← C53×#19240 #27226752
Subgroups — C53×#19240 #27226752
Order 13568.
584 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C53×#3249 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C53×#3209 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C53×#3165 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C53×#2962 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C53×#1694 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C53×#1692 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C53×#1674 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C53×#1672 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C53×#1565 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C53×#1542 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C2×C53×#332 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C53×#533 | C22 | 1 | 1 | yes | characteristic |
| 13 | C53×#533 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C4⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 15 | C53×#501 | — | 2 | 2 | no | — |
| 16 | C53×#500 | C22 | 1 | 2 | yes | — |
| 17 | C53×#498 | C22 | 1 | 2 | yes | — |
| 18 | C53×#494 | — | 2 | 1 | no | — |
| 19 | C53×#487 | — | 2 | 1 | no | — |
| 20 | C53×#477 | — | 2 | 1 | no | — |
| 21 | C53×#477 | C22 | 1 | 2 | yes | — |
| 22 | C53×#467 | — | 2 | 2 | no | — |
| 23 | C53×#462 | — | 2 | 1 | no | — |
| 24 | C53×#462 | C22 | 1 | 2 | yes | — |
| 25 | C53×#462 | C22 | 1 | 2 | yes | — |
| 26 | C53×#462 | C22 | 1 | 2 | yes | — |
| 27 | C53×#451 | — | 2 | 2 | no | — |
| 28 | C53×#446 | — | 2 | 2 | no | — |
| 29 | C53×#446 | C22 | 1 | 2 | yes | — |
| 30 | C8×Q8×C53 | C22 | 1 | 2 | yes | — |
| 31 | C53×#431 | C22 | 1 | 1 | yes | characteristic |
| 32 | C53×#428 | — | 2 | 1 | no | — |
| 33 | C53×#428 | — | 2 | 1 | no | — |
| 34 | C53×#424 | — | 2 | 1 | no | — |
| 35 | C2×C4⋊C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×C4⋊C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 37 | C53×#405 | — | 2 | 1 | no | — |
| 38 | C4×M16×C53 | C22 | 1 | 1 | yes | characteristic |
| 39 | C53×#335 | C22 | 1 | 2 | yes | — |
| 40 | C53×#334 | C22 | 1 | 2 | yes | — |
| 41 | C53×#333 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×#333 | C22 | 1 | 1 | yes | characteristic |
| 43 | C53×#332 | C22 | 1 | 2 | yes | — |
| 44 | C53×#332 | C22 | 1 | 1 | yes | characteristic |
| 45 | C53×#332 | C22 | 1 | 2 | yes | — |
| 46 | C53×#332 | C22 | 1 | 1 | yes | characteristic |
| 47 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 48 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 49 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 50 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 51 | C2×M16×C53 | D4 | 1 | 1 | yes | characteristic |
| 52 | C2×M16×C53 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×C8×C53 | — | 2 | 1 | no | — |
| 54 | C22×C8×C53 | — | 2 | 1 | no | — |
| 55 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 56 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 57 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 58 | C4⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 59 | C4⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 61 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 62 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 63 | #125×C53 | — | 2 | 1 | no | — |
