← C53×#19944 #27227456
Subgroups — C53×#19944 #27227456
Order 13568.
554 conjugacy classes of subgroups.
The subgroup lattice has 364 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C53×#3395 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C53×#3383 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C53×#3374 | C2 | 1 | 2 | yes | maximal |
| 4 | C53×#1707 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C53×#1700 | C2 | 1 | 2 | yes | maximal |
| 6 | C53×#1674 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C53×#1670 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C53×#1653 | C2 | 1 | 2 | yes | maximal |
| 9 | C53×#1653 | C2 | 1 | 2 | yes | maximal |
| 10 | C53×#1591 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C8×Q16×C53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C53×#557 | C22 | 1 | 2 | yes | — |
| 13 | C53×#557 | C22 | 1 | 2 | yes | — |
| 14 | C53×#500 | C22 | 1 | 1 | yes | characteristic |
| 15 | C53×#499 | — | 2 | 1 | no | — |
| 16 | C53×#498 | C22 | 1 | 2 | yes | — |
| 17 | C53×#494 | — | 2 | 1 | no | — |
| 18 | C53×#494 | C22 | 1 | 1 | yes | characteristic |
| 19 | C53×#491 | — | 2 | 2 | no | — |
| 20 | C53×#487 | C22 | 1 | 2 | yes | — |
| 21 | C53×#479 | — | 2 | 2 | no | — |
| 22 | C53×#479 | — | 2 | 2 | no | — |
| 23 | C53×#475 | C22 | 1 | 2 | yes | — |
| 24 | C53×#475 | C22 | 1 | 2 | yes | — |
| 25 | C53×#462 | — | 2 | 2 | no | — |
| 26 | C53×#462 | — | 2 | 2 | no | — |
| 27 | C53×#462 | C22 | 1 | 2 | yes | — |
| 28 | C53×#462 | C22 | 1 | 2 | yes | — |
| 29 | C53×#446 | C22 | 1 | 2 | yes | — |
| 30 | C8×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 31 | C8×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 32 | C53×#441 | — | 2 | 2 | no | — |
| 33 | C4×Q16×C53 | — | 2 | 1 | no | — |
| 34 | C4×Q16×C53 | — | 2 | 1 | no | — |
| 35 | C4×Q16×C53 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×Q16×C53 | C22 | 1 | 1 | yes | characteristic |
| 37 | C53×#335 | C22 | 1 | 1 | yes | characteristic |
| 38 | C53×#335 | C22 | 1 | 1 | yes | characteristic |
| 39 | C53×#332 | C22 | 1 | 2 | yes | — |
| 40 | C53×#332 | C22 | 1 | 2 | yes | — |
| 41 | C53×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 43 | C53×Q8⋊C8 | C22 | 1 | 2 | yes | — |
| 44 | C82×C53 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 46 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 47 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 48 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 49 | C2×Q16×C53 | D4 | 1 | 1 | yes | characteristic |
| 50 | C2×Q16×C53 | D4 | 1 | 1 | yes | characteristic |
| 51 | C4⋊Q8×C53 | — | 2 | 2 | no | — |
| 52 | C4⋊Q8×C53 | — | 2 | 2 | no | — |
| 53 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 54 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 55 | #125×C53 | — | 2 | 2 | no | — |
| 56 | #125×C53 | — | 2 | 2 | no | — |
| 57 | #125×C53 | — | 4 | 2 | no | — |
| 58 | #125×C53 | — | 4 | 2 | no | — |
| 59 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 60 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 61 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 62 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 63 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 65 | C4×Q8×C53 | C23 | 1 | 2 | yes | — |
