← C31×#26505 #21483264
Subgroups — C31×#26505 #21483264
Order 7936.
668 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C31×#3163 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C31×#3082 | C2 | 1 | 2 | yes | maximal |
| 3 | C31×#2950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C31×#2064 | C2 | 1 | 2 | yes | maximal |
| 5 | C31×#2028 | C2 | 1 | 2 | yes | maximal |
| 6 | C31×#1979 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C31×#1971 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C31×#1951 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C31×#1946 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C31×#1857 | C2 | 1 | 2 | yes | maximal |
| 11 | C31×#1773 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C22×Q16×C31 | C22 | 1 | 1 | yes | characteristic |
| 13 | C31×#544 | C22 | 1 | 2 | yes | — |
| 14 | C31×#519 | C22 | 1 | 2 | yes | — |
| 15 | C31×#501 | — | 2 | 2 | no | — |
| 16 | C31×#499 | — | 2 | 1 | no | — |
| 17 | C31×#498 | — | 2 | 1 | no | — |
| 18 | C31×#479 | — | 2 | 2 | no | — |
| 19 | C31×#479 | — | 2 | 2 | no | — |
| 20 | C31×#477 | — | 2 | 2 | no | — |
| 21 | C31×#475 | — | 2 | 2 | no | — |
| 22 | C31×#441 | — | 2 | 1 | no | — |
| 23 | C31×#441 | — | 2 | 1 | no | — |
| 24 | C4×Q16×C31 | — | 2 | 2 | no | — |
| 25 | C2×C31×#108 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C31×#108 | C22 | 1 | 1 | yes | characteristic |
| 27 | C31×#428 | C22 | 1 | 2 | yes | — |
| 28 | C31×#428 | C22 | 1 | 2 | yes | — |
| 29 | C31×#427 | C22 | 1 | 1 | yes | characteristic |
| 30 | C31×#427 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×C31×#106 | C22 | 1 | 1 | yes | characteristic |
| 32 | C31×#424 | C22 | 1 | 2 | yes | — |
| 33 | C31×#419 | C22 | 1 | 2 | yes | — |
| 34 | C31×#419 | C22 | 1 | 2 | yes | — |
| 35 | C2×C31×#103 | C22 | 1 | 2 | yes | — |
| 36 | C2×C31×#101 | C22 | 1 | 2 | yes | — |
| 37 | C31×#405 | C22 | 1 | 1 | yes | characteristic |
| 38 | C31×#405 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×C31×#97 | C22 | 1 | 1 | yes | characteristic |
| 40 | C31×#391 | C22 | 1 | 2 | yes | — |
| 41 | C31×#343 | C22 | 1 | 2 | yes | — |
| 42 | C31×#339 | C22 | 1 | 1 | yes | characteristic |
| 43 | C31×#339 | C22 | 1 | 2 | yes | — |
| 44 | C31×#339 | C22 | 1 | 1 | yes | characteristic |
| 45 | C22×Q8×C31 | C23 | 1 | 2 | yes | — |
| 46 | C2×Q16×C31 | — | 2 | 1 | no | — |
| 47 | C2×Q16×C31 | — | 2 | 1 | no | — |
| 48 | C2×Q16×C31 | — | 2 | 2 | no | — |