| 64 | #125×C53 | — | 2 | 1 | no | — |
| 65 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 66 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 67 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 68 | C22⋊Q8×C53 | D4 | 1 | 2 | yes | — |
| 69 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 70 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 71 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 72 | C4×Q8×C53 | C23 | 1 | 2 | yes | — |
| 73 | #117×C53 | — | 2 | 1 | no | — |
| 74 | #117×C53 | — | 2 | 1 | no | — |
| 75 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 76 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 77 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 78 | #107×C53 | — | 2 | 2 | no | — |
| 79 | #107×C53 | — | 2 | 2 | no | — |
| 80 | #107×C53 | — | 2 | 2 | no | — |
| 81 | #106×C53 | — | 2 | 2 | no | — |
| 82 | #106×C53 | — | 2 | 2 | no | — |
| 83 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 84 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 85 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 86 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 87 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 88 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 89 | C4⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 90 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 92 | #103×C53 | — | 2 | 2 | no | — |
| 93 | #103×C53 | — | 2 | 2 | no | — |
| 94 | #103×C53 | — | 2 | 2 | no | — |
| 95 | #103×C53 | — | 2 | 2 | no | — |
| 96 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 97 | #97×C53 | — | 2 | 2 | no | — |
| 98 | #97×C53 | D4 | 1 | 2 | yes | — |
| 99 | C4×C8×C53 | — | 2 | 2 | no | — |
| 100 | C4×C8×C53 | — | 2 | 1 | no | — |
| 101 | C4×C8×C53 | C23 | 1 | 2 | yes | — |
| 102 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 103 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 104 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 105 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 106 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 107 | C2×Q8×C53 | — | 8 | 1 | no | — |
| 108 | C2×Q8×C53 | — | 8 | 1 | no | — |
| 109 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 110 | C22×C4×C53 | — | 4 | 1 | no | — |
| 111 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C22×C4×C53 | #41 | 1 | 1 | yes | characteristic |
| 114 | Q16×C53 | — | 8 | 2 | no | — |
| 115 | Q16×C53 | — | 8 | 2 | no | — |
| 116 | Q16×C53 | — | 8 | 2 | no | — |
| 117 | M16×C53 | — | 2 | 2 | no | — |
| 118 | M16×C53 | Q16 | 1 | 4 | yes | complemented |
| 119 | C2×C8×C53 | — | 2 | 1 | no | — |
| 120 | C2×C8×C53 | — | 2 | 1 | no | — |
| 121 | C2×C8×C53 | — | 2 | 1 | no | — |
| 122 | C2×C8×C53 | — | 2 | 1 | no | — |
| 123 | C2×C8×C53 | — | 2 | 2 | no | — |
| 124 | C2×C8×C53 | — | 4 | 2 | no | — |
| 125 | C2×C8×C53 | — | 8 | 1 | no | — |
| 126 | C2×C8×C53 | C2×D4 | 1 | 2 | yes | — |
| 127 | C2×C8×C53 | C2×D4 | 1 | 2 | yes | — |