| 66 | #107×C53 | — | 2 | 1 | no | — |
| 67 | #107×C53 | — | 2 | 1 | no | — |
| 68 | #107×C53 | D4 | 1 | 1 | yes | characteristic |
| 69 | #107×C53 | D4 | 1 | 1 | yes | characteristic |
| 70 | #106×C53 | — | 2 | 2 | no | — |
| 71 | #106×C53 | — | 2 | 2 | no | — |
| 72 | #106×C53 | — | 4 | 2 | no | — |
| 73 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 74 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 75 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 76 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 77 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 78 | C4⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 79 | #103×C53 | — | 2 | 2 | no | — |
| 80 | #103×C53 | — | 2 | 2 | no | — |
| 81 | #103×C53 | — | 2 | 2 | no | — |
| 82 | #103×C53 | — | 2 | 2 | no | — |
| 83 | #103×C53 | — | 2 | 2 | no | — |
| 84 | #103×C53 | — | 2 | 2 | no | — |
| 85 | #103×C53 | D4 | 1 | 1 | yes | characteristic |
| 86 | #103×C53 | D4 | 1 | 1 | yes | characteristic |
| 87 | #103×C53 | D4 | 1 | 2 | yes | — |
| 88 | #97×C53 | — | 2 | 2 | no | — |
| 89 | C4×C8×C53 | — | 2 | 1 | no | — |
| 90 | C4×C8×C53 | — | 2 | 1 | no | — |
| 91 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 92 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 95 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 96 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 98 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | Q16×C53 | — | 2 | 2 | no | — |
| 100 | Q16×C53 | — | 2 | 2 | no | — |
| 101 | Q16×C53 | — | 4 | 4 | no | — |
| 102 | Q16×C53 | — | 4 | 2 | no | — |
| 103 | Q16×C53 | — | 8 | 1 | no | — |
| 104 | Q16×C53 | — | 8 | 2 | no | — |
| 105 | C2×C8×C53 | — | 2 | 1 | no | — |
| 106 | C2×C8×C53 | — | 2 | 1 | no | — |
| 107 | C2×C8×C53 | — | 2 | 1 | no | — |
| 108 | C2×C8×C53 | — | 2 | 2 | no | — |
| 109 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 114 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 115 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 116 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 117 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 118 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 119 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 120 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 121 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 122 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 123 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 124 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 125 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 126 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C4⋊C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 128 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C42×C53 | — | 2 | 1 | no | — |
| 130 | C42×C53 | — | 2 | 1 | no | — |
| 131 | C42×C53 | — | 2 | 2 | no | — |
| 132 | C42×C53 | — | 4 | 2 | no | — |
| 133 | C42×C53 | — | 4 | 2 | no | — |
| 134 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 135 | Q8×C53 | — | 2 | 1 | no | — |
| 136 | Q8×C53 | — | 2 | 1 | no | — |
| 137 | Q8×C53 | — | 2 | 2 | no | — |
| 138 | Q8×C53 | — | 2 | 2 | no | — |