| 49 | C2×Q16×C31 | Q8 | 1 | 4 | yes | complemented |
| 50 | C2×M16×C31 | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×M16×C31 | C23 | 1 | 2 | yes | — |
| 52 | C2×M16×C31 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 54 | C22×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 55 | C31×C4⋊Q8 | — | 2 | 2 | no | — |
| 56 | C31×C4⋊Q8 | — | 2 | 2 | no | — |
| 57 | C31×#125 | — | 2 | 2 | no | — |
| 58 | C31×#125 | — | 2 | 2 | no | — |
| 59 | C31×C22⋊Q8 | — | 4 | 2 | no | — |
| 60 | C4×Q8×C31 | — | 2 | 2 | no | — |
| 61 | C4×Q8×C31 | — | 2 | 2 | no | — |
| 62 | C4×Q8×C31 | — | 2 | 2 | no | — |
| 63 | C4×Q8×C31 | — | 2 | 2 | no | — |
| 64 | C31×#117 | — | 4 | 2 | no | — |
| 65 | C31×#117 | C23 | 1 | 1 | yes | characteristic |
| 66 | C31×#117 | C23 | 1 | 1 | yes | characteristic |
| 67 | C31×#117 | C23 | 1 | 2 | yes | — |
| 68 | C2×C4⋊C4×C31 | C23 | 1 | 2 | yes | — |
| 69 | C2×C42×C31 | C23 | 1 | 1 | yes | characteristic |
| 70 | C31×#108 | — | 2 | 2 | no | — |
| 71 | C31×#108 | — | 2 | 2 | no | — |
| 72 | C31×#107 | — | 2 | 2 | no | — |
| 73 | C31×#107 | — | 2 | 2 | no | — |
| 74 | C31×#107 | D4 | 1 | 2 | yes | — |
| 75 | C31×#107 | D4 | 1 | 2 | yes | — |
| 76 | C31×#106 | — | 2 | 1 | no | — |
| 77 | C31×#106 | — | 2 | 1 | no | — |
| 78 | C31×#106 | — | 2 | 2 | no | — |
| 79 | C31×#106 | — | 2 | 2 | no | — |
| 80 | C31×#106 | D4 | 1 | 1 | yes | characteristic |
| 81 | C31×#106 | D4 | 1 | 1 | yes | characteristic |
| 82 | C31×#106 | D4 | 1 | 2 | yes | — |
| 83 | C31×C4⋊C8 | — | 2 | 2 | no | — |
| 84 | C31×C4⋊C8 | — | 2 | 2 | no | — |
| 85 | C31×#103 | — | 2 | 2 | no | — |
| 86 | C31×#103 | — | 2 | 2 | no | — |
| 87 | C31×#103 | — | 2 | 2 | no | — |
| 88 | C31×#103 | — | 2 | 2 | no | — |
| 89 | C31×#103 | — | 2 | 2 | no | — |
| 90 | C31×#103 | — | 2 | 2 | no | — |
| 91 | C31×#101 | — | 2 | 4 | no | — |
| 92 | C31×#97 | — | 2 | 1 | no | — |
| 93 | C31×#97 | — | 2 | 1 | no | — |
| 94 | C31×#97 | — | 2 | 2 | no | — |
| 95 | C4×C8×C31 | — | 2 | 1 | no | — |
| 96 | C4×C8×C31 | — | 2 | 1 | no | — |
| 97 | C31×#95 | — | 4 | 2 | no | — |
| 98 | C2×Q8×C31 | — | 2 | 2 | no | — |
| 99 | C2×Q8×C31 | — | 2 | 2 | no | — |
| 100 | C2×Q8×C31 | — | 2 | 2 | no | — |
| 101 | C2×Q8×C31 | — | 2 | 2 | no | — |
| 102 | C2×Q8×C31 | — | 2 | 2 | no | — |
| 103 | C2×Q8×C31 | — | 4 | 2 | no | — |
| 104 | C2×Q8×C31 | C2×Q8 | 1 | 4 | yes | — |
| 105 | C22×C4×C31 | — | 2 | 2 | no | — |
| 106 | C22×C4×C31 | — | 2 | 1 | no | — |
| 107 | C22×C4×C31 | — | 2 | 2 | no | — |