| 128 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 129 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 130 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 131 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 132 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 133 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 134 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 135 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 136 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 137 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 138 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 139 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 140 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 141 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 142 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 143 | C4⋊C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 144 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 145 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 146 | C42×C53 | — | 2 | 2 | no | — |
| 147 | C42×C53 | — | 4 | 1 | no | — |
| 148 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C42×C53 | #41 | 1 | 1 | yes | characteristic |
| 151 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 152 | C23×C53 | #121 | 1 | 1 | yes | characteristic |
| 153 | Q8×C53 | — | 2 | 2 | no | — |
| 154 | Q8×C53 | — | 2 | 2 | no | — |
| 155 | Q8×C53 | — | 4 | 2 | no | — |
| 156 | Q8×C53 | — | 4 | 1 | no | — |
| 157 | Q8×C53 | — | 4 | 1 | no | — |
| 158 | Q8×C53 | — | 4 | 2 | no | — |
| 159 | Q8×C53 | — | 8 | 1 | no | — |
| 160 | Q8×C53 | — | 8 | 2 | no | — |
| 161 | Q8×C53 | — | 8 | 1 | no | — |
| 162 | C2×C4×C53 | — | 2 | 1 | no | — |
| 163 | C2×C4×C53 | — | 2 | 1 | no | — |
| 164 | C2×C4×C53 | — | 2 | 2 | no | — |
| 165 | C2×C4×C53 | — | 2 | 2 | no | — |
| 166 | C2×C4×C53 | — | 4 | 1 | no | — |
| 167 | C2×C4×C53 | — | 4 | 2 | no | — |
| 168 | C2×C4×C53 | — | 4 | 1 | no | — |
| 169 | C2×C4×C53 | — | 4 | 1 | no | — |
| 170 | C2×C4×C53 | — | 8 | 2 | no | — |
| 171 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C53 | C2×Q16 | 1 | 2 | yes | — |
| 175 | C2×C4×C53 | #137 | 1 | 2 | yes | — |
| 176 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 179 | C8×C53 | — | 2 | 2 | no | — |
| 180 | C8×C53 | — | 4 | 1 | no | — |
| 181 | C8×C53 | — | 4 | 1 | no | — |
| 182 | C8×C53 | — | 4 | 2 | no | — |
| 183 | C8×C53 | — | 4 | 1 | no | — |
| 184 | C8×C53 | — | 4 | 1 | no | — |
| 185 | C8×C53 | C2×Q16 | 1 | 4 | yes | — |
| 186 | #19240 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 187 | C22×C53 | — | 2 | 1 | no | — |
| 188 | C22×C53 | — | 2 | 1 | no | — |
| 189 | C22×C53 | #462 | 1 | 2 | yes | — |
| 190 | C22×C53 | C2×#121 | 1 | 1 | yes | characteristic |
| 191 | C4×C53 | — | 2 | 1 | no | — |
| 192 | C4×C53 | — | 2 | 1 | no | — |
| 193 | C4×C53 | — | 2 | 1 | no | — |
| 194 | C4×C53 | — | 4 | 2 | no | — |
| 195 | C4×C53 | — | 4 | 2 | no | — |
| 196 | C4×C53 | — | 8 | 2 | no | — |
| 197 | C4×C53 | — | 8 | 1 | no | — |
| 198 | C4×C53 | — | 8 | 1 | no | — |
| 199 | C4×C53 | #462 | 1 | 2 | yes | — |
