← C53×#63037 #27270549
Subgroups — C53×#63037 #27270549
Order 13568.
7032 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C53×#3550 | C2 | 1 | 9 | yes | maximal, complemented |
| 2 | C53×#3544 | C2 | 1 | 18 | yes | maximal, complemented |
| 3 | C53×#3522 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | C53×#3503 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C53×#3499 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C53×#3483 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#3482 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×Q82×C53 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×2−1+4×C53 | C22 | 1 | 6 | yes | — |
| 10 | C53×#563 | C22 | 1 | 36 | yes | — |
| 11 | C53×#559 | C22 | 1 | 18 | yes | — |
| 12 | Q82×C53 | C22 | 1 | 1 | yes | characteristic |
| 13 | Q82×C53 | C22 | 1 | 12 | yes | — |
| 14 | Q82×C53 | C22 | 1 | 18 | yes | — |
| 15 | C53×#557 | C22 | 1 | 6 | yes | — |
| 16 | C53×#556 | C22 | 1 | 18 | yes | — |
| 17 | C53×#555 | C22 | 1 | 9 | yes | — |
| 18 | C53×#554 | C22 | 1 | 36 | yes | — |
| 19 | C53×#552 | C22 | 1 | 36 | yes | — |
| 20 | C53×#550 | C22 | 1 | 6 | yes | — |
| 21 | D4×Q8×C53 | C22 | 1 | 2 | yes | — |
| 22 | D4×Q8×C53 | C22 | 1 | 36 | yes | — |
| 23 | C53×#548 | C22 | 1 | 12 | yes | — |
| 24 | C53×#547 | C22 | 1 | 18 | yes | — |
| 25 | C53×#547 | C22 | 1 | 72 | yes | — |
| 26 | C53×#544 | C22 | 1 | 36 | yes | — |
| 27 | C53×#542 | C22 | 1 | 72 | yes | — |
| 28 | C53×#536 | C22 | 1 | 36 | yes | — |
| 29 | C53×#536 | C22 | 1 | 18 | yes | — |
| 30 | C53×#533 | C22 | 1 | 18 | yes | — |
| 31 | C53×#532 | C22 | 1 | 9 | yes | — |
| 32 | C53×#532 | C22 | 1 | 18 | yes | — |
| 33 | C2×C4⋊Q8×C53 | C22 | 1 | 18 | yes | — |
| 34 | C2×C4⋊Q8×C53 | C22 | 1 | 9 | yes | — |
| 35 | C53×#529 | C22 | 1 | 36 | yes | — |
| 36 | C53×#520 | C22 | 1 | 12 | yes | — |
| 37 | C4×#41×C53 | C22 | 1 | 9 | yes | — |
| 38 | C4×#41×C53 | C22 | 1 | 6 | yes | — |
| 39 | C2×C4×Q8×C53 | C22 | 1 | 12 | yes | — |
| 40 | 2−1+4×C53 | — | 4 | 24 | no | — |
| 41 | C2×#41×C53 | C23 | 1 | 6 | yes | — |
| 42 | C2×#41×C53 | C23 | 1 | 9 | yes | — |
| 43 | C2×#41×C53 | C23 | 1 | 6 | yes | — |
| 44 | C2×#41×C53 | C23 | 1 | 36 | yes | — |
| 45 | C22×Q8×C53 | C23 | 1 | 4 | yes | — |
| 46 | C22×Q8×C53 | C23 | 1 | 12 | yes | — |
| 47 | C22×Q8×C53 | C23 | 1 | 18 | yes | — |
| 48 | C4⋊Q8×C53 | C23 | 1 | 18 | yes | — |
| 49 | C4⋊Q8×C53 | C23 | 1 | 9 | yes | — |
| 50 | C4⋊Q8×C53 | C23 | 1 | 18 | yes | — |
| 51 | C4⋊Q8×C53 | C23 | 1 | 18 | yes | — |
| 52 | C4⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 53 | C4⋊Q8×C53 | C23 | 1 | 72 | yes | — |
| 54 | C4⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 55 | #127×C53 | C23 | 1 | 9 | yes | — |
| 56 | #126×C53 | C23 | 1 | 72 | yes | — |
| 57 | #125×C53 | C23 | 1 | 36 | yes | — |
| 58 | #125×C53 | C23 | 1 | 36 | yes | — |
| 59 | #124×C53 | C23 | 1 | 36 | yes | — |
| 60 | #124×C53 | C23 | 1 | 36 | yes | — |
| 61 | #124×C53 | C23 | 1 | 18 | yes | — |
| 62 | #123×C53 | C23 | 1 | 72 | yes | — |
| 63 | #123×C53 | C23 | 1 | 72 | yes | — |
| 64 | C22⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 65 | C22⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 66 | C22⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 67 | C22⋊Q8×C53 | C23 | 1 | 144 | yes | — |
| 68 | #121×C53 | C23 | 1 | 36 | yes | — |
| 69 | #121×C53 | C23 | 1 | 36 | yes | — |
| 70 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 71 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 72 | C4×Q8×C53 | C23 | 1 | 36 | yes | — |
| 73 | C4×Q8×C53 | C23 | 1 | 36 | yes | — |
| 74 | C4×Q8×C53 | C23 | 1 | 2 | yes | — |
| 75 | C4×Q8×C53 | C23 | 1 | 18 | yes | — |
| 76 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 77 | C4×D4×C53 | C23 | 1 | 36 | yes | — |
| 78 | C4×D4×C53 | C23 | 1 | 18 | yes | — |
| 79 | C4×D4×C53 | C23 | 1 | 18 | yes | — |
| 80 | C4×D4×C53 | C23 | 1 | 72 | yes | — |
| 81 | #117×C53 | C23 | 1 | 18 | yes | — |
| 82 | #117×C53 | C23 | 1 | 9 | yes | — |
| 83 | #117×C53 | C23 | 1 | 18 | yes | — |
| 84 | #117×C53 | C23 | 1 | 36 | yes | — |
| 85 | C2×C4⋊C4×C53 | C23 | 1 | 36 | yes | — |
| 86 | C2×C4⋊C4×C53 | C23 | 1 | 36 | yes | — |
| 87 | C2×C42×C53 | C23 | 1 | 18 | yes | — |
| 88 | C2×C42×C53 | C23 | 1 | 9 | yes | — |
| 89 | #41×C53 | — | 2 | 24 | no | — |
| 90 | #41×C53 | — | 2 | 36 | no | — |
| 91 | #41×C53 | — | 4 | 12 | no | — |
| 92 | #41×C53 | — | 4 | 72 | no | — |
| 93 | C2×Q8×C53 | — | 2 | 16 | no | — |
| 94 | C2×Q8×C53 | — | 4 | 24 | no | — |
| 95 | C2×Q8×C53 | — | 4 | 36 | no | — |
| 96 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 97 | C2×Q8×C53 | C24 | 1 | 9 | yes | — |
| 98 | C2×Q8×C53 | C24 | 1 | 36 | yes | — |
| 99 | C2×Q8×C53 | C24 | 1 | 6 | yes | — |
| 100 | C2×Q8×C53 | C24 | 1 | 2 | yes | — |
| 101 | C2×D4×C53 | C24 | 1 | 18 | yes | — |
| 102 | C2×D4×C53 | C24 | 1 | 18 | yes | — |
| 103 | C2×D4×C53 | C24 | 1 | 18 | yes | — |
| 104 | C2×D4×C53 | C24 | 1 | 1 | yes | characteristic |
| 105 | C22×C4×C53 | C24 | 1 | 12 | yes | — |
| 106 | C22×C4×C53 | C24 | 1 | 18 | yes | — |
| 107 | C22×C4×C53 | C24 | 1 | 18 | yes | — |
| 108 | C22×C4×C53 | C24 | 1 | 9 | yes | — |
| 109 | C22×C4×C53 | C24 | 1 | 36 | yes | — |
| 110 | C4⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 111 | C4⋊C4×C53 | C24 | 1 | 18 | yes | — |
| 112 | C4⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 113 | C4⋊C4×C53 | C24 | 1 | 72 | yes | — |
| 114 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 115 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 116 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 117 | C4⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 118 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 119 | C22⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 120 | C22⋊C4×C53 | C24 | 1 | 72 | yes | — |
| 121 | C22⋊C4×C53 | C24 | 1 | 18 | yes | — |
| 122 | C42×C53 | C24 | 1 | 6 | yes | — |
| 123 | C42×C53 | C24 | 1 | 9 | yes | — |
| 124 | C42×C53 | C24 | 1 | 9 | yes | — |
| 125 | C42×C53 | C24 | 1 | 36 | yes | — |
| 126 | C42×C53 | C24 | 1 | 18 | yes | — |
| 127 | C23×C53 | C25 | 1 | 9 | yes | — |
| 128 | C23×C53 | C25 | 1 | 2 | yes | — |
| 129 | Q8×C53 | — | 2 | 18 | no | — |
| 130 | Q8×C53 | — | 2 | 24 | no | — |
| 131 | Q8×C53 | — | 4 | 6 | no | — |
| 132 | Q8×C53 | — | 4 | 36 | no | — |
| 133 | Q8×C53 | 2−1+4 | 1 | 8 | yes | complemented |
| 134 | D4×C53 | — | 2 | 36 | no | — |
| 135 | D4×C53 | — | 2 | 36 | no | — |
| 136 | D4×C53 | — | 4 | 18 | no | — |
| 137 | D4×C53 | H(5,𝔽2) | 1 | 4 | yes | — |
| 138 | C2×C4×C53 | — | 2 | 36 | no | — |
| 139 | C2×C4×C53 | — | 2 | 18 | no | — |
| 140 | C2×C4×C53 | — | 2 | 24 | no | — |
| 141 | C2×C4×C53 | — | 2 | 36 | no | — |
| 142 | C2×C4×C53 | — | 4 | 36 | no | — |
| 143 | C2×C4×C53 | C25 | 1 | 18 | yes | — |
| 144 | C2×C4×C53 | C25 | 1 | 9 | yes | — |
| 145 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 146 | C2×C4×C53 | C25 | 1 | 12 | yes | — |
| 147 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 148 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 149 | #63037 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 150 | C22×C53 | — | 2 | 4 | no | — |
| 151 | C22×C53 | — | 2 | 9 | no | — |
| 152 | C22×C53 | — | 2 | 18 | no | — |
| 153 | C22×C53 | C2×H(5,𝔽2) | 1 | 4 | yes | — |
| 154 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 155 | C4×C53 | — | 2 | 9 | no | — |
| 156 | C4×C53 | — | 2 | 18 | no | — |
| 157 | C4×C53 | — | 2 | 6 | no | — |
| 158 | C4×C53 | — | 2 | 12 | no | — |
| 159 | C4×C53 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 160 | C4×C53 | C2×2−1+4 | 1 | 12 | yes | — |
| 161 | #3550 | C2×C53 | 1 | 9 | yes | complemented |
| 162 | #3544 | C2×C53 | 1 | 18 | yes | complemented |
| 163 | #3522 | C2×C53 | 1 | 12 | yes | complemented |
| 164 | #3503 | C2×C53 | 1 | 6 | yes | complemented |
| 165 | #3499 | C2×C53 | 1 | 9 | yes | complemented |
| 166 | #3483 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 167 | #3482 | C2×C53 | 1 | 6 | yes | complemented |
| 168 | C2×Q82 | C2×C53 | 1 | 2 | yes | complemented |
| 169 | C2×C53 | — | 2 | 4 | no | — |
| 170 | C2×C53 | — | 4 | 9 | no | — |
| 171 | C2×C53 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 172 | C2×C53 | C22×2−1+4 | 1 | 2 | yes | — |
| 173 | C2×2−1+4 | C22×C53 | 1 | 6 | yes | — |
| 174 | #563 | C22×C53 | 1 | 36 | yes | — |
| 175 | #559 | C22×C53 | 1 | 18 | yes | — |
| 176 | Q82 | C22×C53 | 1 | 1 | yes | characteristic |
| 177 | Q82 | C22×C53 | 1 | 12 | yes | — |
| 178 | Q82 | C22×C53 | 1 | 18 | yes | — |
| 179 | #557 | C22×C53 | 1 | 6 | yes | — |
| 180 | #556 | C22×C53 | 1 | 18 | yes | — |
| 181 | #555 | C22×C53 | 1 | 9 | yes | — |
| 182 | #554 | C22×C53 | 1 | 36 | yes | — |
| 183 | #552 | C22×C53 | 1 | 36 | yes | — |
| 184 | #550 | C22×C53 | 1 | 6 | yes | — |
| 185 | D4×Q8 | C22×C53 | 1 | 2 | yes | — |
| 186 | D4×Q8 | C22×C53 | 1 | 36 | yes | — |
| 187 | #548 | C22×C53 | 1 | 12 | yes | — |
| 188 | #547 | C22×C53 | 1 | 18 | yes | — |
| 189 | #547 | C22×C53 | 1 | 72 | yes | — |
| 190 | #544 | C22×C53 | 1 | 36 | yes | — |
| 191 | #542 | C22×C53 | 1 | 72 | yes | — |
| 192 | #536 | C22×C53 | 1 | 36 | yes | — |
| 193 | #536 | C22×C53 | 1 | 18 | yes | — |
| 194 | #533 | C22×C53 | 1 | 18 | yes | — |
| 195 | #532 | C22×C53 | 1 | 9 | yes | — |
| 196 | #532 | C22×C53 | 1 | 18 | yes | — |
| 197 | C2×C4⋊Q8 | C22×C53 | 1 | 18 | yes | — |
| 198 | C2×C4⋊Q8 | C22×C53 | 1 | 9 | yes | — |
| 199 | #529 | C22×C53 | 1 | 36 | yes | — |
| 200 | #520 | C22×C53 | 1 | 12 | yes | — |
| 201 | C4×#41 | C22×C53 | 1 | 9 | yes | — |
| 202 | C4×#41 | C22×C53 | 1 | 6 | yes | — |
| 203 | C2×C4×Q8 | C22×C53 | 1 | 12 | yes | — |
| 204 | C53 | #63037 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 205 | 2−1+4 | — | 4 | 24 | no | — |
| 206 | C2×#41 | C23×C53 | 1 | 6 | yes | — |
| 207 | C2×#41 | C23×C53 | 1 | 9 | yes | — |
| 208 | C2×#41 | C23×C53 | 1 | 6 | yes | — |
| 209 | C2×#41 | C23×C53 | 1 | 36 | yes | — |
| 210 | C22×Q8 | C23×C53 | 1 | 4 | yes | — |
| 211 | C22×Q8 | C23×C53 | 1 | 12 | yes | — |
| 212 | C22×Q8 | C23×C53 | 1 | 18 | yes | — |
| 213 | C4⋊Q8 | C23×C53 | 1 | 18 | yes | — |
| 214 | C4⋊Q8 | C23×C53 | 1 | 9 | yes | — |
| 215 | C4⋊Q8 | C23×C53 | 1 | 18 | yes | — |
| 216 | C4⋊Q8 | C23×C53 | 1 | 18 | yes | — |
| 217 | C4⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 218 | C4⋊Q8 | C23×C53 | 1 | 72 | yes | — |
| 219 | C4⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 220 | #127 | C23×C53 | 1 | 9 | yes | — |
| 221 | #126 | C23×C53 | 1 | 72 | yes | — |
| 222 | #125 | C23×C53 | 1 | 36 | yes | — |
| 223 | #125 | C23×C53 | 1 | 36 | yes | — |
| 224 | #124 | C23×C53 | 1 | 36 | yes | — |
| 225 | #124 | C23×C53 | 1 | 36 | yes | — |
| 226 | #124 | C23×C53 | 1 | 18 | yes | — |
| 227 | #123 | C23×C53 | 1 | 72 | yes | — |
| 228 | #123 | C23×C53 | 1 | 72 | yes | — |
| 229 | C22⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 230 | C22⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 231 | C22⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 232 | C22⋊Q8 | C23×C53 | 1 | 144 | yes | — |
| 233 | #121 | C23×C53 | 1 | 36 | yes | — |
| 234 | #121 | C23×C53 | 1 | 36 | yes | — |
| 235 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 236 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 237 | C4×Q8 | C23×C53 | 1 | 36 | yes | — |
| 238 | C4×Q8 | C23×C53 | 1 | 36 | yes | — |
| 239 | C4×Q8 | C23×C53 | 1 | 2 | yes | — |
| 240 | C4×Q8 | C23×C53 | 1 | 18 | yes | — |
| 241 | C4×D4 | C23×C53 | 1 | 6 | yes | — |
| 242 | C4×D4 | C23×C53 | 1 | 36 | yes | — |
| 243 | C4×D4 | C23×C53 | 1 | 18 | yes | — |
| 244 | C4×D4 | C23×C53 | 1 | 18 | yes | — |
| 245 | C4×D4 | C23×C53 | 1 | 72 | yes | — |
| 246 | #117 | C23×C53 | 1 | 18 | yes | — |
| 247 | #117 | C23×C53 | 1 | 9 | yes | — |
| 248 | #117 | C23×C53 | 1 | 18 | yes | — |
| 249 | #117 | C23×C53 | 1 | 36 | yes | — |
| 250 | C2×C4⋊C4 | C23×C53 | 1 | 36 | yes | — |
| 251 | C2×C4⋊C4 | C23×C53 | 1 | 36 | yes | — |
| 252 | C2×C42 | C23×C53 | 1 | 18 | yes | — |
| 253 | C2×C42 | C23×C53 | 1 | 9 | yes | — |
| 254 | #41 | — | 2 | 24 | no | — |
| 255 | #41 | — | 2 | 36 | no | — |
| 256 | #41 | — | 4 | 12 | no | — |
| 257 | #41 | — | 4 | 72 | no | — |
| 258 | C2×Q8 | — | 2 | 16 | no | — |
| 259 | C2×Q8 | — | 4 | 24 | no | — |
| 260 | C2×Q8 | — | 4 | 36 | no | — |
| 261 | C2×Q8 | C24×C53 | 1 | 12 | yes | — |
| 262 | C2×Q8 | C24×C53 | 1 | 9 | yes | — |
| 263 | C2×Q8 | C24×C53 | 1 | 36 | yes | — |
| 264 | C2×Q8 | C24×C53 | 1 | 6 | yes | — |
| 265 | C2×Q8 | C24×C53 | 1 | 2 | yes | — |
| 266 | C2×D4 | C24×C53 | 1 | 18 | yes | — |
| 267 | C2×D4 | C24×C53 | 1 | 18 | yes | — |
| 268 | C2×D4 | C24×C53 | 1 | 18 | yes | — |
| 269 | C2×D4 | C24×C53 | 1 | 1 | yes | characteristic |
| 270 | C22×C4 | C24×C53 | 1 | 12 | yes | — |
| 271 | C22×C4 | C24×C53 | 1 | 18 | yes | — |
| 272 | C22×C4 | C24×C53 | 1 | 18 | yes | — |
| 273 | C22×C4 | C24×C53 | 1 | 9 | yes | — |
| 274 | C22×C4 | C24×C53 | 1 | 36 | yes | — |
| 275 | C4⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 276 | C4⋊C4 | C24×C53 | 1 | 18 | yes | — |
| 277 | C4⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 278 | C4⋊C4 | C24×C53 | 1 | 72 | yes | — |
| 279 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 280 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 281 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 282 | C4⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 283 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 284 | C22⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 285 | C22⋊C4 | C24×C53 | 1 | 72 | yes | — |
| 286 | C22⋊C4 | C24×C53 | 1 | 18 | yes | — |
| 287 | C42 | C24×C53 | 1 | 6 | yes | — |
| 288 | C42 | C24×C53 | 1 | 9 | yes | — |
| 289 | C42 | C24×C53 | 1 | 9 | yes | — |
| 290 | C42 | C24×C53 | 1 | 36 | yes | — |
| 291 | C42 | C24×C53 | 1 | 18 | yes | — |
| 292 | C23 | C25×C53 | 1 | 9 | yes | — |
| 293 | C23 | C25×C53 | 1 | 2 | yes | — |
| 294 | Q8 | — | 2 | 18 | no | — |
| 295 | Q8 | — | 2 | 24 | no | — |
| 296 | Q8 | — | 4 | 6 | no | — |
| 297 | Q8 | — | 4 | 36 | no | — |
| 298 | Q8 | 2−1+4×C53 | 1 | 8 | yes | complemented |
| 299 | D4 | — | 2 | 36 | no | — |
| 300 | D4 | — | 2 | 36 | no | — |
| 301 | D4 | — | 4 | 18 | no | — |
| 302 | D4 | H(5,𝔽2)×C53 | 1 | 4 | yes | — |
| 303 | C2×C4 | — | 2 | 36 | no | — |
| 304 | C2×C4 | — | 2 | 18 | no | — |
| 305 | C2×C4 | — | 2 | 24 | no | — |
| 306 | C2×C4 | — | 2 | 36 | no | — |
| 307 | C2×C4 | — | 4 | 36 | no | — |
| 308 | C2×C4 | C25×C53 | 1 | 12 | yes | — |
| 309 | C2×C4 | C25×C53 | 1 | 6 | yes | — |
| 310 | C2×C4 | C25×C53 | 1 | 9 | yes | — |
| 311 | C2×C4 | C25×C53 | 1 | 18 | yes | — |
| 312 | C2×C4 | C25×C53 | 1 | 1 | yes | characteristic |
| 313 | C2×C4 | C25×C53 | 1 | 6 | yes | — |
| 314 | C22 | — | 2 | 4 | no | — |
| 315 | C22 | — | 2 | 9 | no | — |
| 316 | C22 | — | 2 | 18 | no | — |
| 317 | C22 | C2×H(5,𝔽2)×C53 | 1 | 4 | yes | — |
| 318 | C22 | C26×C53 | 1 | 1 | yes | characteristic |
| 319 | C4 | — | 2 | 9 | no | — |
| 320 | C4 | — | 2 | 18 | no | — |
| 321 | C4 | — | 2 | 6 | no | — |
| 322 | C4 | — | 2 | 12 | no | — |
| 323 | C4 | C2×H(5,𝔽2)×C53 | 1 | 2 | yes | — |
| 324 | C4 | C2×2−1+4×C53 | 1 | 12 | yes | — |
| 325 | C2 | — | 2 | 4 | no | — |
| 326 | C2 | — | 4 | 9 | no | — |
| 327 | C2 | C22×H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 328 | C2 | C22×2−1+4×C53 | 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