← #27425684
Subgroups — #27425684
Order 13568.
914 conjugacy classes of subgroups.
The subgroup lattice has 668 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16810834 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16810832 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#16810832 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#16810717 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #20279705 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #20277629 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #20276105 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #20275961 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #20275960 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #20275515 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #20275430 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #20275059 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #20275057 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #20274719 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C53×#2068 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C22×Dic212 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×Dic212 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×#11719925 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#13133217 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#13133215 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#13133215 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#13133182 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#13133182 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#13133182 | C22 | 1 | 1 | yes | characteristic |
| 26 | #16810834 | — | 2 | 4 | no | — |
| 27 | #16810832 | — | 2 | 4 | no | — |
| 28 | #16810832 | — | 2 | 4 | no | — |
| 29 | #16810717 | — | 2 | 4 | no | — |
| 30 | C2×#13133146 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#13133146 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#13133142 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#13133142 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#13133141 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#13133140 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#13133140 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#13133140 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#13133140 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#13133140 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×C8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 41 | #16810557 | — | 2 | 1 | no | — |
| 42 | #16810557 | — | 2 | 1 | no | — |
| 43 | #16810528 | C22 | 1 | 1 | yes | characteristic |
| 44 | #16810522 | C22 | 1 | 1 | yes | characteristic |
| 45 | #16810520 | — | 2 | 1 | no | — |
| 46 | #16810520 | — | 2 | 1 | no | — |
| 47 | #16810520 | — | 2 | 1 | no | — |
| 48 | #16810518 | — | 2 | 1 | no | — |
| 49 | #16810492 | — | 2 | 1 | no | — |
| 50 | #16810492 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×#11719919 | C22 | 1 | 1 | yes | characteristic |
| 52 | #16810474 | — | 2 | 1 | no | — |
| 53 | #16810385 | C22 | 1 | 1 | yes | characteristic |
| 54 | #16810378 | C22 | 1 | 1 | yes | characteristic |
| 55 | #16810377 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#107×C53 | C22 | 1 | 1 | yes | characteristic |
| 57 | C2×C4⋊C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 58 | C2×#103×C53 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×#103×C53 | C22 | 1 | 1 | yes | characteristic |
| 60 | C53×#391 | C22 | 1 | 1 | yes | characteristic |
| 61 | C53×#389 | C22 | 1 | 1 | yes | characteristic |
| 62 | C53×#340 | C22 | 1 | 1 | yes | characteristic |
