← C53×#63035 #27270547
Subgroups — C53×#63035 #27270547
Order 13568.
7236 conjugacy classes of subgroups.
The subgroup lattice has 566 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C53×#3551 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | C53×#3550 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C53×#3546 | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | C53×#3514 | C2 | 1 | 12 | yes | maximal, complemented |
| 5 | C53×#3508 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C53×#3500 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C53×#3498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C53×#3497 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C53×#3483 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C53×#3482 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C53×#3480 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | C2×2−1+4×C53 | C22 | 1 | 4 | yes | complemented |
| 13 | C2×H(5,𝔽2)×C53 | C22 | 1 | 2 | yes | — |
| 14 | C53×#563 | C22 | 1 | 12 | yes | complemented |
| 15 | C53×#560 | C22 | 1 | 24 | yes | complemented |
| 16 | C53×#559 | C22 | 1 | 12 | yes | complemented |
| 17 | C53×#559 | C22 | 1 | 6 | yes | complemented |
| 18 | Q82×C53 | C22 | 1 | 3 | yes | complemented |
| 19 | C53×#557 | C22 | 1 | 2 | yes | complemented |
| 20 | C53×#556 | C22 | 1 | 12 | yes | complemented |
| 21 | C53×#556 | C22 | 1 | 6 | yes | complemented |
| 22 | C53×#555 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C53×#555 | C22 | 1 | 12 | yes | complemented |
| 24 | C53×#555 | C22 | 1 | 12 | yes | complemented |
| 25 | C53×#553 | C22 | 1 | 24 | yes | complemented |
| 26 | C53×#552 | C22 | 1 | 12 | yes | complemented |
| 27 | C53×#551 | C22 | 1 | 24 | yes | complemented |
| 28 | C53×#550 | C22 | 1 | 4 | yes | — |
| 29 | C53×#550 | C22 | 1 | 6 | yes | complemented |
| 30 | C53×#550 | C22 | 1 | 12 | yes | complemented |
| 31 | C53×#550 | C22 | 1 | 12 | yes | complemented |
| 32 | D4×Q8×C53 | C22 | 1 | 2 | yes | complemented |
| 33 | D4×Q8×C53 | C22 | 1 | 12 | yes | complemented |
| 34 | C53×#548 | C22 | 1 | 4 | yes | — |
| 35 | C53×#548 | C22 | 1 | 8 | yes | complemented |
| 36 | C53×#548 | C22 | 1 | 24 | yes | complemented |
| 37 | C53×#547 | C22 | 1 | 6 | yes | complemented |
| 38 | C53×#546 | C22 | 1 | 24 | yes | complemented |
| 39 | C53×#546 | C22 | 1 | 24 | yes | complemented |
| 40 | C53×#546 | C22 | 1 | 24 | yes | complemented |
| 41 | D42×C53 | C22 | 1 | 12 | yes | — |
| 42 | C53×#542 | C22 | 1 | 24 | yes | complemented |
| 43 | C53×#540 | C22 | 1 | 24 | yes | complemented |
| 44 | C53×#538 | C22 | 1 | 48 | yes | complemented |
| 45 | C53×#537 | C22 | 1 | 24 | yes | complemented |
| 46 | C53×#536 | C22 | 1 | 12 | yes | complemented |
| 47 | C53×#535 | C22 | 1 | 6 | yes | — |
| 48 | C53×#535 | C22 | 1 | 12 | yes | complemented |
| 49 | C53×#535 | C22 | 1 | 12 | yes | complemented |
| 50 | C53×#533 | C22 | 1 | 6 | yes | complemented |
| 51 | C53×#532 | C22 | 1 | 3 | yes | — |
| 52 | C53×#532 | C22 | 1 | 12 | yes | complemented |
| 53 | C53×#532 | C22 | 1 | 12 | yes | complemented |
| 54 | C53×#532 | C22 | 1 | 12 | yes | complemented |
| 55 | C53×#532 | C22 | 1 | 12 | yes | complemented |
| 56 | C2×#127×C53 | C22 | 1 | 3 | yes | — |
| 57 | C53×#529 | C22 | 1 | 24 | yes | complemented |
| 58 | C53×#529 | C22 | 1 | 12 | yes | complemented |
| 59 | C2×#124×C53 | C22 | 1 | 12 | yes | complemented |
| 60 | C53×#518 | C22 | 1 | 12 | yes | complemented |
| 61 | C4×#41×C53 | C22 | 1 | 1 | yes | characteristic |
| 62 | C4×#41×C53 | C22 | 1 | 4 | yes | complemented |
| 63 | C4×#41×C53 | C22 | 1 | 12 | yes | complemented |
| 64 | C4×#41×C53 | C22 | 1 | 6 | yes | complemented |
| 65 | C2×C4×Q8×C53 | C22 | 1 | 4 | yes | complemented |
| 66 | 2−1+4×C53 | — | 4 | 16 | no | — |
| 67 | H(5,𝔽2)×C53 | — | 4 | 8 | no | — |
| 68 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×#41×C53 | C23 | 1 | 4 | yes | — |
| 70 | C2×#41×C53 | C23 | 1 | 12 | yes | — |
| 71 | C2×#41×C53 | C23 | 1 | 6 | yes | — |
| 72 | C2×#41×C53 | C23 | 1 | 6 | yes | — |
| 73 | C2×#41×C53 | C23 | 1 | 12 | yes | — |
| 74 | C2×#41×C53 | C23 | 1 | 24 | yes | — |
| 75 | C22×Q8×C53 | C23 | 1 | 4 | yes | — |
| 76 | C22×Q8×C53 | C23 | 1 | 12 | yes | — |
| 77 | C22×D4×C53 | C23 | 1 | 12 | yes | — |
| 78 | C22×D4×C53 | C23 | 1 | 12 | yes | — |
| 79 | C22×D4×C53 | C23 | 1 | 6 | yes | — |
| 80 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 81 | C4⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 82 | C4⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 83 | C4⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 84 | C4⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 85 | #127×C53 | C23 | 1 | 3 | yes | — |
| 86 | #127×C53 | C23 | 1 | 12 | yes | — |
| 87 | #127×C53 | C23 | 1 | 6 | yes | — |
| 88 | #127×C53 | C23 | 1 | 12 | yes | — |
| 89 | #127×C53 | C23 | 1 | 12 | yes | — |
| 90 | #126×C53 | C23 | 1 | 24 | yes | — |
| 91 | #126×C53 | C23 | 1 | 48 | yes | — |
| 92 | #125×C53 | C23 | 1 | 12 | yes | — |
| 93 | #125×C53 | C23 | 1 | 12 | yes | — |
| 94 | #124×C53 | C23 | 1 | 12 | yes | — |
| 95 | #124×C53 | C23 | 1 | 12 | yes | — |
| 96 | #124×C53 | C23 | 1 | 24 | yes | — |
| 97 | #124×C53 | C23 | 1 | 24 | yes | — |
| 98 | #124×C53 | C23 | 1 | 6 | yes | — |
| 99 | #124×C53 | C23 | 1 | 4 | yes | — |
| 100 | #124×C53 | C23 | 1 | 24 | yes | — |
| 101 | #124×C53 | C23 | 1 | 24 | yes | — |
| 102 | #123×C53 | C23 | 1 | 24 | yes | — |
| 103 | #123×C53 | C23 | 1 | 48 | yes | — |
| 104 | #123×C53 | C23 | 1 | 24 | yes | — |
| 105 | #123×C53 | C23 | 1 | 24 | yes | — |
| 106 | C22⋊Q8×C53 | C23 | 1 | 24 | yes | — |
| 107 | C22⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 108 | C22⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 109 | C22⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 110 | C22⋊Q8×C53 | C23 | 1 | 48 | yes | — |
| 111 | #121×C53 | C23 | 1 | 24 | yes | — |
| 112 | #121×C53 | C23 | 1 | 12 | yes | — |
| 113 | #121×C53 | C23 | 1 | 12 | yes | — |
| 114 | #121×C53 | C23 | 1 | 12 | yes | — |
| 115 | #121×C53 | C23 | 1 | 4 | yes | — |
| 116 | #121×C53 | C23 | 1 | 24 | yes | — |
| 117 | #121×C53 | C23 | 1 | 24 | yes | — |
| 118 | #121×C53 | C23 | 1 | 24 | yes | — |
| 119 | #121×C53 | C23 | 1 | 24 | yes | — |
| 120 | #121×C53 | C23 | 1 | 24 | yes | — |
| 121 | #121×C53 | C23 | 1 | 24 | yes | — |
| 122 | #121×C53 | C23 | 1 | 48 | yes | — |
| 123 | #120×C53 | C23 | 1 | 24 | yes | — |
| 124 | #120×C53 | C23 | 1 | 48 | yes | — |
| 125 | C4×Q8×C53 | C23 | 1 | 2 | yes | — |
| 126 | C4×Q8×C53 | C23 | 1 | 4 | yes | — |
| 127 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 128 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 129 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 130 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 131 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 132 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 133 | C4×D4×C53 | C23 | 1 | 2 | yes | — |
| 134 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 135 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 136 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 137 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 138 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 139 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 140 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 141 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 142 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 143 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 144 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 145 | #117×C53 | C23 | 1 | 3 | yes | — |
| 146 | #117×C53 | C23 | 1 | 4 | yes | — |
| 147 | #117×C53 | C23 | 1 | 6 | yes | — |
| 148 | #117×C53 | C23 | 1 | 24 | yes | — |
| 149 | #117×C53 | C23 | 1 | 12 | yes | — |
| 150 | #117×C53 | C23 | 1 | 12 | yes | — |
| 151 | #117×C53 | C23 | 1 | 12 | yes | — |
| 152 | C2×C4⋊C4×C53 | C23 | 1 | 12 | yes | — |
| 153 | C2×C22⋊C4×C53 | C23 | 1 | 48 | yes | — |
| 154 | C2×C42×C53 | C23 | 1 | 12 | yes | — |
| 155 | C2×C42×C53 | C23 | 1 | 3 | yes | — |
| 156 | C2×C42×C53 | C23 | 1 | 12 | yes | — |
| 157 | C24×C53 | C24 | 1 | 12 | yes | — |
| 158 | #41×C53 | — | 2 | 4 | no | — |
| 159 | #41×C53 | — | 2 | 16 | no | — |
| 160 | #41×C53 | — | 4 | 12 | no | — |
| 161 | #41×C53 | — | 4 | 24 | no | — |
| 162 | #41×C53 | — | 4 | 12 | no | — |
| 163 | #41×C53 | — | 4 | 24 | no | — |
| 164 | #41×C53 | — | 4 | 48 | no | — |
| 165 | C2×Q8×C53 | — | 2 | 16 | no | — |
| 166 | C2×Q8×C53 | — | 4 | 24 | no | — |
| 167 | C2×Q8×C53 | C24 | 1 | 6 | yes | — |
| 168 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 169 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 170 | C2×Q8×C53 | C24 | 1 | 2 | yes | — |
| 171 | C2×Q8×C53 | C24 | 1 | 1 | yes | characteristic |
| 172 | C2×D4×C53 | — | 4 | 24 | no | — |
| 173 | C2×D4×C53 | — | 4 | 12 | no | — |
| 174 | C2×D4×C53 | — | 4 | 24 | no | — |
| 175 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 176 | C2×D4×C53 | C24 | 1 | 2 | yes | — |
| 177 | C2×D4×C53 | C24 | 1 | 3 | yes | — |
| 178 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 179 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 180 | C2×D4×C53 | C24 | 1 | 24 | yes | — |
| 181 | C2×D4×C53 | C24 | 1 | 24 | yes | — |
| 182 | C2×D4×C53 | C24 | 1 | 24 | yes | — |
| 183 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 184 | C2×D4×C53 | C24 | 1 | 4 | yes | — |
| 185 | C2×D4×C53 | C24 | 1 | 6 | yes | — |
| 186 | C22×C4×C53 | C24 | 1 | 4 | yes | — |
| 187 | C22×C4×C53 | C24 | 1 | 12 | yes | — |
| 188 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 189 | C22×C4×C53 | C24 | 1 | 12 | yes | — |
| 190 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 191 | C22×C4×C53 | C24 | 1 | 24 | yes | — |
| 192 | C22×C4×C53 | C24 | 1 | 12 | yes | — |
| 193 | C22×C4×C53 | C24 | 1 | 24 | yes | — |
| 194 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 195 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 196 | C4⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 197 | C4⋊C4×C53 | C24 | 1 | 2 | yes | — |
| 198 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 199 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 200 | C4⋊C4×C53 | C24 | 1 | 4 | yes | — |
| 201 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 202 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 203 | C4⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 204 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 205 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 206 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 207 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 208 | C22⋊C4×C53 | C24 | 1 | 48 | yes | — |
| 209 | C22⋊C4×C53 | C24 | 1 | 4 | yes | — |
| 210 | C22⋊C4×C53 | C24 | 1 | 8 | yes | — |
| 211 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 212 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 213 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 214 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 215 | C42×C53 | C24 | 1 | 4 | yes | — |
| 216 | C42×C53 | C24 | 1 | 12 | yes | — |
| 217 | C42×C53 | C24 | 1 | 6 | yes | — |
| 218 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 219 | C42×C53 | C24 | 1 | 3 | yes | — |
| 220 | C42×C53 | C24 | 1 | 12 | yes | — |
| 221 | C42×C53 | C24 | 1 | 12 | yes | — |
| 222 | C42×C53 | C24 | 1 | 12 | yes | — |
| 223 | C23×C53 | — | 4 | 12 | no | — |
| 224 | C23×C53 | — | 4 | 24 | no | — |
| 225 | C23×C53 | C25 | 1 | 4 | yes | — |
| 226 | C23×C53 | C25 | 1 | 12 | yes | — |
| 227 | C23×C53 | C25 | 1 | 3 | yes | — |
| 228 | Q8×C53 | — | 2 | 24 | no | — |
| 229 | Q8×C53 | — | 2 | 12 | no | — |
| 230 | Q8×C53 | — | 4 | 12 | no | — |
| 231 | Q8×C53 | — | 4 | 2 | no | — |
| 232 | Q8×C53 | H(5,𝔽2) | 1 | 4 | yes | — |
| 233 | D4×C53 | — | 2 | 6 | no | — |
| 234 | D4×C53 | — | 2 | 24 | no | — |
| 235 | D4×C53 | — | 2 | 24 | no | — |
| 236 | D4×C53 | — | 2 | 4 | no | — |
| 237 | D4×C53 | — | 4 | 6 | no | — |
| 238 | D4×C53 | — | 4 | 12 | no | — |
| 239 | D4×C53 | — | 4 | 24 | no | — |
| 240 | D4×C53 | — | 4 | 24 | no | — |
| 241 | D4×C53 | — | 4 | 12 | no | — |
| 242 | D4×C53 | — | 4 | 4 | no | — |
| 243 | D4×C53 | — | 4 | 24 | no | — |
| 244 | C2×C4×C53 | — | 2 | 6 | no | — |
| 245 | C2×C4×C53 | — | 2 | 24 | no | — |
| 246 | C2×C4×C53 | — | 2 | 24 | no | — |
| 247 | C2×C4×C53 | — | 2 | 12 | no | — |
| 248 | C2×C4×C53 | — | 2 | 8 | no | — |
| 249 | C2×C4×C53 | — | 4 | 24 | no | — |
| 250 | C2×C4×C53 | — | 4 | 24 | no | — |
| 251 | C2×C4×C53 | — | 4 | 12 | no | — |
| 252 | C2×C4×C53 | C25 | 1 | 4 | yes | — |
| 253 | C2×C4×C53 | C25 | 1 | 12 | yes | — |
| 254 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C53 | C25 | 1 | 4 | yes | — |
| 256 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 257 | C2×C4×C53 | C25 | 1 | 12 | yes | — |
| 258 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 259 | C2×C4×C53 | C25 | 1 | 2 | yes | — |
| 260 | #63035 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 261 | C22×C53 | — | 2 | 4 | no | — |
| 262 | C22×C53 | — | 2 | 12 | no | — |
| 263 | C22×C53 | — | 2 | 3 | no | — |
| 264 | C22×C53 | — | 2 | 4 | no | — |
| 265 | C22×C53 | — | 2 | 6 | no | — |
| 266 | C22×C53 | — | 2 | 4 | no | — |
| 267 | C22×C53 | — | 2 | 24 | no | — |
| 268 | C22×C53 | — | 16 | 12 | no | — |
| 269 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 270 | C4×C53 | — | 2 | 1 | no | — |
| 271 | C4×C53 | — | 2 | 4 | no | — |
| 272 | C4×C53 | — | 2 | 12 | no | — |
| 273 | C4×C53 | — | 2 | 4 | no | — |
| 274 | C4×C53 | — | 2 | 6 | no | — |
| 275 | C4×C53 | — | 2 | 12 | no | — |
| 276 | C4×C53 | C2×H(5,𝔽2) | 1 | 6 | yes | — |
| 277 | C4×C53 | #585 | 1 | 4 | yes | — |
| 278 | #3551 | C2×C53 | 1 | 12 | yes | complemented |
| 279 | #3550 | C2×C53 | 1 | 3 | yes | complemented |
| 280 | #3546 | C2×C53 | 1 | 12 | yes | complemented |
| 281 | #3514 | C2×C53 | 1 | 12 | yes | complemented |
| 282 | #3508 | C2×C53 | 1 | 6 | yes | complemented |
| 283 | #3500 | C2×C53 | 1 | 4 | yes | complemented |
| 284 | #3498 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 285 | #3497 | C2×C53 | 1 | 4 | yes | complemented |
| 286 | #3483 | C2×C53 | 1 | 3 | yes | complemented |
| 287 | #3482 | C2×C53 | 1 | 2 | yes | complemented |
| 288 | #3480 | C2×C53 | 1 | 4 | yes | complemented |
| 289 | C2×C53 | — | 4 | 4 | no | — |
| 290 | C2×C53 | — | 4 | 12 | no | — |
| 291 | C2×C53 | — | 4 | 3 | no | — |
| 292 | C2×C53 | C22×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 293 | C2×C53 | C2×#585 | 1 | 2 | yes | — |
| 294 | C2×2−1+4 | C22×C53 | 1 | 4 | yes | complemented |
| 295 | C2×H(5,𝔽2) | C22×C53 | 1 | 2 | yes | — |
| 296 | #563 | C22×C53 | 1 | 12 | yes | complemented |
| 297 | #560 | C22×C53 | 1 | 24 | yes | complemented |
| 298 | #559 | C22×C53 | 1 | 12 | yes | complemented |
| 299 | #559 | C22×C53 | 1 | 6 | yes | complemented |
| 300 | Q82 | C22×C53 | 1 | 3 | yes | complemented |
| 301 | #557 | C22×C53 | 1 | 2 | yes | complemented |
| 302 | #556 | C22×C53 | 1 | 12 | yes | complemented |
| 303 | #556 | C22×C53 | 1 | 6 | yes | complemented |
| 304 | #555 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 305 | #555 | C22×C53 | 1 | 12 | yes | complemented |
| 306 | #555 | C22×C53 | 1 | 12 | yes | complemented |
| 307 | #553 | C22×C53 | 1 | 24 | yes | complemented |
| 308 | #552 | C22×C53 | 1 | 12 | yes | complemented |
| 309 | #551 | C22×C53 | 1 | 24 | yes | complemented |
| 310 | #550 | C22×C53 | 1 | 4 | yes | — |
| 311 | #550 | C22×C53 | 1 | 6 | yes | complemented |
| 312 | #550 | C22×C53 | 1 | 12 | yes | complemented |
| 313 | #550 | C22×C53 | 1 | 12 | yes | complemented |
| 314 | D4×Q8 | C22×C53 | 1 | 2 | yes | complemented |
| 315 | D4×Q8 | C22×C53 | 1 | 12 | yes | complemented |
| 316 | #548 | C22×C53 | 1 | 4 | yes | — |
| 317 | #548 | C22×C53 | 1 | 8 | yes | complemented |
| 318 | #548 | C22×C53 | 1 | 24 | yes | complemented |
| 319 | #547 | C22×C53 | 1 | 6 | yes | complemented |
| 320 | #546 | C22×C53 | 1 | 24 | yes | complemented |
| 321 | #546 | C22×C53 | 1 | 24 | yes | complemented |
| 322 | #546 | C22×C53 | 1 | 24 | yes | complemented |
| 323 | D42 | C22×C53 | 1 | 12 | yes | — |
| 324 | #542 | C22×C53 | 1 | 24 | yes | complemented |
| 325 | #540 | C22×C53 | 1 | 24 | yes | complemented |
| 326 | #538 | C22×C53 | 1 | 48 | yes | complemented |
| 327 | #537 | C22×C53 | 1 | 24 | yes | complemented |
| 328 | #536 | C22×C53 | 1 | 12 | yes | complemented |
| 329 | #535 | C22×C53 | 1 | 6 | yes | — |
| 330 | #535 | C22×C53 | 1 | 12 | yes | complemented |
| 331 | #535 | C22×C53 | 1 | 12 | yes | complemented |
| 332 | #533 | C22×C53 | 1 | 6 | yes | complemented |
| 333 | #532 | C22×C53 | 1 | 3 | yes | — |
| 334 | #532 | C22×C53 | 1 | 12 | yes | complemented |
| 335 | #532 | C22×C53 | 1 | 12 | yes | complemented |
| 336 | #532 | C22×C53 | 1 | 12 | yes | complemented |
| 337 | #532 | C22×C53 | 1 | 12 | yes | complemented |
| 338 | C2×#127 | C22×C53 | 1 | 3 | yes | — |
| 339 | #529 | C22×C53 | 1 | 24 | yes | complemented |
| 340 | #529 | C22×C53 | 1 | 12 | yes | complemented |
| 341 | C2×#124 | C22×C53 | 1 | 12 | yes | complemented |
| 342 | #518 | C22×C53 | 1 | 12 | yes | complemented |
| 343 | C4×#41 | C22×C53 | 1 | 1 | yes | characteristic |
| 344 | C4×#41 | C22×C53 | 1 | 4 | yes | complemented |
| 345 | C4×#41 | C22×C53 | 1 | 12 | yes | complemented |
| 346 | C4×#41 | C22×C53 | 1 | 6 | yes | complemented |
| 347 | C2×C4×Q8 | C22×C53 | 1 | 4 | yes | complemented |
| 348 | C53 | #63035 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 349 | 2−1+4 | — | 4 | 16 | no | — |
| 350 | H(5,𝔽2) | — | 4 | 8 | no | — |
| 351 | C2×#41 | C23×C53 | 1 | 1 | yes | characteristic |
| 352 | C2×#41 | C23×C53 | 1 | 4 | yes | — |
| 353 | C2×#41 | C23×C53 | 1 | 12 | yes | — |
| 354 | C2×#41 | C23×C53 | 1 | 6 | yes | — |
| 355 | C2×#41 | C23×C53 | 1 | 6 | yes | — |
| 356 | C2×#41 | C23×C53 | 1 | 12 | yes | — |
| 357 | C2×#41 | C23×C53 | 1 | 24 | yes | — |
| 358 | C22×Q8 | C23×C53 | 1 | 4 | yes | — |
| 359 | C22×Q8 | C23×C53 | 1 | 12 | yes | — |
| 360 | C22×D4 | C23×C53 | 1 | 12 | yes | — |
| 361 | C22×D4 | C23×C53 | 1 | 12 | yes | — |
| 362 | C22×D4 | C23×C53 | 1 | 6 | yes | — |
| 363 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 364 | C4⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 365 | C4⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 366 | C4⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 367 | C4⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 368 | #127 | C23×C53 | 1 | 3 | yes | — |
| 369 | #127 | C23×C53 | 1 | 12 | yes | — |
| 370 | #127 | C23×C53 | 1 | 6 | yes | — |
| 371 | #127 | C23×C53 | 1 | 12 | yes | — |
| 372 | #127 | C23×C53 | 1 | 12 | yes | — |
| 373 | #126 | C23×C53 | 1 | 24 | yes | — |
| 374 | #126 | C23×C53 | 1 | 48 | yes | — |
| 375 | #125 | C23×C53 | 1 | 12 | yes | — |
| 376 | #125 | C23×C53 | 1 | 12 | yes | — |
| 377 | #124 | C23×C53 | 1 | 12 | yes | — |
| 378 | #124 | C23×C53 | 1 | 12 | yes | — |
| 379 | #124 | C23×C53 | 1 | 24 | yes | — |
| 380 | #124 | C23×C53 | 1 | 24 | yes | — |
| 381 | #124 | C23×C53 | 1 | 6 | yes | — |
| 382 | #124 | C23×C53 | 1 | 4 | yes | — |
| 383 | #124 | C23×C53 | 1 | 24 | yes | — |
| 384 | #124 | C23×C53 | 1 | 24 | yes | — |
| 385 | #123 | C23×C53 | 1 | 24 | yes | — |
| 386 | #123 | C23×C53 | 1 | 48 | yes | — |
| 387 | #123 | C23×C53 | 1 | 24 | yes | — |
| 388 | #123 | C23×C53 | 1 | 24 | yes | — |
| 389 | C22⋊Q8 | C23×C53 | 1 | 24 | yes | — |
| 390 | C22⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 391 | C22⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 392 | C22⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 393 | C22⋊Q8 | C23×C53 | 1 | 48 | yes | — |
| 394 | #121 | C23×C53 | 1 | 24 | yes | — |
| 395 | #121 | C23×C53 | 1 | 12 | yes | — |
| 396 | #121 | C23×C53 | 1 | 12 | yes | — |
| 397 | #121 | C23×C53 | 1 | 12 | yes | — |
| 398 | #121 | C23×C53 | 1 | 4 | yes | — |
| 399 | #121 | C23×C53 | 1 | 24 | yes | — |
| 400 | #121 | C23×C53 | 1 | 24 | yes | — |
| 401 | #121 | C23×C53 | 1 | 24 | yes | — |
| 402 | #121 | C23×C53 | 1 | 24 | yes | — |
| 403 | #121 | C23×C53 | 1 | 24 | yes | — |
| 404 | #121 | C23×C53 | 1 | 24 | yes | — |
| 405 | #121 | C23×C53 | 1 | 48 | yes | — |
| 406 | #120 | C23×C53 | 1 | 24 | yes | — |
| 407 | #120 | C23×C53 | 1 | 48 | yes | — |
| 408 | C4×Q8 | C23×C53 | 1 | 2 | yes | — |
| 409 | C4×Q8 | C23×C53 | 1 | 4 | yes | — |
| 410 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 411 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 412 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 413 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 414 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 415 | C4×D4 | C23×C53 | 1 | 6 | yes | — |
| 416 | C4×D4 | C23×C53 | 1 | 2 | yes | — |
| 417 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 418 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 419 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 420 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 421 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 422 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 423 | C4×D4 | C23×C53 | 1 | 6 | yes | — |
| 424 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 425 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 426 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 427 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 428 | #117 | C23×C53 | 1 | 3 | yes | — |
| 429 | #117 | C23×C53 | 1 | 4 | yes | — |
| 430 | #117 | C23×C53 | 1 | 6 | yes | — |
| 431 | #117 | C23×C53 | 1 | 24 | yes | — |
| 432 | #117 | C23×C53 | 1 | 12 | yes | — |
| 433 | #117 | C23×C53 | 1 | 12 | yes | — |
| 434 | #117 | C23×C53 | 1 | 12 | yes | — |
| 435 | C2×C4⋊C4 | C23×C53 | 1 | 12 | yes | — |
| 436 | C2×C22⋊C4 | C23×C53 | 1 | 48 | yes | — |
| 437 | C2×C42 | C23×C53 | 1 | 12 | yes | — |
| 438 | C2×C42 | C23×C53 | 1 | 3 | yes | — |
| 439 | C2×C42 | C23×C53 | 1 | 12 | yes | — |
| 440 | C24 | C24×C53 | 1 | 12 | yes | — |
| 441 | #41 | — | 2 | 4 | no | — |
| 442 | #41 | — | 2 | 16 | no | — |
| 443 | #41 | — | 4 | 12 | no | — |
| 444 | #41 | — | 4 | 24 | no | — |
| 445 | #41 | — | 4 | 12 | no | — |
| 446 | #41 | — | 4 | 24 | no | — |
| 447 | #41 | — | 4 | 48 | no | — |
| 448 | C2×Q8 | — | 2 | 16 | no | — |
| 449 | C2×Q8 | — | 4 | 24 | no | — |
| 450 | C2×Q8 | C24×C53 | 1 | 6 | yes | — |
| 451 | C2×Q8 | C24×C53 | 1 | 12 | yes | — |
| 452 | C2×Q8 | C24×C53 | 1 | 12 | yes | — |
| 453 | C2×Q8 | C24×C53 | 1 | 2 | yes | — |
| 454 | C2×Q8 | C24×C53 | 1 | 1 | yes | characteristic |
| 455 | C2×D4 | — | 4 | 24 | no | — |
| 456 | C2×D4 | — | 4 | 12 | no | — |
| 457 | C2×D4 | — | 4 | 24 | no | — |
| 458 | C2×D4 | C24×C53 | 1 | 12 | yes | — |
| 459 | C2×D4 | C24×C53 | 1 | 2 | yes | — |
| 460 | C2×D4 | C24×C53 | 1 | 3 | yes | — |
| 461 | C2×D4 | C24×C53 | 1 | 12 | yes | — |
| 462 | C2×D4 | C24×C53 | 1 | 12 | yes | — |
| 463 | C2×D4 | C24×C53 | 1 | 24 | yes | — |
| 464 | C2×D4 | C24×C53 | 1 | 24 | yes | — |
| 465 | C2×D4 | C24×C53 | 1 | 24 | yes | — |
| 466 | C2×D4 | C24×C53 | 1 | 12 | yes | — |
| 467 | C2×D4 | C24×C53 | 1 | 4 | yes | — |
| 468 | C2×D4 | C24×C53 | 1 | 6 | yes | — |
| 469 | C22×C4 | C24×C53 | 1 | 4 | yes | — |
| 470 | C22×C4 | C24×C53 | 1 | 12 | yes | — |
| 471 | C22×C4 | C24×C53 | 1 | 6 | yes | — |
| 472 | C22×C4 | C24×C53 | 1 | 12 | yes | — |
| 473 | C22×C4 | C24×C53 | 1 | 3 | yes | — |
| 474 | C22×C4 | C24×C53 | 1 | 24 | yes | — |
| 475 | C22×C4 | C24×C53 | 1 | 12 | yes | — |
| 476 | C22×C4 | C24×C53 | 1 | 24 | yes | — |
| 477 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 478 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 479 | C4⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 480 | C4⋊C4 | C24×C53 | 1 | 2 | yes | — |
| 481 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 482 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 483 | C4⋊C4 | C24×C53 | 1 | 4 | yes | — |
| 484 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 485 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 486 | C4⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 487 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 488 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 489 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 490 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 491 | C22⋊C4 | C24×C53 | 1 | 48 | yes | — |
| 492 | C22⋊C4 | C24×C53 | 1 | 4 | yes | — |
| 493 | C22⋊C4 | C24×C53 | 1 | 8 | yes | — |
| 494 | C22⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 495 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 496 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 497 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 498 | C42 | C24×C53 | 1 | 4 | yes | — |
| 499 | C42 | C24×C53 | 1 | 12 | yes | — |
| 500 | C42 | C24×C53 | 1 | 6 | yes | — |
| 501 | C42 | C24×C53 | 1 | 1 | yes | characteristic |
| 502 | C42 | C24×C53 | 1 | 3 | yes | — |
| 503 | C42 | C24×C53 | 1 | 12 | yes | — |
| 504 | C42 | C24×C53 | 1 | 12 | yes | — |
| 505 | C42 | C24×C53 | 1 | 12 | yes | — |
| 506 | C23 | — | 4 | 12 | no | — |
| 507 | C23 | — | 4 | 24 | no | — |
| 508 | C23 | C25×C53 | 1 | 3 | yes | — |
| 509 | C23 | C25×C53 | 1 | 12 | yes | — |
| 510 | C23 | C25×C53 | 1 | 4 | yes | — |
| 511 | Q8 | — | 2 | 24 | no | — |
| 512 | Q8 | — | 2 | 12 | no | — |
| 513 | Q8 | — | 4 | 12 | no | — |
| 514 | Q8 | — | 4 | 2 | no | — |
| 515 | Q8 | H(5,𝔽2)×C53 | 1 | 4 | yes | — |
| 516 | D4 | — | 2 | 6 | no | — |
| 517 | D4 | — | 2 | 24 | no | — |
| 518 | D4 | — | 2 | 24 | no | — |
| 519 | D4 | — | 2 | 4 | no | — |
| 520 | D4 | — | 4 | 6 | no | — |
| 521 | D4 | — | 4 | 12 | no | — |
| 522 | D4 | — | 4 | 24 | no | — |
| 523 | D4 | — | 4 | 24 | no | — |
| 524 | D4 | — | 4 | 12 | no | — |
| 525 | D4 | — | 4 | 4 | no | — |
| 526 | D4 | — | 4 | 24 | no | — |
| 527 | C2×C4 | — | 2 | 6 | no | — |
| 528 | C2×C4 | — | 2 | 24 | no | — |
| 529 | C2×C4 | — | 2 | 24 | no | — |
| 530 | C2×C4 | — | 2 | 12 | no | — |
| 531 | C2×C4 | — | 2 | 8 | no | — |
| 532 | C2×C4 | — | 4 | 24 | no | — |
| 533 | C2×C4 | — | 4 | 24 | no | — |
| 534 | C2×C4 | — | 4 | 12 | no | — |
| 535 | C2×C4 | C25×C53 | 1 | 4 | yes | — |
| 536 | C2×C4 | C25×C53 | 1 | 12 | yes | — |
| 537 | C2×C4 | C25×C53 | 1 | 6 | yes | — |
| 538 | C2×C4 | C25×C53 | 1 | 4 | yes | — |
| 539 | C2×C4 | C25×C53 | 1 | 1 | yes | characteristic |
| 540 | C2×C4 | C25×C53 | 1 | 12 | yes | — |
| 541 | C2×C4 | C25×C53 | 1 | 3 | yes | — |
| 542 | C2×C4 | C25×C53 | 1 | 2 | yes | — |
| 543 | C22 | — | 2 | 4 | no | — |
| 544 | C22 | — | 2 | 12 | no | — |
| 545 | C22 | — | 2 | 3 | no | — |
| 546 | C22 | — | 2 | 4 | no | — |
| 547 | C22 | — | 2 | 6 | no | — |
| 548 | C22 | — | 2 | 4 | no | — |
| 549 | C22 | — | 2 | 24 | no | — |
| 550 | C22 | — | 16 | 12 | no | — |
| 551 | C22 | C26×C53 | 1 | 1 | yes | characteristic |
| 552 | C4 | — | 2 | 1 | no | — |
| 553 | C4 | — | 2 | 4 | no | — |
| 554 | C4 | — | 2 | 12 | no | — |
| 555 | C4 | — | 2 | 4 | no | — |
| 556 | C4 | — | 2 | 6 | no | — |
| 557 | C4 | — | 2 | 12 | no | — |
| 558 | C4 | C2×H(5,𝔽2)×C53 | 1 | 6 | yes | — |
| 559 | C4 | C53×#585 | 1 | 4 | yes | — |
| 560 | C2 | — | 4 | 3 | no | — |
| 561 | C2 | — | 4 | 12 | no | — |
| 562 | C2 | — | 4 | 4 | no | — |
| 563 | C2 | C22×H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 564 | C2 | C2×C53×#585 | 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