← #28264753
Subgroups — #28264753
Order 13568.
1682 conjugacy classes of subgroups.
The subgroup lattice has 680 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20288523 | C2 | 1 | 2 | yes | maximal |
| 2 | #20287679 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #20287644 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20287608 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20287603 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20287603 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20287598 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20285251 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #20285227 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #20284555 | C2 | 1 | 2 | yes | maximal |
| 11 | #20284551 | C2 | 1 | 2 | yes | maximal |
| 12 | #20284519 | C2 | 1 | 2 | yes | maximal |
| 13 | #20283647 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #20283584 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #20283582 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C2×#16810717 | C2 | 1 | 1 | yes | maximal, characteristic |
| 17 | C53×#3164 | C2 | 1 | 1 | yes | maximal, characteristic |
| 18 | C22×Dic212 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16811353 | — | 2 | 2 | no | — |
| 20 | #16811353 | C22 | 1 | 4 | yes | — |
| 21 | #16811350 | — | 2 | 2 | no | — |
| 22 | #16811350 | — | 2 | 2 | no | — |
| 23 | #16811350 | C22 | 1 | 4 | yes | — |
| 24 | #16811350 | C22 | 1 | 4 | yes | — |
| 25 | #16811348 | — | 2 | 2 | no | — |
| 26 | #16811348 | C22 | 1 | 4 | yes | — |
| 27 | #16811254 | C22 | 1 | 2 | yes | — |
| 28 | #16811252 | — | 2 | 4 | no | — |
| 29 | #16811176 | C22 | 1 | 2 | yes | — |
| 30 | #16811176 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16811175 | — | 2 | 4 | no | — |
| 32 | #16811100 | C22 | 1 | 2 | yes | — |
| 33 | #16811100 | C22 | 1 | 2 | yes | — |
| 34 | C2×#13133182 | C22 | 1 | 2 | yes | — |
| 35 | #16811031 | C22 | 1 | 4 | yes | — |
| 36 | #16811027 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16811027 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16811027 | C22 | 1 | 2 | yes | — |
| 39 | #16811024 | C22 | 1 | 1 | yes | characteristic |
| 40 | #16811024 | C22 | 1 | 1 | yes | characteristic |
| 41 | #16811024 | C22 | 1 | 2 | yes | — |
| 42 | #16811023 | C22 | 1 | 2 | yes | — |
| 43 | #16811020 | C22 | 1 | 2 | yes | — |
| 44 | #16810933 | C22 | 1 | 4 | yes | — |
| 45 | #16810933 | C22 | 1 | 4 | yes | — |
| 46 | #16810929 | C22 | 1 | 4 | yes | — |
| 47 | #16810929 | C22 | 1 | 4 | yes | — |
| 48 | #16810927 | C22 | 1 | 4 | yes | — |
| 49 | #16810927 | C22 | 1 | 4 | yes | — |
| 50 | #16810917 | C22 | 1 | 4 | yes | — |
| 51 | #16810917 | C22 | 1 | 4 | yes | — |
| 52 | #16810915 | C22 | 1 | 4 | yes | — |
| 53 | #16810907 | C22 | 1 | 4 | yes | — |
| 54 | #16810907 | C22 | 1 | 4 | yes | — |
| 55 | #16810905 | C22 | 1 | 4 | yes | — |
| 56 | #16810751 | C22 | 1 | 2 | yes | — |
| 57 | #16810751 | C22 | 1 | 2 | yes | — |
| 58 | C8×Dic106 | C22 | 1 | 2 | yes | — |
| 59 | C8×Dic106 | C22 | 1 | 2 | yes | — |
| 60 | #16810731 | C22 | 1 | 4 | yes | — |
| 61 | #16810729 | C22 | 1 | 4 | yes | — |
| 62 | C4×Dic212 | C22 | 1 | 2 | yes | — |
| 63 | C4×Dic212 | C22 | 1 | 2 | yes | — |
| 64 | #16810717 | C22 | 1 | 2 | yes | — |
| 65 | #16810717 | C22 | 1 | 2 | yes | — |
| 66 | #16810717 | C22 | 1 | 2 | yes | — |
| 67 | #16810717 | C22 | 1 | 2 | yes | — |
| 68 | #16810717 | C22 | 1 | 2 | yes | — |
| 69 | #16810717 | C22 | 1 | 2 | yes | — |
| 70 | #16810663 | C22 | 1 | 2 | yes | — |
| 71 | #16810661 | C22 | 1 | 1 | yes | characteristic |
| 72 | #16810659 | C22 | 1 | 2 | yes | — |
| 73 | #16810651 | C22 | 1 | 1 | yes | characteristic |
| 74 | #16810650 | C22 | 1 | 1 | yes | characteristic |
| 75 | #16810646 | C22 | 1 | 1 | yes | characteristic |
| 76 | #16810633 | C22 | 1 | 2 | yes | — |
| 77 | #16810631 | C22 | 1 | 2 | yes | — |
| 78 | C2×#13133140 | C22 | 1 | 2 | yes | — |
| 79 | #16810578 | C22 | 1 | 1 | yes | characteristic |
| 80 | C2×C8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 81 | C53×#544 | C22 | 1 | 2 | yes | — |
| 82 | C53×#501 | C22 | 1 | 4 | yes | — |
| 83 | C53×#500 | C22 | 1 | 2 | yes | — |
| 84 | C53×#499 | C22 | 1 | 2 | yes | — |
| 85 | C53×#428 | C22 | 1 | 2 | yes | — |
| 86 | C53×#427 | C22 | 1 | 1 | yes | characteristic |
| 87 | C2×#107×C53 | C22 | 1 | 1 | yes | characteristic |
| 88 | C53×#405 | C22 | 1 | 1 | yes | characteristic |
| 89 | C22×Dic106 | C23 | 1 | 2 | yes | — |
| 90 | C2×Dic212 | Q8 | 1 | 8 | yes | complemented |
| 91 | C2×Dic212 | C23 | 1 | 2 | yes | — |
| 92 | C2×Dic212 | C23 | 1 | 2 | yes | — |
| 93 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 94 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 95 | #13133216 | — | 2 | 2 | no | — |
| 96 | #13133216 | — | 2 | 4 | no | — |
| 97 | #13133216 | — | 2 | 4 | no | — |
| 98 | #13133216 | — | 2 | 4 | no | — |
| 99 | #13133216 | D4 | 1 | 1 | yes | characteristic |
| 100 | #13133216 | D4 | 1 | 1 | yes | characteristic |
| 101 | #13133216 | C23 | 1 | 2 | yes | — |
| 102 | #13133216 | C23 | 1 | 2 | yes | — |
| 103 | #13133216 | C23 | 1 | 4 | yes | — |
| 104 | #13133215 | — | 2 | 4 | no | — |
| 105 | #13133215 | — | 2 | 4 | no | — |
| 106 | #13133215 | — | 2 | 4 | no | — |
| 107 | #13133208 | — | 2 | 2 | no | — |
| 108 | #13133208 | D4 | 1 | 1 | yes | characteristic |
| 109 | #13133208 | D4 | 1 | 1 | yes | characteristic |
| 110 | #13133208 | C23 | 1 | 2 | yes | — |
| 111 | #13133208 | C23 | 1 | 2 | yes | — |
| 112 | #13133208 | C23 | 1 | 4 | yes | — |
| 113 | #13133207 | — | 2 | 4 | no | — |
| 114 | #13133207 | — | 2 | 4 | no | — |
| 115 | #13133207 | — | 2 | 4 | no | — |
| 116 | #13133207 | — | 2 | 4 | no | — |
| 117 | #13133207 | — | 2 | 4 | no | — |
| 118 | #13133207 | — | 2 | 4 | no | — |
| 119 | #13133196 | — | 2 | 4 | no | — |
| 120 | #13133194 | — | 2 | 2 | no | — |
| 121 | #13133194 | — | 2 | 2 | no | — |
| 122 | #13133194 | D4 | 1 | 2 | yes | — |
| 123 | #13133194 | D4 | 1 | 2 | yes | — |
| 124 | Q8×Dic53 | — | 2 | 4 | no | — |
| 125 | C4×Dic106 | — | 2 | 2 | no | — |
| 126 | C4×Dic106 | — | 2 | 2 | no | — |
| 127 | C4×Dic106 | — | 2 | 2 | no | — |
| 128 | C4×Dic106 | — | 2 | 2 | no | — |
| 129 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 130 | C4×Dic106 | C23 | 1 | 2 | yes | — |
| 131 | C4×Dic106 | C23 | 1 | 4 | yes | — |
| 132 | C4×Dic106 | C23 | 1 | 4 | yes | — |
| 133 | #13133182 | — | 2 | 2 | no | — |
| 134 | #13133182 | — | 2 | 2 | no | — |
| 135 | #13133182 | — | 2 | 4 | no | — |
| 136 | #13133182 | — | 2 | 4 | no | — |
| 137 | #13133182 | — | 2 | 2 | no | — |
| 138 | #13133182 | — | 2 | 2 | no | — |
| 139 | #13133182 | — | 2 | 4 | no | — |
| 140 | #13133182 | C23 | 1 | 4 | yes | — |
| 141 | #13133182 | C23 | 1 | 4 | yes | — |
| 142 | #13133182 | C23 | 1 | 4 | yes | — |
| 143 | #13133182 | C23 | 1 | 4 | yes | — |
| 144 | #13133176 | C23 | 1 | 2 | yes | — |
| 145 | #13133176 | C23 | 1 | 1 | yes | characteristic |
| 146 | #13133173 | — | 2 | 4 | no | — |
| 147 | #13133173 | — | 2 | 4 | no | — |
| 148 | C2×#11719919 | — | 2 | 2 | no | — |
| 149 | C2×C4×Dic53 | — | 2 | 2 | no | — |
| 150 | C2×C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 151 | #13133151 | C23 | 1 | 1 | yes | characteristic |
| 152 | #13133151 | C23 | 1 | 1 | yes | characteristic |
| 153 | #13133150 | C23 | 1 | 2 | yes | — |
| 154 | #13133150 | C23 | 1 | 2 | yes | — |
| 155 | #13133150 | C23 | 1 | 4 | yes | — |
| 156 | #13133149 | C23 | 1 | 2 | yes | — |
| 157 | #13133148 | C23 | 1 | 2 | yes | — |
| 158 | #13133148 | C23 | 1 | 2 | yes | — |
| 159 | #13133148 | C23 | 1 | 4 | yes | — |
| 160 | C4⋊#88322 | C23 | 1 | 2 | yes | — |
| 161 | C4⋊#88322 | C23 | 1 | 2 | yes | — |
| 162 | #13133146 | C23 | 1 | 2 | yes | — |
| 163 | #13133146 | C23 | 1 | 2 | yes | — |
| 164 | #13133146 | C23 | 1 | 2 | yes | — |
| 165 | #13133146 | C23 | 1 | 2 | yes | — |
| 166 | #13133142 | C23 | 1 | 4 | yes | — |
| 167 | #13133142 | C23 | 1 | 4 | yes | — |
| 168 | #13133140 | C23 | 1 | 4 | yes | — |
| 169 | #13133140 | C23 | 1 | 4 | yes | — |
| 170 | #13133140 | C23 | 1 | 4 | yes | — |
| 171 | #13133140 | C23 | 1 | 4 | yes | — |
| 172 | #13133127 | C23 | 1 | 2 | yes | — |
| 173 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 174 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 175 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 176 | C8×Dic53 | C23 | 1 | 2 | yes | — |
| 177 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 178 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 179 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 180 | C4⋊Q8×C53 | — | 2 | 2 | no | — |
| 181 | C4⋊Q8×C53 | C23 | 1 | 4 | yes | — |
| 182 | #125×C53 | — | 2 | 2 | no | — |
| 183 | #125×C53 | C23 | 1 | 4 | yes | — |
| 184 | C22⋊Q8×C53 | — | 2 | 4 | no | — |
| 185 | #117×C53 | C23 | 1 | 2 | yes | — |
| 186 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 187 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 188 | #107×C53 | C23 | 1 | 1 | yes | characteristic |
| 189 | #107×C53 | C23 | 1 | 2 | yes | — |
| 190 | #107×C53 | C23 | 1 | 1 | yes | characteristic |
| 191 | #107×C53 | C23 | 1 | 4 | yes | — |
| 192 | #107×C53 | C23 | 1 | 2 | yes | — |
| 193 | #106×C53 | C23 | 1 | 2 | yes | — |
| 194 | #106×C53 | C23 | 1 | 4 | yes | — |
| 195 | #97×C53 | C23 | 1 | 2 | yes | — |
| 196 | C4×C8×C53 | C23 | 1 | 2 | yes | — |
| 197 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 198 | C22×C4×C53 | — | 2 | 2 | no | — |
| 199 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 200 | C22×Dic53 | — | 2 | 2 | no | — |
| 201 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C2×Dic106 | — | 2 | 2 | no | — |
| 204 | C2×Dic106 | — | 2 | 4 | no | — |
| 205 | C2×Dic106 | — | 2 | 2 | no | — |
| 206 | C2×Dic106 | — | 2 | 4 | no | — |
| 207 | C2×Dic106 | — | 2 | 2 | no | — |
| 208 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 209 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 210 | C2×Dic106 | C2×Q8 | 1 | 8 | yes | — |
| 211 | C2×Dic106 | C24 | 1 | 4 | yes | — |
| 212 | M16×C53 | — | 2 | 2 | no | — |
| 213 | C2×C8×C53 | C2×Q8 | 1 | 4 | yes | — |
| 214 | C2×C8×C53 | C24 | 1 | 2 | yes | — |
| 215 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 216 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 217 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 218 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 219 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 220 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 221 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C4⋊C4×C53 | C24 | 1 | 2 | yes | — |
| 224 | C4⋊C4×C53 | C24 | 1 | 4 | yes | — |
| 225 | C4⋊C4×C53 | C24 | 1 | 2 | yes | — |
| 226 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 227 | C22⋊C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 228 | C42×C53 | — | 2 | 2 | no | — |
| 229 | C42×C53 | C24 | 1 | 2 | yes | — |
| 230 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 231 | C22⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 232 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 233 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 234 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 235 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 238 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 239 | C4⋊Dic53 | C24 | 1 | 2 | yes | — |
| 240 | C4⋊Dic53 | C24 | 1 | 2 | yes | — |
| 241 | #11719919 | — | 2 | 4 | no | — |
| 242 | #11719919 | — | 2 | 4 | no | — |
| 243 | #11719919 | — | 2 | 4 | no | — |
| 244 | #11719919 | — | 2 | 4 | no | — |
| 245 | #11719919 | — | 2 | 4 | no | — |
| 246 | #11719919 | — | 2 | 4 | no | — |
| 247 | #11719919 | — | 2 | 2 | no | — |
| 248 | #11719919 | — | 2 | 2 | no | — |
| 249 | #11719919 | — | 2 | 4 | no | — |
| 250 | #11719919 | — | 2 | 4 | no | — |
| 251 | #11719919 | — | 2 | 2 | no | — |
| 252 | #11719919 | — | 2 | 2 | no | — |
| 253 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 254 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 255 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 256 | #11719919 | C2×D4 | 1 | 2 | yes | — |
| 257 | C4×Dic53 | — | 2 | 4 | no | — |
| 258 | C4×Dic53 | — | 2 | 4 | no | — |
| 259 | C4×Dic53 | — | 2 | 2 | no | — |
| 260 | C4×Dic53 | — | 2 | 4 | no | — |
| 261 | C4×Dic53 | — | 2 | 4 | no | — |
| 262 | C4×Dic53 | — | 2 | 4 | no | — |
| 263 | C4×Dic53 | — | 2 | 4 | no | — |
| 264 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C4×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 267 | C4×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 268 | C4×Dic53 | C24 | 1 | 2 | yes | — |
| 269 | #11719917 | — | 2 | 2 | no | — |
| 270 | C2×#88322 | — | 2 | 2 | no | — |
| 271 | C2×#88322 | C24 | 1 | 1 | yes | characteristic |
| 272 | C2×#88322 | C24 | 1 | 1 | yes | characteristic |
| 273 | C2×#88322 | C24 | 1 | 2 | yes | — |
| 274 | Dic212 | C2×Q8 | 1 | 8 | yes | — |
| 275 | Dic212 | C2×Q8 | 1 | 8 | yes | — |
| 276 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 277 | Q8×C53 | — | 8 | 4 | no | — |
| 278 | C2×C4×C53 | — | 2 | 4 | no | — |
| 279 | C2×C4×C53 | — | 2 | 2 | no | — |
| 280 | C2×C4×C53 | — | 2 | 2 | no | — |
| 281 | C2×C4×C53 | — | 8 | 2 | no | — |
| 282 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 283 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 284 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×C4×C53 | C22×Q8 | 1 | 2 | yes | — |
| 286 | C2×C4×C53 | 2−1+4 | 1 | 2 | yes | — |
| 287 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 288 | C2×Dic53 | — | 2 | 8 | no | — |
| 289 | C2×Dic53 | — | 2 | 4 | no | — |
| 290 | C2×Dic53 | — | 2 | 2 | no | — |
| 291 | C2×Dic53 | — | 2 | 2 | no | — |
| 292 | C2×Dic53 | — | 2 | 2 | no | — |
| 293 | C2×Dic53 | — | 4 | 1 | no | — |
| 294 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 295 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 296 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 298 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 300 | Dic106 | — | 2 | 8 | no | — |
| 301 | Dic106 | — | 2 | 4 | no | — |
| 302 | Dic106 | — | 2 | 4 | no | — |
| 303 | Dic106 | — | 4 | 2 | no | — |
| 304 | Dic106 | — | 4 | 4 | no | — |
| 305 | Dic106 | — | 8 | 4 | no | — |
| 306 | Dic106 | — | 8 | 2 | no | — |
| 307 | Dic106 | C22×Q8 | 1 | 8 | yes | — |
| 308 | C8×C53 | — | 2 | 2 | no | — |
| 309 | C8×C53 | C22×Q8 | 1 | 2 | yes | — |
| 310 | C8×C53 | C22×Q8 | 1 | 2 | yes | — |
| 311 | #88322 | — | 2 | 1 | no | — |
| 312 | #88322 | — | 2 | 1 | no | — |
| 313 | #88322 | — | 2 | 2 | no | — |
| 314 | #61372 | — | 53 | 1 | no | maximal, Sylow |
| 315 | C22×C53 | — | 2 | 1 | no | — |
| 316 | C22×C53 | — | 2 | 1 | no | — |
| 317 | C22×C53 | D4×Q8 | 1 | 2 | yes | — |
| 318 | C22×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 319 | C4×C53 | — | 2 | 2 | no | — |
| 320 | C4×C53 | — | 2 | 2 | no | — |
| 321 | C4×C53 | — | 4 | 4 | no | — |
| 322 | C4×C53 | — | 4 | 2 | no | — |
| 323 | C4×C53 | — | 4 | 2 | no | — |
| 324 | C4×C53 | D4×Q8 | 1 | 2 | yes | — |
| 325 | C4×C53 | C23×Q8 | 1 | 1 | yes | characteristic |
| 326 | C4×C53 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 327 | Dic53 | — | 2 | 1 | no | — |
| 328 | Dic53 | — | 2 | 2 | no | — |
| 329 | Dic53 | — | 2 | 1 | no | — |
| 330 | Dic53 | — | 2 | 8 | no | — |
| 331 | Dic53 | — | 2 | 2 | no | — |
| 332 | Dic53 | — | 2 | 1 | no | — |
| 333 | Dic53 | — | 4 | 2 | no | — |
| 334 | Dic53 | — | 4 | 2 | no | — |
| 335 | Dic53 | #578 | 1 | 2 | yes | — |
| 336 | #3502 | — | 53 | 2 | no | — |
| 337 | #3390 | — | 53 | 4 | no | — |
| 338 | #3387 | — | 53 | 4 | no | — |
| 339 | #3383 | — | 53 | 2 | no | — |
| 340 | #3383 | — | 53 | 2 | no | — |
| 341 | #3383 | — | 53 | 2 | no | — |
| 342 | Q8×Q16 | — | 53 | 2 | no | — |
| 343 | #3164 | — | 53 | 1 | no | — |
| 344 | #3164 | D53 | 1 | 1 | yes | characteristic |
| 345 | #3160 | — | 53 | 1 | no | — |
| 346 | #3082 | — | 53 | 2 | no | — |
| 347 | #3082 | — | 53 | 2 | no | — |
| 348 | #3078 | — | 53 | 2 | no | — |
| 349 | #2960 | — | 53 | 1 | no | — |
| 350 | #2950 | — | 53 | 1 | no | — |
| 351 | #2950 | — | 53 | 1 | no | — |
| 352 | C2×C4×Q16 | — | 53 | 1 | no | — |
| 353 | C2×C53 | — | 2 | 2 | no | — |
| 354 | C2×C53 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 355 | C2×C53 | C2×#578 | 1 | 1 | yes | characteristic |
| 356 | C2×C53 | #3584 | 1 | 1 | yes | characteristic |
| 357 | C22×Q16 | — | 53 | 1 | no | — |
| 358 | Q82 | — | 53 | 4 | no | — |
| 359 | Q82 | — | 106 | 2 | no | — |
| 360 | #557 | — | 53 | 4 | no | — |
| 361 | #557 | — | 53 | 4 | no | — |
| 362 | #557 | — | 53 | 4 | no | — |
| 363 | #557 | — | 106 | 2 | no | — |
| 364 | #557 | — | 106 | 2 | no | — |
| 365 | #557 | — | 106 | 2 | no | — |
| 366 | #544 | — | 53 | 2 | no | — |
| 367 | #544 | — | 106 | 4 | no | — |
| 368 | #544 | C2×D53 | 1 | 2 | yes | — |
| 369 | #533 | — | 53 | 2 | no | — |
| 370 | #533 | — | 53 | 1 | no | — |
| 371 | #533 | — | 106 | 4 | no | — |
| 372 | #519 | — | 53 | 2 | no | — |
| 373 | #519 | — | 53 | 2 | no | — |
| 374 | C2×C4×Q8 | — | 53 | 2 | no | — |
| 375 | #501 | — | 53 | 4 | no | — |
| 376 | #501 | C2×D53 | 1 | 4 | yes | — |
| 377 | #500 | — | 53 | 1 | no | — |
| 378 | #500 | — | 53 | 2 | no | — |
| 379 | #500 | — | 53 | 1 | no | — |
| 380 | #500 | C2×D53 | 1 | 2 | yes | — |
| 381 | #499 | — | 53 | 1 | no | — |
| 382 | #499 | — | 53 | 1 | no | — |
| 383 | #499 | — | 53 | 2 | no | — |
| 384 | #499 | — | 53 | 2 | no | — |
| 385 | #499 | C2×D53 | 1 | 2 | yes | — |
| 386 | #498 | — | 53 | 2 | no | — |
| 387 | #479 | — | 53 | 4 | no | — |
| 388 | #479 | — | 53 | 4 | no | — |
| 389 | #479 | — | 53 | 4 | no | — |
| 390 | #479 | — | 53 | 4 | no | — |
| 391 | #479 | — | 53 | 4 | no | — |
| 392 | #479 | — | 53 | 4 | no | — |
| 393 | #477 | — | 53 | 4 | no | — |
| 394 | #477 | — | 53 | 4 | no | — |
| 395 | #477 | — | 53 | 4 | no | — |
| 396 | #475 | — | 53 | 4 | no | — |
| 397 | #475 | — | 53 | 4 | no | — |
| 398 | #475 | — | 53 | 4 | no | — |
| 399 | #446 | — | 53 | 2 | no | — |
| 400 | #446 | — | 53 | 2 | no | — |
| 401 | C8×Q8 | — | 53 | 2 | no | — |
| 402 | C8×Q8 | — | 53 | 2 | no | — |
| 403 | #441 | — | 53 | 4 | no | — |
| 404 | #441 | — | 53 | 4 | no | — |
| 405 | C4×Q16 | — | 53 | 2 | no | — |
| 406 | C4×Q16 | — | 53 | 2 | no | — |
| 407 | C4×Q16 | — | 53 | 2 | no | — |
| 408 | C4×Q16 | — | 53 | 2 | no | — |
| 409 | C4×Q16 | — | 53 | 2 | no | — |
| 410 | C4×Q16 | — | 53 | 2 | no | — |
| 411 | C4×Q16 | — | 53 | 2 | no | — |
| 412 | C4×Q16 | — | 53 | 2 | no | — |
| 413 | #428 | — | 53 | 2 | no | — |
| 414 | #428 | C2×D53 | 1 | 2 | yes | — |
| 415 | #427 | — | 53 | 1 | no | — |
| 416 | #427 | — | 53 | 2 | no | — |
| 417 | #427 | C2×D53 | 1 | 1 | yes | characteristic |
| 418 | C2×#107 | C2×D53 | 1 | 1 | yes | characteristic |
| 419 | #424 | — | 53 | 1 | no | — |
| 420 | #424 | — | 53 | 1 | no | — |
| 421 | #423 | — | 53 | 1 | no | — |
| 422 | #419 | — | 53 | 2 | no | — |
| 423 | #419 | — | 53 | 2 | no | — |
| 424 | C2×#103 | — | 53 | 2 | no | — |
| 425 | #405 | — | 53 | 1 | no | — |
| 426 | #405 | C2×D53 | 1 | 1 | yes | characteristic |
| 427 | C2×C4×C8 | — | 53 | 1 | no | — |
| 428 | C53 | #61372 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 429 | C22×Q8 | — | 53 | 2 | no | — |
| 430 | C2×Q16 | — | 53 | 8 | no | — |
| 431 | C2×Q16 | — | 53 | 2 | no | — |
| 432 | C2×Q16 | — | 53 | 2 | no | — |
| 433 | C2×M16 | — | 53 | 1 | no | — |
| 434 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 435 | C22×C8 | — | 53 | 1 | no | — |
| 436 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 437 | C4⋊Q8 | — | 2 | 2 | no | — |
| 438 | C4⋊Q8 | — | 53 | 1 | no | — |
| 439 | C4⋊Q8 | — | 53 | 1 | no | — |
| 440 | C4⋊Q8 | — | 53 | 2 | no | — |
| 441 | C4⋊Q8 | — | 53 | 2 | no | — |
| 442 | C4⋊Q8 | — | 53 | 4 | no | — |
| 443 | C4⋊Q8 | — | 106 | 2 | no | — |
| 444 | C4⋊Q8 | — | 106 | 4 | no | — |
| 445 | C4⋊Q8 | — | 106 | 4 | no | — |
| 446 | C4⋊Q8 | — | 106 | 4 | no | — |
| 447 | C4⋊Q8 | — | 106 | 4 | no | — |
| 448 | C4⋊Q8 | — | 106 | 4 | no | — |
| 449 | C4⋊Q8 | — | 106 | 4 | no | — |
| 450 | C4⋊Q8 | C22×D53 | 1 | 4 | yes | — |
| 451 | #125 | — | 2 | 2 | no | — |
| 452 | #125 | — | 53 | 1 | no | — |
| 453 | #125 | — | 53 | 1 | no | — |
| 454 | #125 | — | 53 | 2 | no | — |
| 455 | #125 | — | 53 | 2 | no | — |
| 456 | #125 | — | 53 | 4 | no | — |
| 457 | #125 | — | 106 | 4 | no | — |
| 458 | #125 | — | 106 | 4 | no | — |
| 459 | #125 | — | 106 | 2 | no | — |
| 460 | #125 | — | 106 | 4 | no | — |
| 461 | #125 | — | 106 | 4 | no | — |
| 462 | #125 | — | 106 | 4 | no | — |
| 463 | #125 | — | 106 | 4 | no | — |
| 464 | #125 | C22×D53 | 1 | 4 | yes | — |
| 465 | C22⋊Q8 | — | 2 | 4 | no | — |
| 466 | C22⋊Q8 | — | 53 | 2 | no | — |
| 467 | C22⋊Q8 | — | 53 | 2 | no | — |
| 468 | C22⋊Q8 | — | 106 | 2 | no | — |
| 469 | C22⋊Q8 | — | 106 | 2 | no | — |
| 470 | C22⋊Q8 | — | 106 | 4 | no | — |
| 471 | C4×Q8 | — | 53 | 2 | no | — |
| 472 | C4×Q8 | — | 53 | 2 | no | — |
| 473 | C4×Q8 | — | 53 | 4 | no | — |
| 474 | C4×Q8 | — | 53 | 4 | no | — |
| 475 | C4×Q8 | — | 53 | 4 | no | — |
| 476 | C4×Q8 | — | 53 | 4 | no | — |
| 477 | C4×Q8 | — | 53 | 4 | no | — |
| 478 | C4×Q8 | — | 53 | 4 | no | — |
| 479 | C4×Q8 | — | 106 | 2 | no | — |
| 480 | C4×Q8 | — | 106 | 2 | no | — |
| 481 | C4×Q8 | — | 106 | 2 | no | — |
| 482 | C4×Q8 | — | 106 | 2 | no | — |
| 483 | C4×Q8 | — | 106 | 2 | no | — |
| 484 | C4×Q8 | — | 106 | 2 | no | — |
| 485 | C4×Q8 | — | 106 | 4 | no | — |
| 486 | C4×Q8 | — | 106 | 4 | no | — |
| 487 | C4×Q8 | — | 106 | 4 | no | — |
| 488 | C4×Q8 | — | 106 | 4 | no | — |
| 489 | C4×Q8 | — | 106 | 2 | no | — |
| 490 | C4×Q8 | — | 106 | 2 | no | — |
| 491 | #117 | — | 53 | 1 | no | — |
| 492 | #117 | — | 53 | 2 | no | — |
| 493 | #117 | — | 106 | 4 | no | — |
| 494 | #117 | — | 106 | 4 | no | — |
| 495 | #117 | C22×D53 | 1 | 2 | yes | — |
| 496 | #117 | C22×D53 | 1 | 1 | yes | characteristic |
| 497 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 498 | C2×C4⋊C4 | C22×D53 | 1 | 2 | yes | — |
| 499 | C2×C42 | — | 53 | 1 | no | — |
| 500 | C2×C42 | — | 106 | 2 | no | — |
| 501 | #107 | — | 53 | 1 | no | — |
| 502 | #107 | — | 53 | 1 | no | — |
| 503 | #107 | — | 53 | 2 | no | — |
| 504 | #107 | — | 53 | 2 | no | — |
| 505 | #107 | — | 53 | 4 | no | — |
| 506 | #107 | C22×D53 | 1 | 2 | yes | — |
| 507 | #107 | C22×D53 | 1 | 2 | yes | — |
| 508 | #107 | C22×D53 | 1 | 1 | yes | characteristic |
| 509 | #107 | C22×D53 | 1 | 1 | yes | characteristic |
| 510 | #107 | C22×D53 | 1 | 4 | yes | — |
| 511 | #106 | — | 53 | 2 | no | — |
| 512 | #106 | — | 53 | 2 | no | — |
| 513 | #106 | — | 53 | 2 | no | — |
| 514 | #106 | — | 53 | 4 | no | — |
| 515 | #106 | C22×D53 | 1 | 2 | yes | — |
| 516 | #106 | C22×D53 | 1 | 4 | yes | — |
| 517 | C4⋊C8 | — | 53 | 2 | no | — |
| 518 | C4⋊C8 | — | 53 | 2 | no | — |
| 519 | C4⋊C8 | — | 53 | 2 | no | — |
| 520 | C4⋊C8 | — | 53 | 2 | no | — |
| 521 | C4⋊C8 | — | 53 | 2 | no | — |
| 522 | C4⋊C8 | — | 53 | 2 | no | — |
| 523 | #103 | — | 53 | 4 | no | — |
| 524 | #103 | — | 53 | 4 | no | — |
| 525 | #103 | — | 53 | 4 | no | — |
| 526 | #103 | — | 53 | 4 | no | — |
| 527 | #103 | — | 53 | 4 | no | — |
| 528 | #103 | — | 53 | 4 | no | — |
| 529 | #97 | — | 53 | 2 | no | — |
| 530 | #97 | C22×D53 | 1 | 2 | yes | — |
| 531 | C4×C8 | — | 53 | 1 | no | — |
| 532 | C4×C8 | — | 53 | 1 | no | — |
| 533 | C4×C8 | — | 53 | 1 | no | — |
| 534 | C4×C8 | — | 53 | 1 | no | — |
| 535 | C4×C8 | — | 53 | 2 | no | — |
| 536 | C4×C8 | C22×D53 | 1 | 2 | yes | — |
| 537 | C2×Q8 | — | 2 | 4 | no | — |
| 538 | C2×Q8 | — | 53 | 2 | no | — |
| 539 | C2×Q8 | — | 53 | 2 | no | — |
| 540 | C2×Q8 | — | 53 | 8 | no | — |
| 541 | C2×Q8 | — | 53 | 4 | no | — |
| 542 | C2×Q8 | — | 106 | 2 | no | — |
| 543 | C2×Q8 | — | 106 | 4 | no | — |
| 544 | C2×Q8 | — | 106 | 2 | no | — |
| 545 | C2×Q8 | — | 106 | 2 | no | — |
| 546 | C2×Q8 | — | 106 | 4 | no | — |
| 547 | C22×C4 | — | 2 | 2 | no | — |
| 548 | C22×C4 | — | 53 | 1 | no | — |
| 549 | C22×C4 | — | 53 | 1 | no | — |
| 550 | C22×C4 | — | 106 | 2 | no | — |
| 551 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 552 | Q16 | — | 53 | 8 | no | — |
| 553 | Q16 | — | 53 | 8 | no | — |
| 554 | M16 | — | 2 | 2 | no | — |
| 555 | M16 | — | 106 | 2 | no | — |
| 556 | C2×C8 | — | 53 | 1 | no | — |
| 557 | C2×C8 | — | 53 | 1 | no | — |
| 558 | C2×C8 | — | 53 | 2 | no | — |
| 559 | C2×C8 | — | 106 | 2 | no | — |
| 560 | C2×C8 | Q8×D53 | 1 | 4 | yes | — |
| 561 | C2×C8 | C23×D53 | 1 | 2 | yes | — |
| 562 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 563 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 564 | C4⋊C4 | — | 2 | 2 | no | — |
| 565 | C4⋊C4 | — | 2 | 4 | no | — |
| 566 | C4⋊C4 | — | 2 | 4 | no | — |
| 567 | C4⋊C4 | — | 2 | 4 | no | — |
| 568 | C4⋊C4 | — | 53 | 1 | no | — |
| 569 | C4⋊C4 | — | 53 | 1 | no | — |
| 570 | C4⋊C4 | — | 53 | 2 | no | — |
| 571 | C4⋊C4 | — | 53 | 2 | no | — |
| 572 | C4⋊C4 | — | 53 | 2 | no | — |
| 573 | C4⋊C4 | — | 53 | 2 | no | — |
| 574 | C4⋊C4 | — | 53 | 2 | no | — |
| 575 | C4⋊C4 | — | 53 | 2 | no | — |
| 576 | C4⋊C4 | — | 53 | 2 | no | — |
| 577 | C4⋊C4 | — | 53 | 2 | no | — |
| 578 | C4⋊C4 | — | 106 | 4 | no | — |
| 579 | C4⋊C4 | — | 106 | 4 | no | — |
| 580 | C4⋊C4 | — | 106 | 4 | no | — |
| 581 | C4⋊C4 | — | 106 | 4 | no | — |
| 582 | C4⋊C4 | — | 106 | 2 | no | — |
| 583 | C4⋊C4 | — | 106 | 2 | no | — |
| 584 | C4⋊C4 | — | 106 | 2 | no | — |
| 585 | C4⋊C4 | — | 106 | 4 | no | — |
| 586 | C4⋊C4 | — | 106 | 2 | no | — |
| 587 | C4⋊C4 | — | 106 | 4 | no | — |
| 588 | C4⋊C4 | — | 106 | 2 | no | — |
| 589 | C4⋊C4 | — | 106 | 2 | no | — |
| 590 | C4⋊C4 | — | 106 | 4 | no | — |
| 591 | C4⋊C4 | — | 106 | 4 | no | — |
| 592 | C4⋊C4 | — | 106 | 4 | no | — |
| 593 | C4⋊C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 594 | C4⋊C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 595 | C4⋊C4 | C23×D53 | 1 | 2 | yes | — |
| 596 | C4⋊C4 | C23×D53 | 1 | 4 | yes | — |
| 597 | C4⋊C4 | C23×D53 | 1 | 2 | yes | — |
| 598 | C22⋊C4 | — | 2 | 2 | no | — |
| 599 | C22⋊C4 | — | 53 | 2 | no | — |
| 600 | C22⋊C4 | — | 106 | 2 | no | — |
| 601 | C22⋊C4 | D4×D53 | 1 | 2 | yes | — |
| 602 | C42 | — | 2 | 2 | no | — |
| 603 | C42 | — | 53 | 1 | no | — |
| 604 | C42 | — | 53 | 1 | no | — |
| 605 | C42 | — | 53 | 1 | no | — |
| 606 | C42 | — | 53 | 1 | no | — |
| 607 | C42 | — | 53 | 2 | no | — |
| 608 | C42 | — | 106 | 4 | no | — |
| 609 | C42 | — | 106 | 4 | no | — |
| 610 | C42 | — | 106 | 4 | no | — |
| 611 | C42 | — | 106 | 4 | no | — |
| 612 | C42 | — | 106 | 2 | no | — |
| 613 | C42 | — | 106 | 4 | no | — |
| 614 | C42 | — | 106 | 4 | no | — |
| 615 | C42 | C23×D53 | 1 | 2 | yes | — |
| 616 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 617 | Q8 | — | 8 | 4 | no | — |
| 618 | Q8 | — | 53 | 8 | no | — |
| 619 | Q8 | — | 106 | 4 | no | — |
| 620 | Q8 | — | 106 | 8 | no | — |
| 621 | Q8 | — | 106 | 4 | no | — |
| 622 | Q8 | — | 424 | 4 | no | — |
| 623 | Q8 | — | 424 | 2 | no | — |
| 624 | Q8 | — | 212 | 2 | no | — |
| 625 | Q8 | — | 212 | 4 | no | — |
| 626 | C2×C4 | — | 2 | 2 | no | — |
| 627 | C2×C4 | — | 2 | 2 | no | — |
| 628 | C2×C4 | — | 2 | 4 | no | — |
| 629 | C2×C4 | — | 8 | 2 | no | — |
| 630 | C2×C4 | — | 53 | 1 | no | — |
| 631 | C2×C4 | — | 53 | 1 | no | — |
| 632 | C2×C4 | — | 53 | 1 | no | — |
| 633 | C2×C4 | — | 53 | 1 | no | — |
| 634 | C2×C4 | — | 53 | 2 | no | — |
| 635 | C2×C4 | — | 53 | 2 | no | — |
| 636 | C2×C4 | — | 106 | 2 | no | — |
| 637 | C2×C4 | — | 106 | 8 | no | — |
| 638 | C2×C4 | — | 106 | 4 | no | — |
| 639 | C2×C4 | — | 106 | 2 | no | — |
| 640 | C2×C4 | — | 106 | 2 | no | — |
| 641 | C2×C4 | — | 212 | 1 | no | — |
| 642 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 643 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 644 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 645 | C2×C4 | C2×Q8×D53 | 1 | 2 | yes | — |
| 646 | C2×C4 | #13133265 | 1 | 2 | yes | — |
| 647 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 648 | C8 | — | 2 | 2 | no | — |
| 649 | C8 | — | 106 | 1 | no | — |
| 650 | C8 | — | 106 | 1 | no | — |
| 651 | C8 | — | 106 | 2 | no | — |
| 652 | C8 | C2×Q8×D53 | 1 | 2 | yes | — |
| 653 | C8 | C2×Q8×D53 | 1 | 2 | yes | — |
| 654 | C22 | — | 2 | 1 | no | — |
| 655 | C22 | — | 2 | 1 | no | — |
| 656 | C22 | #16811288 | 1 | 2 | yes | — |
| 657 | C22 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 658 | C4 | — | 2 | 2 | no | — |
| 659 | C4 | — | 2 | 2 | no | — |
| 660 | C4 | — | 4 | 2 | no | — |
| 661 | C4 | — | 4 | 4 | no | — |
| 662 | C4 | — | 4 | 2 | no | — |
| 663 | C4 | — | 53 | 2 | no | — |
| 664 | C4 | — | 106 | 8 | no | — |
| 665 | C4 | — | 106 | 1 | no | — |
| 666 | C4 | — | 106 | 2 | no | — |
| 667 | C4 | — | 106 | 1 | no | — |
| 668 | C4 | — | 106 | 1 | no | — |
| 669 | C4 | — | 106 | 2 | no | — |
| 670 | C4 | — | 212 | 2 | no | — |
| 671 | C4 | — | 212 | 2 | no | — |
| 672 | C4 | #16811288 | 1 | 2 | yes | — |
| 673 | C4 | C22×Q8×D53 | 1 | 1 | yes | characteristic |
| 674 | C4 | C2×#13133265 | 1 | 1 | yes | characteristic |
| 675 | C2 | — | 2 | 2 | no | — |
| 676 | C2 | C2×#16811288 | 1 | 1 | yes | characteristic |
| 677 | C2 | #578×D53 | 1 | 1 | yes | characteristic |
| 678 | C2 | #20289483 | 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