| 200 | C4×C53 | C22×Q16 | 1 | 1 | yes | characteristic |
| 201 | C4×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 202 | C4×C53 | #576 | 1 | 1 | yes | characteristic |
| 203 | C4×C53 | #577 | 1 | 1 | yes | characteristic |
| 204 | #3249 | C2×C53 | 1 | 1 | yes | characteristic |
| 205 | #3209 | C2×C53 | 1 | 1 | yes | characteristic |
| 206 | #3165 | C2×C53 | 1 | 1 | yes | characteristic |
| 207 | #2962 | C2×C53 | 1 | 1 | yes | characteristic |
| 208 | #1694 | C2×C53 | 1 | 2 | yes | complemented |
| 209 | #1692 | C2×C53 | 1 | 2 | yes | complemented |
| 210 | #1674 | C2×C53 | 1 | 2 | yes | complemented |
| 211 | #1672 | C2×C53 | 1 | 2 | yes | complemented |
| 212 | #1565 | C2×C53 | 1 | 1 | yes | characteristic |
| 213 | #1542 | C2×C53 | 1 | 1 | yes | characteristic |
| 214 | C2×#332 | C2×C53 | 1 | 1 | yes | characteristic |
| 215 | C2×C53 | — | 2 | 2 | no | — |
| 216 | C2×C53 | C2×#462 | 1 | 1 | yes | characteristic |
| 217 | C2×C53 | #3062 | 1 | 1 | yes | characteristic |
| 218 | C2×C53 | #3069 | 1 | 1 | yes | characteristic |
| 219 | #533 | C22×C53 | 1 | 1 | yes | characteristic |
| 220 | #533 | C22×C53 | 1 | 1 | yes | characteristic |
| 221 | C2×C4⋊Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 222 | #501 | — | 2 | 2 | no | — |
| 223 | #500 | C22×C53 | 1 | 2 | yes | — |
| 224 | #498 | C22×C53 | 1 | 2 | yes | — |
| 225 | #494 | — | 2 | 1 | no | — |
| 226 | #487 | — | 2 | 1 | no | — |
| 227 | #477 | — | 2 | 1 | no | — |
| 228 | #477 | C22×C53 | 1 | 2 | yes | — |
| 229 | #467 | — | 2 | 2 | no | — |
| 230 | #462 | — | 2 | 1 | no | — |
| 231 | #462 | C22×C53 | 1 | 2 | yes | — |
| 232 | #462 | C22×C53 | 1 | 2 | yes | — |
| 233 | #462 | C22×C53 | 1 | 2 | yes | — |
| 234 | #451 | — | 2 | 2 | no | — |
| 235 | #446 | — | 2 | 2 | no | — |
| 236 | #446 | C22×C53 | 1 | 2 | yes | — |
| 237 | C8×Q8 | C22×C53 | 1 | 2 | yes | — |
| 238 | #431 | C22×C53 | 1 | 1 | yes | characteristic |
| 239 | #428 | — | 2 | 1 | no | — |
| 240 | #428 | — | 2 | 1 | no | — |
| 241 | #424 | — | 2 | 1 | no | — |
| 242 | C2×C4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 243 | C2×C4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 244 | #405 | — | 2 | 1 | no | — |
| 245 | C4×M16 | C22×C53 | 1 | 1 | yes | characteristic |
| 246 | #335 | C22×C53 | 1 | 2 | yes | — |
| 247 | #334 | C22×C53 | 1 | 2 | yes | — |
| 248 | #333 | C22×C53 | 1 | 1 | yes | characteristic |
| 249 | #333 | C22×C53 | 1 | 1 | yes | characteristic |
| 250 | #332 | C22×C53 | 1 | 2 | yes | — |
| 251 | #332 | C22×C53 | 1 | 2 | yes | — |
| 252 | #332 | C22×C53 | 1 | 1 | yes | characteristic |
| 253 | #332 | C22×C53 | 1 | 1 | yes | characteristic |
| 254 | C53 | #19240 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 255 | C22×Q8 | — | 2 | 1 | no | — |
| 256 | C2×Q16 | — | 2 | 2 | no | — |
| 257 | C2×Q16 | — | 2 | 2 | no | — |
| 258 | C2×Q16 | — | 2 | 2 | no | — |
| 259 | C2×M16 | D4×C53 | 1 | 1 | yes | characteristic |
| 260 | C2×M16 | D4×C53 | 1 | 1 | yes | characteristic |
| 261 | C22×C8 | — | 2 | 1 | no | — |
| 262 | C22×C8 | — | 2 | 1 | no | — |
| 263 | C4⋊Q8 | — | 2 | 1 | no | — |
| 264 | C4⋊Q8 | — | 2 | 1 | no | — |
| 265 | C4⋊Q8 | — | 2 | 1 | no | — |
| 266 | C4⋊Q8 | D4×C53 | 1 | 1 | yes | characteristic |
| 267 | C4⋊Q8 | D4×C53 | 1 | 1 | yes | characteristic |
| 268 | C4⋊Q8 | C23×C53 | 1 | 2 | yes | — |
| 269 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 270 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 271 | #125 | — | 2 | 1 | no | — |
| 272 | #125 | — | 2 | 1 | no | — |
| 273 | C22⋊Q8 | — | 2 | 1 | no | — |
| 274 | C22⋊Q8 | — | 2 | 1 | no | — |
| 275 | C22⋊Q8 | — | 2 | 1 | no | — |
| 276 | C22⋊Q8 | D4×C53 | 1 | 2 | yes | — |
| 277 | C4×Q8 | — | 2 | 1 | no | — |
| 278 | C4×Q8 | — | 2 | 1 | no | — |
| 279 | C4×Q8 | — | 2 | 1 | no | — |
| 280 | C4×Q8 | C23×C53 | 1 | 2 | yes | — |
| 281 | #117 | — | 2 | 1 | no | — |
| 282 | #117 | — | 2 | 1 | no | — |
| 283 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 284 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 285 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 286 | #107 | — | 2 | 2 | no | — |
| 287 | #107 | — | 2 | 2 | no | — |
| 288 | #107 | — | 2 | 2 | no | — |
| 289 | #106 | — | 2 | 2 | no | — |
| 290 | #106 | — | 2 | 2 | no | — |
| 291 | C4⋊C8 | — | 2 | 2 | no | — |
| 292 | C4⋊C8 | — | 2 | 2 | no | — |
| 293 | C4⋊C8 | — | 2 | 1 | no | — |
| 294 | C4⋊C8 | — | 2 | 1 | no | — |
| 295 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 296 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 297 | C4⋊C8 | C23×C53 | 1 | 2 | yes | — |
| 298 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 299 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 300 | #103 | — | 2 | 2 | no | — |
| 301 | #103 | — | 2 | 2 | no | — |
| 302 | #103 | — | 2 | 2 | no | — |
| 303 | #103 | — | 2 | 2 | no | — |
| 304 | C22⋊C8 | — | 2 | 1 | no | — |
| 305 | #97 | — | 2 | 2 | no | — |
| 306 | #97 | D4×C53 | 1 | 2 | yes | — |
| 307 | C4×C8 | — | 2 | 2 | no | — |
| 308 | C4×C8 | — | 2 | 1 | no | — |
| 309 | C4×C8 | C23×C53 | 1 | 2 | yes | — |
| 310 | C2×Q8 | — | 2 | 1 | no | — |
| 311 | C2×Q8 | — | 2 | 1 | no | — |
| 312 | C2×Q8 | — | 2 | 2 | no | — |
| 313 | C2×Q8 | — | 2 | 1 | no | — |
| 314 | C2×Q8 | — | 4 | 1 | no | — |
| 315 | C2×Q8 | — | 8 | 1 | no | — |
| 316 | C2×Q8 | — | 8 | 1 | no | — |
| 317 | C2×Q8 | C2×D4×C53 | 1 | 2 | yes | — |
| 318 | C22×C4 | — | 4 | 1 | no | — |
| 319 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 320 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 321 | C22×C4 | #41×C53 | 1 | 1 | yes | characteristic |
| 322 | Q16 | — | 8 | 2 | no | — |
| 323 | Q16 | — | 8 | 2 | no | — |
| 324 | Q16 | — | 8 | 2 | no | — |
| 325 | M16 | — | 2 | 2 | no | — |
| 326 | M16 | Q16×C53 | 1 | 4 | yes | complemented |
| 327 | C2×C8 | — | 2 | 1 | no | — |
| 328 | C2×C8 | — | 2 | 1 | no | — |
| 329 | C2×C8 | — | 2 | 1 | no | — |
| 330 | C2×C8 | — | 2 | 1 | no | — |
| 331 | C2×C8 | — | 2 | 2 | no | — |
| 332 | C2×C8 | — | 4 | 2 | no | — |
| 333 | C2×C8 | — | 8 | 1 | no | — |
| 334 | C2×C8 | C2×D4×C53 | 1 | 2 | yes | — |
| 335 | C2×C8 | C2×D4×C53 | 1 | 2 | yes | — |
| 336 | C4⋊C4 | — | 2 | 1 | no | — |
| 337 | C4⋊C4 | — | 2 | 1 | no | — |
| 338 | C4⋊C4 | — | 2 | 1 | no | — |
| 339 | C4⋊C4 | — | 2 | 2 | no | — |
| 340 | C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C4⋊C4 | — | 2 | 1 | no | — |
| 342 | C4⋊C4 | — | 2 | 1 | no | — |
| 343 | C4⋊C4 | — | 2 | 2 | no | — |
| 344 | C4⋊C4 | — | 2 | 1 | no | — |
| 345 | C4⋊C4 | — | 2 | 2 | no | — |
| 346 | C4⋊C4 | — | 2 | 1 | no | — |
| 347 | C4⋊C4 | — | 4 | 1 | no | — |
| 348 | C4⋊C4 | — | 4 | 1 | no | — |
| 349 | C4⋊C4 | — | 4 | 1 | no | — |
| 350 | C4⋊C4 | — | 4 | 1 | no | — |
| 351 | C4⋊C4 | C2×D4×C53 | 1 | 2 | yes | — |
| 352 | C22⋊C4 | — | 2 | 2 | no | — |
| 353 | C22⋊C4 | — | 4 | 1 | no | — |
| 354 | C42 | — | 2 | 2 | no | — |
| 355 | C42 | — | 4 | 1 | no | — |
| 356 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 357 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 358 | C42 | #41×C53 | 1 | 1 | yes | characteristic |
| 359 | C42 | C24×C53 | 1 | 1 | yes | characteristic |
| 360 | C23 | #121×C53 | 1 | 1 | yes | characteristic |
| 361 | Q8 | — | 2 | 2 | no | — |
| 362 | Q8 | — | 2 | 2 | no | — |
| 363 | Q8 | — | 4 | 1 | no | — |
| 364 | Q8 | — | 4 | 2 | no | — |
| 365 | Q8 | — | 4 | 2 | no | — |
| 366 | Q8 | — | 4 | 1 | no | — |
| 367 | Q8 | — | 8 | 1 | no | — |
| 368 | Q8 | — | 8 | 1 | no | — |
| 369 | Q8 | — | 8 | 2 | no | — |
| 370 | C2×C4 | — | 2 | 1 | no | — |
| 371 | C2×C4 | — | 2 | 1 | no | — |
| 372 | C2×C4 | — | 2 | 2 | no | — |
| 373 | C2×C4 | — | 2 | 2 | no | — |
| 374 | C2×C4 | — | 4 | 1 | no | — |
| 375 | C2×C4 | — | 4 | 1 | no | — |
| 376 | C2×C4 | — | 4 | 1 | no | — |
| 377 | C2×C4 | — | 4 | 2 | no | — |
| 378 | C2×C4 | — | 8 | 2 | no | — |
| 379 | C2×C4 | #121×C53 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | #121×C53 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | #121×C53 | 1 | 1 | yes | characteristic |
| 382 | C2×C4 | C2×Q16×C53 | 1 | 2 | yes | — |
| 383 | C2×C4 | #137×C53 | 1 | 2 | yes | — |
| 384 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 386 | C2×C4 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 387 | C8 | — | 2 | 2 | no | — |
| 388 | C8 | — | 4 | 1 | no | — |
| 389 | C8 | — | 4 | 1 | no | — |
| 390 | C8 | — | 4 | 2 | no | — |
| 391 | C8 | — | 4 | 1 | no | — |
| 392 | C8 | — | 4 | 1 | no | — |
| 393 | C8 | C2×Q16×C53 | 1 | 4 | yes | — |
| 394 | C22 | — | 2 | 1 | no | — |
| 395 | C22 | — | 2 | 1 | no | — |
| 396 | C22 | C53×#462 | 1 | 2 | yes | — |
| 397 | C22 | C2×#121×C53 | 1 | 1 | yes | characteristic |
| 398 | C4 | — | 2 | 1 | no | — |
| 399 | C4 | — | 2 | 1 | no | — |
| 400 | C4 | — | 2 | 1 | no | — |
| 401 | C4 | — | 4 | 2 | no | — |
| 402 | C4 | — | 4 | 2 | no | — |
| 403 | C4 | — | 8 | 2 | no | — |
| 404 | C4 | — | 8 | 1 | no | — |
| 405 | C4 | — | 8 | 1 | no | — |
| 406 | C4 | C53×#462 | 1 | 2 | yes | — |
| 407 | C4 | C22×Q16×C53 | 1 | 1 | yes | characteristic |
| 408 | C4 | C2×#137×C53 | 1 | 1 | yes | characteristic |
| 409 | C4 | C53×#576 | 1 | 1 | yes | characteristic |
| 410 | C4 | C53×#577 | 1 | 1 | yes | characteristic |
| 411 | C2 | — | 2 | 2 | no | — |
| 412 | C2 | C2×C53×#462 | 1 | 1 | yes | characteristic |
| 413 | C2 | C53×#3062 | 1 | 1 | yes | characteristic |
| 414 | C2 | C53×#3069 | 1 | 1 | yes | characteristic |
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