| 108 | C22×C4×C31 | C24 | 1 | 1 | yes | characteristic |
| 109 | Q16×C31 | — | 2 | 4 | no | — |
| 110 | Q16×C31 | — | 2 | 4 | no | — |
| 111 | M16×C31 | — | 2 | 1 | no | — |
| 112 | M16×C31 | — | 2 | 2 | no | — |
| 113 | M16×C31 | — | 2 | 2 | no | — |
| 114 | M16×C31 | — | 2 | 1 | no | — |
| 115 | M16×C31 | — | 2 | 1 | no | — |
| 116 | M16×C31 | #41 | 1 | 2 | yes | — |
| 117 | C2×C8×C31 | — | 2 | 1 | no | — |
| 118 | C2×C8×C31 | — | 2 | 1 | no | — |
| 119 | C2×C8×C31 | — | 2 | 1 | no | — |
| 120 | C2×C8×C31 | — | 2 | 1 | no | — |
| 121 | C2×C8×C31 | — | 2 | 2 | no | — |
| 122 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C8×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C8×C31 | C2×Q8 | 1 | 2 | yes | — |
| 127 | C2×C8×C31 | #41 | 1 | 2 | yes | — |
| 128 | C4⋊C4×C31 | — | 2 | 2 | no | — |
| 129 | C4⋊C4×C31 | — | 2 | 2 | no | — |
| 130 | C4⋊C4×C31 | — | 4 | 2 | no | — |
| 131 | C4⋊C4×C31 | — | 4 | 2 | no | — |
| 132 | C4⋊C4×C31 | — | 4 | 2 | no | — |
| 133 | C4⋊C4×C31 | — | 4 | 2 | no | — |
| 134 | C4⋊C4×C31 | — | 4 | 2 | no | — |
| 135 | C4⋊C4×C31 | C2×D4 | 1 | 2 | yes | — |
| 136 | C4⋊C4×C31 | C2×D4 | 1 | 2 | yes | — |
| 137 | C4⋊C4×C31 | C2×D4 | 1 | 2 | yes | — |
| 138 | C4⋊C4×C31 | C2×D4 | 1 | 2 | yes | — |
| 139 | C22⋊C4×C31 | — | 2 | 1 | no | — |
| 140 | C22⋊C4×C31 | — | 2 | 2 | no | — |
| 141 | C22⋊C4×C31 | — | 2 | 1 | no | — |
| 142 | C42×C31 | — | 2 | 1 | no | — |
| 143 | C42×C31 | — | 2 | 1 | no | — |
| 144 | C42×C31 | — | 2 | 2 | no | — |
| 145 | C42×C31 | — | 2 | 1 | no | — |
| 146 | C42×C31 | — | 2 | 1 | no | — |
| 147 | C42×C31 | — | 4 | 2 | no | — |
| 148 | C42×C31 | — | 4 | 2 | no | — |
| 149 | #26505 | C31 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 150 | C23×C31 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 151 | Q8×C31 | — | 2 | 4 | no | — |
| 152 | Q8×C31 | — | 2 | 4 | no | — |
| 153 | Q8×C31 | — | 4 | 2 | no | — |
| 154 | Q8×C31 | — | 4 | 2 | no | — |
| 155 | Q8×C31 | — | 16 | 2 | no | — |
| 156 | C2×C4×C31 | — | 2 | 2 | no | — |
| 157 | C2×C4×C31 | — | 2 | 2 | no | — |
| 158 | C2×C4×C31 | — | 2 | 2 | no | — |
| 159 | C2×C4×C31 | — | 2 | 2 | no | — |
| 160 | C2×C4×C31 | — | 2 | 4 | no | — |
| 161 | C2×C4×C31 | — | 4 | 2 | no | — |
| 162 | C2×C4×C31 | — | 4 | 2 | no | — |
| 163 | C2×C4×C31 | — | 4 | 2 | no | — |
| 164 | C2×C4×C31 | — | 4 | 1 | no | — |
| 165 | C2×C4×C31 | — | 4 | 2 | no | — |
| 166 | C2×C4×C31 | — | 8 | 2 | no | — |
| 167 | C2×C4×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C4×C31 | C22×Q8 | 1 | 1 | yes | characteristic |
