← C53×#63036 #27270548
Subgroups — C53×#63036 #27270548
Order 13568.
6608 conjugacy classes of subgroups.
The subgroup lattice has 596 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C53×#3567 | C2 | 1 | 8 | yes | maximal, complemented |
| 2 | C53×#3562 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | C53×#3556 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C53×#3554 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C53×#3521 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | C53×#3517 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C53×#3508 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C53×#3507 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | C53×#3482 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C53×#3480 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | C53×#564 | C22 | 1 | 4 | yes | complemented |
| 12 | C53×#562 | C22 | 1 | 24 | yes | complemented |
| 13 | C53×#560 | C22 | 1 | 8 | yes | — |
| 14 | C53×#559 | C22 | 1 | 6 | yes | — |
| 15 | C53×#559 | C22 | 1 | 6 | yes | — |
| 16 | C53×#559 | C22 | 1 | 12 | yes | complemented |
| 17 | C53×#557 | C22 | 1 | 6 | yes | complemented |
| 18 | C53×#557 | C22 | 1 | 3 | yes | complemented |
| 19 | C53×#557 | C22 | 1 | 6 | yes | complemented |
| 20 | C53×#556 | C22 | 1 | 6 | yes | — |
| 21 | C53×#556 | C22 | 1 | 3 | yes | complemented |
| 22 | C53×#556 | C22 | 1 | 12 | yes | complemented |
| 23 | C53×#556 | C22 | 1 | 12 | yes | complemented |
| 24 | C53×#554 | C22 | 1 | 12 | yes | complemented |
| 25 | C53×#553 | C22 | 1 | 12 | yes | complemented |
| 26 | C53×#553 | C22 | 1 | 24 | yes | complemented |
| 27 | C53×#553 | C22 | 1 | 24 | yes | complemented |
| 28 | C53×#552 | C22 | 1 | 6 | yes | — |
| 29 | C53×#552 | C22 | 1 | 12 | yes | complemented |
| 30 | C53×#552 | C22 | 1 | 24 | yes | complemented |
| 31 | C53×#551 | C22 | 1 | 24 | yes | — |
| 32 | C53×#550 | C22 | 1 | 6 | yes | — |
| 33 | C53×#550 | C22 | 1 | 6 | yes | — |
| 34 | C53×#550 | C22 | 1 | 12 | yes | complemented |
| 35 | D4×Q8×C53 | C22 | 1 | 3 | yes | complemented |
| 36 | C53×#548 | C22 | 1 | 6 | yes | — |
| 37 | C53×#548 | C22 | 1 | 12 | yes | complemented |
| 38 | C53×#547 | C22 | 1 | 6 | yes | — |
| 39 | C53×#547 | C22 | 1 | 3 | yes | complemented |
| 40 | C53×#547 | C22 | 1 | 12 | yes | complemented |
| 41 | C53×#546 | C22 | 1 | 12 | yes | — |
| 42 | C53×#546 | C22 | 1 | 12 | yes | — |
| 43 | C53×#542 | C22 | 1 | 12 | yes | complemented |
| 44 | C53×#541 | C22 | 1 | 12 | yes | — |
| 45 | C53×#540 | C22 | 1 | 12 | yes | — |
| 46 | C53×#540 | C22 | 1 | 12 | yes | complemented |
| 47 | C53×#540 | C22 | 1 | 24 | yes | complemented |
| 48 | C53×#539 | C22 | 1 | 24 | yes | complemented |
| 49 | C53×#539 | C22 | 1 | 24 | yes | complemented |
| 50 | C53×#538 | C22 | 1 | 24 | yes | — |
| 51 | C53×#536 | C22 | 1 | 12 | yes | complemented |
| 52 | C53×#535 | C22 | 1 | 6 | yes | — |
| 53 | C53×#533 | C22 | 1 | 3 | yes | — |
| 54 | C53×#533 | C22 | 1 | 6 | yes | complemented |
| 55 | C53×#532 | C22 | 1 | 6 | yes | — |
| 56 | C53×#532 | C22 | 1 | 6 | yes | — |
| 57 | C53×#532 | C22 | 1 | 12 | yes | complemented |
| 58 | C2×#127×C53 | C22 | 1 | 1 | yes | characteristic |
| 59 | C53×#529 | C22 | 1 | 12 | yes | — |
| 60 | C53×#529 | C22 | 1 | 12 | yes | complemented |
| 61 | C53×#529 | C22 | 1 | 24 | yes | complemented |
| 62 | C53×#529 | C22 | 1 | 6 | yes | complemented |
| 63 | C53×#529 | C22 | 1 | 12 | yes | complemented |
| 64 | C2×#126×C53 | C22 | 1 | 8 | yes | — |
| 65 | C53×#520 | C22 | 1 | 12 | yes | complemented |
| 66 | C53×#518 | C22 | 1 | 6 | yes | — |
| 67 | C4×#41×C53 | C22 | 1 | 3 | yes | — |
| 68 | C4×#41×C53 | C22 | 1 | 12 | yes | complemented |
| 69 | C4×#41×C53 | C22 | 1 | 6 | yes | complemented |
| 70 | C2×C4×Q8×C53 | C22 | 1 | 6 | yes | complemented |
| 71 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 72 | C2×#41×C53 | C23 | 1 | 12 | yes | — |
| 73 | C2×#41×C53 | C23 | 1 | 6 | yes | — |
| 74 | C2×#41×C53 | C23 | 1 | 12 | yes | — |
| 75 | C22×Q8×C53 | C23 | 1 | 6 | yes | — |
| 76 | C22×D4×C53 | C23 | 1 | 6 | yes | — |
| 77 | C4⋊Q8×C53 | C23 | 1 | 3 | yes | — |
| 78 | C4⋊Q8×C53 | C23 | 1 | 3 | yes | — |
| 79 | C4⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 80 | C4⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 81 | C4⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 82 | #127×C53 | C23 | 1 | 6 | yes | — |
| 83 | #127×C53 | C23 | 1 | 2 | yes | — |
| 84 | #127×C53 | C23 | 1 | 12 | yes | — |
| 85 | #127×C53 | C23 | 1 | 8 | yes | — |
| 86 | #126×C53 | C23 | 1 | 12 | yes | — |
| 87 | #126×C53 | C23 | 1 | 24 | yes | — |
| 88 | #126×C53 | C23 | 1 | 8 | yes | — |
| 89 | #126×C53 | C23 | 1 | 8 | yes | — |
| 90 | #126×C53 | C23 | 1 | 12 | yes | — |
| 91 | #126×C53 | C23 | 1 | 24 | yes | — |
| 92 | #126×C53 | C23 | 1 | 12 | yes | — |
| 93 | #126×C53 | C23 | 1 | 8 | yes | — |
| 94 | #126×C53 | C23 | 1 | 8 | yes | — |
| 95 | #125×C53 | C23 | 1 | 12 | yes | — |
| 96 | #125×C53 | C23 | 1 | 6 | yes | — |
| 97 | #125×C53 | C23 | 1 | 24 | yes | — |
| 98 | #125×C53 | C23 | 1 | 12 | yes | — |
| 99 | #125×C53 | C23 | 1 | 6 | yes | — |
| 100 | #125×C53 | C23 | 1 | 12 | yes | — |
| 101 | #125×C53 | C23 | 1 | 24 | yes | — |
| 102 | #124×C53 | C23 | 1 | 12 | yes | — |
| 103 | #124×C53 | C23 | 1 | 12 | yes | — |
| 104 | #124×C53 | C23 | 1 | 6 | yes | — |
| 105 | #124×C53 | C23 | 1 | 12 | yes | — |
| 106 | #124×C53 | C23 | 1 | 24 | yes | — |
| 107 | #124×C53 | C23 | 1 | 12 | yes | — |
| 108 | #123×C53 | C23 | 1 | 12 | yes | — |
| 109 | #123×C53 | C23 | 1 | 12 | yes | — |
| 110 | #123×C53 | C23 | 1 | 24 | yes | — |
| 111 | #123×C53 | C23 | 1 | 24 | yes | — |
| 112 | #123×C53 | C23 | 1 | 24 | yes | — |
| 113 | #123×C53 | C23 | 1 | 24 | yes | — |
| 114 | #123×C53 | C23 | 1 | 12 | yes | — |
| 115 | #123×C53 | C23 | 1 | 24 | yes | — |
| 116 | #123×C53 | C23 | 1 | 24 | yes | — |
| 117 | C22⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 118 | C22⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 119 | C22⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 120 | C22⋊Q8×C53 | C23 | 1 | 24 | yes | — |
| 121 | C22⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 122 | C22⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 123 | C22⋊Q8×C53 | C23 | 1 | 6 | yes | — |
| 124 | C22⋊Q8×C53 | C23 | 1 | 12 | yes | — |
| 125 | C22⋊Q8×C53 | C23 | 1 | 24 | yes | — |
| 126 | C22⋊Q8×C53 | C23 | 1 | 24 | yes | — |
| 127 | #121×C53 | C23 | 1 | 12 | yes | — |
| 128 | #121×C53 | C23 | 1 | 12 | yes | — |
| 129 | #121×C53 | C23 | 1 | 24 | yes | — |
| 130 | #121×C53 | C23 | 1 | 6 | yes | — |
| 131 | #121×C53 | C23 | 1 | 12 | yes | — |
| 132 | #121×C53 | C23 | 1 | 12 | yes | — |
| 133 | #121×C53 | C23 | 1 | 12 | yes | — |
| 134 | #121×C53 | C23 | 1 | 24 | yes | — |
| 135 | #121×C53 | C23 | 1 | 24 | yes | — |
| 136 | #121×C53 | C23 | 1 | 24 | yes | — |
| 137 | #121×C53 | C23 | 1 | 24 | yes | — |
| 138 | #120×C53 | C23 | 1 | 24 | yes | — |
| 139 | C4×Q8×C53 | C23 | 1 | 3 | yes | — |
| 140 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 141 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 142 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 143 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 144 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 145 | C4×Q8×C53 | C23 | 1 | 3 | yes | — |
| 146 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 147 | C4×Q8×C53 | C23 | 1 | 6 | yes | — |
| 148 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 149 | C4×Q8×C53 | C23 | 1 | 12 | yes | — |
| 150 | C4×D4×C53 | C23 | 1 | 3 | yes | — |
| 151 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 152 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 153 | C4×D4×C53 | C23 | 1 | 3 | yes | — |
| 154 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 155 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 156 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 157 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 158 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 159 | C4×D4×C53 | C23 | 1 | 6 | yes | — |
| 160 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 161 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 162 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 163 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 164 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 165 | C4×D4×C53 | C23 | 1 | 24 | yes | — |
| 166 | C4×D4×C53 | C23 | 1 | 12 | yes | — |
| 167 | #117×C53 | C23 | 1 | 3 | yes | — |
| 168 | #117×C53 | C23 | 1 | 6 | yes | — |
| 169 | #117×C53 | C23 | 1 | 6 | yes | — |
| 170 | #117×C53 | C23 | 1 | 24 | yes | — |
| 171 | #117×C53 | C23 | 1 | 12 | yes | — |
| 172 | #117×C53 | C23 | 1 | 6 | yes | — |
| 173 | #117×C53 | C23 | 1 | 12 | yes | — |
| 174 | #117×C53 | C23 | 1 | 24 | yes | — |
| 175 | C2×C4⋊C4×C53 | C23 | 1 | 6 | yes | — |
| 176 | C2×C4⋊C4×C53 | C23 | 1 | 12 | yes | — |
| 177 | C2×C4⋊C4×C53 | C23 | 1 | 24 | yes | — |
| 178 | C2×C22⋊C4×C53 | C23 | 1 | 24 | yes | — |
| 179 | C2×C42×C53 | C23 | 1 | 6 | yes | — |
| 180 | C2×C42×C53 | C23 | 1 | 12 | yes | — |
| 181 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 182 | C2×C42×C53 | C23 | 1 | 8 | yes | — |
| 183 | C24×C53 | C24 | 1 | 4 | yes | — |
| 184 | #41×C53 | — | 4 | 6 | no | — |
| 185 | #41×C53 | — | 4 | 24 | no | — |
| 186 | #41×C53 | — | 4 | 24 | no | — |
| 187 | #41×C53 | — | 4 | 12 | no | — |
| 188 | C2×Q8×C53 | — | 4 | 12 | no | — |
| 189 | C2×Q8×C53 | C24 | 1 | 3 | yes | — |
| 190 | C2×Q8×C53 | C24 | 1 | 6 | yes | — |
| 191 | C2×Q8×C53 | C24 | 1 | 6 | yes | — |
| 192 | C2×Q8×C53 | C24 | 1 | 12 | yes | — |
| 193 | C2×D4×C53 | — | 4 | 12 | no | — |
| 194 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 195 | C2×D4×C53 | C24 | 1 | 3 | yes | — |
| 196 | C2×D4×C53 | C24 | 1 | 6 | yes | — |
| 197 | C2×D4×C53 | C24 | 1 | 24 | yes | — |
| 198 | C2×D4×C53 | C24 | 1 | 24 | yes | — |
| 199 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 200 | C2×D4×C53 | C24 | 1 | 12 | yes | — |
| 201 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 202 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 203 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 204 | C22×C4×C53 | C24 | 1 | 24 | yes | — |
| 205 | C22×C4×C53 | C24 | 1 | 12 | yes | — |
| 206 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 207 | C22×C4×C53 | C24 | 1 | 12 | yes | — |
| 208 | C22×C4×C53 | C24 | 1 | 24 | yes | — |
| 209 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 210 | C4⋊C4×C53 | C24 | 1 | 3 | yes | — |
| 211 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 212 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 213 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 214 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 215 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 216 | C4⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 217 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 218 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 219 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 220 | C4⋊C4×C53 | C24 | 1 | 3 | yes | — |
| 221 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 222 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 223 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 224 | C4⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 225 | C4⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 226 | C4⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 227 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 228 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 229 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 230 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 231 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 232 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 233 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 234 | C22⋊C4×C53 | C24 | 1 | 24 | yes | — |
| 235 | C22⋊C4×C53 | C24 | 1 | 6 | yes | — |
| 236 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 237 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 238 | C22⋊C4×C53 | C24 | 1 | 12 | yes | — |
| 239 | C42×C53 | C24 | 1 | 12 | yes | — |
| 240 | C42×C53 | C24 | 1 | 6 | yes | — |
| 241 | C42×C53 | C24 | 1 | 3 | yes | — |
| 242 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 243 | C42×C53 | C24 | 1 | 6 | yes | — |
| 244 | C42×C53 | C24 | 1 | 12 | yes | — |
| 245 | C42×C53 | C24 | 1 | 6 | yes | — |
| 246 | C42×C53 | C24 | 1 | 12 | yes | — |
| 247 | C42×C53 | C24 | 1 | 8 | yes | — |
| 248 | C42×C53 | C24 | 1 | 8 | yes | — |
| 249 | C23×C53 | — | 4 | 12 | no | — |
| 250 | C23×C53 | C25 | 1 | 6 | yes | — |
| 251 | C23×C53 | C25 | 1 | 8 | yes | — |
| 252 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 253 | Q8×C53 | — | 2 | 6 | no | — |
| 254 | Q8×C53 | — | 2 | 12 | no | — |
| 255 | Q8×C53 | — | 2 | 12 | no | — |
| 256 | Q8×C53 | — | 4 | 12 | no | — |
| 257 | D4×C53 | — | 2 | 24 | no | — |
| 258 | D4×C53 | — | 2 | 6 | no | — |
| 259 | D4×C53 | — | 4 | 12 | no | — |
| 260 | D4×C53 | — | 4 | 24 | no | — |
| 261 | D4×C53 | — | 4 | 12 | no | — |
| 262 | D4×C53 | — | 4 | 24 | no | — |
| 263 | D4×C53 | — | 4 | 6 | no | — |
| 264 | C2×C4×C53 | — | 2 | 6 | no | — |
| 265 | C2×C4×C53 | — | 2 | 12 | no | — |
| 266 | C2×C4×C53 | — | 2 | 12 | no | — |
| 267 | C2×C4×C53 | — | 4 | 12 | no | — |
| 268 | C2×C4×C53 | — | 4 | 12 | no | — |
| 269 | C2×C4×C53 | — | 4 | 24 | no | — |
| 270 | C2×C4×C53 | — | 4 | 24 | no | — |
| 271 | C2×C4×C53 | — | 4 | 6 | no | — |
| 272 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 273 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 274 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 275 | C2×C4×C53 | C25 | 1 | 12 | yes | — |
| 276 | C2×C4×C53 | C25 | 1 | 12 | yes | — |
| 277 | C2×C4×C53 | C25 | 1 | 6 | yes | — |
| 278 | C2×C4×C53 | C25 | 1 | 3 | yes | — |
| 279 | #63036 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 280 | C22×C53 | — | 2 | 6 | no | — |
| 281 | C22×C53 | — | 2 | 6 | no | — |
| 282 | C22×C53 | — | 2 | 3 | no | — |
| 283 | C22×C53 | — | 2 | 6 | no | — |
| 284 | C22×C53 | — | 2 | 24 | no | — |
| 285 | C22×C53 | — | 16 | 4 | no | — |
| 286 | C22×C53 | C26 | 1 | 1 | yes | characteristic |
| 287 | C4×C53 | — | 2 | 6 | no | — |
| 288 | C4×C53 | — | 2 | 6 | no | — |
| 289 | C4×C53 | — | 2 | 3 | no | — |
| 290 | C4×C53 | — | 2 | 12 | no | — |
| 291 | C4×C53 | — | 2 | 12 | no | — |
| 292 | C4×C53 | — | 2 | 6 | no | — |
| 293 | C4×C53 | #585 | 1 | 6 | yes | — |
| 294 | #3567 | C2×C53 | 1 | 8 | yes | complemented |
| 295 | #3562 | C2×C53 | 1 | 12 | yes | complemented |
| 296 | #3556 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 297 | #3554 | C2×C53 | 1 | 6 | yes | complemented |
| 298 | #3521 | C2×C53 | 1 | 12 | yes | complemented |
| 299 | #3517 | C2×C53 | 1 | 6 | yes | complemented |
| 300 | #3508 | C2×C53 | 1 | 3 | yes | complemented |
| 301 | #3507 | C2×C53 | 1 | 6 | yes | complemented |
| 302 | #3482 | C2×C53 | 1 | 3 | yes | complemented |
| 303 | #3480 | C2×C53 | 1 | 6 | yes | complemented |
| 304 | C2×C53 | — | 4 | 6 | no | — |
| 305 | C2×C53 | — | 4 | 8 | no | — |
| 306 | C2×C53 | — | 4 | 1 | no | — |
| 307 | C2×C53 | C2×#585 | 1 | 3 | yes | — |
| 308 | #564 | C22×C53 | 1 | 4 | yes | complemented |
| 309 | #562 | C22×C53 | 1 | 24 | yes | complemented |
| 310 | #560 | C22×C53 | 1 | 8 | yes | — |
| 311 | #559 | C22×C53 | 1 | 6 | yes | — |
| 312 | #559 | C22×C53 | 1 | 6 | yes | — |
| 313 | #559 | C22×C53 | 1 | 12 | yes | complemented |
| 314 | #557 | C22×C53 | 1 | 6 | yes | complemented |
| 315 | #557 | C22×C53 | 1 | 3 | yes | complemented |
| 316 | #557 | C22×C53 | 1 | 6 | yes | complemented |
| 317 | #556 | C22×C53 | 1 | 6 | yes | — |
| 318 | #556 | C22×C53 | 1 | 3 | yes | complemented |
| 319 | #556 | C22×C53 | 1 | 12 | yes | complemented |
| 320 | #556 | C22×C53 | 1 | 12 | yes | complemented |
| 321 | #554 | C22×C53 | 1 | 12 | yes | complemented |
| 322 | #553 | C22×C53 | 1 | 12 | yes | complemented |
| 323 | #553 | C22×C53 | 1 | 24 | yes | complemented |
| 324 | #553 | C22×C53 | 1 | 24 | yes | complemented |
| 325 | #552 | C22×C53 | 1 | 6 | yes | — |
| 326 | #552 | C22×C53 | 1 | 12 | yes | complemented |
| 327 | #552 | C22×C53 | 1 | 24 | yes | complemented |
| 328 | #551 | C22×C53 | 1 | 24 | yes | — |
| 329 | #550 | C22×C53 | 1 | 6 | yes | — |
| 330 | #550 | C22×C53 | 1 | 6 | yes | — |
| 331 | #550 | C22×C53 | 1 | 12 | yes | complemented |
| 332 | D4×Q8 | C22×C53 | 1 | 3 | yes | complemented |
| 333 | #548 | C22×C53 | 1 | 6 | yes | — |
| 334 | #548 | C22×C53 | 1 | 12 | yes | complemented |
| 335 | #547 | C22×C53 | 1 | 6 | yes | — |
| 336 | #547 | C22×C53 | 1 | 3 | yes | complemented |
| 337 | #547 | C22×C53 | 1 | 12 | yes | complemented |
| 338 | #546 | C22×C53 | 1 | 12 | yes | — |
| 339 | #546 | C22×C53 | 1 | 12 | yes | — |
| 340 | #542 | C22×C53 | 1 | 12 | yes | complemented |
| 341 | #541 | C22×C53 | 1 | 12 | yes | — |
| 342 | #540 | C22×C53 | 1 | 12 | yes | — |
| 343 | #540 | C22×C53 | 1 | 12 | yes | complemented |
| 344 | #540 | C22×C53 | 1 | 24 | yes | complemented |
| 345 | #539 | C22×C53 | 1 | 24 | yes | complemented |
| 346 | #539 | C22×C53 | 1 | 24 | yes | complemented |
| 347 | #538 | C22×C53 | 1 | 24 | yes | — |
| 348 | #536 | C22×C53 | 1 | 12 | yes | complemented |
| 349 | #535 | C22×C53 | 1 | 6 | yes | — |
| 350 | #533 | C22×C53 | 1 | 3 | yes | — |
| 351 | #533 | C22×C53 | 1 | 6 | yes | complemented |
| 352 | #532 | C22×C53 | 1 | 6 | yes | — |
| 353 | #532 | C22×C53 | 1 | 6 | yes | — |
| 354 | #532 | C22×C53 | 1 | 12 | yes | complemented |
| 355 | C2×#127 | C22×C53 | 1 | 1 | yes | characteristic |
| 356 | #529 | C22×C53 | 1 | 12 | yes | — |
| 357 | #529 | C22×C53 | 1 | 12 | yes | complemented |
| 358 | #529 | C22×C53 | 1 | 24 | yes | complemented |
| 359 | #529 | C22×C53 | 1 | 6 | yes | complemented |
| 360 | #529 | C22×C53 | 1 | 12 | yes | complemented |
| 361 | C2×#126 | C22×C53 | 1 | 8 | yes | — |
| 362 | #520 | C22×C53 | 1 | 12 | yes | complemented |
| 363 | #518 | C22×C53 | 1 | 6 | yes | — |
| 364 | C4×#41 | C22×C53 | 1 | 3 | yes | — |
| 365 | C4×#41 | C22×C53 | 1 | 12 | yes | complemented |
| 366 | C4×#41 | C22×C53 | 1 | 6 | yes | complemented |
| 367 | C2×C4×Q8 | C22×C53 | 1 | 6 | yes | complemented |
| 368 | C53 | #63036 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 369 | C2×#41 | C23×C53 | 1 | 3 | yes | — |
| 370 | C2×#41 | C23×C53 | 1 | 12 | yes | — |
| 371 | C2×#41 | C23×C53 | 1 | 6 | yes | — |
| 372 | C2×#41 | C23×C53 | 1 | 12 | yes | — |
| 373 | C22×Q8 | C23×C53 | 1 | 6 | yes | — |
| 374 | C22×D4 | C23×C53 | 1 | 6 | yes | — |
| 375 | C4⋊Q8 | C23×C53 | 1 | 3 | yes | — |
| 376 | C4⋊Q8 | C23×C53 | 1 | 3 | yes | — |
| 377 | C4⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 378 | C4⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 379 | C4⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 380 | #127 | C23×C53 | 1 | 6 | yes | — |
| 381 | #127 | C23×C53 | 1 | 2 | yes | — |
| 382 | #127 | C23×C53 | 1 | 12 | yes | — |
| 383 | #127 | C23×C53 | 1 | 8 | yes | — |
| 384 | #126 | C23×C53 | 1 | 12 | yes | — |
| 385 | #126 | C23×C53 | 1 | 24 | yes | — |
| 386 | #126 | C23×C53 | 1 | 8 | yes | — |
| 387 | #126 | C23×C53 | 1 | 8 | yes | — |
| 388 | #126 | C23×C53 | 1 | 12 | yes | — |
| 389 | #126 | C23×C53 | 1 | 24 | yes | — |
| 390 | #126 | C23×C53 | 1 | 12 | yes | — |
| 391 | #126 | C23×C53 | 1 | 8 | yes | — |
| 392 | #126 | C23×C53 | 1 | 8 | yes | — |
| 393 | #125 | C23×C53 | 1 | 12 | yes | — |
| 394 | #125 | C23×C53 | 1 | 6 | yes | — |
| 395 | #125 | C23×C53 | 1 | 24 | yes | — |
| 396 | #125 | C23×C53 | 1 | 12 | yes | — |
| 397 | #125 | C23×C53 | 1 | 6 | yes | — |
| 398 | #125 | C23×C53 | 1 | 12 | yes | — |
| 399 | #125 | C23×C53 | 1 | 24 | yes | — |
| 400 | #124 | C23×C53 | 1 | 12 | yes | — |
| 401 | #124 | C23×C53 | 1 | 12 | yes | — |
| 402 | #124 | C23×C53 | 1 | 6 | yes | — |
| 403 | #124 | C23×C53 | 1 | 12 | yes | — |
| 404 | #124 | C23×C53 | 1 | 24 | yes | — |
| 405 | #124 | C23×C53 | 1 | 12 | yes | — |
| 406 | #123 | C23×C53 | 1 | 12 | yes | — |
| 407 | #123 | C23×C53 | 1 | 12 | yes | — |
| 408 | #123 | C23×C53 | 1 | 24 | yes | — |
| 409 | #123 | C23×C53 | 1 | 24 | yes | — |
| 410 | #123 | C23×C53 | 1 | 24 | yes | — |
| 411 | #123 | C23×C53 | 1 | 24 | yes | — |
| 412 | #123 | C23×C53 | 1 | 12 | yes | — |
| 413 | #123 | C23×C53 | 1 | 24 | yes | — |
| 414 | #123 | C23×C53 | 1 | 24 | yes | — |
| 415 | C22⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 416 | C22⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 417 | C22⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 418 | C22⋊Q8 | C23×C53 | 1 | 24 | yes | — |
| 419 | C22⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 420 | C22⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 421 | C22⋊Q8 | C23×C53 | 1 | 6 | yes | — |
| 422 | C22⋊Q8 | C23×C53 | 1 | 12 | yes | — |
| 423 | C22⋊Q8 | C23×C53 | 1 | 24 | yes | — |
| 424 | C22⋊Q8 | C23×C53 | 1 | 24 | yes | — |
| 425 | #121 | C23×C53 | 1 | 12 | yes | — |
| 426 | #121 | C23×C53 | 1 | 12 | yes | — |
| 427 | #121 | C23×C53 | 1 | 24 | yes | — |
| 428 | #121 | C23×C53 | 1 | 6 | yes | — |
| 429 | #121 | C23×C53 | 1 | 12 | yes | — |
| 430 | #121 | C23×C53 | 1 | 12 | yes | — |
| 431 | #121 | C23×C53 | 1 | 12 | yes | — |
| 432 | #121 | C23×C53 | 1 | 24 | yes | — |
| 433 | #121 | C23×C53 | 1 | 24 | yes | — |
| 434 | #121 | C23×C53 | 1 | 24 | yes | — |
| 435 | #121 | C23×C53 | 1 | 24 | yes | — |
| 436 | #120 | C23×C53 | 1 | 24 | yes | — |
| 437 | C4×Q8 | C23×C53 | 1 | 3 | yes | — |
| 438 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 439 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 440 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 441 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 442 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 443 | C4×Q8 | C23×C53 | 1 | 3 | yes | — |
| 444 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 445 | C4×Q8 | C23×C53 | 1 | 6 | yes | — |
| 446 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 447 | C4×Q8 | C23×C53 | 1 | 12 | yes | — |
| 448 | C4×D4 | C23×C53 | 1 | 3 | yes | — |
| 449 | C4×D4 | C23×C53 | 1 | 6 | yes | — |
| 450 | C4×D4 | C23×C53 | 1 | 6 | yes | — |
| 451 | C4×D4 | C23×C53 | 1 | 3 | yes | — |
| 452 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 453 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 454 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 455 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 456 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 457 | C4×D4 | C23×C53 | 1 | 6 | yes | — |
| 458 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 459 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 460 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 461 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 462 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 463 | C4×D4 | C23×C53 | 1 | 24 | yes | — |
| 464 | C4×D4 | C23×C53 | 1 | 12 | yes | — |
| 465 | #117 | C23×C53 | 1 | 3 | yes | — |
| 466 | #117 | C23×C53 | 1 | 6 | yes | — |
| 467 | #117 | C23×C53 | 1 | 6 | yes | — |
| 468 | #117 | C23×C53 | 1 | 24 | yes | — |
| 469 | #117 | C23×C53 | 1 | 12 | yes | — |
| 470 | #117 | C23×C53 | 1 | 6 | yes | — |
| 471 | #117 | C23×C53 | 1 | 12 | yes | — |
| 472 | #117 | C23×C53 | 1 | 24 | yes | — |
| 473 | C2×C4⋊C4 | C23×C53 | 1 | 6 | yes | — |
| 474 | C2×C4⋊C4 | C23×C53 | 1 | 12 | yes | — |
| 475 | C2×C4⋊C4 | C23×C53 | 1 | 24 | yes | — |
| 476 | C2×C22⋊C4 | C23×C53 | 1 | 24 | yes | — |
| 477 | C2×C42 | C23×C53 | 1 | 6 | yes | — |
| 478 | C2×C42 | C23×C53 | 1 | 12 | yes | — |
| 479 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 480 | C2×C42 | C23×C53 | 1 | 8 | yes | — |
| 481 | C24 | C24×C53 | 1 | 4 | yes | — |
| 482 | #41 | — | 4 | 6 | no | — |
| 483 | #41 | — | 4 | 24 | no | — |
| 484 | #41 | — | 4 | 24 | no | — |
| 485 | #41 | — | 4 | 12 | no | — |
| 486 | C2×Q8 | — | 4 | 12 | no | — |
| 487 | C2×Q8 | C24×C53 | 1 | 3 | yes | — |
| 488 | C2×Q8 | C24×C53 | 1 | 6 | yes | — |
| 489 | C2×Q8 | C24×C53 | 1 | 6 | yes | — |
| 490 | C2×Q8 | C24×C53 | 1 | 12 | yes | — |
| 491 | C2×D4 | — | 4 | 12 | no | — |
| 492 | C2×D4 | C24×C53 | 1 | 12 | yes | — |
| 493 | C2×D4 | C24×C53 | 1 | 3 | yes | — |
| 494 | C2×D4 | C24×C53 | 1 | 6 | yes | — |
| 495 | C2×D4 | C24×C53 | 1 | 24 | yes | — |
| 496 | C2×D4 | C24×C53 | 1 | 24 | yes | — |
| 497 | C2×D4 | C24×C53 | 1 | 12 | yes | — |
| 498 | C2×D4 | C24×C53 | 1 | 12 | yes | — |
| 499 | C22×C4 | C24×C53 | 1 | 6 | yes | — |
| 500 | C22×C4 | C24×C53 | 1 | 6 | yes | — |
| 501 | C22×C4 | C24×C53 | 1 | 3 | yes | — |
| 502 | C22×C4 | C24×C53 | 1 | 24 | yes | — |
| 503 | C22×C4 | C24×C53 | 1 | 12 | yes | — |
| 504 | C22×C4 | C24×C53 | 1 | 6 | yes | — |
| 505 | C22×C4 | C24×C53 | 1 | 12 | yes | — |
| 506 | C22×C4 | C24×C53 | 1 | 24 | yes | — |
| 507 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 508 | C4⋊C4 | C24×C53 | 1 | 3 | yes | — |
| 509 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 510 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 511 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 512 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 513 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 514 | C4⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 515 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 516 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 517 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 518 | C4⋊C4 | C24×C53 | 1 | 3 | yes | — |
| 519 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 520 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 521 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 522 | C4⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 523 | C4⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 524 | C4⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 525 | C22⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 526 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 527 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 528 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 529 | C22⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 530 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 531 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 532 | C22⋊C4 | C24×C53 | 1 | 24 | yes | — |
| 533 | C22⋊C4 | C24×C53 | 1 | 6 | yes | — |
| 534 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 535 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 536 | C22⋊C4 | C24×C53 | 1 | 12 | yes | — |
| 537 | C42 | C24×C53 | 1 | 12 | yes | — |
| 538 | C42 | C24×C53 | 1 | 6 | yes | — |
| 539 | C42 | C24×C53 | 1 | 3 | yes | — |
| 540 | C42 | C24×C53 | 1 | 1 | yes | characteristic |
| 541 | C42 | C24×C53 | 1 | 6 | yes | — |
| 542 | C42 | C24×C53 | 1 | 12 | yes | — |
| 543 | C42 | C24×C53 | 1 | 6 | yes | — |
| 544 | C42 | C24×C53 | 1 | 12 | yes | — |
| 545 | C42 | C24×C53 | 1 | 8 | yes | — |
| 546 | C42 | C24×C53 | 1 | 8 | yes | — |
| 547 | C23 | — | 4 | 12 | no | — |
| 548 | C23 | C25×C53 | 1 | 1 | yes | characteristic |
| 549 | C23 | C25×C53 | 1 | 8 | yes | — |
| 550 | C23 | C25×C53 | 1 | 6 | yes | — |
| 551 | Q8 | — | 2 | 6 | no | — |
| 552 | Q8 | — | 2 | 12 | no | — |
| 553 | Q8 | — | 2 | 12 | no | — |
| 554 | Q8 | — | 4 | 12 | no | — |
| 555 | D4 | — | 2 | 24 | no | — |
| 556 | D4 | — | 2 | 6 | no | — |
| 557 | D4 | — | 4 | 12 | no | — |
| 558 | D4 | — | 4 | 24 | no | — |
| 559 | D4 | — | 4 | 12 | no | — |
| 560 | D4 | — | 4 | 24 | no | — |
| 561 | D4 | — | 4 | 6 | no | — |
| 562 | C2×C4 | — | 2 | 6 | no | — |
| 563 | C2×C4 | — | 2 | 12 | no | — |
| 564 | C2×C4 | — | 2 | 12 | no | — |
| 565 | C2×C4 | — | 4 | 12 | no | — |
| 566 | C2×C4 | — | 4 | 12 | no | — |
| 567 | C2×C4 | — | 4 | 24 | no | — |
| 568 | C2×C4 | — | 4 | 24 | no | — |
| 569 | C2×C4 | — | 4 | 6 | no | — |
| 570 | C2×C4 | C25×C53 | 1 | 6 | yes | — |
| 571 | C2×C4 | C25×C53 | 1 | 6 | yes | — |
| 572 | C2×C4 | C25×C53 | 1 | 12 | yes | — |
| 573 | C2×C4 | C25×C53 | 1 | 12 | yes | — |
| 574 | C2×C4 | C25×C53 | 1 | 3 | yes | — |
| 575 | C2×C4 | C25×C53 | 1 | 6 | yes | — |
| 576 | C2×C4 | C25×C53 | 1 | 3 | yes | — |
| 577 | C22 | — | 2 | 6 | no | — |
| 578 | C22 | — | 2 | 6 | no | — |
| 579 | C22 | — | 2 | 3 | no | — |
| 580 | C22 | — | 2 | 6 | no | — |
| 581 | C22 | — | 2 | 24 | no | — |
| 582 | C22 | — | 16 | 4 | no | — |
| 583 | C22 | C26×C53 | 1 | 1 | yes | characteristic |
| 584 | C4 | — | 2 | 6 | no | — |
| 585 | C4 | — | 2 | 6 | no | — |
| 586 | C4 | — | 2 | 3 | no | — |
| 587 | C4 | — | 2 | 12 | no | — |
| 588 | C4 | — | 2 | 12 | no | — |
| 589 | C4 | — | 2 | 6 | no | — |
| 590 | C4 | C53×#585 | 1 | 6 | yes | — |
| 591 | C2 | — | 4 | 1 | no | — |
| 592 | C2 | — | 4 | 8 | no | — |
| 593 | C2 | — | 4 | 6 | no | — |
| 594 | C2 | C2×C53×#585 | 1 | 3 | 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