← C53×#63048 #27270560
Subgroups — C53×#63048 #27270560
Order 13568.
6912 conjugacy classes of subgroups.
The subgroup lattice has 392 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C53×#3561 | C2 | 1 | 18 | yes | maximal, complemented |
| 2 | C53×#3550 | C2 | 1 | 9 | yes | maximal, complemented |
| 3 | C53×#3540 | C2 | 1 | 18 | yes | maximal, complemented |
| 4 | C53×#3529 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C53×#3518 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C53×#3500 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C53×#3486 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×2−1+4×C53 | C22 | 1 | 3 | yes | — |
| 9 | C2×H(5,𝔽2)×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C23×Q8×C53 | C22 | 1 | 2 | yes | complemented |
| 11 | C53×#563 | C22 | 1 | 9 | yes | complemented |
| 12 | C53×#563 | C22 | 1 | 18 | yes | complemented |
| 13 | C53×#562 | C22 | 1 | 18 | yes | complemented |
| 14 | C53×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C53×H(3,𝔽4) | C22 | 1 | 12 | yes | complemented |
| 16 | C53×#560 | C22 | 1 | 18 | yes | complemented |
| 17 | C53×#559 | C22 | 1 | 18 | yes | complemented |
| 18 | Q82×C53 | C22 | 1 | 2 | yes | complemented |
| 19 | Q82×C53 | C22 | 1 | 6 | yes | complemented |
| 20 | C53×#556 | C22 | 1 | 36 | yes | complemented |
| 21 | C53×#556 | C22 | 1 | 18 | yes | complemented |
| 22 | C53×#555 | C22 | 1 | 18 | yes | complemented |
| 23 | C53×#551 | C22 | 1 | 36 | yes | complemented |
| 24 | D4×Q8×C53 | C22 | 1 | 6 | yes | complemented |
| 25 | D4×Q8×C53 | C22 | 1 | 36 | yes | complemented |
| 26 | C53×#548 | C22 | 1 | 12 | yes | complemented |
| 27 | C53×#548 | C22 | 1 | 36 | yes | complemented |
| 28 | C53×#546 | C22 | 1 | 36 | yes | complemented |
| 29 | C53×#543 | C22 | 1 | 12 | yes | complemented |
| 30 | C53×#542 | C22 | 1 | 36 | yes | complemented |
| 31 | C53×#542 | C22 | 1 | 72 | yes | complemented |
| 32 | C53×#538 | C22 | 1 | 36 | yes | complemented |
| 33 | C53×#536 | C22 | 1 | 18 | yes | complemented |
| 34 | C53×#536 | C22 | 1 | 18 | yes | complemented |
| 35 | C53×#536 | C22 | 1 | 9 | yes | complemented |
| 36 | C53×#535 | C22 | 1 | 9 | yes | — |
| 37 | C53×#533 | C22 | 1 | 18 | yes | complemented |
| 38 | C53×#532 | C22 | 1 | 9 | yes | — |
| 39 | C53×#529 | C22 | 1 | 18 | yes | complemented |
| 40 | C2×#124×C53 | C22 | 1 | 9 | yes | complemented |
| 41 | C53×#525 | C22 | 1 | 18 | yes | complemented |
| 42 | C53×#525 | C22 | 1 | 18 | yes | complemented |
| 43 | C53×#519 | C22 | 1 | 6 | yes | complemented |
| 44 | C4×#41×C53 | C22 | 1 | 3 | yes | complemented |
| 45 | 2−1+4×C53 | — | 4 | 12 | no | — |
| 46 | H(5,𝔽2)×C53 | — | 4 | 4 | no | — |
| 47 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 48 | C2×#41×C53 | C23 | 1 | 9 | yes | — |
| 49 | C2×#41×C53 | C23 | 1 | 18 | yes | — |
| 50 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 51 | C22×Q8×C53 | — | 4 | 8 | no | — |
| 52 | C22×Q8×C53 | C23 | 1 | 6 | yes | — |
| 53 | C22×Q8×C53 | C23 | 1 | 9 | yes | — |
| 54 | C22×Q8×C53 | C23 | 1 | 18 | yes | — |
| 55 | C22×D4×C53 | C23 | 1 | 9 | yes | — |
| 56 | C23×C4×C53 | C23 | 1 | 6 | yes | — |
| 57 | C4⋊Q8×C53 | C23 | 1 | 9 | yes | — |
| 58 | C4⋊Q8×C53 | C23 | 1 | 18 | yes | — |
| 59 | C4⋊Q8×C53 | C23 | 1 | 18 | yes | — |
| 60 | C4⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 61 | #127×C53 | C23 | 1 | 9 | yes | — |
| 62 | #126×C53 | C23 | 1 | 36 | yes | — |
| 63 | #126×C53 | C23 | 1 | 72 | yes | — |
| 64 | #125×C53 | C23 | 1 | 18 | yes | — |
| 65 | #124×C53 | C23 | 1 | 9 | yes | — |
| 66 | #124×C53 | C23 | 1 | 18 | yes | — |
| 67 | #124×C53 | C23 | 1 | 36 | yes | — |
| 68 | #124×C53 | C23 | 1 | 6 | yes | — |
| 69 | #124×C53 | C23 | 1 | 3 | yes | — |
| 70 | #124×C53 | C23 | 1 | 36 | yes | — |
| 71 | #124×C53 | C23 | 1 | 72 | yes | — |
| 72 | #123×C53 | C23 | 1 | 36 | yes | — |
| 73 | #123×C53 | C23 | 1 | 18 | yes | — |
| 74 | #123×C53 | C23 | 1 | 18 | yes | — |
| 75 | #123×C53 | C23 | 1 | 36 | yes | — |
| 76 | #123×C53 | C23 | 1 | 36 | yes | — |
| 77 | C22⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 78 | C22⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 79 | C22⋊Q8×C53 | C23 | 1 | 18 | yes | — |
| 80 | C22⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 81 | C22⋊Q8×C53 | C23 | 1 | 36 | yes | — |
| 82 | C22⋊Q8×C53 | C23 | 1 | 72 | yes | — |
| 83 | #121×C53 | C23 | 1 | 36 | yes | — |
| 84 | #121×C53 | C23 | 1 | 36 | yes | — |
| 85 | #121×C53 | C23 | 1 | 18 | yes | — |
| 86 | #121×C53 | C23 | 1 | 36 | yes | — |
| 87 | #120×C53 | C23 | 1 | 6 | yes | — |
| 88 | #120×C53 | C23 | 1 | 18 | yes | — |
| 89 | #120×C53 | C23 | 1 | 36 | yes | — |
| 90 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 91 | C4×Q8×C53 | C23 | 1 | 36 | yes | — |
| 92 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 93 | C4×Q8×C53 | C23 | 1 | 36 | yes | — |
| 94 | C4×D4×C53 | C23 | 1 | 18 | yes | — |
| 95 | C4×D4×C53 | C23 | 1 | 18 | yes | — |
| 96 | C4×D4×C53 | C23 | 1 | 36 | yes | — |
| 97 | C4×D4×C53 | C23 | 1 | 72 | yes | — |
| 98 | #117×C53 | C23 | 1 | 9 | yes | — |
| 99 | #117×C53 | C23 | 1 | 18 | yes | — |
| 100 | #117×C53 | C23 | 1 | 18 | yes | — |
| 101 | #117×C53 | C23 | 1 | 36 | yes | — |
| 102 | C2×C22⋊C4×C53 | C23 | 1 | 36 | yes | — |
| 103 | C2×C42×C53 | C23 | 1 | 9 | yes | — |
| 104 | C24×C53 | C24 | 1 | 6 | yes | — |
| 105 | C24×C53 | C24 | 1 | 2 | yes | — |
| 106 | #41×C53 | — | 2 | 12 | no | — |
| 107 | #41×C53 | — | 4 | 6 | no | — |
| 108 | #41×C53 | — | 4 | 18 | no | — |
| 109 | #41×C53 | — | 4 | 36 | no | — |
| 110 | C2×Q8×C53 | — | 2 | 24 | no | — |
| 111 | C2×Q8×C53 | — | 4 | 36 | no | — |
| 112 | C2×Q8×C53 | — | 4 | 18 | no | — |
| 113 | C2×Q8×C53 | C24 | 1 | 18 | yes | — |
| 114 | C2×Q8×C53 | C24 | 1 | 2 | yes | — |
| 115 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 116 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 117 | C2×Q8×C53 | C24 | 1 | 9 | yes | — |
| 118 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 119 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 120 | C2×D4×C53 | — | 4 | 18 | no | — |
| 121 | C2×D4×C53 | C24 | 1 | 9 | yes | — |
| 122 | C2×D4×C53 | C24 | 1 | 36 | yes | — |
| 123 | C2×D4×C53 | C24 | 1 | 6 | yes | — |
| 124 | C2×D4×C53 | C24 | 1 | 18 | yes | — |
| 125 | C2×D4×C53 | C24 | 1 | 3 | yes | — |
| 126 | C2×D4×C53 | C24 | 1 | 9 | yes | — |
| 127 | C22×C4×C53 | — | 4 | 12 | no | — |
| 128 | C22×C4×C53 | C24 | 1 | 9 | yes | — |
| 129 | C22×C4×C53 | C24 | 1 | 18 | yes | — |
| 130 | C22×C4×C53 | C24 | 1 | 18 | yes | — |
| 131 | C22×C4×C53 | C24 | 1 | 18 | yes | — |
| 132 | C22×C4×C53 | C24 | 1 | 18 | yes | — |
| 133 | C4⋊C4×C53 | C24 | 1 | 18 | yes | — |
| 134 | C4⋊C4×C53 | C24 | 1 | 18 | yes | — |
| 135 | C4⋊C4×C53 | C24 | 1 | 18 | yes | — |
| 136 | C4⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 137 | C4⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 138 | C4⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 139 | C22⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 140 | C22⋊C4×C53 | C24 | 1 | 72 | yes | — |
| 141 | C22⋊C4×C53 | C24 | 1 | 18 | yes | — |
| 142 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 143 | C22⋊C4×C53 | C24 | 1 | 18 | yes | — |
| 144 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 145 | C22⋊C4×C53 | C24 | 1 | 36 | yes | — |
| 146 | C42×C53 | C24 | 1 | 3 | yes | — |
| 147 | C42×C53 | C24 | 1 | 18 | yes | — |
| 148 | C42×C53 | C24 | 1 | 9 | yes | — |
| 149 | C42×C53 | C24 | 1 | 36 | yes | — |
| 150 | C23×C53 | — | 4 | 2 | no | — |
| 151 | C23×C53 | — | 4 | 4 | no | — |
| 152 | C23×C53 | — | 4 | 6 | no | — |
| 153 | C23×C53 | — | 4 | 12 | no | — |
| 154 | C23×C53 | C25 | 1 | 6 | yes | — |
| 155 | C23×C53 | C25 | 1 | 9 | yes | — |
| 156 | Q8×C53 | — | 2 | 36 | no | — |
| 157 | Q8×C53 | — | 4 | 12 | no | — |
| 158 | Q8×C53 | — | 4 | 9 | no | — |
| 159 | Q8×C53 | — | 4 | 2 | no | — |
| 160 | Q8×C53 | — | 4 | 12 | no | — |
| 161 | Q8×C53 | — | 4 | 1 | no | — |
| 162 | Q8×C53 | H(5,𝔽2) | 1 | 4 | yes | — |
| 163 | D4×C53 | — | 2 | 18 | no | — |
| 164 | D4×C53 | — | 4 | 9 | no | — |
| 165 | D4×C53 | — | 4 | 6 | no | — |
| 166 | D4×C53 | — | 4 | 36 | no | — |
| 167 | D4×C53 | — | 4 | 3 | no | — |
| 168 | D4×C53 | — | 4 | 18 | no | — |
| 169 | C2×C4×C53 | — | 2 | 36 | no | — |
| 170 | C2×C4×C53 | — | 2 | 18 | no | — |
| 171 | C2×C4×C53 | — | 4 | 18 | no | — |
| 172 | C2×C4×C53 | — | 4 | 18 | no | — |
| 173 | C2×C4×C53 | — | 4 | 18 | no | — |
| 174 | C2×C4×C53 | C25 | 1 | 18 | yes | — |
| 175 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 176 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 177 | C2×C4×C53 | C25 | 1 | 18 | yes | — |
| 178 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 179 | #63048 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 180 | C22×C53 | — | 2 | 6 | no | — |
| 181 | C22×C53 | — | 2 | 9 | no | — |
| 182 | C22×C53 | — | 2 | 18 | no | — |
| 183 | C22×C53 | — | 2 | 12 | no | — |
| 184 | C22×C53 | — | 4 | 8 | no | — |
| 185 | C22×C53 | — | 16 | 6 | no | — |
| 186 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 187 | C4×C53 | — | 2 | 3 | no | — |
| 188 | C4×C53 | — | 2 | 18 | no | — |
| 189 | C4×C53 | — | 2 | 6 | no | — |
| 190 | C4×C53 | — | 2 | 18 | no | — |
| 191 | C4×C53 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 192 | #3561 | C2×C53 | 1 | 18 | yes | complemented |
| 193 | #3550 | C2×C53 | 1 | 9 | yes | complemented |
| 194 | #3540 | C2×C53 | 1 | 18 | yes | complemented |
| 195 | #3529 | C2×C53 | 1 | 3 | yes | complemented |
| 196 | #3518 | C2×C53 | 1 | 6 | yes | complemented |
| 197 | #3500 | C2×C53 | 1 | 3 | yes | complemented |
| 198 | #3486 | C2×C53 | 1 | 6 | yes | complemented |
| 199 | C2×C53 | — | 4 | 6 | no | — |
| 200 | C2×C53 | — | 4 | 9 | no | — |
| 201 | C2×C53 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 202 | C2×C53 | 2−1+6 | 1 | 2 | yes | — |
| 203 | C2×2−1+4 | C22×C53 | 1 | 3 | yes | — |
| 204 | C2×H(5,𝔽2) | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 205 | C23×Q8 | C22×C53 | 1 | 2 | yes | complemented |
| 206 | #563 | C22×C53 | 1 | 9 | yes | complemented |
| 207 | #563 | C22×C53 | 1 | 18 | yes | complemented |
| 208 | #562 | C22×C53 | 1 | 18 | yes | complemented |
| 209 | H(3,𝔽4) | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 210 | H(3,𝔽4) | C22×C53 | 1 | 12 | yes | complemented |
| 211 | #560 | C22×C53 | 1 | 18 | yes | complemented |
| 212 | #559 | C22×C53 | 1 | 18 | yes | complemented |
| 213 | Q82 | C22×C53 | 1 | 2 | yes | complemented |
| 214 | Q82 | C22×C53 | 1 | 6 | yes | complemented |
| 215 | #556 | C22×C53 | 1 | 36 | yes | complemented |
| 216 | #556 | C22×C53 | 1 | 18 | yes | complemented |
| 217 | #555 | C22×C53 | 1 | 18 | yes | complemented |
| 218 | #551 | C22×C53 | 1 | 36 | yes | complemented |
| 219 | D4×Q8 | C22×C53 | 1 | 6 | yes | complemented |
| 220 | D4×Q8 | C22×C53 | 1 | 36 | yes | complemented |
| 221 | #548 | C22×C53 | 1 | 12 | yes | complemented |
| 222 | #548 | C22×C53 | 1 | 36 | yes | complemented |
| 223 | #546 | C22×C53 | 1 | 36 | yes | complemented |
| 224 | #543 | C22×C53 | 1 | 12 | yes | complemented |
| 225 | #542 | C22×C53 | 1 | 36 | yes | complemented |
| 226 | #542 | C22×C53 | 1 | 72 | yes | complemented |
| 227 | #538 | C22×C53 | 1 | 36 | yes | complemented |
| 228 | #536 | C22×C53 | 1 | 18 | yes | complemented |
| 229 | #536 | C22×C53 | 1 | 18 | yes | complemented |
| 230 | #536 | C22×C53 | 1 | 9 | yes | complemented |
| 231 | #535 | C22×C53 | 1 | 9 | yes | — |
| 232 | #533 | C22×C53 | 1 | 18 | yes | complemented |
| 233 | #532 | C22×C53 | 1 | 9 | yes | — |
| 234 | #529 | C22×C53 | 1 | 18 | yes | complemented |
| 235 | C2×#124 | C22×C53 | 1 | 9 | yes | complemented |
| 236 | #525 | C22×C53 | 1 | 18 | yes | complemented |
| 237 | #525 | C22×C53 | 1 | 18 | yes | complemented |
| 238 | #519 | C22×C53 | 1 | 6 | yes | complemented |
| 239 | C4×#41 | C22×C53 | 1 | 3 | yes | complemented |
| 240 | C53 | #63048 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 241 | 2−1+4 | — | 4 | 12 | no | — |
| 242 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 243 | C2×#41 | C23×C53 | 1 | 3 | yes | — |
| 244 | C2×#41 | C23×C53 | 1 | 9 | yes | — |
| 245 | C2×#41 | C23×C53 | 1 | 18 | yes | — |
| 246 | C2×#41 | C23×C53 | 1 | 3 | yes | — |
| 247 | C22×Q8 | — | 4 | 8 | no | — |
| 248 | C22×Q8 | C23×C53 | 1 | 6 | yes | — |
| 249 | C22×Q8 | C23×C53 | 1 | 9 | yes | — |
| 250 | C22×Q8 | C23×C53 | 1 | 18 | yes | — |
| 251 | C22×D4 | C23×C53 | 1 | 9 | yes | — |
| 252 | C23×C4 | C23×C53 | 1 | 6 | yes | — |
| 253 | C4⋊Q8 | C23×C53 | 1 | 9 | yes | — |
| 254 | C4⋊Q8 | C23×C53 | 1 | 18 | yes | — |
| 255 | C4⋊Q8 | C23×C53 | 1 | 18 | yes | — |
| 256 | C4⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 257 | #127 | C23×C53 | 1 | 9 | yes | — |
| 258 | #126 | C23×C53 | 1 | 36 | yes | — |
| 259 | #126 | C23×C53 | 1 | 72 | yes | — |
| 260 | #125 | C23×C53 | 1 | 18 | yes | — |
| 261 | #124 | C23×C53 | 1 | 9 | yes | — |
| 262 | #124 | C23×C53 | 1 | 18 | yes | — |
| 263 | #124 | C23×C53 | 1 | 36 | yes | — |
| 264 | #124 | C23×C53 | 1 | 6 | yes | — |
| 265 | #124 | C23×C53 | 1 | 3 | yes | — |
| 266 | #124 | C23×C53 | 1 | 36 | yes | — |
| 267 | #124 | C23×C53 | 1 | 72 | yes | — |
| 268 | #123 | C23×C53 | 1 | 36 | yes | — |
| 269 | #123 | C23×C53 | 1 | 18 | yes | — |
| 270 | #123 | C23×C53 | 1 | 18 | yes | — |
| 271 | #123 | C23×C53 | 1 | 36 | yes | — |
| 272 | #123 | C23×C53 | 1 | 36 | yes | — |
| 273 | C22⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 274 | C22⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 275 | C22⋊Q8 | C23×C53 | 1 | 18 | yes | — |
| 276 | C22⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 277 | C22⋊Q8 | C23×C53 | 1 | 36 | yes | — |
| 278 | C22⋊Q8 | C23×C53 | 1 | 72 | yes | — |
| 279 | #121 | C23×C53 | 1 | 36 | yes | — |
| 280 | #121 | C23×C53 | 1 | 36 | yes | — |
| 281 | #121 | C23×C53 | 1 | 18 | yes | — |
| 282 | #121 | C23×C53 | 1 | 36 | yes | — |
| 283 | #120 | C23×C53 | 1 | 6 | yes | — |
| 284 | #120 | C23×C53 | 1 | 18 | yes | — |
| 285 | #120 | C23×C53 | 1 | 36 | yes | — |
| 286 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 287 | C4×Q8 | C23×C53 | 1 | 36 | yes | — |
| 288 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 289 | C4×Q8 | C23×C53 | 1 | 36 | yes | — |
| 290 | C4×D4 | C23×C53 | 1 | 18 | yes | — |
| 291 | C4×D4 | C23×C53 | 1 | 18 | yes | — |
| 292 | C4×D4 | C23×C53 | 1 | 36 | yes | — |
| 293 | C4×D4 | C23×C53 | 1 | 72 | yes | — |
| 294 | #117 | C23×C53 | 1 | 9 | yes | — |
| 295 | #117 | C23×C53 | 1 | 18 | yes | — |
| 296 | #117 | C23×C53 | 1 | 18 | yes | — |
| 297 | #117 | C23×C53 | 1 | 36 | yes | — |
| 298 | C2×C22⋊C4 | C23×C53 | 1 | 36 | yes | — |
| 299 | C2×C42 | C23×C53 | 1 | 9 | yes | — |
| 300 | C24 | C24×C53 | 1 | 6 | yes | — |
| 301 | C24 | C24×C53 | 1 | 2 | yes | — |
| 302 | #41 | — | 2 | 12 | no | — |
| 303 | #41 | — | 4 | 6 | no | — |
| 304 | #41 | — | 4 | 18 | no | — |
| 305 | #41 | — | 4 | 36 | no | — |
| 306 | C2×Q8 | — | 2 | 24 | no | — |
| 307 | C2×Q8 | — | 4 | 36 | no | — |
| 308 | C2×Q8 | — | 4 | 18 | no | — |
| 309 | C2×Q8 | C24×C53 | 1 | 18 | yes | — |
| 310 | C2×Q8 | C24×C53 | 1 | 2 | yes | — |
| 311 | C2×Q8 | C24×C53 | 1 | 12 | yes | — |
| 312 | C2×Q8 | C24×C53 | 1 | 12 | yes | — |
| 313 | C2×Q8 | C24×C53 | 1 | 9 | yes | — |
| 314 | C2×Q8 | C24×C53 | 1 | 1 | yes | characteristic |
| 315 | C2×Q8 | C24×C53 | 1 | 1 | yes | characteristic |
| 316 | C2×D4 | — | 4 | 18 | no | — |
| 317 | C2×D4 | C24×C53 | 1 | 9 | yes | — |
| 318 | C2×D4 | C24×C53 | 1 | 36 | yes | — |
| 319 | C2×D4 | C24×C53 | 1 | 6 | yes | — |
| 320 | C2×D4 | C24×C53 | 1 | 18 | yes | — |
| 321 | C2×D4 | C24×C53 | 1 | 3 | yes | — |
| 322 | C2×D4 | C24×C53 | 1 | 9 | yes | — |
| 323 | C22×C4 | — | 4 | 12 | no | — |
| 324 | C22×C4 | C24×C53 | 1 | 9 | yes | — |
| 325 | C22×C4 | C24×C53 | 1 | 18 | yes | — |
| 326 | C22×C4 | C24×C53 | 1 | 18 | yes | — |
| 327 | C22×C4 | C24×C53 | 1 | 18 | yes | — |
| 328 | C22×C4 | C24×C53 | 1 | 18 | yes | — |
| 329 | C4⋊C4 | C24×C53 | 1 | 18 | yes | — |
| 330 | C4⋊C4 | C24×C53 | 1 | 18 | yes | — |
| 331 | C4⋊C4 | C24×C53 | 1 | 18 | yes | — |
| 332 | C4⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 333 | C4⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 334 | C4⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 335 | C22⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 336 | C22⋊C4 | C24×C53 | 1 | 72 | yes | — |
| 337 | C22⋊C4 | C24×C53 | 1 | 18 | yes | — |
| 338 | C22⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 339 | C22⋊C4 | C24×C53 | 1 | 18 | yes | — |
| 340 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 341 | C22⋊C4 | C24×C53 | 1 | 36 | yes | — |
| 342 | C42 | C24×C53 | 1 | 3 | yes | — |
| 343 | C42 | C24×C53 | 1 | 18 | yes | — |
| 344 | C42 | C24×C53 | 1 | 9 | yes | — |
| 345 | C42 | C24×C53 | 1 | 36 | yes | — |
| 346 | C23 | — | 4 | 2 | no | — |
| 347 | C23 | — | 4 | 4 | no | — |
| 348 | C23 | — | 4 | 6 | no | — |
| 349 | C23 | — | 4 | 12 | no | — |
| 350 | C23 | C25×C53 | 1 | 9 | yes | — |
| 351 | C23 | C25×C53 | 1 | 6 | yes | — |
| 352 | Q8 | — | 2 | 36 | no | — |
| 353 | Q8 | — | 4 | 12 | no | — |
| 354 | Q8 | — | 4 | 9 | no | — |
| 355 | Q8 | — | 4 | 2 | no | — |
| 356 | Q8 | — | 4 | 12 | no | — |
| 357 | Q8 | — | 4 | 1 | no | — |
| 358 | Q8 | H(5,𝔽2)×C53 | 1 | 4 | yes | — |
| 359 | D4 | — | 2 | 18 | no | — |
| 360 | D4 | — | 4 | 9 | no | — |
| 361 | D4 | — | 4 | 6 | no | — |
| 362 | D4 | — | 4 | 36 | no | — |
| 363 | D4 | — | 4 | 3 | no | — |
| 364 | D4 | — | 4 | 18 | no | — |
| 365 | C2×C4 | — | 2 | 36 | no | — |
| 366 | C2×C4 | — | 2 | 18 | no | — |
| 367 | C2×C4 | — | 4 | 18 | no | — |
| 368 | C2×C4 | — | 4 | 18 | no | — |
| 369 | C2×C4 | — | 4 | 18 | no | — |
| 370 | C2×C4 | C25×C53 | 1 | 18 | yes | — |
| 371 | C2×C4 | C25×C53 | 1 | 6 | yes | — |
| 372 | C2×C4 | C25×C53 | 1 | 3 | yes | — |
| 373 | C2×C4 | C25×C53 | 1 | 18 | yes | — |
| 374 | C2×C4 | C25×C53 | 1 | 3 | yes | — |
| 375 | C22 | — | 2 | 6 | no | — |
| 376 | C22 | — | 2 | 9 | no | — |
| 377 | C22 | — | 2 | 18 | no | — |
| 378 | C22 | — | 2 | 12 | no | — |
| 379 | C22 | — | 4 | 8 | no | — |
| 380 | C22 | — | 16 | 6 | no | — |
| 381 | C22 | C26×C53 | 1 | 1 | yes | characteristic |
| 382 | C4 | — | 2 | 3 | no | — |
| 383 | C4 | — | 2 | 18 | no | — |
| 384 | C4 | — | 2 | 6 | no | — |
| 385 | C4 | — | 2 | 18 | no | — |
| 386 | C4 | C2×H(5,𝔽2)×C53 | 1 | 6 | yes | — |
| 387 | C2 | — | 4 | 6 | no | — |
| 388 | C2 | — | 4 | 9 | no | — |
| 389 | C2 | C22×H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 390 | C2 | C53×2−1+6 | 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