| 170 | C2×C4×C31 | C2×#41 | 1 | 1 | yes | characteristic |
| 171 | C2×C4×C31 | C2×#41 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C31 | 2−1+4 | 1 | 1 | yes | characteristic |
| 173 | C8×C31 | — | 2 | 1 | no | — |
| 174 | C8×C31 | — | 2 | 1 | no | — |
| 175 | C8×C31 | — | 2 | 2 | no | — |
| 176 | C8×C31 | — | 4 | 2 | no | — |
| 177 | C8×C31 | — | 4 | 1 | no | — |
| 178 | C8×C31 | C22⋊Q8 | 1 | 2 | yes | — |
| 179 | C8×C31 | C22⋊Q8 | 1 | 2 | yes | — |
| 180 | #3163 | C2×C31 | 1 | 1 | yes | characteristic |
| 181 | #3082 | C2×C31 | 1 | 2 | yes | — |
| 182 | #2950 | C2×C31 | 1 | 1 | yes | characteristic |
| 183 | #2064 | C2×C31 | 1 | 2 | yes | — |
| 184 | #2028 | C2×C31 | 1 | 2 | yes | — |
| 185 | #1979 | C2×C31 | 1 | 1 | yes | characteristic |
| 186 | #1971 | C2×C31 | 1 | 1 | yes | characteristic |
| 187 | #1951 | C2×C31 | 1 | 1 | yes | characteristic |
| 188 | #1946 | C2×C31 | 1 | 1 | yes | characteristic |
| 189 | #1857 | C2×C31 | 1 | 2 | yes | — |
| 190 | #1773 | C2×C31 | 1 | 1 | yes | characteristic |
| 191 | C22×C31 | — | 2 | 2 | no | — |
| 192 | C22×C31 | #542 | 1 | 1 | yes | characteristic |
| 193 | C22×C31 | D42 | 1 | 1 | yes | characteristic |
| 194 | C22×C31 | #554 | 1 | 1 | yes | characteristic |
| 195 | C4×C31 | — | 4 | 4 | no | — |
| 196 | C4×C31 | — | 4 | 2 | no | — |
| 197 | C4×C31 | — | 4 | 2 | no | — |
| 198 | C4×C31 | — | 4 | 2 | no | — |
| 199 | C4×C31 | — | 4 | 2 | no | — |
| 200 | C4×C31 | — | 8 | 1 | no | — |
| 201 | C4×C31 | — | 8 | 2 | no | — |
| 202 | C4×C31 | C2×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 203 | C4×C31 | #532 | 1 | 1 | yes | characteristic |
| 204 | C4×C31 | #548 | 1 | 1 | yes | characteristic |
| 205 | C4×C31 | D4×Q8 | 1 | 1 | yes | characteristic |
| 206 | C22×Q16 | C22×C31 | 1 | 1 | yes | characteristic |
| 207 | #544 | C22×C31 | 1 | 2 | yes | — |
| 208 | #519 | C22×C31 | 1 | 2 | yes | — |
| 209 | #501 | — | 2 | 2 | no | — |
| 210 | #499 | — | 2 | 1 | no | — |
| 211 | #498 | — | 2 | 1 | no | — |
| 212 | #479 | — | 2 | 2 | no | — |
| 213 | #479 | — | 2 | 2 | no | — |
| 214 | #477 | — | 2 | 2 | no | — |
| 215 | #475 | — | 2 | 2 | no | — |
| 216 | #441 | — | 2 | 1 | no | — |
| 217 | #441 | — | 2 | 1 | no | — |
| 218 | C4×Q16 | — | 2 | 2 | no | — |
| 219 | C2×#108 | C22×C31 | 1 | 1 | yes | characteristic |
| 220 | C2×#108 | C22×C31 | 1 | 1 | yes | characteristic |
| 221 | #428 | C22×C31 | 1 | 2 | yes | — |