| 139 | Q8×C53 | — | 2 | 1 | no | — |
| 140 | Q8×C53 | — | 4 | 2 | no | — |
| 141 | Q8×C53 | — | 4 | 2 | no | — |
| 142 | Q8×C53 | — | 4 | 2 | no | — |
| 143 | Q8×C53 | — | 4 | 2 | no | — |
| 144 | Q8×C53 | #135 | 1 | 2 | yes | — |
| 145 | C2×C4×C53 | — | 2 | 1 | no | — |
| 146 | C2×C4×C53 | — | 2 | 2 | no | — |
| 147 | C2×C4×C53 | — | 2 | 1 | no | — |
| 148 | C2×C4×C53 | — | 2 | 1 | no | — |
| 149 | C2×C4×C53 | — | 2 | 2 | no | — |
| 150 | C2×C4×C53 | — | 2 | 1 | no | — |
| 151 | C2×C4×C53 | — | 4 | 2 | no | — |
| 152 | C2×C4×C53 | — | 4 | 2 | no | — |
| 153 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 156 | C8×C53 | — | 2 | 2 | no | — |
| 157 | C8×C53 | — | 2 | 1 | no | — |
| 158 | C8×C53 | — | 2 | 1 | no | — |
| 159 | C8×C53 | — | 2 | 1 | no | — |
| 160 | C8×C53 | — | 4 | 2 | no | — |
| 161 | C8×C53 | — | 4 | 1 | no | — |
| 162 | C8×C53 | — | 4 | 1 | no | — |
| 163 | C8×C53 | #137 | 1 | 2 | yes | — |
| 164 | #19944 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 165 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 166 | C4×C53 | — | 2 | 2 | no | — |
| 167 | C4×C53 | — | 2 | 1 | no | — |
| 168 | C4×C53 | — | 4 | 2 | no | — |
| 169 | C4×C53 | — | 4 | 1 | no | — |
| 170 | C4×C53 | — | 4 | 1 | no | — |
| 171 | C4×C53 | — | 4 | 2 | no | — |
| 172 | C4×C53 | — | 4 | 1 | no | — |
| 173 | C4×C53 | — | 8 | 2 | no | — |
| 174 | C4×C53 | — | 8 | 2 | no | — |
| 175 | C4×C53 | C2×#135 | 1 | 1 | yes | characteristic |
| 176 | C4×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 177 | C4×C53 | #577 | 1 | 1 | yes | characteristic |
| 178 | C4×C53 | #578 | 1 | 1 | yes | characteristic |
| 179 | #3395 | C2×C53 | 1 | 1 | yes | characteristic |
| 180 | #3383 | C2×C53 | 1 | 1 | yes | characteristic |
| 181 | #3374 | C2×C53 | 1 | 2 | yes | — |
| 182 | #1707 | C2×C53 | 1 | 1 | yes | characteristic |
| 183 | #1700 | C2×C53 | 1 | 2 | yes | — |
| 184 | #1674 | C2×C53 | 1 | 1 | yes | characteristic |
| 185 | #1670 | C2×C53 | 1 | 1 | yes | characteristic |
| 186 | #1653 | C2×C53 | 1 | 2 | yes | — |
| 187 | #1653 | C2×C53 | 1 | 2 | yes | — |
| 188 | #1591 | C2×C53 | 1 | 1 | yes | characteristic |
| 189 | C8×Q16 | C2×C53 | 1 | 1 | yes | characteristic |
| 190 | C2×C53 | #3278 | 1 | 1 | yes | characteristic |
| 191 | C2×C53 | #3285 | 1 | 1 | yes | characteristic |
| 192 | C2×C53 | #3293 | 1 | 1 | yes | characteristic |
| 193 | #557 | C22×C53 | 1 | 2 | yes | — |
| 194 | #557 | C22×C53 | 1 | 2 | yes | — |
| 195 | #500 | C22×C53 | 1 | 1 | yes | characteristic |
| 196 | #499 | — | 2 | 1 | no | — |
| 197 | #498 | C22×C53 | 1 | 2 | yes | — |
| 198 | #494 | — | 2 | 1 | no | — |
| 199 | #494 | C22×C53 | 1 | 1 | yes | characteristic |
| 200 | #491 | — | 2 | 2 | no | — |
| 201 | #487 | C22×C53 | 1 | 2 | yes | — |
| 202 | #479 | — | 2 | 2 | no | — |
| 203 | #479 | — | 2 | 2 | no | — |
| 204 | #475 | C22×C53 | 1 | 2 | yes | — |
| 205 | #475 | C22×C53 | 1 | 2 | yes | — |
| 206 | #462 | — | 2 | 2 | no | — |
| 207 | #462 | — | 2 | 2 | no | — |
| 208 | #462 | C22×C53 | 1 | 2 | yes | — |
| 209 | #462 | C22×C53 | 1 | 2 | yes | — |
| 210 | #446 | C22×C53 | 1 | 2 | yes | — |
| 211 | C8×Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 212 | C8×Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 213 | #441 | — | 2 | 2 | no | — |
| 214 | C4×Q16 | — | 2 | 1 | no | — |
| 215 | C4×Q16 | — | 2 | 1 | no | — |
| 216 | C4×Q16 | C22×C53 | 1 | 1 | yes | characteristic |
| 217 | C4×Q16 | C22×C53 | 1 | 1 | yes | characteristic |
| 218 | #335 | C22×C53 | 1 | 1 | yes | characteristic |
| 219 | #335 | C22×C53 | 1 | 1 | yes | characteristic |
| 220 | #332 | C22×C53 | 1 | 2 | yes | — |
| 221 | #332 | C22×C53 | 1 | 2 | yes | — |
| 222 | Q8⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 223 | Q8⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 224 | Q8⋊C8 | C22×C53 | 1 | 2 | yes | — |
| 225 | C82 | C22×C53 | 1 | 1 | yes | characteristic |
| 226 | C53 | #19944 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 227 | C2×Q16 | — | 2 | 2 | no | — |
| 228 | C2×Q16 | — | 2 | 2 | no | — |
| 229 | C2×Q16 | — | 2 | 1 | no | — |
| 230 | C2×Q16 | — | 2 | 1 | no | — |
| 231 | C2×Q16 | D4×C53 | 1 | 1 | yes | characteristic |
| 232 | C2×Q16 | D4×C53 | 1 | 1 | yes | characteristic |
| 233 | C4⋊Q8 | — | 2 | 2 | no | — |
| 234 | C4⋊Q8 | — | 2 | 2 | no | — |
| 235 | C4⋊Q8 | C23×C53 | 1 | 2 | yes | — |
| 236 | C4⋊Q8 | C23×C53 | 1 | 2 | yes | — |
| 237 | #125 | — | 2 | 2 | no | — |
| 238 | #125 | — | 2 | 2 | no | — |
| 239 | #125 | — | 4 | 2 | no | — |
| 240 | #125 | — | 4 | 2 | no | — |
| 241 | C4×Q8 | — | 2 | 2 | no | — |
| 242 | C4×Q8 | — | 2 | 2 | no | — |
| 243 | C4×Q8 | — | 2 | 2 | no | — |
| 244 | C4×Q8 | — | 2 | 2 | no | — |
| 245 | C4×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 246 | C4×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 247 | C4×Q8 | C23×C53 | 1 | 2 | yes | — |
| 248 | #107 | — | 2 | 1 | no | — |
| 249 | #107 | — | 2 | 1 | no | — |
| 250 | #107 | D4×C53 | 1 | 1 | yes | characteristic |
| 251 | #107 | D4×C53 | 1 | 1 | yes | characteristic |
| 252 | #106 | — | 2 | 2 | no | — |
| 253 | #106 | — | 2 | 2 | no | — |
| 254 | #106 | — | 4 | 2 | no | — |
| 255 | C4⋊C8 | — | 2 | 1 | no | — |
| 256 | C4⋊C8 | — | 2 | 1 | no | — |
| 257 | C4⋊C8 | — | 2 | 2 | no | — |
| 258 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 259 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 260 | C4⋊C8 | C23×C53 | 1 | 2 | yes | — |
| 261 | #103 | — | 2 | 2 | no | — |
| 262 | #103 | — | 2 | 2 | no | — |
| 263 | #103 | — | 2 | 2 | no | — |
| 264 | #103 | — | 2 | 2 | no | — |
| 265 | #103 | — | 2 | 2 | no | — |
| 266 | #103 | — | 2 | 2 | no | — |
| 267 | #103 | D4×C53 | 1 | 1 | yes | characteristic |
| 268 | #103 | D4×C53 | 1 | 2 | yes | — |
| 269 | #103 | D4×C53 | 1 | 1 | yes | characteristic |
| 270 | #97 | — | 2 | 2 | no | — |
| 271 | C4×C8 | — | 2 | 1 | no | — |
| 272 | C4×C8 | — | 2 | 1 | no | — |
| 273 | C4×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 274 | C4×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 275 | C4×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 276 | C2×Q8 | — | 2 | 2 | no | — |
| 277 | C2×Q8 | — | 2 | 2 | no | — |
| 278 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 279 | C2×Q8 | C2×D4×C53 | 1 | 2 | yes | — |
| 280 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 281 | Q16 | — | 2 | 2 | no | — |
| 282 | Q16 | — | 2 | 2 | no | — |
| 283 | Q16 | — | 4 | 4 | no | — |
| 284 | Q16 | — | 4 | 2 | no | — |
| 285 | Q16 | — | 8 | 1 | no | — |
| 286 | Q16 | — | 8 | 2 | no | — |
| 287 | C2×C8 | — | 2 | 1 | no | — |
| 288 | C2×C8 | — | 2 | 1 | no | — |
| 289 | C2×C8 | — | 2 | 1 | no | — |
| 290 | C2×C8 | — | 2 | 2 | no | — |
| 291 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 292 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 293 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 294 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 295 | C4⋊C4 | — | 2 | 1 | no | — |
| 296 | C4⋊C4 | — | 2 | 1 | no | — |
| 297 | C4⋊C4 | — | 2 | 2 | no | — |
| 298 | C4⋊C4 | — | 2 | 2 | no | — |
| 299 | C4⋊C4 | — | 2 | 2 | no | — |
| 300 | C4⋊C4 | — | 2 | 2 | no | — |
| 301 | C4⋊C4 | — | 2 | 2 | no | — |
| 302 | C4⋊C4 | — | 4 | 2 | no | — |
| 303 | C4⋊C4 | — | 4 | 2 | no | — |
| 304 | C4⋊C4 | — | 4 | 2 | no | — |
| 305 | C4⋊C4 | — | 4 | 2 | no | — |
| 306 | C4⋊C4 | — | 4 | 2 | no | — |
| 307 | C4⋊C4 | — | 4 | 2 | no | — |
| 308 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 309 | C4⋊C4 | C2×D4×C53 | 1 | 2 | yes | — |
| 310 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 311 | C42 | — | 2 | 1 | no | — |
| 312 | C42 | — | 2 | 1 | no | — |
| 313 | C42 | — | 2 | 2 | no | — |
| 314 | C42 | — | 4 | 2 | no | — |
| 315 | C42 | — | 4 | 2 | no | — |
| 316 | C42 | C24×C53 | 1 | 1 | yes | characteristic |
| 317 | Q8 | — | 2 | 1 | no | — |
| 318 | Q8 | — | 2 | 1 | no | — |
| 319 | Q8 | — | 2 | 2 | no | — |
| 320 | Q8 | — | 2 | 2 | no | — |
| 321 | Q8 | — | 2 | 1 | no | — |
| 322 | Q8 | — | 4 | 2 | no | — |
| 323 | Q8 | — | 4 | 2 | no | — |
| 324 | Q8 | — | 4 | 2 | no | — |
| 325 | Q8 | — | 4 | 2 | no | — |
| 326 | Q8 | #135×C53 | 1 | 2 | yes | — |
| 327 | C2×C4 | — | 2 | 1 | no | — |
| 328 | C2×C4 | — | 2 | 1 | no | — |
| 329 | C2×C4 | — | 2 | 2 | no | — |
| 330 | C2×C4 | — | 2 | 2 | no | — |
| 331 | C2×C4 | — | 2 | 1 | no | — |
| 332 | C2×C4 | — | 2 | 1 | no | — |
| 333 | C2×C4 | — | 4 | 2 | no | — |
| 334 | C2×C4 | — | 4 | 2 | no | — |
| 335 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 336 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 338 | C8 | — | 2 | 2 | no | — |
| 339 | C8 | — | 2 | 1 | no | — |
| 340 | C8 | — | 2 | 1 | no | — |
| 341 | C8 | — | 2 | 1 | no | — |
| 342 | C8 | — | 4 | 2 | no | — |
| 343 | C8 | — | 4 | 1 | no | — |
| 344 | C8 | — | 4 | 1 | no | — |
| 345 | C8 | #137×C53 | 1 | 2 | yes | — |
| 346 | C22 | D42×C53 | 1 | 1 | yes | characteristic |
| 347 | C4 | — | 2 | 2 | no | — |
| 348 | C4 | — | 2 | 1 | no | — |
| 349 | C4 | — | 4 | 2 | no | — |
| 350 | C4 | — | 4 | 1 | no | — |
| 351 | C4 | — | 4 | 1 | no | — |
| 352 | C4 | — | 4 | 2 | no | — |
| 353 | C4 | — | 4 | 1 | no | — |
| 354 | C4 | — | 8 | 2 | no | — |
| 355 | C4 | — | 8 | 2 | no | — |
| 356 | C4 | C2×#135×C53 | 1 | 1 | yes | characteristic |
| 357 | C4 | C2×#137×C53 | 1 | 1 | yes | characteristic |
| 358 | C4 | C53×#577 | 1 | 1 | yes | characteristic |
| 359 | C4 | C53×#578 | 1 | 1 | yes | characteristic |
| 360 | C2 | C53×#3278 | 1 | 1 | yes | characteristic |
| 361 | C2 | C53×#3285 | 1 | 1 | yes | characteristic |
| 362 | C2 | C53×#3293 | 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