| 63 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 64 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 65 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×Dic212 | — | 2 | 2 | no | — |
| 67 | C2×Dic212 | — | 2 | 2 | no | — |
| 68 | C2×Dic212 | — | 2 | 2 | no | — |
| 69 | C2×Dic212 | — | 2 | 2 | no | — |
| 70 | C2×Dic212 | — | 2 | 2 | no | — |
| 71 | C2×Dic212 | D4 | 1 | 4 | yes | — |
| 72 | C2×#11719925 | — | 2 | 2 | no | — |
| 73 | C2×#11719925 | — | 2 | 2 | no | — |
| 74 | C2×#11719925 | — | 2 | 2 | no | — |
| 75 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 76 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 77 | #13133217 | — | 2 | 2 | no | — |
| 78 | #13133217 | — | 4 | 1 | no | — |
| 79 | #13133215 | — | 2 | 2 | no | — |
| 80 | #13133215 | — | 2 | 2 | no | — |
| 81 | #13133215 | — | 2 | 2 | no | — |
| 82 | #13133215 | — | 4 | 1 | no | — |
| 83 | C4×Dic106 | — | 2 | 2 | no | — |
| 84 | C4×Dic106 | — | 4 | 1 | no | — |
| 85 | #13133182 | — | 2 | 2 | no | — |
| 86 | #13133182 | — | 2 | 2 | no | — |
| 87 | #13133182 | — | 2 | 2 | no | — |
| 88 | #13133182 | — | 2 | 2 | no | — |
| 89 | #13133182 | — | 4 | 1 | no | — |
| 90 | #13133182 | D4 | 1 | 4 | yes | — |
| 91 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 92 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 93 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 94 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×#11719919 | — | 2 | 1 | no | — |
| 96 | C2×#11719919 | — | 2 | 1 | no | — |
| 97 | C2×#11719919 | — | 2 | 1 | no | — |
| 98 | C2×#11719919 | — | 2 | 1 | no | — |
| 99 | C2×#11719919 | — | 2 | 1 | no | — |
| 100 | C2×#11719919 | — | 2 | 1 | no | — |
| 101 | C2×#11719919 | — | 2 | 1 | no | — |
| 102 | C2×#11719919 | — | 2 | 1 | no | — |
| 103 | C2×#11719919 | — | 2 | 1 | no | — |
| 104 | C2×#11719919 | — | 2 | 1 | no | — |
| 105 | C2×#11719919 | D4 | 1 | 1 | yes | characteristic |
| 106 | C2×#11719919 | D4 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 108 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 109 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 110 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 111 | C2×C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 113 | #13133146 | — | 2 | 2 | no | — |
| 114 | #13133146 | — | 2 | 2 | no | — |
| 115 | #13133142 | — | 2 | 2 | no | — |
| 116 | #13133142 | — | 2 | 2 | no | — |
| 117 | #13133141 | — | 4 | 1 | no | — |
| 118 | #13133140 | — | 2 | 2 | no | — |
| 119 | #13133140 | — | 2 | 2 | no | — |
| 120 | #13133140 | — | 2 | 2 | no | — |
| 121 | #13133140 | — | 2 | 2 | no | — |
| 122 | #13133140 | — | 4 | 1 | no | — |
| 123 | C8×Dic53 | — | 2 | 2 | no | — |
| 124 | #13133124 | — | 2 | 1 | no | — |
| 125 | #13133124 | — | 2 | 1 | no | — |
| 126 | #13133124 | — | 2 | 1 | no | — |
| 127 | #13133124 | D4 | 1 | 1 | yes | characteristic |
| 128 | #13133124 | D4 | 1 | 1 | yes | characteristic |
| 129 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 130 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 131 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 133 | C2×C4⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 134 | C2×C4⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 135 | C2×C4⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 136 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 137 | #107×C53 | — | 2 | 2 | no | — |
| 138 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 139 | #103×C53 | — | 2 | 2 | no | — |
| 140 | #103×C53 | — | 2 | 2 | no | — |
| 141 | #95×C53 | — | 2 | 1 | no | — |
| 142 | #95×C53 | — | 2 | 1 | no | — |
| 143 | #95×C53 | — | 2 | 1 | no | — |
| 144 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 145 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 146 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 147 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 148 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 149 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 150 | C22×C4×C53 | — | 2 | 1 | no | — |
| 151 | C22×C4×C53 | — | 2 | 1 | no | — |
| 152 | C22×C4×C53 | — | 2 | 1 | no | — |
| 153 | C22×C4×C53 | — | 2 | 1 | no | — |
| 154 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 157 | C22×Dic53 | — | 2 | 1 | no | — |
| 158 | C22×Dic53 | — | 2 | 1 | no | — |
| 159 | C22×Dic53 | — | 2 | 1 | no | — |
| 160 | C22×Dic53 | — | 2 | 1 | no | — |
| 161 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C2×Dic106 | — | 2 | 1 | no | — |
| 166 | C2×Dic106 | — | 2 | 1 | no | — |
| 167 | C2×Dic106 | — | 2 | 1 | no | — |
| 168 | C2×Dic106 | — | 2 | 1 | no | — |
| 169 | C2×Dic106 | — | 2 | 1 | no | — |
| 170 | C2×Dic106 | — | 2 | 1 | no | — |
| 171 | C2×Dic106 | — | 2 | 1 | no | — |
| 172 | C2×Dic106 | — | 2 | 1 | no | — |
| 173 | C2×Dic106 | — | 2 | 1 | no | — |
| 174 | C2×Dic106 | — | 2 | 1 | no | — |
| 175 | C2×Dic106 | — | 2 | 1 | no | — |
| 176 | C2×Dic106 | — | 2 | 1 | no | — |
| 177 | C2×Dic106 | — | 2 | 1 | no | — |
| 178 | C2×Dic106 | — | 2 | 1 | no | — |
| 179 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 180 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 181 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 182 | C2×Dic106 | #41 | 1 | 2 | yes | — |
| 183 | C2×C8×C53 | — | 2 | 1 | no | — |
| 184 | C2×C8×C53 | — | 2 | 1 | no | — |
| 185 | C2×C8×C53 | — | 2 | 1 | no | — |
| 186 | C2×C8×C53 | — | 2 | 1 | no | — |
| 187 | C2×C8×C53 | — | 2 | 1 | no | — |
| 188 | C2×C8×C53 | C2×D4 | 1 | 2 | yes | — |
| 189 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 190 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 191 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 192 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 193 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 194 | C4⋊C4×C53 | — | 8 | 1 | no | — |
| 195 | C4⋊C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 196 | C42×C53 | — | 2 | 1 | no | — |
| 197 | C42×C53 | — | 2 | 1 | no | — |
| 198 | #11719925 | — | 4 | 4 | no | — |
| 199 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 200 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 201 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 202 | C4⋊Dic53 | — | 4 | 2 | no | — |
| 203 | C4⋊Dic53 | — | 8 | 1 | no | — |
| 204 | #11719919 | — | 2 | 4 | no | — |
| 205 | #11719919 | — | 2 | 2 | no | — |
| 206 | #11719919 | — | 4 | 2 | no | — |
| 207 | #11719919 | — | 4 | 2 | no | — |
| 208 | #11719919 | — | 4 | 2 | no | — |
| 209 | #11719919 | — | 4 | 2 | no | — |
| 210 | #11719919 | — | 4 | 2 | no | — |
| 211 | #11719919 | — | 4 | 2 | no | — |
| 212 | #11719919 | — | 4 | 2 | no | — |
| 213 | #11719919 | — | 4 | 2 | no | — |
| 214 | #11719919 | — | 8 | 1 | no | — |
| 215 | #11719919 | Q16 | 1 | 4 | yes | complemented |
| 216 | C4×Dic53 | — | 2 | 1 | no | — |
| 217 | C4×Dic53 | — | 2 | 1 | no | — |
| 218 | C4×Dic53 | — | 2 | 4 | no | — |
| 219 | C4×Dic53 | — | 4 | 2 | no | — |
| 220 | C4×Dic53 | — | 4 | 2 | no | — |
| 221 | C4×Dic53 | — | 4 | 2 | no | — |
| 222 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 223 | C4×Dic53 | #41 | 1 | 2 | yes | — |
| 224 | C2×#88322 | — | 2 | 1 | no | — |
| 225 | C2×#88322 | — | 2 | 1 | no | — |
| 226 | C2×#88322 | — | 2 | 1 | no | — |
| 227 | C2×#88322 | — | 2 | 1 | no | — |
| 228 | C2×#88322 | — | 2 | 1 | no | — |
| 229 | C2×#88322 | — | 2 | 1 | no | — |
| 230 | Dic212 | — | 2 | 8 | no | — |
| 231 | Dic212 | — | 4 | 4 | no | — |
| 232 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 233 | Q8×C53 | — | 4 | 1 | no | — |
| 234 | Q8×C53 | — | 4 | 1 | no | — |
| 235 | Q8×C53 | — | 4 | 1 | no | — |
| 236 | Q8×C53 | — | 4 | 1 | no | — |
| 237 | C2×C4×C53 | — | 2 | 1 | no | — |
| 238 | C2×C4×C53 | — | 2 | 1 | no | — |
| 239 | C2×C4×C53 | — | 2 | 2 | no | — |
| 240 | C2×C4×C53 | — | 2 | 1 | no | — |
| 241 | C2×C4×C53 | — | 2 | 1 | no | — |
| 242 | C2×C4×C53 | — | 2 | 1 | no | — |
| 243 | C2×C4×C53 | — | 4 | 1 | no | — |
| 244 | C2×C4×C53 | — | 4 | 1 | no | — |
| 245 | C2×C4×C53 | — | 4 | 1 | no | — |
| 246 | C2×C4×C53 | — | 4 | 1 | no | — |
| 247 | C2×C4×C53 | — | 4 | 1 | no | — |
| 248 | C2×C4×C53 | — | 4 | 1 | no | — |
| 249 | C2×C4×C53 | — | 4 | 1 | no | — |
| 250 | C2×C4×C53 | — | 4 | 1 | no | — |
| 251 | C2×C4×C53 | — | 4 | 1 | no | — |
| 252 | C2×C4×C53 | — | 4 | 1 | no | — |
| 253 | C2×C4×C53 | — | 4 | 1 | no | — |
| 254 | C2×C4×C53 | C2×Q16 | 1 | 2 | yes | — |
| 255 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C53 | 2−1+4 | 1 | 1 | yes | characteristic |
| 261 | C2×Dic53 | — | 2 | 2 | no | — |
| 262 | C2×Dic53 | — | 2 | 2 | no | — |
| 263 | C2×Dic53 | — | 2 | 1 | no | — |
| 264 | C2×Dic53 | — | 2 | 2 | no | — |
| 265 | C2×Dic53 | — | 2 | 1 | no | — |
| 266 | C2×Dic53 | — | 2 | 1 | no | — |
| 267 | C2×Dic53 | — | 2 | 1 | no | — |
| 268 | C2×Dic53 | — | 2 | 2 | no | — |
| 269 | C2×Dic53 | — | 2 | 1 | no | — |
| 270 | C2×Dic53 | — | 2 | 1 | no | — |
| 271 | C2×Dic53 | — | 2 | 1 | no | — |
| 272 | C2×Dic53 | — | 4 | 1 | no | — |
| 273 | C2×Dic53 | — | 4 | 1 | no | — |
| 274 | C2×Dic53 | — | 4 | 1 | no | — |
| 275 | C2×Dic53 | — | 4 | 1 | no | — |
| 276 | C2×Dic53 | — | 4 | 1 | no | — |
| 277 | C2×Dic53 | — | 4 | 1 | no | — |
| 278 | C2×Dic53 | — | 4 | 1 | no | — |
| 279 | C2×Dic53 | — | 4 | 1 | no | — |
| 280 | C2×Dic53 | #121 | 1 | 2 | yes | — |
| 281 | C2×Dic53 | #121 | 1 | 2 | yes | — |
| 282 | C2×Dic53 | C2×Q16 | 1 | 2 | yes | — |
| 283 | C2×Dic53 | C2×Q16 | 1 | 2 | yes | — |
| 284 | C2×Dic53 | #137 | 1 | 2 | yes | — |
| 285 | Dic106 | — | 2 | 2 | no | — |
| 286 | Dic106 | — | 2 | 2 | no | — |
| 287 | Dic106 | — | 2 | 2 | no | — |
| 288 | Dic106 | — | 2 | 2 | no | — |
| 289 | Dic106 | — | 2 | 2 | no | — |
| 290 | Dic106 | — | 4 | 1 | no | — |
| 291 | Dic106 | — | 4 | 1 | no | — |
| 292 | Dic106 | — | 4 | 1 | no | — |
| 293 | Dic106 | — | 4 | 1 | no | — |
| 294 | Dic106 | — | 4 | 1 | no | — |
| 295 | Dic106 | — | 4 | 1 | no | — |
| 296 | Dic106 | #121 | 1 | 4 | yes | — |
| 297 | C8×C53 | — | 2 | 2 | no | — |
| 298 | C8×C53 | — | 4 | 1 | no | — |
| 299 | #88322 | — | 4 | 1 | no | — |
| 300 | #88322 | — | 4 | 1 | no | — |
| 301 | #24732 | — | 53 | 1 | no | maximal, Sylow |
| 302 | C22×C53 | C2×#121 | 1 | 1 | yes | characteristic |
| 303 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 304 | C22×C53 | #548 | 1 | 1 | yes | characteristic |
| 305 | C22×C53 | C22×Q16 | 1 | 1 | yes | characteristic |
| 306 | C22×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 307 | C22×C53 | #577 | 1 | 1 | yes | characteristic |
| 308 | C22×C53 | #578 | 1 | 1 | yes | characteristic |
| 309 | C4×C53 | — | 2 | 2 | no | — |
| 310 | C4×C53 | — | 4 | 1 | no | — |
| 311 | C4×C53 | — | 4 | 2 | no | — |
| 312 | C4×C53 | — | 8 | 1 | no | — |
| 313 | C4×C53 | — | 8 | 1 | no | — |
| 314 | C4×C53 | — | 8 | 1 | no | — |
| 315 | C4×C53 | C2×#121 | 1 | 1 | yes | characteristic |
| 316 | C4×C53 | #537 | 1 | 1 | yes | characteristic |
| 317 | C4×C53 | #547 | 1 | 1 | yes | characteristic |
| 318 | C4×C53 | #553 | 1 | 1 | yes | characteristic |
| 319 | Dic53 | — | 2 | 4 | no | — |
| 320 | Dic53 | — | 2 | 2 | no | — |
| 321 | Dic53 | — | 2 | 2 | no | — |
| 322 | Dic53 | — | 4 | 2 | no | — |
| 323 | Dic53 | — | 4 | 1 | no | — |
| 324 | Dic53 | — | 8 | 1 | no | — |
| 325 | Dic53 | — | 8 | 1 | no | — |
| 326 | Dic53 | #462 | 1 | 4 | yes | complemented |
| 327 | C2×#462 | — | 53 | 1 | no | — |
| 328 | C2×#462 | — | 53 | 1 | no | — |
| 329 | C2×#462 | — | 53 | 1 | no | — |
| 330 | C2×C4×Q16 | — | 53 | 1 | no | — |
| 331 | #2546 | — | 53 | 1 | no | — |
| 332 | Q8×C4⋊C4 | — | 53 | 1 | no | — |
| 333 | #2068 | — | 53 | 1 | no | — |
| 334 | #2068 | D53 | 1 | 1 | yes | characteristic |
| 335 | #2043 | — | 53 | 1 | no | — |
| 336 | #2043 | — | 53 | 1 | no | — |
| 337 | #1956 | — | 53 | 1 | no | — |
| 338 | #1939 | — | 53 | 1 | no | — |
| 339 | #1878 | — | 53 | 1 | no | — |
| 340 | #1878 | — | 53 | 1 | no | — |
| 341 | #1803 | — | 53 | 1 | no | — |
| 342 | C2×C53 | #2416 | 1 | 1 | yes | characteristic |
| 343 | C2×C53 | C2×#462 | 1 | 1 | yes | characteristic |
| 344 | C2×C53 | #3046 | 1 | 1 | yes | characteristic |
| 345 | C2×C53 | #3278 | 1 | 1 | yes | characteristic |
| 346 | C2×C53 | D4×Q16 | 1 | 1 | yes | characteristic |
| 347 | C2×C53 | #3363 | 1 | 1 | yes | characteristic |
| 348 | C2×C53 | #3374 | 1 | 1 | yes | characteristic |
| 349 | C22×Q16 | — | 53 | 1 | no | — |
| 350 | C22×Q16 | — | 53 | 1 | no | — |
| 351 | C22×Q16 | — | 53 | 1 | no | — |
| 352 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 353 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 354 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 355 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 356 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 357 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 358 | C2×C4×Q8 | — | 53 | 1 | no | — |
| 359 | #462 | — | 106 | 4 | no | — |
| 360 | #462 | — | 106 | 4 | no | — |
| 361 | #462 | — | 106 | 4 | no | — |
| 362 | C4×Q16 | — | 106 | 4 | no | — |
| 363 | C2×#107 | C2×D53 | 1 | 1 | yes | characteristic |
| 364 | C2×C4⋊C8 | — | 53 | 1 | no | — |
| 365 | C2×C4⋊C8 | — | 53 | 1 | no | — |
| 366 | C2×C4⋊C8 | C2×D53 | 1 | 1 | yes | characteristic |
| 367 | C2×#103 | — | 53 | 1 | no | — |
| 368 | C2×#103 | — | 53 | 1 | no | — |
| 369 | C2×#103 | — | 53 | 1 | no | — |
| 370 | C2×#103 | — | 53 | 1 | no | — |
| 371 | C2×#103 | — | 53 | 1 | no | — |
| 372 | C2×#103 | — | 53 | 1 | no | — |
| 373 | C2×#103 | — | 53 | 1 | no | — |
| 374 | C2×#103 | — | 53 | 1 | no | — |
| 375 | C2×#103 | C2×D53 | 1 | 1 | yes | characteristic |
| 376 | C2×#103 | C2×D53 | 1 | 1 | yes | characteristic |
| 377 | C2×C4×C8 | — | 53 | 1 | no | — |
| 378 | #398 | — | 106 | 1 | no | — |
| 379 | #398 | — | 106 | 1 | no | — |
| 380 | #391 | — | 53 | 1 | no | — |
| 381 | #391 | C2×D53 | 1 | 1 | yes | characteristic |
| 382 | #389 | — | 53 | 1 | no | — |
| 383 | #389 | — | 106 | 1 | no | — |
| 384 | #389 | — | 106 | 1 | no | — |
| 385 | #389 | — | 106 | 1 | no | — |
| 386 | #389 | — | 106 | 1 | no | — |
| 387 | #389 | C2×D53 | 1 | 1 | yes | characteristic |
| 388 | #384 | — | 53 | 1 | no | — |
| 389 | #384 | — | 106 | 1 | no | — |
| 390 | C4×C4⋊C4 | — | 53 | 1 | no | — |
| 391 | C4×C4⋊C4 | — | 106 | 1 | no | — |
| 392 | #340 | — | 53 | 1 | no | — |
| 393 | #340 | C2×D53 | 1 | 1 | yes | characteristic |
| 394 | #336 | — | 53 | 1 | no | — |
| 395 | #336 | — | 53 | 1 | no | — |
| 396 | C53 | #24732 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 397 | C22×Q8 | — | 53 | 1 | no | — |
| 398 | C22×Q8 | — | 53 | 1 | no | — |
| 399 | C22×Q8 | — | 53 | 1 | no | — |
| 400 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 401 | C2×Q16 | — | 53 | 4 | no | — |
| 402 | C2×Q16 | — | 106 | 2 | no | — |
| 403 | C2×Q16 | — | 106 | 2 | no | — |
| 404 | C2×Q16 | — | 106 | 2 | no | — |
| 405 | C2×Q16 | — | 106 | 2 | no | — |
| 406 | C2×Q16 | — | 106 | 2 | no | — |
| 407 | C2×Q16 | — | 106 | 2 | no | — |
| 408 | C2×Q16 | — | 106 | 2 | no | — |
| 409 | C2×Q16 | — | 106 | 2 | no | — |
| 410 | C22×C8 | — | 53 | 1 | no | — |
| 411 | C22×C8 | — | 53 | 1 | no | — |
| 412 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 413 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 414 | C4⋊Q8 | — | 106 | 2 | no | — |
| 415 | C4⋊Q8 | — | 106 | 2 | no | — |
| 416 | C4⋊Q8 | — | 106 | 2 | no | — |
| 417 | C4⋊Q8 | — | 106 | 2 | no | — |
| 418 | C4⋊Q8 | — | 212 | 1 | no | — |
| 419 | C4⋊Q8 | — | 212 | 1 | no | — |
| 420 | C4×Q8 | — | 53 | 4 | no | — |
| 421 | C4×Q8 | — | 106 | 2 | no | — |
| 422 | C4×Q8 | — | 106 | 2 | no | — |
| 423 | C4×Q8 | — | 106 | 2 | no | — |
| 424 | C4×Q8 | — | 106 | 2 | no | — |
| 425 | C4×Q8 | — | 106 | 2 | no | — |
| 426 | C4×Q8 | — | 212 | 1 | no | — |
| 427 | C4×Q8 | — | 212 | 1 | no | — |
| 428 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 429 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 430 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 431 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 432 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 433 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 434 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 435 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 436 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 437 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 438 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 439 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 440 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 441 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 442 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 443 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 444 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 445 | C2×C4⋊C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 446 | C2×C4⋊C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 447 | C2×C4⋊C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 448 | C2×C42 | — | 53 | 1 | no | — |
| 449 | C2×C42 | — | 53 | 1 | no | — |
| 450 | C2×C42 | — | 106 | 1 | no | — |
| 451 | C2×C42 | — | 106 | 1 | no | — |
| 452 | C2×C42 | — | 106 | 1 | no | — |
| 453 | C2×C42 | — | 106 | 1 | no | — |
| 454 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 455 | #107 | — | 2 | 2 | no | — |
| 456 | C4⋊C8 | — | 2 | 2 | no | — |
| 457 | C4⋊C8 | — | 106 | 2 | no | — |
| 458 | C4⋊C8 | — | 106 | 2 | no | — |
| 459 | #103 | — | 2 | 2 | no | — |
| 460 | #103 | — | 2 | 2 | no | — |
| 461 | #103 | — | 106 | 2 | no | — |
| 462 | #103 | — | 106 | 2 | no | — |
| 463 | #103 | — | 106 | 2 | no | — |
| 464 | #103 | — | 106 | 2 | no | — |
| 465 | #103 | — | 106 | 2 | no | — |
| 466 | #103 | — | 106 | 2 | no | — |
| 467 | #103 | — | 212 | 1 | no | — |
| 468 | #103 | — | 212 | 1 | no | — |
| 469 | C4×C8 | — | 106 | 2 | no | — |
| 470 | #95 | — | 2 | 1 | no | — |
| 471 | #95 | — | 2 | 1 | no | — |
| 472 | #95 | — | 2 | 1 | no | — |
| 473 | #95 | — | 53 | 1 | no | — |
| 474 | #95 | — | 53 | 1 | no | — |
| 475 | #95 | — | 106 | 1 | no | — |
| 476 | #95 | — | 106 | 1 | no | — |
| 477 | #95 | — | 106 | 1 | no | — |
| 478 | C2×Q8 | — | 2 | 1 | no | — |
| 479 | C2×Q8 | — | 2 | 1 | no | — |
| 480 | C2×Q8 | — | 2 | 1 | no | — |
| 481 | C2×Q8 | — | 2 | 1 | no | — |
| 482 | C2×Q8 | — | 2 | 1 | no | — |
| 483 | C2×Q8 | — | 2 | 1 | no | — |
| 484 | C2×Q8 | — | 53 | 2 | no | — |
| 485 | C2×Q8 | — | 53 | 2 | no | — |
| 486 | C2×Q8 | — | 53 | 2 | no | — |
| 487 | C2×Q8 | — | 53 | 2 | no | — |
| 488 | C2×Q8 | — | 106 | 1 | no | — |
| 489 | C2×Q8 | — | 106 | 1 | no | — |
| 490 | C2×Q8 | — | 106 | 1 | no | — |
| 491 | C2×Q8 | — | 106 | 1 | no | — |
| 492 | C2×Q8 | — | 106 | 1 | no | — |
| 493 | C2×Q8 | — | 106 | 1 | no | — |
| 494 | C2×Q8 | — | 106 | 1 | no | — |
| 495 | C2×Q8 | — | 106 | 1 | no | — |
| 496 | C2×Q8 | — | 106 | 1 | no | — |
| 497 | C2×Q8 | — | 106 | 1 | no | — |
| 498 | C2×Q8 | — | 106 | 1 | no | — |
| 499 | C2×Q8 | — | 106 | 1 | no | — |
| 500 | C2×Q8 | — | 106 | 1 | no | — |
| 501 | C2×Q8 | — | 106 | 1 | no | — |
| 502 | C22×C4 | — | 2 | 1 | no | — |
| 503 | C22×C4 | — | 2 | 1 | no | — |
| 504 | C22×C4 | — | 2 | 1 | no | — |
| 505 | C22×C4 | — | 2 | 1 | no | — |
| 506 | C22×C4 | — | 53 | 1 | no | — |
| 507 | C22×C4 | — | 53 | 1 | no | — |
| 508 | C22×C4 | — | 53 | 1 | no | — |
| 509 | C22×C4 | — | 53 | 1 | no | — |
| 510 | C22×C4 | — | 106 | 1 | no | — |
| 511 | C22×C4 | — | 106 | 1 | no | — |
| 512 | C22×C4 | — | 106 | 1 | no | — |
| 513 | C22×C4 | — | 106 | 1 | no | — |
| 514 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 515 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 516 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 517 | Q16 | — | 106 | 8 | no | — |
| 518 | Q16 | — | 212 | 4 | no | — |
| 519 | Q16 | — | 212 | 4 | no | — |
| 520 | C2×C8 | — | 2 | 1 | no | — |
| 521 | C2×C8 | — | 2 | 1 | no | — |
| 522 | C2×C8 | — | 2 | 1 | no | — |
| 523 | C2×C8 | — | 2 | 1 | no | — |
| 524 | C2×C8 | — | 2 | 1 | no | — |
| 525 | C2×C8 | — | 106 | 1 | no | — |
| 526 | C2×C8 | — | 106 | 1 | no | — |
| 527 | C2×C8 | — | 106 | 1 | no | — |
| 528 | C2×C8 | — | 106 | 1 | no | — |
| 529 | C2×C8 | — | 106 | 1 | no | — |
| 530 | C2×C8 | — | 106 | 1 | no | — |
| 531 | C2×C8 | D4×D53 | 1 | 2 | yes | — |
| 532 | C4⋊C4 | — | 2 | 1 | no | — |
| 533 | C4⋊C4 | — | 2 | 1 | no | — |
| 534 | C4⋊C4 | — | 2 | 1 | no | — |
| 535 | C4⋊C4 | — | 2 | 1 | no | — |
| 536 | C4⋊C4 | — | 2 | 1 | no | — |
| 537 | C4⋊C4 | — | 8 | 1 | no | — |
| 538 | C4⋊C4 | — | 53 | 4 | no | — |
| 539 | C4⋊C4 | — | 106 | 2 | no | — |
| 540 | C4⋊C4 | — | 106 | 4 | no | — |
| 541 | C4⋊C4 | — | 106 | 1 | no | — |
| 542 | C4⋊C4 | — | 106 | 1 | no | — |
| 543 | C4⋊C4 | — | 424 | 1 | no | — |
| 544 | C4⋊C4 | — | 424 | 1 | no | — |
| 545 | C4⋊C4 | — | 212 | 2 | no | — |
| 546 | C4⋊C4 | — | 212 | 2 | no | — |
| 547 | C4⋊C4 | — | 212 | 2 | no | — |
| 548 | C4⋊C4 | — | 212 | 2 | no | — |
| 549 | C4⋊C4 | — | 212 | 2 | no | — |
| 550 | C4⋊C4 | — | 212 | 2 | no | — |
| 551 | C4⋊C4 | — | 212 | 2 | no | — |
| 552 | C4⋊C4 | — | 212 | 2 | no | — |
| 553 | C4⋊C4 | — | 212 | 2 | no | — |
| 554 | C4⋊C4 | — | 212 | 2 | no | — |
| 555 | C4⋊C4 | D4×D53 | 1 | 2 | yes | — |
| 556 | C42 | — | 2 | 1 | no | — |
| 557 | C42 | — | 2 | 1 | no | — |
| 558 | C42 | — | 53 | 2 | no | — |
| 559 | C42 | — | 53 | 2 | no | — |
| 560 | C42 | — | 106 | 4 | no | — |
| 561 | C42 | — | 106 | 1 | no | — |
| 562 | C42 | — | 106 | 1 | no | — |
| 563 | C42 | — | 212 | 2 | no | — |
| 564 | C42 | — | 212 | 2 | no | — |
| 565 | C42 | — | 212 | 2 | no | — |
| 566 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 567 | Q8 | — | 4 | 1 | no | — |
| 568 | Q8 | — | 4 | 1 | no | — |
| 569 | Q8 | — | 4 | 1 | no | — |
| 570 | Q8 | — | 4 | 1 | no | — |
| 571 | Q8 | — | 53 | 4 | no | — |
| 572 | Q8 | — | 106 | 2 | no | — |
| 573 | Q8 | — | 106 | 2 | no | — |
| 574 | Q8 | — | 106 | 2 | no | — |
| 575 | Q8 | — | 106 | 2 | no | — |
| 576 | Q8 | — | 106 | 2 | no | — |
| 577 | Q8 | — | 212 | 1 | no | — |
| 578 | Q8 | — | 212 | 1 | no | — |
| 579 | Q8 | — | 212 | 1 | no | — |
| 580 | Q8 | — | 212 | 1 | no | — |
| 581 | Q8 | — | 212 | 1 | no | — |
| 582 | Q8 | — | 212 | 1 | no | — |
| 583 | C2×C4 | — | 2 | 1 | no | — |
| 584 | C2×C4 | — | 2 | 1 | no | — |
| 585 | C2×C4 | — | 2 | 2 | no | — |
| 586 | C2×C4 | — | 2 | 1 | no | — |
| 587 | C2×C4 | — | 2 | 1 | no | — |
| 588 | C2×C4 | — | 2 | 1 | no | — |
| 589 | C2×C4 | — | 4 | 1 | no | — |
| 590 | C2×C4 | — | 4 | 1 | no | — |
| 591 | C2×C4 | — | 4 | 1 | no | — |
| 592 | C2×C4 | — | 4 | 1 | no | — |
| 593 | C2×C4 | — | 4 | 1 | no | — |
| 594 | C2×C4 | — | 4 | 1 | no | — |
| 595 | C2×C4 | — | 4 | 1 | no | — |
| 596 | C2×C4 | — | 4 | 1 | no | — |
| 597 | C2×C4 | — | 4 | 1 | no | — |
| 598 | C2×C4 | — | 4 | 1 | no | — |
| 599 | C2×C4 | — | 4 | 1 | no | — |
| 600 | C2×C4 | — | 53 | 2 | no | — |
| 601 | C2×C4 | — | 53 | 2 | no | — |
| 602 | C2×C4 | — | 53 | 2 | no | — |
| 603 | C2×C4 | — | 53 | 2 | no | — |
| 604 | C2×C4 | — | 53 | 2 | no | — |
| 605 | C2×C4 | — | 106 | 2 | no | — |
| 606 | C2×C4 | — | 106 | 2 | no | — |
| 607 | C2×C4 | — | 106 | 1 | no | — |
| 608 | C2×C4 | — | 106 | 1 | no | — |
| 609 | C2×C4 | — | 106 | 1 | no | — |
| 610 | C2×C4 | — | 106 | 1 | no | — |
| 611 | C2×C4 | — | 106 | 2 | no | — |
| 612 | C2×C4 | — | 106 | 1 | no | — |
| 613 | C2×C4 | — | 106 | 1 | no | — |
| 614 | C2×C4 | — | 106 | 1 | no | — |
| 615 | C2×C4 | — | 106 | 2 | no | — |
| 616 | C2×C4 | — | 212 | 1 | no | — |
| 617 | C2×C4 | — | 212 | 1 | no | — |
| 618 | C2×C4 | — | 212 | 1 | no | — |
| 619 | C2×C4 | — | 212 | 1 | no | — |
| 620 | C2×C4 | — | 212 | 1 | no | — |
| 621 | C2×C4 | — | 212 | 1 | no | — |
| 622 | C2×C4 | — | 212 | 1 | no | — |
| 623 | C2×C4 | — | 212 | 1 | no | — |
| 624 | C2×C4 | Q16×D53 | 1 | 2 | yes | — |
| 625 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 627 | C2×C4 | #41×D53 | 1 | 1 | yes | characteristic |
| 628 | C2×C4 | #41×D53 | 1 | 1 | yes | characteristic |
| 629 | C2×C4 | #13133263 | 1 | 1 | yes | characteristic |
| 630 | C2×C4 | #13133265 | 1 | 1 | yes | characteristic |
| 631 | C8 | — | 2 | 2 | no | — |
| 632 | C8 | — | 4 | 1 | no | — |
| 633 | C8 | — | 212 | 1 | no | — |
| 634 | C8 | — | 212 | 1 | no | — |
| 635 | C22 | #121×D53 | 1 | 1 | yes | characteristic |
| 636 | C22 | #16811257 | 1 | 1 | yes | characteristic |
| 637 | C22 | #16811283 | 1 | 1 | yes | characteristic |
| 638 | C22 | C2×Q16×D53 | 1 | 1 | yes | characteristic |
| 639 | C22 | #137×D53 | 1 | 1 | yes | characteristic |
| 640 | C22 | #16811433 | 1 | 1 | yes | characteristic |
| 641 | C22 | #16811437 | 1 | 1 | yes | characteristic |
| 642 | C4 | — | 2 | 2 | no | — |
| 643 | C4 | — | 4 | 2 | no | — |
| 644 | C4 | — | 4 | 1 | no | — |
| 645 | C4 | — | 8 | 1 | no | — |
| 646 | C4 | — | 8 | 1 | no | — |
| 647 | C4 | — | 8 | 1 | no | — |
| 648 | C4 | — | 53 | 4 | no | — |
| 649 | C4 | — | 106 | 2 | no | — |
| 650 | C4 | — | 106 | 2 | no | — |
| 651 | C4 | — | 106 | 4 | no | — |
| 652 | C4 | — | 424 | 1 | no | — |
| 653 | C4 | — | 424 | 1 | no | — |
| 654 | C4 | — | 212 | 2 | no | — |
| 655 | C4 | — | 212 | 1 | no | — |
| 656 | C4 | #121×D53 | 1 | 1 | yes | characteristic |
| 657 | C4 | #16811203 | 1 | 1 | yes | characteristic |
| 658 | C4 | #16811275 | 1 | 1 | yes | characteristic |
| 659 | C4 | #16811324 | 1 | 1 | yes | characteristic |
| 660 | C2 | #20278150 | 1 | 1 | yes | characteristic |
| 661 | C2 | #462×D53 | 1 | 1 | yes | characteristic |
| 662 | C2 | #20284266 | 1 | 1 | yes | characteristic |
| 663 | C2 | #20286378 | 1 | 1 | yes | characteristic |
| 664 | C2 | #20286464 | 1 | 1 | yes | characteristic |
| 665 | C2 | #20287392 | 1 | 1 | yes | characteristic |
| 666 | C2 | #20287521 | 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