 4 | 6 | no | — |
| 233 | #532 | — | 2 | 3 | no | — |
| 234 | #532 | — | 2 | 3 | no | — |
| 235 | #532 | — | 4 | 3 | no | — |
| 236 | #532 | — | 4 | 3 | no | — |
| 237 | #532 | — | 4 | 3 | no | — |
| 238 | #532 | — | 4 | 3 | no | — |
| 239 | #532 | — | 4 | 3 | no | — |
| 240 | #532 | — | 4 | 3 | no | — |
| 241 | #532 | C22⋊C4 | 1 | 6 | yes | — |
| 242 | #532 | C22⋊C4 | 1 | 6 | yes | — |
| 243 | #532 | C22×C4 | 1 | 6 | yes | — |
| 244 | #532 | C22×C4 | 1 | 6 | yes | — |
| 245 | #532 | C22×C4 | 1 | 6 | yes | — |
| 246 | #532 | C22×C4 | 1 | 3 | yes | — |
| 247 | #532 | C22×C4 | 1 | 3 | yes | — |
| 248 | #532 | C2×D4 | 1 | 6 | yes | — |
| 249 | #532 | C2×D4 | 1 | 6 | yes | — |
| 250 | #532 | C24 | 1 | 3 | yes | — |
| 251 | #532 | C24 | 1 | 1 | yes | characteristic |
| 252 | C2×C4⋊Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 253 | C2×C4⋊Q8 | C22×C4 | 1 | 3 | yes | — |
| 254 | C2×C4⋊Q8 | C22×C4 | 1 | 3 | yes | — |
| 255 | C2×#127 | — | 2 | 3 | no | — |
| 256 | C2×#127 | — | 2 | 3 | no | — |
| 257 | C2×#127 | — | 2 | 3 | no | — |
| 258 | C2×#127 | — | 4 | 3 | no | — |
| 259 | C2×#127 | — | 4 | 3 | no | — |
| 260 | C2×#127 | — | 4 | 3 | no | — |
| 261 | C2×#127 | C22×C4 | 1 | 6 | yes | — |
| 262 | C2×#127 | C22×C4 | 1 | 6 | yes | — |
| 263 | C2×#127 | C22×C4 | 1 | 3 | yes | — |
| 264 | C2×#127 | C22×C4 | 1 | 3 | yes | — |
| 265 | C2×#127 | C24 | 1 | 3 | yes | — |
| 266 | C2×#124 | — | 2 | 3 | no | — |
| 267 | C2×#124 | C22⋊C4 | 1 | 6 | yes | — |
| 268 | C2×#124 | C2×D4 | 1 | 6 | yes | — |
| 269 | #525 | — | 4 | 6 | no | — |
| 270 | #525 | — | 4 | 6 | no | — |
| 271 | C2×#121 | — | 4 | 6 | no | — |
| 272 | C2×#121 | — | 4 | 3 | no | — |
| 273 | C2×#121 | — | 4 | 3 | no | — |
| 274 | C2×#121 | — | 4 | 3 | no | — |
| 275 | C2×#120 | — | 4 | 6 | no | — |
| 276 | #520 | — | 8 | 8 | no | — |
| 277 | #519 | — | 4 | 4 | no | — |
| 278 | #518 | — | 4 | 12 | no | — |
| 279 | C4×#41 | — | 2 | 3 | no | — |
| 280 | C4×#41 | — | 2 | 1 | no | — |
| 281 | C4×#41 | — | 8 | 8 | no | — |
| 282 | C4×#41 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 283 | C4×#41 | C22⋊C4 | 1 | 3 | yes | — |
| 284 | C4×#41 | C22×C4 | 1 | 1 | yes | characteristic |
| 285 | C4×#41 | C22×C4 | 1 | 3 | yes | — |
| 286 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 287 | C2×C4×D4 | — | 2 | 3 | no | — |
| 288 | C2×C4×D4 | — | 4 | 3 | no | — |
| 289 | C2×C4×D4 | — | 4 | 3 | no | — |
| 290 | C2×C4×D4 | — | 4 | 3 | no | — |
| 291 | C2×#117 | — | 4 | 12 | no | — |
| 292 | C2×#117 | C22⋊C4 | 1 | 3 | yes | — |
| 293 | C22×C42 | C22×C4 | 1 | 3 | yes | — |
| 294 | #497 | — | 2 | 12 | no | — |
| 295 | #497 | — | 2 | 12 | no | — |
| 296 | #497 | — | 2 | 6 | no | — |
| 297 | #497 | — | 2 | 2 | no | — |
| 298 | #496 | — | 2 | 12 | no | — |
| 299 | #496 | — | 2 | 12 | no | — |
| 300 | #496 | — | 2 | 6 | no | — |
| 301 | #496 | — | 2 | 12 | no | — |
| 302 | #496 | — | 2 | 24 | no | — |
| 303 | #496 | — | 2 | 12 | no | — |
| 304 | #496 | — | 2 | 6 | no | — |
| 305 | #496 | — | 2 | 12 | no | — |
| 306 | #495 | — | 2 | 24 | no | — |
| 307 | #495 | — | 2 | 12 | no | — |
| 308 | #495 | — | 2 | 12 | no | — |
| 309 | #494 | C22×C4 | 1 | 2 | yes | — |
| 310 | #494 | C22×C4 | 1 | 6 | yes | — |
| 311 | #493 | — | 2 | 12 | no | — |
| 312 | #493 | — | 2 | 12 | no | — |
| 313 | #493 | C22×C4 | 1 | 6 | yes | — |
| 314 | #493 | C22×C4 | 1 | 12 | yes | — |
| 315 | #493 | C24 | 1 | 6 | yes | — |
| 316 | #492 | — | 2 | 12 | no | — |
| 317 | #492 | — | 2 | 12 | no | — |
| 318 | #492 | C22×C4 | 1 | 12 | yes | — |
| 319 | #492 | C22×C4 | 1 | 6 | yes | — |
| 320 | #492 | C22×C4 | 1 | 6 | yes | — |
| 321 | #492 | C22×C4 | 1 | 6 | yes | — |
| 322 | #492 | C24 | 1 | 2 | yes | — |
| 323 | #410 | — | 2 | 8 | no | — |
| 324 | #410 | — | 2 | 24 | no | — |
| 325 | #410 | — | 4 | 12 | no | — |
| 326 | #410 | — | 4 | 12 | no | — |
| 327 | #410 | — | 4 | 12 | no | — |
| 328 | #410 | — | 4 | 12 | no | — |
| 329 | C2×#99 | — | 2 | 24 | no | — |
| 330 | C2×#99 | — | 4 | 12 | no | — |
| 331 | C2×#99 | — | 4 | 24 | no | — |
| 332 | #405 | — | 2 | 6 | no | — |
| 333 | #405 | — | 2 | 6 | no | — |
| 334 | #405 | — | 2 | 12 | no | — |
| 335 | C4×M16 | — | 2 | 3 | no | — |
| 336 | C4×M16 | — | 2 | 3 | no | — |
| 337 | C4×M16 | — | 2 | 3 | no | — |
| 338 | C4×M16 | — | 2 | 3 | no | — |
| 339 | C4×M16 | C22×C4 | 1 | 1 | yes | characteristic |
| 340 | C4×M16 | C22×C4 | 1 | 3 | yes | — |
| 341 | C4×M16 | C22×C4 | 1 | 6 | yes | — |
| 342 | C4×M16 | C22×C4 | 1 | 6 | yes | — |
| 343 | C2×#97 | — | 2 | 3 | no | — |
| 344 | C2×#97 | — | 2 | 3 | no | — |
| 345 | C2×C4×C8 | C22×C4 | 1 | 6 | yes | — |
| 346 | C2×C4×C8 | C22×C4 | 1 | 6 | yes | — |
| 347 | #354 | — | 2 | 8 | no | — |
| 348 | #354 | — | 2 | 24 | no | — |
| 349 | #353 | — | 2 | 24 | no | — |
| 350 | #353 | C24 | 1 | 16 | yes | — |
| 351 | C25 | — | 4 | 3 | no | — |
| 352 | 2−1+4 | — | 4 | 8 | no | — |
| 353 | 2−1+4 | — | 4 | 24 | no | — |
| 354 | 2−1+4 | — | 8 | 8 | no | — |
| 355 | H(5,𝔽2) | — | 4 | 24 | no | — |
| 356 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 357 | H(5,𝔽2) | — | 4 | 16 | no | — |
| 358 | H(5,𝔽2) | — | 4 | 48 | no | — |
| 359 | H(5,𝔽2) | — | 8 | 24 | no | — |
| 360 | H(5,𝔽2) | — | 8 | 24 | no | — |
| 361 | H(5,𝔽2) | — | 8 | 8 | no | — |
| 362 | C2×#41 | — | 2 | 8 | no | — |
| 363 | C2×#41 | — | 2 | 2 | no | — |
| 364 | C2×#41 | — | 2 | 6 | no | — |
| 365 | C2×#41 | — | 2 | 6 | no | — |
| 366 | C2×#41 | — | 2 | 12 | no | — |
| 367 | C2×#41 | — | 2 | 6 | no | — |
| 368 | C2×#41 | — | 2 | 6 | no | — |
| 369 | C2×#41 | — | 2 | 6 | no | — |
| 370 | C2×#41 | — | 2 | 6 | no | — |
| 371 | C2×#41 | — | 2 | 6 | no | — |
| 372 | C2×#41 | — | 2 | 6 | no | — |
| 373 | C2×#41 | — | 2 | 6 | no | — |
| 374 | C2×#41 | — | 4 | 12 | no | — |
| 375 | C2×#41 | — | 4 | 12 | no | — |
| 376 | C2×#41 | — | 4 | 12 | no | — |
| 377 | C2×#41 | — | 4 | 12 | no | — |
| 378 | C2×#41 | — | 4 | 12 | no | — |
| 379 | C2×#41 | — | 4 | 12 | no | — |
| 380 | C2×#41 | — | 4 | 8 | no | — |
| 381 | C2×#41 | — | 4 | 8 | no | — |
| 382 | C2×#41 | — | 4 | 6 | no | — |
| 383 | C2×#41 | — | 4 | 2 | no | — |
| 384 | C2×#41 | — | 4 | 3 | no | — |
| 385 | C2×#41 | — | 4 | 3 | no | — |
| 386 | C2×#41 | — | 8 | 12 | no | — |
| 387 | C2×#41 | — | 8 | 12 | no | — |
| 388 | C2×#41 | — | 8 | 4 | no | — |
| 389 | C2×#41 | — | 8 | 4 | no | — |
| 390 | C2×#41 | #99 | 1 | 3 | yes | — |
| 391 | C2×#41 | #99 | 1 | 1 | yes | characteristic |
| 392 | C2×#41 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 393 | C2×#41 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 394 | C2×#41 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 395 | C2×#41 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 396 | C2×#41 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 397 | C2×#41 | C22×D4 | 1 | 2 | yes | — |
| 398 | C2×#41 | C22×D4 | 1 | 6 | yes | — |
| 399 | C22×Q8 | — | 2 | 2 | no | — |
| 400 | C22×Q8 | — | 2 | 6 | no | — |
| 401 | C22×Q8 | — | 2 | 1 | no | — |
| 402 | C22×Q8 | #99 | 1 | 1 | yes | characteristic |
| 403 | C22×Q8 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 404 | C22×Q8 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 405 | C22×D4 | — | 2 | 6 | no | — |
| 406 | C22×D4 | — | 2 | 6 | no | — |
| 407 | C22×D4 | — | 2 | 6 | no | — |
| 408 | C22×D4 | — | 2 | 6 | no | — |
| 409 | C22×D4 | — | 2 | 12 | no | — |
| 410 | C22×D4 | — | 2 | 3 | no | — |
| 411 | C22×D4 | — | 2 | 6 | no | — |
| 412 | C22×D4 | — | 2 | 6 | no | — |
| 413 | C22×D4 | — | 4 | 12 | no | — |
| 414 | C22×D4 | — | 4 | 12 | no | — |
| 415 | C22×D4 | — | 4 | 3 | no | — |
| 416 | C22×D4 | — | 4 | 3 | no | — |
| 417 | C22×D4 | — | 4 | 3 | no | — |
| 418 | C22×D4 | — | 4 | 6 | no | — |
| 419 | C22×D4 | — | 4 | 6 | no | — |
| 420 | C22×D4 | — | 4 | 6 | no | — |
| 421 | C22×D4 | — | 4 | 6 | no | — |
| 422 | C22×D4 | — | 4 | 6 | no | — |
| 423 | C22×D4 | — | 4 | 3 | no | — |
| 424 | C22×D4 | — | 4 | 12 | no | — |
| 425 | C22×D4 | — | 4 | 6 | no | — |
| 426 | C22×D4 | — | 4 | 6 | no | — |
| 427 | C22×D4 | — | 4 | 3 | no | — |
| 428 | C22×D4 | — | 4 | 3 | no | — |
| 429 | C22×D4 | — | 4 | 3 | no | — |
| 430 | C22×D4 | — | 8 | 12 | no | — |
| 431 | C22×D4 | — | 8 | 12 | no | — |
| 432 | C22×D4 | — | 16 | 12 | no | — |
| 433 | C22×D4 | #99 | 1 | 3 | yes | — |
| 434 | C22×D4 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 435 | C22×D4 | C22×D4 | 1 | 6 | yes | — |
| 436 | C23×C4 | — | 2 | 3 | no | — |
| 437 | C23×C4 | — | 2 | 6 | no | — |
| 438 | C23×C4 | — | 2 | 6 | no | — |
| 439 | C23×C4 | — | 4 | 3 | no | — |
| 440 | C23×C4 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 441 | #137 | — | 4 | 12 | no | — |
| 442 | #137 | — | 4 | 12 | no | — |
| 443 | #137 | — | 4 | 4 | no | — |
| 444 | #137 | — | 4 | 4 | no | — |
| 445 | #137 | — | 4 | 48 | no | — |
| 446 | #137 | — | 4 | 48 | no | — |
| 447 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 448 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 449 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 450 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 451 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 452 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 453 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 454 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 455 | AGL(1,ℤ/8) | — | 4 | 96 | no | — |
| 456 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 457 | AGL(1,ℤ/8) | — | 4 | 48 | no | — |
| 458 | #135 | — | 4 | 48 | no | — |
| 459 | #135 | — | 4 | 48 | no | — |
| 460 | #135 | — | 4 | 96 | no | — |
| 461 | C2×Q16 | — | 2 | 4 | no | — |
| 462 | C2×Q16 | — | 2 | 12 | no | — |
| 463 | C2×SD16 | — | 2 | 24 | no | — |
| 464 | C2×SD16 | — | 2 | 12 | no | — |
| 465 | C2×SD16 | — | 2 | 12 | no | — |
| 466 | C2×SD16 | — | 2 | 12 | no | — |
| 467 | C2×SD16 | — | 2 | 4 | no | — |
| 468 | C2×SD16 | — | 4 | 48 | no | — |
| 469 | C2×SD16 | — | 4 | 48 | no | — |
| 470 | C2×D8 | — | 2 | 12 | no | — |
| 471 | C2×D8 | — | 2 | 24 | no | — |
| 472 | C2×D8 | — | 2 | 12 | no | — |
| 473 | C2×D8 | — | 4 | 48 | no | — |
| 474 | C2×D8 | — | 4 | 48 | no | — |
| 475 | #131 | — | 2 | 16 | no | — |
| 476 | #131 | — | 2 | 48 | no | — |
| 477 | C2×M16 | — | 2 | 24 | no | — |
| 478 | C2×M16 | — | 2 | 24 | no | — |
| 479 | C2×M16 | — | 2 | 1 | no | — |
| 480 | C2×M16 | — | 2 | 3 | no | — |
| 481 | C2×M16 | — | 2 | 6 | no | — |
| 482 | C2×M16 | — | 2 | 6 | no | — |
| 483 | C22×C8 | — | 2 | 6 | no | — |
| 484 | C22×C8 | — | 2 | 6 | no | — |
| 485 | C4⋊Q8 | — | 2 | 1 | no | — |
| 486 | C4⋊Q8 | — | 4 | 3 | no | — |
| 487 | C4⋊Q8 | — | 4 | 3 | no | — |
| 488 | C4⋊Q8 | — | 4 | 1 | no | — |
| 489 | C4⋊Q8 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 490 | C4⋊Q8 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 491 | C4⋊Q8 | C23×C4 | 1 | 2 | yes | — |
| 492 | C4⋊Q8 | C23×C4 | 1 | 3 | yes | — |
| 493 | C4⋊Q8 | C23×C4 | 1 | 1 | yes | characteristic |
| 494 | #127 | — | 2 | 3 | no | — |
| 495 | #127 | — | 2 | 6 | no | — |
| 496 | #127 | — | 2 | 6 | no | — |
| 497 | #127 | — | 4 | 3 | no | — |
| 498 | #127 | — | 4 | 3 | no | — |
| 499 | #127 | — | 4 | 3 | no | — |
| 500 | #127 | — | 4 | 6 | no | — |
| 501 | #127 | — | 4 | 6 | no | — |
| 502 | #127 | — | 4 | 6 | no | — |
| 503 | #127 | — | 4 | 6 | no | — |
| 504 | #127 | — | 4 | 6 | no | — |
| 505 | #127 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 506 | #127 | C23×C4 | 1 | 6 | yes | — |
| 507 | #127 | C23×C4 | 1 | 3 | yes | — |
| 508 | #127 | C22×D4 | 1 | 6 | yes | — |
| 509 | #127 | C25 | 1 | 1 | yes | characteristic |
| 510 | #124 | — | 2 | 6 | no | — |
| 511 | #124 | — | 2 | 6 | no | — |
| 512 | #124 | — | 4 | 6 | no | — |
| 513 | #124 | — | 4 | 6 | no | — |
| 514 | #124 | — | 4 | 6 | no | — |
| 515 | #124 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 516 | #124 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 517 | #124 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 518 | #124 | C22×D4 | 1 | 2 | yes | — |
| 519 | #124 | C22×D4 | 1 | 6 | yes | — |
| 520 | #123 | — | 4 | 12 | no | — |
| 521 | #123 | — | 4 | 6 | no | — |
| 522 | #123 | — | 4 | 6 | no | — |
| 523 | C22⋊Q8 | — | 4 | 6 | no | — |
| 524 | C22⋊Q8 | — | 4 | 12 | no | — |
| 525 | C22⋊Q8 | — | 4 | 6 | no | — |
| 526 | #121 | — | 4 | 6 | no | — |
| 527 | #121 | — | 4 | 6 | no | — |
| 528 | #121 | — | 4 | 12 | no | — |
| 529 | #121 | — | 4 | 24 | no | — |
| 530 | #121 | — | 4 | 12 | no | — |
| 531 | #121 | — | 4 | 12 | no | — |
| 532 | #121 | — | 4 | 3 | no | — |
| 533 | #121 | — | 4 | 1 | no | — |
| 534 | #121 | — | 4 | 6 | no | — |
| 535 | #121 | — | 4 | 6 | no | — |
| 536 | #121 | — | 4 | 6 | no | — |
| 537 | #121 | — | 4 | 3 | no | — |
| 538 | #121 | — | 4 | 6 | no | — |
| 539 | #121 | — | 4 | 6 | no | — |
| 540 | #121 | — | 4 | 3 | no | — |
| 541 | #121 | — | 4 | 6 | no | — |
| 542 | #121 | — | 4 | 6 | no | — |
| 543 | #121 | — | 4 | 6 | no | — |
| 544 | #121 | — | 4 | 6 | no | — |
| 545 | #120 | — | 4 | 6 | no | — |
| 546 | #120 | — | 4 | 6 | no | — |
| 547 | #120 | — | 4 | 12 | no | — |
| 548 | #120 | — | 4 | 12 | no | — |
| 549 | #120 | — | 4 | 12 | no | — |
| 550 | #120 | — | 4 | 24 | no | — |
| 551 | C4×Q8 | — | 2 | 3 | no | — |
| 552 | C4×Q8 | — | 2 | 1 | no | — |
| 553 | C4×Q8 | — | 2 | 3 | no | — |
| 554 | C4×Q8 | — | 2 | 1 | no | — |
| 555 | C4×Q8 | — | 8 | 16 | no | — |
| 556 | C4×D4 | — | 2 | 6 | no | — |
| 557 | C4×D4 | — | 2 | 3 | no | — |
| 558 | C4×D4 | — | 2 | 3 | no | — |
| 559 | C4×D4 | — | 2 | 3 | no | — |
| 560 | C4×D4 | — | 2 | 6 | no | — |
| 561 | C4×D4 | — | 2 | 3 | no | — |
| 562 | C4×D4 | — | 4 | 3 | no | — |
| 563 | C4×D4 | — | 4 | 1 | no | — |
| 564 | C4×D4 | — | 4 | 6 | no | — |
| 565 | C4×D4 | — | 4 | 6 | no | — |
| 566 | C4×D4 | — | 4 | 6 | no | — |
| 567 | C4×D4 | — | 4 | 3 | no | — |
| 568 | C4×D4 | — | 4 | 6 | no | — |
| 569 | C4×D4 | — | 4 | 6 | no | — |
| 570 | C4×D4 | — | 4 | 3 | no | — |
| 571 | C4×D4 | — | 4 | 6 | no | — |
| 572 | C4×D4 | — | 4 | 6 | no | — |
| 573 | C4×D4 | — | 4 | 6 | no | — |
| 574 | C4×D4 | — | 4 | 6 | no | — |
| 575 | C4×D4 | — | 8 | 48 | no | — |
| 576 | #117 | — | 2 | 3 | no | — |
| 577 | #117 | — | 2 | 3 | no | — |
| 578 | #117 | — | 4 | 8 | no | — |
| 579 | #117 | — | 4 | 24 | no | — |
| 580 | #117 | — | 8 | 12 | no | — |
| 581 | #117 | — | 8 | 12 | no | — |
| 582 | #117 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 583 | #117 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 584 | #117 | C2×C22⋊C4 | 1 | 6 | yes | — |
| 585 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 586 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 587 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 588 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 589 | C2×C4⋊C4 | — | 8 | 12 | no | — |
| 590 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 591 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 592 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 593 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 594 | C2×C22⋊C4 | — | 4 | 24 | no | — |
| 595 | C2×C42 | — | 2 | 3 | no | — |
| 596 | C2×C42 | — | 2 | 3 | no | — |
| 597 | C2×C42 | — | 2 | 3 | no | — |
| 598 | C2×C42 | — | 8 | 12 | no | — |
| 599 | C2×C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 600 | C2×C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 601 | C2×C42 | C2×C22⋊C4 | 1 | 3 | yes | — |
| 602 | C2×C42 | C23×C4 | 1 | 3 | yes | — |
| 603 | C2×C42 | C23×C4 | 1 | 3 | yes | — |
| 604 | C2×C42 | C23×C4 | 1 | 1 | yes | characteristic |
| 605 | #99 | — | 2 | 16 | no | — |
| 606 | #99 | — | 4 | 24 | no | — |
| 607 | #99 | — | 4 | 24 | no | — |
| 608 | #99 | — | 4 | 8 | no | — |
| 609 | #97 | — | 2 | 1 | no | — |
| 610 | #97 | — | 2 | 3 | no | — |
| 611 | #97 | — | 2 | 6 | no | — |
| 612 | #97 | — | 2 | 6 | no | — |
| 613 | C4×C8 | — | 2 | 6 | no | — |
| 614 | C4×C8 | — | 2 | 6 | no | — |
| 615 | C4×C8 | C23×C4 | 1 | 6 | yes | — |
| 616 | C4×C8 | C23×C4 | 1 | 2 | yes | — |
| 617 | C24 | — | 2 | 6 | no | — |
| 618 | C24 | — | 2 | 6 | no | — |
| 619 | C24 | — | 4 | 3 | no | — |
| 620 | C24 | — | 4 | 6 | no | — |
| 621 | C24 | — | 4 | 6 | no | — |
| 622 | C24 | — | 8 | 6 | no | — |
| 623 | C24 | — | 8 | 6 | no | — |
| 624 | C24 | — | 16 | 12 | no | — |
| 625 | C24 | C2×#99 | 1 | 3 | yes | — |
| 626 | #41 | — | 2 | 4 | no | — |
| 627 | #41 | — | 2 | 12 | no | — |
| 628 | #41 | — | 2 | 12 | no | — |
| 629 | #41 | — | 4 | 12 | no | — |
| 630 | #41 | — | 4 | 12 | no | — |
| 631 | #41 | — | 4 | 6 | no | — |
| 632 | #41 | — | 4 | 6 | no | — |
| 633 | #41 | — | 4 | 2 | no | — |
| 634 | #41 | — | 4 | 2 | no | — |
| 635 | #41 | — | 4 | 24 | no | — |
| 636 | #41 | — | 4 | 24 | no | — |
| 637 | #41 | — | 4 | 24 | no | — |
| 638 | #41 | — | 4 | 8 | no | — |
| 639 | #41 | — | 4 | 24 | no | — |
| 640 | #41 | — | 4 | 12 | no | — |
| 641 | #41 | — | 4 | 12 | no | — |
| 642 | #41 | — | 8 | 6 | no | — |
| 643 | #41 | — | 8 | 6 | no | — |
| 644 | #41 | — | 8 | 12 | no | — |
| 645 | #41 | — | 8 | 12 | no | — |
| 646 | #41 | — | 8 | 12 | no | — |
| 647 | #41 | — | 8 | 24 | no | — |
| 648 | #41 | — | 8 | 12 | no | — |
| 649 | #41 | — | 8 | 12 | no | — |
| 650 | #41 | — | 8 | 24 | no | — |
| 651 | #41 | — | 8 | 8 | no | — |
| 652 | #41 | — | 8 | 12 | no | — |
| 653 | #41 | #353 | 1 | 8 | yes | — |
| 654 | C2×Q8 | — | 2 | 4 | no | — |
| 655 | C2×Q8 | — | 2 | 6 | no | — |
| 656 | C2×Q8 | — | 2 | 6 | no | — |
| 657 | C2×Q8 | — | 2 | 2 | no | — |
| 658 | C2×Q8 | — | 4 | 12 | no | — |
| 659 | C2×Q8 | — | 4 | 12 | no | — |
| 660 | C2×Q8 | — | 4 | 2 | no | — |
| 661 | C2×Q8 | — | 4 | 2 | no | — |
| 662 | C2×Q8 | — | 4 | 8 | no | — |
| 663 | C2×Q8 | — | 4 | 1 | no | — |
| 664 | C2×Q8 | — | 8 | 12 | no | — |
| 665 | C2×Q8 | C2×#99 | 1 | 3 | yes | — |
| 666 | C2×Q8 | C2×#99 | 1 | 1 | yes | characteristic |
| 667 | C2×Q8 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 668 | C2×Q8 | C22×C22⋊C4 | 1 | 2 | yes | — |
| 669 | C2×D4 | — | 2 | 12 | no | — |
| 670 | C2×D4 | — | 2 | 12 | no | — |
| 671 | C2×D4 | — | 2 | 6 | no | — |
| 672 | C2×D4 | — | 2 | 2 | no | — |
| 673 | C2×D4 | — | 2 | 6 | no | — |
| 674 | C2×D4 | — | 2 | 6 | no | — |
| 675 | C2×D4 | — | 2 | 6 | no | — |
| 676 | C2×D4 | — | 2 | 6 | no | — |
| 677 | C2×D4 | — | 2 | 6 | no | — |
| 678 | C2×D4 | — | 4 | 12 | no | — |
| 679 | C2×D4 | — | 4 | 12 | no | — |
| 680 | C2×D4 | — | 4 | 24 | no | — |
| 681 | C2×D4 | — | 4 | 24 | no | — |
| 682 | C2×D4 | — | 4 | 6 | no | — |
| 683 | C2×D4 | — | 4 | 6 | no | — |
| 684 | C2×D4 | — | 4 | 3 | no | — |
| 685 | C2×D4 | — | 4 | 1 | no | — |
| 686 | C2×D4 | — | 4 | 6 | no | — |
| 687 | C2×D4 | — | 4 | 6 | no | — |
| 688 | C2×D4 | — | 4 | 6 | no | — |
| 689 | C2×D4 | — | 4 | 6 | no | — |
| 690 | C2×D4 | — | 4 | 12 | no | — |
| 691 | C2×D4 | — | 4 | 12 | no | — |
| 692 | C2×D4 | — | 4 | 24 | no | — |
| 693 | C2×D4 | — | 4 | 6 | no | — |
| 694 | C2×D4 | — | 4 | 6 | no | — |
| 695 | C2×D4 | — | 4 | 6 | no | — |
| 696 | C2×D4 | — | 4 | 6 | no | — |
| 697 | C2×D4 | — | 4 | 3 | no | — |
| 698 | C2×D4 | — | 8 | 6 | no | — |
| 699 | C2×D4 | — | 8 | 6 | no | — |
| 700 | C2×D4 | — | 8 | 12 | no | — |
| 701 | C2×D4 | — | 8 | 12 | no | — |
| 702 | C2×D4 | — | 8 | 12 | no | — |
| 703 | C2×D4 | — | 8 | 12 | no | — |
| 704 | C2×D4 | — | 8 | 24 | no | — |
| 705 | C2×D4 | — | 8 | 48 | no | — |
| 706 | C2×D4 | — | 8 | 24 | no | — |
| 707 | C2×D4 | — | 8 | 12 | no | — |
| 708 | C2×D4 | — | 8 | 6 | no | — |
| 709 | C2×D4 | — | 8 | 6 | no | — |
| 710 | C2×D4 | — | 8 | 24 | no | — |
| 711 | C2×D4 | — | 8 | 12 | no | — |
| 712 | C2×D4 | — | 16 | 6 | no | — |
| 713 | C2×D4 | — | 16 | 6 | no | — |
| 714 | C2×D4 | — | 16 | 12 | no | — |
| 715 | C2×D4 | — | 16 | 12 | no | — |
| 716 | C2×D4 | — | 16 | 12 | no | — |
| 717 | C2×D4 | — | 16 | 12 | no | — |
| 718 | C2×D4 | — | 16 | 12 | no | — |
| 719 | C2×D4 | C2×#99 | 1 | 6 | yes | — |
| 720 | C2×D4 | C2×#99 | 1 | 3 | yes | — |
| 721 | C2×D4 | C2×#99 | 1 | 3 | yes | — |
| 722 | C2×D4 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 723 | C2×D4 | C23×D4 | 1 | 2 | yes | — |
| 724 | C22×C4 | — | 2 | 12 | no | — |
| 725 | C22×C4 | — | 2 | 1 | no | — |
| 726 | C22×C4 | — | 2 | 3 | no | — |
| 727 | C22×C4 | — | 2 | 3 | no | — |
| 728 | C22×C4 | — | 2 | 6 | no | — |
| 729 | C22×C4 | — | 2 | 3 | no | — |
| 730 | C22×C4 | — | 2 | 3 | no | — |
| 731 | C22×C4 | — | 2 | 3 | no | — |
| 732 | C22×C4 | — | 2 | 6 | no | — |
| 733 | C22×C4 | — | 2 | 2 | no | — |
| 734 | C22×C4 | — | 2 | 6 | no | — |
| 735 | C22×C4 | — | 2 | 6 | no | — |
| 736 | C22×C4 | — | 2 | 6 | no | — |
| 737 | C22×C4 | — | 2 | 12 | no | — |
| 738 | C22×C4 | — | 4 | 12 | no | — |
| 739 | C22×C4 | — | 4 | 12 | no | — |
| 740 | C22×C4 | — | 4 | 1 | no | — |
| 741 | C22×C4 | — | 4 | 6 | no | — |
| 742 | C22×C4 | — | 4 | 6 | no | — |
| 743 | C22×C4 | — | 8 | 6 | no | — |
| 744 | C22×C4 | — | 8 | 6 | no | — |
| 745 | C22×C4 | — | 8 | 6 | no | — |
| 746 | C22×C4 | — | 8 | 6 | no | — |
| 747 | C22×C4 | — | 8 | 6 | no | — |
| 748 | C22×C4 | — | 8 | 24 | no | — |
| 749 | C22×C4 | C2×#99 | 1 | 3 | yes | — |
| 750 | C22×C4 | C2×#99 | 1 | 3 | yes | — |
| 751 | C22×C4 | C2×#99 | 1 | 3 | yes | — |
| 752 | C22×C4 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 753 | C22×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 754 | C22×C4 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 755 | Q16 | — | 4 | 8 | no | — |
| 756 | Q16 | — | 4 | 24 | no | — |
| 757 | SD16 | — | 4 | 24 | no | — |
| 758 | SD16 | — | 4 | 48 | no | — |
| 759 | SD16 | — | 4 | 24 | no | — |
| 760 | SD16 | — | 4 | 24 | no | — |
| 761 | SD16 | — | 4 | 8 | no | — |
| 762 | D8 | — | 4 | 24 | no | — |
| 763 | D8 | — | 4 | 48 | no | — |
| 764 | D8 | — | 4 | 24 | no | — |
| 765 | M16 | — | 2 | 4 | no | — |
| 766 | M16 | — | 2 | 12 | no | — |
| 767 | M16 | — | 2 | 24 | no | — |
| 768 | M16 | — | 2 | 24 | no | — |
| 769 | C2×C8 | — | 2 | 24 | no | — |
| 770 | C2×C8 | — | 2 | 24 | no | — |
| 771 | C2×C8 | — | 2 | 6 | no | — |
| 772 | C2×C8 | — | 2 | 2 | no | — |
| 773 | C4⋊C4 | — | 2 | 6 | no | — |
| 774 | C4⋊C4 | — | 2 | 3 | no | — |
| 775 | C4⋊C4 | — | 2 | 3 | no | — |
| 776 | C4⋊C4 | — | 4 | 3 | no | — |
| 777 | C4⋊C4 | — | 4 | 1 | no | — |
| 778 | C4⋊C4 | — | 4 | 6 | no | — |
| 779 | C4⋊C4 | — | 4 | 6 | no | — |
| 780 | C4⋊C4 | — | 4 | 2 | no | — |
| 781 | C4⋊C4 | — | 4 | 2 | no | — |
| 782 | C4⋊C4 | — | 8 | 8 | no | — |
| 783 | C4⋊C4 | — | 8 | 24 | no | — |
| 784 | C22⋊C4 | — | 2 | 3 | no | — |
| 785 | C22⋊C4 | — | 2 | 3 | no | — |
| 786 | C22⋊C4 | — | 2 | 6 | no | — |
| 787 | C22⋊C4 | — | 4 | 6 | no | — |
| 788 | C22⋊C4 | — | 4 | 2 | no | — |
| 789 | C22⋊C4 | — | 4 | 12 | no | — |
| 790 | C22⋊C4 | — | 4 | 6 | no | — |
| 791 | C22⋊C4 | — | 4 | 6 | no | — |
| 792 | C22⋊C4 | — | 4 | 12 | no | — |
| 793 | C22⋊C4 | — | 4 | 12 | no | — |
| 794 | C22⋊C4 | — | 4 | 16 | no | — |
| 795 | C22⋊C4 | — | 8 | 24 | no | — |
| 796 | C42 | — | 2 | 1 | no | — |
| 797 | C42 | — | 2 | 3 | no | — |
| 798 | C42 | — | 2 | 3 | no | — |
| 799 | C42 | — | 2 | 3 | no | — |
| 800 | C42 | — | 2 | 3 | no | — |
| 801 | C42 | — | 2 | 3 | no | — |
| 802 | C42 | — | 8 | 8 | no | — |
| 803 | C42 | — | 8 | 24 | no | — |
| 804 | C42 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 805 | C42 | C22×C22⋊C4 | 1 | 3 | yes | — |
| 806 | C42 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 807 | C42 | C24×C4 | 1 | 1 | yes | characteristic |
| 808 | C23 | — | 2 | 6 | no | — |
| 809 | C23 | — | 2 | 2 | no | — |
| 810 | C23 | — | 2 | 6 | no | — |
| 811 | C23 | — | 4 | 12 | no | — |
| 812 | C23 | — | 4 | 6 | no | — |
| 813 | C23 | — | 8 | 6 | no | — |
| 814 | C23 | — | 8 | 3 | no | — |
| 815 | C23 | — | 8 | 3 | no | — |
| 816 | C23 | — | 8 | 12 | no | — |
| 817 | C23 | — | 8 | 3 | no | — |
| 818 | C23 | — | 8 | 12 | no | — |
| 819 | C23 | — | 8 | 12 | no | — |
| 820 | C23 | — | 16 | 6 | no | — |
| 821 | C23 | — | 16 | 6 | no | — |
| 822 | C23 | — | 16 | 12 | no | — |
| 823 | C23 | — | 16 | 12 | no | — |
| 824 | C23 | — | 32 | 12 | no | — |
| 825 | C23 | — | 32 | 12 | no | — |
| 826 | C23 | C22×#99 | 1 | 3 | yes | — |
| 827 | C23 | C22×#99 | 1 | 1 | yes | characteristic |
| 828 | C23 | C22×#99 | 1 | 3 | yes | — |
| 829 | Q8 | — | 2 | 6 | no | — |
| 830 | Q8 | — | 4 | 2 | no | — |
| 831 | Q8 | — | 4 | 6 | no | — |
| 832 | Q8 | — | 4 | 4 | no | — |
| 833 | Q8 | — | 4 | 12 | no | — |
| 834 | Q8 | — | 8 | 6 | no | — |
| 835 | Q8 | — | 8 | 2 | no | — |
| 836 | Q8 | C2×#353 | 1 | 4 | yes | — |
| 837 | D4 | — | 2 | 12 | no | — |
| 838 | D4 | — | 2 | 6 | no | — |
| 839 | D4 | — | 4 | 6 | no | — |
| 840 | D4 | — | 4 | 2 | no | — |
| 841 | D4 | — | 4 | 12 | no | — |
| 842 | D4 | — | 4 | 24 | no | — |
| 843 | D4 | — | 4 | 12 | no | — |
| 844 | D4 | — | 8 | 6 | no | — |
| 845 | D4 | — | 8 | 12 | no | — |
| 846 | D4 | — | 8 | 12 | no | — |
| 847 | D4 | — | 8 | 6 | no | — |
| 848 | D4 | — | 8 | 2 | no | — |
| 849 | D4 | — | 8 | 2 | no | — |
| 850 | D4 | — | 8 | 6 | no | — |
| 851 | D4 | — | 8 | 6 | no | — |
| 852 | D4 | — | 8 | 6 | no | — |
| 853 | D4 | — | 8 | 12 | no | — |
| 854 | D4 | — | 8 | 12 | no | — |
| 855 | D4 | — | 8 | 12 | no | — |
| 856 | D4 | — | 8 | 6 | no | — |
| 857 | D4 | — | 8 | 12 | no | — |
| 858 | D4 | — | 16 | 6 | no | — |
| 859 | D4 | — | 16 | 6 | no | — |
| 860 | D4 | — | 16 | 12 | no | — |
| 861 | D4 | — | 16 | 12 | no | — |
| 862 | D4 | C2×#353 | 1 | 12 | yes | — |
| 863 | C2×C4 | — | 2 | 6 | no | — |
| 864 | C2×C4 | — | 2 | 1 | no | — |
| 865 | C2×C4 | — | 2 | 6 | no | — |
| 866 | C2×C4 | — | 2 | 2 | no | — |
| 867 | C2×C4 | — | 2 | 6 | no | — |
| 868 | C2×C4 | — | 2 | 6 | no | — |
| 869 | C2×C4 | — | 2 | 1 | no | — |
| 870 | C2×C4 | — | 2 | 3 | no | — |
| 871 | C2×C4 | — | 2 | 3 | no | — |
| 872 | C2×C4 | — | 2 | 2 | no | — |
| 873 | C2×C4 | — | 2 | 6 | no | — |
| 874 | C2×C4 | — | 4 | 2 | no | — |
| 875 | C2×C4 | — | 4 | 6 | no | — |
| 876 | C2×C4 | — | 4 | 6 | no | — |
| 877 | C2×C4 | — | 4 | 12 | no | — |
| 878 | C2×C4 | — | 4 | 2 | no | — |
| 879 | C2×C4 | — | 4 | 12 | no | — |
| 880 | C2×C4 | — | 4 | 2 | no | — |
| 881 | C2×C4 | — | 4 | 6 | no | — |
| 882 | C2×C4 | — | 4 | 6 | no | — |
| 883 | C2×C4 | — | 4 | 12 | no | — |
| 884 | C2×C4 | — | 4 | 2 | no | — |
| 885 | C2×C4 | — | 8 | 12 | no | — |
| 886 | C2×C4 | — | 8 | 12 | no | — |
| 887 | C2×C4 | — | 8 | 6 | no | — |
| 888 | C2×C4 | — | 8 | 3 | no | — |
| 889 | C2×C4 | — | 8 | 3 | no | — |
| 890 | C2×C4 | — | 8 | 3 | no | — |
| 891 | C2×C4 | — | 8 | 1 | no | — |
| 892 | C2×C4 | — | 8 | 1 | no | — |
| 893 | C2×C4 | — | 8 | 12 | no | — |
| 894 | C2×C4 | — | 8 | 16 | no | — |
| 895 | C2×C4 | — | 32 | 24 | no | — |
| 896 | C2×C4 | C2×#353 | 1 | 12 | yes | — |
| 897 | C2×C4 | C22×#99 | 1 | 3 | yes | — |
| 898 | C2×C4 | C22×#99 | 1 | 1 | yes | characteristic |
| 899 | C2×C4 | C22×#99 | 1 | 3 | yes | — |
| 900 | C2×C4 | C23×C22⋊C4 | 1 | 1 | yes | characteristic |
| 901 | C8 | — | 2 | 12 | no | — |
| 902 | C8 | — | 2 | 4 | no | — |
| 903 | C22 | — | 2 | 1 | no | — |
| 904 | C22 | — | 2 | 3 | no | — |
| 905 | C22 | — | 4 | 3 | no | — |
| 906 | C22 | — | 4 | 1 | no | — |
| 907 | C22 | — | 4 | 3 | no | — |
| 908 | C22 | — | 4 | 2 | no | — |
| 909 | C22 | — | 4 | 6 | no | — |
| 910 | C22 | — | 8 | 6 | no | — |
| 911 | C22 | — | 8 | 2 | no | — |
| 912 | C22 | — | 8 | 6 | no | — |
| 913 | C22 | — | 8 | 12 | no | — |
| 914 | C22 | — | 8 | 6 | no | — |
| 915 | C22 | — | 16 | 12 | no | — |
| 916 | C22 | — | 16 | 6 | no | — |
| 917 | C22 | — | 16 | 6 | no | — |
| 918 | C22 | — | 32 | 12 | no | — |
| 919 | C22 | — | 32 | 6 | no | — |
| 920 | C22 | — | 32 | 12 | no | — |
| 921 | C22 | C22×#353 | 1 | 6 | yes | — |
| 922 | C22 | C23×#99 | 1 | 1 | yes | characteristic |
| 923 | C4 | — | 2 | 2 | no | — |
| 924 | C4 | — | 2 | 1 | no | — |
| 925 | C4 | — | 2 | 3 | no | — |
| 926 | C4 | — | 4 | 1 | no | — |
| 927 | C4 | — | 4 | 3 | no | — |
| 928 | C4 | — | 4 | 3 | no | — |
| 929 | C4 | — | 4 | 2 | no | — |
| 930 | C4 | — | 4 | 6 | no | — |
| 931 | C4 | — | 8 | 2 | no | — |
| 932 | C4 | — | 16 | 16 | no | — |
| 933 | C4 | C22×#353 | 1 | 2 | yes | — |
| 934 | C4 | C22×#353 | 1 | 6 | yes | — |
| 935 | C2 | — | 2 | 1 | no | — |
| 936 | C2 | — | 2 | 6 | no | — |
| 937 | C2 | — | 4 | 1 | no | — |
| 938 | C2 | — | 4 | 3 | no | — |
| 939 | C2 | — | 8 | 2 | no | — |
| 940 | C2 | — | 8 | 6 | no | — |
| 941 | C2 | — | 16 | 6 | no | — |
| 942 | C2 | C23×#353 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C23×#353 |
| commutator | C42 | C24×C4 |
| Frattini, cosocle | #127 | C25 |
| prime radical | #10575254 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ C22×#41 ◁ #62812 ◁ G | |
| LECS | G ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #7622466 | C2 | semidirect |
| 3. #512616 | C2 | semidirect |
| 4. #512613 | C2 | semidirect |
| 5. #512601 | C2 | semidirect |
| 6. C2×#13585 | C2 | semidirect |
| 9. C2×#3498 | C4 | semidirect |
| 12. #60647 | C4 | semidirect |
| 14. #60646 | C4 | semidirect |
| 17. #60639 | C4 | semidirect |
| 19. C2×#3151 | C4 | semidirect |
| 22. C4×#568 | C4 | semidirect |
| 25. #33360 | C22 | semidirect |
| 26. #33359 | C22 | semidirect |
| 28. C2×#2126 | C22 | semidirect |
| 29. #13586 | C22 | semidirect |
| 30. #13585 | C22 | semidirect |
| 31. #13585 | C22 | semidirect |
| 32. #13584 | C22 | semidirect |
| 33. #13583 | C22 | semidirect |
| 34. C2×#1408 | C22 | semidirect |
| 57. #3498 | C2×C4 | semidirect |
| 58. #3498 | C2×C4 | semidirect |
| 69. C2×#532 | C2×C4 | semidirect |
| 71. C22×#127 | C2×C4 | semidirect |
| 84. #3152 | C2×C4 | semidirect |
| 85. #3152 | C2×C4 | semidirect |
| 86. #3152 | C2×C4 | semidirect |
| 92. #3151 | C2×C4 | semidirect |
| 93. #3151 | C2×C4 | semidirect |
| 94. #3151 | C2×C4 | semidirect |
| 95. #3151 | C2×C4 | semidirect |
| 96. #3151 | C2×C4 | semidirect |
| 104. #3147 | C2×C4 | semidirect |
| 105. #3147 | C2×C4 | semidirect |
| 107. C2×#493 | C2×C4 | semidirect |
| 109. C2×#492 | C2×C4 | semidirect |
| 110. C2×#492 | C2×C4 | semidirect |
| 119. C4×#131 | C2×C4 | semidirect |
| 120. C4×#131 | C2×C4 | semidirect |
| 122. C2×C4×M16 | C2×C4 | semidirect |
| 123. C2×C4×M16 | C2×C4 | semidirect |
| 130. #2126 | C23 | semidirect |
| 132. C2×#353 | C23 | semidirect |
| 133. #1409 | C23 | semidirect |
| 134. #1408 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10575254 | 2 |
| #7622466 | 2 |
| #512616 | 2 |
| #512613 | 2 |
| #512601 | 2 |
| C2×#13585 | 2 |