| 222 | #428 | C22×C31 | 1 | 2 | yes | — |
| 223 | #427 | C22×C31 | 1 | 1 | yes | characteristic |
| 224 | #427 | C22×C31 | 1 | 1 | yes | characteristic |
| 225 | C2×#106 | C22×C31 | 1 | 1 | yes | characteristic |
| 226 | #424 | C22×C31 | 1 | 2 | yes | — |
| 227 | #419 | C22×C31 | 1 | 2 | yes | — |
| 228 | #419 | C22×C31 | 1 | 2 | yes | — |
| 229 | C2×#103 | C22×C31 | 1 | 2 | yes | — |
| 230 | C2×#101 | C22×C31 | 1 | 2 | yes | — |
| 231 | #405 | C22×C31 | 1 | 1 | yes | characteristic |
| 232 | #405 | C22×C31 | 1 | 1 | yes | characteristic |
| 233 | C2×#97 | C22×C31 | 1 | 1 | yes | characteristic |
| 234 | #391 | C22×C31 | 1 | 2 | yes | — |
| 235 | #343 | C22×C31 | 1 | 2 | yes | — |
| 236 | #339 | C22×C31 | 1 | 1 | yes | characteristic |
| 237 | #339 | C22×C31 | 1 | 2 | yes | — |
| 238 | #339 | C22×C31 | 1 | 1 | yes | characteristic |
| 239 | C2×C31 | — | 2 | 1 | no | — |
| 240 | C2×C31 | — | 2 | 1 | no | — |
| 241 | C2×C31 | #2452 | 1 | 1 | yes | characteristic |
| 242 | C2×C31 | #3289 | 1 | 2 | yes | — |
| 243 | C22×Q8 | C23×C31 | 1 | 2 | yes | — |
| 244 | C2×Q16 | — | 2 | 1 | no | — |
| 245 | C2×Q16 | — | 2 | 1 | no | — |
| 246 | C2×Q16 | — | 2 | 2 | no | — |
| 247 | C2×Q16 | Q8×C31 | 1 | 4 | yes | complemented |
| 248 | C2×M16 | C23×C31 | 1 | 1 | yes | characteristic |
| 249 | C2×M16 | C23×C31 | 1 | 2 | yes | — |
| 250 | C2×M16 | C23×C31 | 1 | 1 | yes | characteristic |
| 251 | C22×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 252 | C22×C8 | C23×C31 | 1 | 1 | yes | characteristic |
| 253 | C4⋊Q8 | — | 2 | 2 | no | — |
| 254 | C4⋊Q8 | — | 2 | 2 | no | — |
| 255 | #125 | — | 2 | 2 | no | — |
| 256 | #125 | — | 2 | 2 | no | — |
| 257 | C22⋊Q8 | — | 4 | 2 | no | — |
| 258 | C4×Q8 | — | 2 | 2 | no | — |
| 259 | C4×Q8 | — | 2 | 2 | no | — |
| 260 | C4×Q8 | — | 2 | 2 | no | — |
| 261 | C4×Q8 | — | 2 | 2 | no | — |
| 262 | #117 | — | 4 | 2 | no | — |
| 263 | #117 | C23×C31 | 1 | 1 | yes | characteristic |
| 264 | #117 | C23×C31 | 1 | 2 | yes | — |
| 265 | #117 | C23×C31 | 1 | 1 | yes | characteristic |
| 266 | C2×C4⋊C4 | C23×C31 | 1 | 2 | yes | — |
| 267 | C2×C42 | C23×C31 | 1 | 1 | yes | characteristic |
| 268 | #108 | — | 2 | 2 | no | — |
| 269 | #108 | — | 2 | 2 | no | — |
| 270 | #107 | — | 2 | 2 | no | — |
| 271 | #107 | — | 2 | 2 | no | — |
| 272 | #107 | D4×C31 | 1 | 2 | yes | — |
| 273 | #107 | D4×C31 | 1 | 2 | yes | — |
| 274 | #106 | — | 2 | 1 | no | — |
| 275 | #106 | — | 2 | 1 | no | — |
| 276 | #106 | — | 2 | 2 | no | — |
| 277 | #106 | — | 2 | 2 | no | — |
| 278 | #106 | D4×C31 | 1 | 1 | yes | characteristic |
| 279 | #106 | D4×C31 | 1 | 1 | yes | characteristic |
| 280 | #106 | D4×C31 | 1 | 2 | yes | — |
| 281 | C4⋊C8 | — | 2 | 2 | no | — |
| 282 | C4⋊C8 | — | 2 | 2 | no | — |
| 283 | #103 | — | 2 | 2 | no | — |
| 284 | #103 | — | 2 | 2 | no | — |
| 285 | #103 | — | 2 | 2 | no | — |
| 286 | #103 | — | 2 | 2 | no | — |
| 287 | #103 | — | 2 | 2 | no | — |
| 288 | #103 | — | 2 | 2 | no | — |
| 289 | #101 | — | 2 | 4 | no | — |
| 290 | #97 | — | 2 | 1 | no | — |
| 291 | #97 | — | 2 | 1 | no | — |
| 292 | #97 | — | 2 | 2 | no | — |
| 293 | C4×C8 | — | 2 | 1 | no | — |
| 294 | C4×C8 | — | 2 | 1 | no | — |
| 295 | #95 | — | 4 | 2 | no | — |
| 296 | C31 | #26505 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 297 | C2×Q8 | — | 2 | 2 | no | — |
| 298 | C2×Q8 | — | 2 | 2 | no | — |
| 299 | C2×Q8 | — | 2 | 2 | no | — |
| 300 | C2×Q8 | — | 2 | 2 | no | — |
| 301 | C2×Q8 | — | 2 | 2 | no | — |
| 302 | C2×Q8 | — | 4 | 2 | no | — |
| 303 | C2×Q8 | C2×Q8×C31 | 1 | 4 | yes | — |
| 304 | C22×C4 | — | 2 | 2 | no | — |
| 305 | C22×C4 | — | 2 | 1 | no | — |
| 306 | C22×C4 | — | 2 | 2 | no | — |
| 307 | C22×C4 | C24×C31 | 1 | 1 | yes | characteristic |
| 308 | Q16 | — | 2 | 4 | no | — |
| 309 | Q16 | — | 2 | 4 | no | — |
| 310 | M16 | — | 2 | 1 | no | — |
| 311 | M16 | — | 2 | 2 | no | — |
| 312 | M16 | — | 2 | 2 | no | — |
| 313 | M16 | — | 2 | 1 | no | — |
| 314 | M16 | — | 2 | 1 | no | — |
| 315 | M16 | #41×C31 | 1 | 2 | yes | — |
| 316 | C2×C8 | — | 2 | 1 | no | — |
| 317 | C2×C8 | — | 2 | 1 | no | — |
| 318 | C2×C8 | — | 2 | 1 | no | — |
| 319 | C2×C8 | — | 2 | 1 | no | — |
| 320 | C2×C8 | — | 2 | 2 | no | — |
| 321 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 322 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 323 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 324 | C2×C8 | C2×D4×C31 | 1 | 1 | yes | characteristic |
| 325 | C2×C8 | C2×Q8×C31 | 1 | 2 | yes | — |
| 326 | C2×C8 | #41×C31 | 1 | 2 | yes | — |
| 327 | C4⋊C4 | — | 2 | 2 | no | — |
| 328 | C4⋊C4 | — | 2 | 2 | no | — |
| 329 | C4⋊C4 | — | 4 | 2 | no | — |
| 330 | C4⋊C4 | — | 4 | 2 | no | — |
| 331 | C4⋊C4 | — | 4 | 2 | no | — |
| 332 | C4⋊C4 | — | 4 | 2 | no | — |
| 333 | C4⋊C4 | — | 4 | 2 | no | — |
| 334 | C4⋊C4 | C2×D4×C31 | 1 | 2 | yes | — |
| 335 | C4⋊C4 | C2×D4×C31 | 1 | 2 | yes | — |
| 336 | C4⋊C4 | C2×D4×C31 | 1 | 2 | yes | — |
| 337 | C4⋊C4 | C2×D4×C31 | 1 | 2 | yes | — |
| 338 | C22⋊C4 | — | 2 | 1 | no | — |
| 339 | C22⋊C4 | — | 2 | 2 | no | — |
| 340 | C22⋊C4 | — | 2 | 1 | no | — |
| 341 | C42 | — | 2 | 1 | no | — |
| 342 | C42 | — | 2 | 1 | no | — |
| 343 | C42 | — | 2 | 2 | no | — |
| 344 | C42 | — | 2 | 1 | no | — |
| 345 | C42 | — | 2 | 1 | no | — |
| 346 | C42 | — | 4 | 2 | no | — |
| 347 | C42 | — | 4 | 2 | no | — |
| 348 | C23 | C31×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 349 | Q8 | — | 2 | 4 | no | — |
| 350 | Q8 | — | 2 | 4 | no | — |
| 351 | Q8 | — | 4 | 2 | no | — |
| 352 | Q8 | — | 4 | 2 | no | — |
| 353 | Q8 | — | 16 | 2 | no | — |
| 354 | C2×C4 | — | 2 | 2 | no | — |
| 355 | C2×C4 | — | 2 | 2 | no | — |
| 356 | C2×C4 | — | 2 | 2 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 2 | 4 | no | — |
| 359 | C2×C4 | — | 4 | 2 | no | — |
| 360 | C2×C4 | — | 4 | 2 | no | — |
| 361 | C2×C4 | — | 4 | 2 | no | — |
| 362 | C2×C4 | — | 4 | 1 | no | — |
| 363 | C2×C4 | — | 4 | 2 | no | — |
| 364 | C2×C4 | — | 8 | 2 | no | — |
| 365 | C2×C4 | C22×D4×C31 | 1 | 1 | yes | characteristic |
| 366 | C2×C4 | C22×D4×C31 | 1 | 1 | yes | characteristic |
| 367 | C2×C4 | C22×Q8×C31 | 1 | 1 | yes | characteristic |
| 368 | C2×C4 | C2×#41×C31 | 1 | 1 | yes | characteristic |
| 369 | C2×C4 | C2×#41×C31 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | C31×2−1+4 | 1 | 1 | yes | characteristic |
| 371 | C8 | — | 2 | 1 | no | — |
| 372 | C8 | — | 2 | 1 | no | — |
| 373 | C8 | — | 2 | 2 | no | — |
| 374 | C8 | — | 4 | 2 | no | — |
| 375 | C8 | — | 4 | 1 | no | — |
| 376 | C8 | C31×C22⋊Q8 | 1 | 2 | yes | — |
| 377 | C8 | C31×C22⋊Q8 | 1 | 2 | yes | — |
| 378 | C22 | — | 2 | 2 | no | — |
| 379 | C22 | C31×#542 | 1 | 1 | yes | characteristic |
| 380 | C22 | D42×C31 | 1 | 1 | yes | characteristic |
| 381 | C22 | C31×#554 | 1 | 1 | yes | characteristic |
| 382 | C4 | — | 4 | 4 | no | — |
| 383 | C4 | — | 4 | 2 | no | — |
| 384 | C4 | — | 4 | 2 | no | — |
| 385 | C4 | — | 4 | 2 | no | — |
| 386 | C4 | — | 4 | 2 | no | — |
| 387 | C4 | — | 8 | 1 | no | — |
| 388 | C4 | — | 8 | 2 | no | — |
| 389 | C4 | C2×C31×C22⋊Q8 | 1 | 1 | yes | characteristic |
| 390 | C4 | C31×#532 | 1 | 1 | yes | characteristic |
| 391 | C4 | C31×#548 | 1 | 1 | yes | characteristic |
| 392 | C4 | D4×Q8×C31 | 1 | 1 | yes | characteristic |
| 393 | C2 | — | 2 | 1 | no | — |
| 394 | C2 | — | 2 | 1 | no | — |
| 395 | C2 | C31×#2452 | 1 | 1 | yes | characteristic |
| 396 | C2 | C31×#3289 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta