← #28256988
Subgroups — #28256988
Order 13568.
1910 conjugacy classes of subgroups.
The subgroup lattice has 594 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20288010 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #20286110 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #20286109 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20286102 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20286090 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20286073 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #20284504 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #20284322 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #20284163 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #423×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#3253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#13133236 | C22 | 1 | 4 | yes | — |
| 13 | C2×M16×D53 | C22 | 1 | 2 | yes | — |
| 14 | #16811180 | C22 | 1 | 2 | yes | — |
| 15 | #16811178 | C22 | 1 | 2 | yes | — |
| 16 | #16811178 | C22 | 1 | 2 | yes | — |
| 17 | #16811171 | C22 | 1 | 2 | yes | — |
| 18 | #16811171 | C22 | 1 | 2 | yes | — |
| 19 | #16811155 | — | 2 | 2 | no | — |
| 20 | #16811155 | C22 | 1 | 4 | yes | — |
| 21 | #16811154 | — | 2 | 2 | no | — |
| 22 | #16811154 | C22 | 1 | 4 | yes | — |
| 23 | #16811152 | — | 2 | 2 | no | — |
| 24 | #16811152 | — | 2 | 2 | no | — |
| 25 | #16811133 | — | 2 | 2 | no | — |
| 26 | #16811133 | C22 | 1 | 4 | yes | — |
| 27 | #16811130 | — | 2 | 2 | no | — |
| 28 | #41×Dic53 | — | 2 | 2 | no | — |
| 29 | C4×#11719947 | — | 2 | 2 | no | — |
| 30 | C4×#11719947 | C22 | 1 | 4 | yes | — |
| 31 | C2×C42×D53 | C22 | 1 | 1 | yes | characteristic |
| 32 | #16810933 | C22 | 1 | 8 | yes | complemented |
| 33 | #16810925 | C22 | 1 | 8 | yes | complemented |
| 34 | #16810915 | C22 | 1 | 4 | yes | complemented |
| 35 | #16810909 | C22 | 1 | 4 | yes | complemented |
| 36 | #16810903 | C22 | 1 | 4 | yes | complemented |
| 37 | #16810882 | C22 | 1 | 4 | yes | — |
| 38 | #16810881 | C22 | 1 | 4 | yes | — |
| 39 | #16810873 | C22 | 1 | 4 | yes | — |
| 40 | #16810868 | C22 | 1 | 8 | yes | — |
| 41 | #16810867 | C22 | 1 | 8 | yes | — |
| 42 | #16810844 | C22 | 1 | 8 | yes | complemented |
| 43 | #16810836 | C22 | 1 | 8 | yes | complemented |
| 44 | #16810834 | C22 | 1 | 4 | yes | complemented |
| 45 | #16810828 | C22 | 1 | 4 | yes | complemented |
| 46 | #16810820 | C22 | 1 | 4 | yes | complemented |
| 47 | #16810658 | C22 | 1 | 4 | yes | — |
| 48 | #16810647 | C22 | 1 | 1 | yes | characteristic |
| 49 | #16810646 | C22 | 1 | 2 | yes | — |
| 50 | #16810645 | C22 | 1 | 4 | yes | — |
| 51 | C4⋊C8×D53 | C22 | 1 | 4 | yes | — |
| 52 | #16810616 | C22 | 1 | 8 | yes | — |
| 53 | C53×#532 | C22 | 1 | 2 | yes | — |
| 54 | C53×#476 | C22 | 1 | 4 | yes | complemented |
| 55 | C53×#469 | C22 | 1 | 4 | yes | — |
| 56 | C53×#459 | C22 | 1 | 4 | yes | complemented |
| 57 | C53×#423 | C22 | 1 | 1 | yes | characteristic |
| 58 | C2×#11719947 | — | 2 | 2 | no | — |
| 59 | C2×#11719947 | C23 | 1 | 4 | yes | — |
| 60 | C22×C4×D53 | D4 | 1 | 2 | yes | — |
| 61 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 62 | #13133236 | — | 4 | 8 | no | — |
| 63 | C2×Dic212 | C23 | 1 | 4 | yes | — |
| 64 | C2×#11719923 | C23 | 1 | 8 | yes | — |
| 65 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 66 | C2×#11719912 | C23 | 1 | 4 | yes | — |
| 67 | M16×D53 | — | 4 | 4 | no | — |
| 68 | C2×C8×D53 | C23 | 1 | 4 | yes | — |
| 69 | #13133217 | C23 | 1 | 2 | yes | — |
| 70 | #13133217 | C23 | 1 | 2 | yes | — |
| 71 | #13133210 | — | 2 | 4 | no | — |
| 72 | #13133210 | — | 2 | 4 | no | — |
| 73 | #13133209 | — | 2 | 2 | no | — |
| 74 | #13133208 | — | 2 | 2 | no | — |
| 75 | #13133208 | C23 | 1 | 4 | yes | — |
| 76 | #13133204 | — | 2 | 2 | no | — |
| 77 | #13133204 | C23 | 1 | 4 | yes | — |
| 78 | #13133199 | — | 2 | 4 | no | — |
| 79 | #13133199 | — | 2 | 4 | no | — |
| 80 | #13133198 | — | 2 | 4 | no | — |
| 81 | #13133197 | — | 2 | 2 | no | — |
| 82 | #13133197 | C23 | 1 | 4 | yes | — |
| 83 | #13133196 | — | 2 | 2 | no | — |
| 84 | #13133196 | C23 | 1 | 4 | yes | — |
| 85 | #13133193 | — | 2 | 2 | no | — |
| 86 | #13133193 | — | 2 | 2 | no | — |
| 87 | #13133188 | — | 2 | 2 | no | — |
| 88 | #13133188 | — | 2 | 2 | no | — |
| 89 | #13133188 | — | 2 | 2 | no | — |
| 90 | #13133188 | C23 | 1 | 4 | yes | — |
| 91 | #13133185 | — | 2 | 4 | no | — |
| 92 | Q8×Dic53 | — | 2 | 2 | no | — |
| 93 | Q8×Dic53 | — | 2 | 2 | no | — |
| 94 | C4×Dic106 | — | 2 | 2 | no | — |
| 95 | C4×Dic106 | C23 | 1 | 4 | yes | — |
| 96 | #13133182 | — | 2 | 2 | no | — |
| 97 | #13133182 | C23 | 1 | 4 | yes | — |
| 98 | D4×Dic53 | — | 2 | 2 | no | — |
| 99 | D4×Dic53 | — | 2 | 2 | no | — |
| 100 | D4×Dic53 | — | 2 | 2 | no | — |
| 101 | D4×Dic53 | — | 2 | 4 | no | — |
| 102 | D4×Dic53 | — | 2 | 4 | no | — |
| 103 | D4×Dic53 | C23 | 1 | 4 | yes | — |
| 104 | C4×C22⋊D53 | — | 2 | 4 | no | — |
| 105 | C4×C22⋊D53 | — | 2 | 4 | no | — |
| 106 | #13133177 | — | 2 | 4 | no | — |
| 107 | #13133177 | — | 2 | 4 | no | — |
| 108 | #13133176 | — | 2 | 4 | no | — |
| 109 | #13133176 | — | 2 | 2 | no | — |
| 110 | #13133175 | — | 2 | 2 | no | — |
| 111 | #13133175 | C23 | 1 | 4 | yes | — |
| 112 | #13133173 | — | 2 | 4 | no | — |
| 113 | #13133173 | — | 2 | 4 | no | — |
| 114 | C2×C4×Dic53 | — | 2 | 4 | no | — |
| 115 | C2×C4×Dic53 | D4 | 1 | 2 | yes | — |
| 116 | C2×C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 117 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 118 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 119 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 120 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 121 | C42×D53 | C23 | 1 | 2 | yes | — |
| 122 | C42×D53 | C23 | 1 | 2 | yes | — |
| 123 | #13133150 | C23 | 1 | 8 | yes | — |
| 124 | #13133149 | C23 | 1 | 4 | yes | — |
| 125 | C4⋊#88322 | C23 | 1 | 4 | yes | — |
| 126 | #13133146 | C23 | 1 | 8 | yes | — |
| 127 | #13133142 | C23 | 1 | 8 | yes | — |
| 128 | #13133140 | C23 | 1 | 8 | yes | — |
| 129 | #13133138 | C23 | 1 | 8 | yes | — |
| 130 | C2×#41×C53 | — | 2 | 2 | no | — |
| 131 | C2×D8×C53 | C23 | 1 | 4 | yes | — |
| 132 | C2×M16×C53 | C23 | 1 | 2 | yes | — |
| 133 | C4⋊Q8×C53 | C23 | 1 | 2 | yes | — |
| 134 | #127×C53 | C23 | 1 | 2 | yes | — |
| 135 | #124×C53 | — | 2 | 2 | no | — |
| 136 | #121×C53 | — | 2 | 2 | no | — |
| 137 | #121×C53 | C23 | 1 | 4 | yes | — |
| 138 | C4×D4×C53 | — | 2 | 2 | no | — |
| 139 | C4×D4×C53 | C23 | 1 | 4 | yes | — |
| 140 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 141 | #106×C53 | C23 | 1 | 4 | yes | — |
| 142 | C4⋊C8×C53 | C23 | 1 | 4 | yes | — |
| 143 | #102×C53 | C23 | 1 | 8 | yes | — |
| 144 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | #41×C53 | — | 4 | 8 | no | — |
| 146 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 147 | C2×D4×C53 | — | 2 | 4 | no | — |
| 148 | C2×D4×C53 | — | 2 | 2 | no | — |
| 149 | C2×D4×C53 | — | 2 | 2 | no | — |
| 150 | C2×D4×C53 | C24 | 1 | 4 | yes | — |
| 151 | C22×C4×C53 | — | 2 | 4 | no | — |
| 152 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 153 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 154 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 155 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 156 | C22×Dic53 | — | 2 | 4 | no | — |
| 157 | C22×Dic53 | — | 2 | 4 | no | — |
| 158 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C22×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 160 | #11719947 | — | 2 | 8 | no | — |
| 161 | #11719947 | — | 2 | 8 | no | — |
| 162 | #11719947 | — | 4 | 8 | no | — |
| 163 | C2×C4×D53 | — | 2 | 2 | no | — |
| 164 | C2×C4×D53 | — | 2 | 2 | no | — |
| 165 | C2×C4×D53 | — | 4 | 4 | no | — |
| 166 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 169 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 170 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 171 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 172 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 173 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 174 | C2×Dic106 | — | 2 | 2 | no | — |
| 175 | C2×Dic106 | C24 | 1 | 4 | yes | — |
| 176 | D8×C53 | — | 4 | 4 | no | — |
| 177 | M16×C53 | — | 4 | 2 | no | — |
| 178 | C2×C8×C53 | C24 | 1 | 4 | yes | — |
| 179 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 180 | C4⋊C4×C53 | C24 | 1 | 4 | yes | — |
| 181 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 182 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 183 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C42×C53 | C24 | 1 | 2 | yes | — |
| 186 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 187 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 188 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 189 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 190 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 191 | #11719923 | — | 4 | 8 | no | — |
| 192 | #11719921 | — | 2 | 4 | no | — |
| 193 | #11719921 | — | 2 | 4 | no | — |
| 194 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 195 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 196 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 197 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 198 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 199 | C4⋊Dic53 | C24 | 1 | 4 | yes | — |
| 200 | #11719919 | — | 2 | 4 | no | — |
| 201 | #11719919 | — | 2 | 4 | no | — |
| 202 | #11719919 | — | 2 | 4 | no | — |
| 203 | #11719919 | — | 2 | 4 | no | — |
| 204 | C4×Dic53 | — | 2 | 4 | no | — |
| 205 | C4×Dic53 | — | 2 | 4 | no | — |
| 206 | C4×Dic53 | — | 2 | 4 | no | — |
| 207 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 210 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 211 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 212 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 213 | C4×Dic53 | C24 | 1 | 2 | yes | — |
| 214 | #11719917 | — | 4 | 2 | no | — |
| 215 | C2×#88322 | C24 | 1 | 4 | yes | — |
| 216 | Dic212 | — | 4 | 4 | no | — |
| 217 | #11719912 | — | 4 | 4 | no | — |
| 218 | C8×D53 | — | 2 | 8 | no | — |
| 219 | C23×C53 | — | 2 | 4 | no | — |
| 220 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 221 | C22×D53 | — | 2 | 2 | no | — |
| 222 | C22×D53 | — | 4 | 2 | no | — |
| 223 | C22×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C22×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 225 | Q8×C53 | — | 4 | 4 | no | — |
| 226 | D4×C53 | — | 2 | 4 | no | — |
| 227 | D4×C53 | — | 2 | 4 | no | — |
| 228 | D4×C53 | — | 4 | 4 | no | — |
| 229 | D4×C53 | — | 4 | 8 | no | — |
| 230 | D4×C53 | — | 4 | 4 | no | — |
| 231 | C2×C4×C53 | — | 2 | 4 | no | — |
| 232 | C2×C4×C53 | — | 2 | 1 | no | — |
| 233 | C2×C4×C53 | — | 2 | 1 | no | — |
| 234 | C2×C4×C53 | — | 2 | 4 | no | — |
| 235 | C2×C4×C53 | — | 4 | 8 | no | — |
| 236 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 237 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 239 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 240 | C22⋊D53 | — | 4 | 8 | no | — |
| 241 | C22⋊D53 | — | 4 | 8 | no | — |
| 242 | C2×Dic53 | — | 2 | 2 | no | — |
| 243 | C2×Dic53 | — | 2 | 4 | no | — |
| 244 | C2×Dic53 | — | 2 | 4 | no | — |
| 245 | C2×Dic53 | — | 4 | 2 | no | — |
| 246 | C2×Dic53 | — | 4 | 8 | no | — |
| 247 | C2×Dic53 | — | 4 | 8 | no | — |
| 248 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 249 | C2×Dic53 | C22×D4 | 1 | 2 | yes | — |
| 250 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 252 | C4×D53 | — | 2 | 2 | no | — |
| 253 | C4×D53 | — | 2 | 4 | no | — |
| 254 | C4×D53 | — | 2 | 4 | no | — |
| 255 | C4×D53 | — | 2 | 1 | no | — |
| 256 | C4×D53 | — | 2 | 1 | no | — |
| 257 | C4×D53 | — | 2 | 2 | no | — |
| 258 | C4×D53 | — | 4 | 2 | no | — |
| 259 | C4×D53 | — | 4 | 2 | no | — |
| 260 | C4×D53 | H(5,𝔽2) | 1 | 2 | yes | — |
| 261 | C4×D53 | 2−1+4 | 1 | 2 | yes | — |
| 262 | Dic106 | — | 2 | 4 | no | — |
| 263 | Dic106 | — | 2 | 4 | no | — |
| 264 | Dic106 | — | 4 | 4 | no | — |
| 265 | C8×C53 | — | 2 | 4 | no | — |
| 266 | #88322 | — | 2 | 4 | no | — |
| 267 | #60907 | — | 53 | 1 | no | maximal, Sylow |
| 268 | C22×C53 | — | 2 | 1 | no | — |
| 269 | C22×C53 | — | 2 | 2 | no | — |
| 270 | C22×C53 | — | 4 | 4 | no | — |
| 271 | C22×C53 | — | 4 | 4 | no | — |
| 272 | C22×C53 | — | 4 | 4 | no | — |
| 273 | C22×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×D53 | — | 2 | 2 | no | — |
| 275 | C2×D53 | — | 2 | 1 | no | — |
| 276 | C2×D53 | — | 2 | 2 | no | — |
| 277 | C2×D53 | — | 4 | 4 | no | — |
| 278 | C2×D53 | #537 | 1 | 2 | yes | — |
| 279 | C4×C53 | — | 2 | 1 | no | — |
| 280 | C4×C53 | — | 2 | 2 | no | — |
| 281 | C4×C53 | — | 4 | 4 | no | — |
| 282 | C4×C53 | #575 | 1 | 4 | yes | — |
| 283 | C4×C53 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 284 | C4×C53 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 285 | Dic53 | — | 2 | 1 | no | — |
| 286 | Dic53 | — | 2 | 2 | no | — |
| 287 | Dic53 | — | 2 | 2 | no | — |
| 288 | Dic53 | — | 4 | 4 | no | — |
| 289 | Dic53 | — | 4 | 4 | no | — |
| 290 | Dic53 | #537 | 1 | 2 | yes | — |
| 291 | #3444 | — | 53 | 2 | no | — |
| 292 | #3256 | — | 53 | 4 | no | — |
| 293 | #3255 | — | 53 | 1 | no | — |
| 294 | #3254 | — | 53 | 2 | no | — |
| 295 | #3253 | D53 | 1 | 1 | yes | characteristic, complemented |
| 296 | #3252 | — | 53 | 4 | no | — |
| 297 | #3251 | — | 53 | 4 | no | — |
| 298 | #3076 | — | 53 | 4 | no | — |
| 299 | #3054 | — | 53 | 4 | no | — |
| 300 | #3035 | — | 53 | 4 | no | — |
| 301 | C2×#423 | — | 53 | 1 | no | — |
| 302 | C2×C53 | — | 4 | 1 | no | — |
| 303 | C2×C53 | — | 8 | 4 | no | — |
| 304 | C2×C53 | C2×#537 | 1 | 1 | yes | characteristic |
| 305 | C2×C53 | C2×#575 | 1 | 2 | yes | — |
| 306 | D53 | — | 2 | 2 | no | — |
| 307 | D53 | — | 4 | 1 | no | — |
| 308 | C2×#135 | — | 53 | 4 | no | — |
| 309 | C22×M16 | — | 53 | 2 | no | — |
| 310 | #533 | — | 53 | 2 | no | — |
| 311 | #533 | — | 53 | 2 | no | — |
| 312 | #533 | — | 53 | 2 | no | — |
| 313 | #532 | — | 53 | 2 | no | — |
| 314 | #532 | — | 53 | 2 | no | — |
| 315 | #532 | C2×D53 | 1 | 2 | yes | — |
| 316 | #529 | — | 53 | 4 | no | — |
| 317 | #529 | — | 53 | 4 | no | — |
| 318 | #529 | — | 106 | 2 | no | — |
| 319 | #529 | — | 106 | 2 | no | — |
| 320 | #529 | — | 106 | 2 | no | — |
| 321 | #529 | — | 106 | 2 | no | — |
| 322 | #525 | — | 53 | 4 | no | — |
| 323 | #525 | — | 106 | 2 | no | — |
| 324 | #525 | — | 106 | 2 | no | — |
| 325 | C4×#41 | — | 53 | 4 | no | — |
| 326 | C4×#41 | — | 106 | 2 | no | — |
| 327 | C4×#41 | — | 106 | 2 | no | — |
| 328 | C22×C42 | — | 53 | 1 | no | — |
| 329 | #479 | — | 53 | 8 | no | — |
| 330 | #478 | — | 53 | 8 | no | — |
| 331 | #477 | — | 53 | 4 | no | — |
| 332 | #476 | C2×D53 | 1 | 4 | yes | complemented |
| 333 | #475 | — | 53 | 4 | no | — |
| 334 | #474 | — | 53 | 4 | no | — |
| 335 | #470 | — | 53 | 4 | no | — |
| 336 | #470 | — | 53 | 4 | no | — |
| 337 | #469 | — | 53 | 4 | no | — |
| 338 | #469 | C2×D53 | 1 | 4 | yes | — |
| 339 | #468 | — | 53 | 8 | no | — |
| 340 | #468 | — | 53 | 8 | no | — |
| 341 | #464 | — | 53 | 8 | no | — |
| 342 | #463 | — | 53 | 8 | no | — |
| 343 | #462 | — | 53 | 4 | no | — |
| 344 | #461 | — | 53 | 4 | no | — |
| 345 | #460 | — | 53 | 4 | no | — |
| 346 | #459 | C2×D53 | 1 | 4 | yes | complemented |
| 347 | #427 | — | 53 | 4 | no | — |
| 348 | #423 | — | 53 | 2 | no | — |
| 349 | #423 | — | 53 | 1 | no | — |
| 350 | #423 | — | 53 | 4 | no | — |
| 351 | #423 | C2×D53 | 1 | 1 | yes | characteristic |
| 352 | C2×C4⋊C8 | — | 53 | 4 | no | — |
| 353 | #416 | — | 53 | 8 | no | — |
| 354 | C53 | #60907 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 355 | C2×#41 | — | 2 | 2 | no | — |
| 356 | C2×#41 | — | 53 | 4 | no | — |
| 357 | C2×#41 | — | 106 | 2 | no | — |
| 358 | C23×C4 | — | 53 | 1 | no | — |
| 359 | C23×C4 | — | 53 | 2 | no | — |
| 360 | #135 | — | 212 | 8 | no | — |
| 361 | C2×Q16 | — | 53 | 4 | no | — |
| 362 | C2×SD16 | — | 53 | 8 | no | — |
| 363 | C2×D8 | C22×D53 | 1 | 4 | yes | — |
| 364 | C2×M16 | — | 53 | 2 | no | — |
| 365 | C2×M16 | — | 53 | 4 | no | — |
| 366 | C2×M16 | — | 212 | 4 | no | — |
| 367 | C2×M16 | C22×D53 | 1 | 2 | yes | — |
| 368 | C22×C8 | — | 53 | 4 | no | — |
| 369 | C4⋊Q8 | — | 53 | 2 | no | — |
| 370 | C4⋊Q8 | — | 53 | 2 | no | — |
| 371 | C4⋊Q8 | C22×D53 | 1 | 2 | yes | — |
| 372 | #127 | C22×D53 | 1 | 2 | yes | — |
| 373 | #126 | — | 106 | 4 | no | — |
| 374 | #126 | — | 106 | 4 | no | — |
| 375 | #125 | — | 53 | 4 | no | — |
| 376 | #125 | — | 106 | 2 | no | — |
| 377 | #125 | — | 106 | 2 | no | — |
| 378 | #124 | — | 2 | 2 | no | — |
| 379 | #124 | — | 53 | 4 | no | — |
| 380 | #124 | — | 106 | 2 | no | — |
| 381 | #123 | — | 106 | 4 | no | — |
| 382 | #123 | — | 106 | 4 | no | — |
| 383 | #123 | — | 106 | 4 | no | — |
| 384 | C22⋊Q8 | — | 53 | 4 | no | — |
| 385 | C22⋊Q8 | — | 53 | 4 | no | — |
| 386 | C22⋊Q8 | — | 106 | 2 | no | — |
| 387 | C22⋊Q8 | — | 106 | 2 | no | — |
| 388 | C22⋊Q8 | — | 106 | 2 | no | — |
| 389 | C22⋊Q8 | — | 106 | 2 | no | — |
| 390 | #121 | — | 2 | 2 | no | — |
| 391 | #121 | — | 53 | 4 | no | — |
| 392 | #121 | — | 106 | 2 | no | — |
| 393 | #121 | — | 106 | 2 | no | — |
| 394 | #121 | — | 106 | 2 | no | — |
| 395 | #121 | C22×D53 | 1 | 4 | yes | — |
| 396 | #120 | — | 106 | 4 | no | — |
| 397 | C4×Q8 | — | 53 | 4 | no | — |
| 398 | C4×Q8 | — | 53 | 4 | no | — |
| 399 | C4×Q8 | — | 106 | 2 | no | — |
| 400 | C4×Q8 | — | 106 | 2 | no | — |
| 401 | C4×Q8 | — | 106 | 2 | no | — |
| 402 | C4×Q8 | — | 106 | 2 | no | — |
| 403 | C4×D4 | — | 2 | 2 | no | — |
| 404 | C4×D4 | — | 53 | 4 | no | — |
| 405 | C4×D4 | — | 106 | 2 | no | — |
| 406 | C4×D4 | — | 106 | 2 | no | — |
| 407 | C4×D4 | — | 106 | 2 | no | — |
| 408 | C4×D4 | — | 106 | 4 | no | — |
| 409 | C4×D4 | — | 106 | 4 | no | — |
| 410 | C4×D4 | — | 106 | 4 | no | — |
| 411 | C4×D4 | — | 106 | 4 | no | — |
| 412 | C4×D4 | — | 106 | 4 | no | — |
| 413 | C4×D4 | — | 106 | 4 | no | — |
| 414 | C4×D4 | C22×D53 | 1 | 4 | yes | — |
| 415 | #117 | — | 53 | 4 | no | — |
| 416 | #117 | — | 106 | 4 | no | — |
| 417 | #117 | — | 106 | 4 | no | — |
| 418 | #117 | — | 106 | 4 | no | — |
| 419 | #117 | — | 106 | 2 | no | — |
| 420 | #117 | — | 106 | 2 | no | — |
| 421 | C2×C42 | — | 53 | 2 | no | — |
| 422 | C2×C42 | — | 53 | 1 | no | — |
| 423 | C2×C42 | — | 53 | 1 | no | — |
| 424 | C2×C42 | — | 53 | 1 | no | — |
| 425 | C2×C42 | — | 53 | 1 | no | — |
| 426 | C2×C42 | — | 53 | 1 | no | — |
| 427 | C2×C42 | — | 53 | 2 | no | — |
| 428 | C2×C42 | — | 53 | 2 | no | — |
| 429 | C2×C42 | — | 106 | 4 | no | — |
| 430 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 431 | #107 | — | 53 | 8 | no | — |
| 432 | #106 | — | 53 | 4 | no | — |
| 433 | #106 | C22×D53 | 1 | 4 | yes | — |
| 434 | C4⋊C8 | — | 53 | 8 | no | — |
| 435 | C4⋊C8 | — | 53 | 4 | no | — |
| 436 | C4⋊C8 | C22×D53 | 1 | 4 | yes | — |
| 437 | #103 | — | 53 | 8 | no | — |
| 438 | #103 | — | 53 | 8 | no | — |
| 439 | #102 | — | 53 | 8 | no | — |
| 440 | #102 | C22×D53 | 1 | 8 | yes | — |
| 441 | C24 | — | 53 | 1 | no | — |
| 442 | #41 | — | 4 | 8 | no | — |
| 443 | #41 | — | 106 | 8 | no | — |
| 444 | #41 | — | 106 | 8 | no | — |
| 445 | #41 | — | 212 | 8 | no | — |
| 446 | C2×Q8 | — | 2 | 2 | no | — |
| 447 | C2×Q8 | — | 53 | 4 | no | — |
| 448 | C2×Q8 | — | 106 | 2 | no | — |
| 449 | C2×D4 | — | 2 | 4 | no | — |
| 450 | C2×D4 | — | 2 | 2 | no | — |
| 451 | C2×D4 | — | 2 | 2 | no | — |
| 452 | C2×D4 | — | 106 | 4 | no | — |
| 453 | C2×D4 | — | 106 | 4 | no | — |
| 454 | C2×D4 | C23×D53 | 1 | 4 | yes | — |
| 455 | C22×C4 | — | 2 | 4 | no | — |
| 456 | C22×C4 | — | 53 | 1 | no | — |
| 457 | C22×C4 | — | 53 | 1 | no | — |
| 458 | C22×C4 | — | 53 | 2 | no | — |
| 459 | C22×C4 | — | 53 | 2 | no | — |
| 460 | C22×C4 | — | 53 | 1 | no | — |
| 461 | C22×C4 | — | 53 | 2 | no | — |
| 462 | C22×C4 | — | 53 | 1 | no | — |
| 463 | C22×C4 | — | 53 | 1 | no | — |
| 464 | C22×C4 | — | 53 | 2 | no | — |
| 465 | C22×C4 | — | 53 | 2 | no | — |
| 466 | C22×C4 | — | 106 | 2 | no | — |
| 467 | C22×C4 | — | 106 | 2 | no | — |
| 468 | C22×C4 | — | 106 | 4 | no | — |
| 469 | C22×C4 | — | 106 | 4 | no | — |
| 470 | C22×C4 | — | 212 | 4 | no | — |
| 471 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 472 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 473 | Q16 | — | 212 | 4 | no | — |
| 474 | SD16 | — | 212 | 8 | no | — |
| 475 | D8 | — | 4 | 4 | no | — |
| 476 | M16 | — | 4 | 2 | no | — |
| 477 | M16 | — | 212 | 4 | no | — |
| 478 | M16 | — | 212 | 2 | no | — |
| 479 | C2×C8 | — | 53 | 4 | no | — |
| 480 | C2×C8 | — | 106 | 8 | no | — |
| 481 | C2×C8 | C23×D53 | 1 | 4 | yes | — |
| 482 | C4⋊C4 | — | 2 | 2 | no | — |
| 483 | C4⋊C4 | — | 53 | 4 | no | — |
| 484 | C4⋊C4 | — | 106 | 4 | no | — |
| 485 | C4⋊C4 | — | 106 | 4 | no | — |
| 486 | C4⋊C4 | — | 106 | 4 | no | — |
| 487 | C4⋊C4 | — | 106 | 4 | no | — |
| 488 | C4⋊C4 | — | 106 | 4 | no | — |
| 489 | C4⋊C4 | — | 106 | 2 | no | — |
| 490 | C4⋊C4 | — | 106 | 2 | no | — |
| 491 | C4⋊C4 | — | 106 | 2 | no | — |
| 492 | C4⋊C4 | — | 106 | 4 | no | — |
| 493 | C4⋊C4 | C23×D53 | 1 | 4 | yes | — |
| 494 | C22⋊C4 | — | 2 | 4 | no | — |
| 495 | C22⋊C4 | — | 2 | 4 | no | — |
| 496 | C22⋊C4 | — | 106 | 4 | no | — |
| 497 | C22⋊C4 | — | 106 | 4 | no | — |
| 498 | C22⋊C4 | — | 106 | 4 | no | — |
| 499 | C22⋊C4 | — | 106 | 4 | no | — |
| 500 | C22⋊C4 | — | 106 | 4 | no | — |
| 501 | C22⋊C4 | — | 106 | 4 | no | — |
| 502 | C22⋊C4 | — | 106 | 4 | no | — |
| 503 | C42 | — | 53 | 2 | no | — |
| 504 | C42 | — | 53 | 1 | no | — |
| 505 | C42 | — | 53 | 2 | no | — |
| 506 | C42 | — | 53 | 2 | no | — |
| 507 | C42 | — | 53 | 2 | no | — |
| 508 | C42 | — | 53 | 1 | no | — |
| 509 | C42 | — | 53 | 2 | no | — |
| 510 | C42 | — | 106 | 4 | no | — |
| 511 | C42 | — | 106 | 4 | no | — |
| 512 | C42 | — | 106 | 4 | no | — |
| 513 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 514 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 515 | C42 | C23×D53 | 1 | 2 | yes | — |
| 516 | C23 | — | 2 | 4 | no | — |
| 517 | C23 | — | 53 | 1 | no | — |
| 518 | C23 | — | 53 | 1 | no | — |
| 519 | C23 | — | 106 | 2 | no | — |
| 520 | C23 | — | 212 | 2 | no | — |
| 521 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 522 | Q8 | — | 4 | 4 | no | — |
| 523 | Q8 | — | 106 | 4 | no | — |
| 524 | Q8 | — | 106 | 4 | no | — |
| 525 | Q8 | — | 212 | 4 | no | — |
| 526 | D4 | — | 2 | 4 | no | — |
| 527 | D4 | — | 2 | 4 | no | — |
| 528 | D4 | — | 4 | 4 | no | — |
| 529 | D4 | — | 4 | 8 | no | — |
| 530 | D4 | — | 4 | 4 | no | — |
| 531 | D4 | — | 212 | 8 | no | — |
| 532 | D4 | — | 212 | 8 | no | — |
| 533 | C2×C4 | — | 2 | 4 | no | — |
| 534 | C2×C4 | — | 2 | 1 | no | — |
| 535 | C2×C4 | — | 2 | 1 | no | — |
| 536 | C2×C4 | — | 2 | 4 | no | — |
| 537 | C2×C4 | — | 4 | 8 | no | — |
| 538 | C2×C4 | — | 53 | 1 | no | — |
| 539 | C2×C4 | — | 53 | 2 | no | — |
| 540 | C2×C4 | — | 53 | 2 | no | — |
| 541 | C2×C4 | — | 53 | 2 | no | — |
| 542 | C2×C4 | — | 53 | 1 | no | — |
| 543 | C2×C4 | — | 53 | 2 | no | — |
| 544 | C2×C4 | — | 106 | 2 | no | — |
| 545 | C2×C4 | — | 106 | 2 | no | — |
| 546 | C2×C4 | — | 106 | 2 | no | — |
| 547 | C2×C4 | — | 106 | 4 | no | — |
| 548 | C2×C4 | — | 106 | 4 | no | — |
| 549 | C2×C4 | — | 106 | 1 | no | — |
| 550 | C2×C4 | — | 106 | 1 | no | — |
| 551 | C2×C4 | — | 106 | 4 | no | — |
| 552 | C2×C4 | — | 106 | 4 | no | — |
| 553 | C2×C4 | — | 212 | 2 | no | — |
| 554 | C2×C4 | — | 212 | 2 | no | — |
| 555 | C2×C4 | — | 212 | 8 | no | — |
| 556 | C2×C4 | — | 212 | 2 | no | — |
| 557 | C2×C4 | — | 212 | 8 | no | — |
| 558 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 559 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 560 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 561 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 562 | C8 | — | 2 | 4 | no | — |
| 563 | C8 | — | 106 | 4 | no | — |
| 564 | C22 | — | 2 | 1 | no | — |
| 565 | C22 | — | 2 | 2 | no | — |
| 566 | C22 | — | 4 | 4 | no | — |
| 567 | C22 | — | 4 | 4 | no | — |
| 568 | C22 | — | 4 | 4 | no | — |
| 569 | C22 | — | 53 | 2 | no | — |
| 570 | C22 | — | 106 | 2 | no | — |
| 571 | C22 | — | 106 | 1 | no | — |
| 572 | C22 | — | 106 | 2 | no | — |
| 573 | C22 | — | 212 | 4 | no | — |
| 574 | C22 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 575 | C4 | — | 2 | 1 | no | — |
| 576 | C4 | — | 2 | 2 | no | — |
| 577 | C4 | — | 4 | 4 | no | — |
| 578 | C4 | — | 53 | 2 | no | — |
| 579 | C4 | — | 106 | 1 | no | — |
| 580 | C4 | — | 106 | 2 | no | — |
| 581 | C4 | — | 106 | 2 | no | — |
| 582 | C4 | — | 212 | 4 | no | — |
| 583 | C4 | — | 212 | 4 | no | — |
| 584 | C4 | #16811419 | 1 | 4 | yes | — |
| 585 | C4 | H(5,𝔽2)×D53 | 1 | 1 | yes | characteristic |
| 586 | C4 | 2−1+4×D53 | 1 | 1 | yes | characteristic |
| 587 | C2 | — | 4 | 1 | no | — |
| 588 | C2 | — | 8 | 4 | no | — |
| 589 | C2 | — | 106 | 2 | no | — |
| 590 | C2 | — | 212 | 1 | no | — |
| 591 | C2 | #537×D53 | 1 | 1 | yes | characteristic |
| 592 | C2 | C2×#16811419 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta