Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2130 conjugacy classes of subgroups.
The subgroup lattice has 570 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20282998 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #20281853 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #20281822 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20281301 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20281158 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20280817 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20278469 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #20278249 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #20277415 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#16810485 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#2646 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C23×C4×D53 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#13133192 | C22 | 1 | 2 | yes | — |
| 14 | C2×#13133192 | C22 | 1 | 4 | yes | — |
| 15 | C2×#13133192 | C22 | 1 | 2 | yes | — |
| 16 | C2×#13133191 | C22 | 1 | 2 | yes | — |
| 17 | C2×#13133191 | C22 | 1 | 4 | yes | — |
| 18 | C2×#13133187 | C22 | 1 | 4 | yes | — |
| 19 | C2×#13133177 | C22 | 1 | 4 | yes | — |
| 20 | C22×#11719921 | C22 | 1 | 2 | yes | — |
| 21 | #16810565 | C22 | 1 | 4 | yes | complemented |
| 22 | #16810560 | C22 | 1 | 4 | yes | complemented |
| 23 | #16810552 | C22 | 1 | 4 | yes | complemented |
| 24 | #16810549 | C22 | 1 | 4 | yes | complemented |
| 25 | #16810545 | C22 | 1 | 4 | yes | — |
| 26 | #16810541 | C22 | 1 | 4 | yes | — |
| 27 | #16810540 | C22 | 1 | 4 | yes | — |
| 28 | #16810540 | C22 | 1 | 4 | yes | complemented |
| 29 | #16810533 | C22 | 1 | 4 | yes | — |
| 30 | #16810533 | C22 | 1 | 4 | yes | complemented |
| 31 | #16810524 | C22 | 1 | 4 | yes | — |
| 32 | #16810515 | C22 | 1 | 4 | yes | — |
| 33 | #16810513 | C22 | 1 | 4 | yes | complemented |
| 34 | #16810513 | C22 | 1 | 4 | yes | complemented |
| 35 | #16810509 | C22 | 1 | 4 | yes | complemented |
| 36 | #16810506 | C22 | 1 | 4 | yes | complemented |
| 37 | #16810501 | C22 | 1 | 4 | yes | — |
| 38 | #16810501 | C22 | 1 | 4 | yes | — |
| 39 | #16810501 | C22 | 1 | 4 | yes | — |
| 40 | #16810501 | C22 | 1 | 4 | yes | complemented |
| 41 | #16810501 | C22 | 1 | 4 | yes | complemented |
| 42 | #16810500 | C22 | 1 | 4 | yes | — |
| 43 | #16810500 | C22 | 1 | 4 | yes | — |
| 44 | #16810494 | C22 | 1 | 4 | yes | complemented |
| 45 | #16810485 | C22 | 1 | 4 | yes | — |
| 46 | #16810485 | C22 | 1 | 4 | yes | — |
| 47 | #16810485 | C22 | 1 | 4 | yes | complemented |
| 48 | #16810480 | C22 | 1 | 2 | yes | — |
| 49 | #16810480 | C22 | 1 | 2 | yes | — |
| 50 | C2×#13133124 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#13133124 | C22 | 1 | 2 | yes | — |
| 52 | C53×#400 | C22 | 1 | 4 | yes | complemented |
| 53 | C53×#398 | C22 | 1 | 4 | yes | complemented |
| 54 | C53×#385 | C22 | 1 | 4 | yes | — |
| 55 | C53×#380 | C22 | 1 | 2 | yes | — |
| 56 | C2×#95×C53 | C22 | 1 | 1 | yes | characteristic |
| 57 | C24×D53 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×D212 | C23 | 1 | 4 | yes | — |
| 59 | C22×D212 | C23 | 1 | 4 | yes | — |
| 60 | C22×D212 | C23 | 1 | 2 | yes | — |
| 61 | C22×D212 | C23 | 1 | 4 | yes | — |
| 62 | C22×C22⋊D53 | C23 | 1 | 4 | yes | — |
| 63 | C23×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 64 | C23×Dic53 | C23 | 1 | 2 | yes | — |
| 65 | C22×C4×D53 | — | 2 | 4 | no | — |
| 66 | C22×C4×D53 | — | 4 | 4 | no | — |
| 67 | C22×C4×D53 | C23 | 1 | 2 | yes | — |
| 68 | C22×C4×D53 | C23 | 1 | 2 | yes | — |
| 69 | C22×C4×D53 | C23 | 1 | 4 | yes | — |
| 70 | #13133192 | — | 4 | 4 | no | — |
| 71 | #13133192 | — | 4 | 4 | no | — |
| 72 | #13133192 | — | 4 | 8 | no | — |
| 73 | #13133191 | — | 2 | 8 | no | — |
| 74 | #13133191 | — | 4 | 8 | no | — |
| 75 | #13133187 | — | 4 | 8 | no | — |
| 76 | #13133177 | — | 4 | 8 | no | — |
| 77 | C2×C4⋊Dic53 | C23 | 1 | 2 | yes | — |
| 78 | C2×C4⋊Dic53 | C23 | 1 | 4 | yes | — |
| 79 | C2×#11719919 | C23 | 1 | 4 | yes | — |
| 80 | C2×#11719921 | — | 4 | 4 | no | — |
| 81 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 82 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 83 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 84 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 85 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 86 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 87 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 88 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 89 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 90 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 91 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 92 | C2×#11719921 | C23 | 1 | 4 | yes | — |
| 93 | C2×C4×Dic53 | C23 | 1 | 4 | yes | — |
| 94 | #13133124 | C23 | 1 | 4 | yes | — |
| 95 | #13133124 | C23 | 1 | 4 | yes | — |
| 96 | #13133124 | C23 | 1 | 4 | yes | — |
| 97 | #13133124 | C23 | 1 | 4 | yes | — |
| 98 | #13133124 | C23 | 1 | 4 | yes | — |
| 99 | #13133124 | C23 | 1 | 4 | yes | — |
| 100 | #13133124 | C23 | 1 | 4 | yes | — |
| 101 | C23×C4×C53 | C23 | 1 | 2 | yes | — |
| 102 | C23×C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×C4⋊C4×C53 | C23 | 1 | 4 | yes | — |
| 104 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 105 | C2×C4⋊C4×C53 | C23 | 1 | 4 | yes | — |
| 106 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 107 | C2×C22⋊C4×C53 | C23 | 1 | 4 | yes | — |
| 108 | #95×C53 | C23 | 1 | 4 | yes | — |
| 109 | #95×C53 | C23 | 1 | 4 | yes | — |
| 110 | #95×C53 | C23 | 1 | 4 | yes | — |
| 111 | #95×C53 | C23 | 1 | 4 | yes | — |
| 112 | C24×C53 | C24 | 1 | 1 | yes | characteristic |
| 113 | C23×D53 | — | 2 | 2 | no | — |
| 114 | C23×D53 | — | 2 | 4 | no | — |
| 115 | C23×D53 | — | 2 | 4 | no | — |
| 116 | C23×D53 | — | 4 | 1 | no | — |
| 117 | C23×D53 | — | 4 | 1 | no | — |
| 118 | C23×D53 | C24 | 1 | 4 | yes | — |
| 119 | C23×D53 | C24 | 1 | 2 | yes | — |
| 120 | C22×C4×C53 | — | 2 | 4 | no | — |
| 121 | C22×C4×C53 | — | 4 | 2 | no | — |
| 122 | C22×C4×C53 | — | 4 | 2 | no | — |
| 123 | C22×C4×C53 | — | 4 | 2 | no | — |
| 124 | C22×C4×C53 | #41 | 1 | 4 | yes | — |
| 125 | C22×C4×C53 | C24 | 1 | 4 | yes | — |
| 126 | C22×C4×C53 | C24 | 1 | 4 | yes | — |
| 127 | C22×C4×C53 | C24 | 1 | 4 | yes | — |
| 128 | C22×C4×C53 | C24 | 1 | 2 | yes | — |
| 129 | C2×C22⋊D53 | — | 2 | 8 | no | — |
| 130 | C2×C22⋊D53 | — | 2 | 8 | no | — |
| 131 | C2×C22⋊D53 | — | 2 | 8 | no | — |
| 132 | C22×Dic53 | — | 2 | 2 | no | — |
| 133 | C22×Dic53 | — | 2 | 4 | no | — |
| 134 | C22×Dic53 | — | 4 | 2 | no | — |
| 135 | C22×Dic53 | — | 4 | 2 | no | — |
| 136 | C22×Dic53 | — | 4 | 2 | no | — |
| 137 | C22×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 138 | C22×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 139 | C22×Dic53 | C24 | 1 | 4 | yes | — |
| 140 | C22×Dic53 | C24 | 1 | 4 | yes | — |
| 141 | C2×D212 | — | 2 | 8 | no | — |
| 142 | C2×D212 | — | 2 | 8 | no | — |
| 143 | C2×D212 | — | 2 | 4 | no | — |
| 144 | C2×D212 | — | 4 | 4 | no | — |
| 145 | C2×D212 | — | 4 | 4 | no | — |
| 146 | C2×D212 | — | 4 | 4 | no | — |
| 147 | C2×D212 | — | 4 | 2 | no | — |
| 148 | C2×D212 | — | 4 | 2 | no | — |
| 149 | C2×D212 | — | 4 | 4 | no | — |
| 150 | C2×D212 | — | 4 | 4 | no | — |
| 151 | C2×D212 | — | 4 | 4 | no | — |
| 152 | C2×D212 | — | 4 | 4 | no | — |
| 153 | C2×C4×D53 | — | 2 | 4 | no | — |
| 154 | C2×C4×D53 | — | 2 | 4 | no | — |
| 155 | C2×C4×D53 | — | 2 | 4 | no | — |
| 156 | C2×C4×D53 | — | 2 | 4 | no | — |
| 157 | C2×C4×D53 | — | 4 | 2 | no | — |
| 158 | C2×C4×D53 | — | 4 | 2 | no | — |
| 159 | C2×C4×D53 | — | 4 | 16 | no | — |
| 160 | C2×C4×D53 | — | 4 | 4 | no | — |
| 161 | C2×C4×D53 | — | 4 | 4 | no | — |
| 162 | C2×C4×D53 | — | 4 | 4 | no | — |
| 163 | C4⋊C4×C53 | — | 4 | 4 | no | — |
| 164 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 165 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 166 | C4⋊C4×C53 | — | 4 | 4 | no | — |
| 167 | C22⋊C4×C53 | — | 2 | 8 | no | — |
| 168 | #11719921 | — | 2 | 8 | no | — |
| 169 | #11719921 | — | 2 | 8 | no | — |
| 170 | #11719921 | — | 4 | 4 | no | — |
| 171 | #11719921 | — | 4 | 4 | no | — |
| 172 | #11719921 | — | 4 | 4 | no | — |
| 173 | #11719921 | — | 4 | 4 | no | — |
| 174 | #11719921 | — | 4 | 4 | no | — |
| 175 | #11719921 | — | 4 | 4 | no | — |
| 176 | #11719921 | — | 4 | 4 | no | — |
| 177 | #11719921 | — | 4 | 4 | no | — |
| 178 | #11719921 | — | 4 | 4 | no | — |
| 179 | #11719921 | — | 4 | 4 | no | — |
| 180 | C4⋊Dic53 | — | 2 | 4 | no | — |
| 181 | C4⋊Dic53 | — | 4 | 4 | no | — |
| 182 | #11719919 | — | 4 | 4 | no | — |
| 183 | C4×Dic53 | — | 4 | 4 | no | — |
| 184 | C23×C53 | — | 2 | 2 | no | — |
| 185 | C23×C53 | — | 2 | 1 | no | — |
| 186 | C23×C53 | — | 2 | 1 | no | — |
| 187 | C23×C53 | C2×#41 | 1 | 2 | yes | — |
| 188 | C23×C53 | H(5,𝔽2) | 1 | 4 | yes | — |
| 189 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 190 | C22×D53 | — | 2 | 8 | no | — |
| 191 | C22×D53 | — | 2 | 2 | no | — |
| 192 | C22×D53 | — | 2 | 2 | no | — |
| 193 | C22×D53 | — | 2 | 2 | no | — |
| 194 | C22×D53 | — | 2 | 2 | no | — |
| 195 | C22×D53 | — | 2 | 2 | no | — |
| 196 | C22×D53 | — | 2 | 2 | no | — |
| 197 | C22×D53 | — | 2 | 4 | no | — |
| 198 | C22×D53 | — | 2 | 4 | no | — |
| 199 | C22×D53 | — | 2 | 4 | no | — |
| 200 | C22×D53 | — | 2 | 4 | no | — |
| 201 | C22×D53 | — | 2 | 4 | no | — |
| 202 | C22×D53 | — | 2 | 4 | no | — |
| 203 | C22×D53 | — | 2 | 4 | no | — |
| 204 | C22×D53 | — | 4 | 8 | no | — |
| 205 | C22×D53 | — | 4 | 8 | no | — |
| 206 | C22×D53 | — | 4 | 4 | no | — |
| 207 | C22×D53 | — | 4 | 4 | no | — |
| 208 | C22×D53 | H(5,𝔽2) | 1 | 4 | yes | — |
| 209 | C2×C4×C53 | — | 2 | 2 | no | — |
| 210 | C2×C4×C53 | — | 2 | 2 | no | — |
| 211 | C2×C4×C53 | — | 2 | 4 | no | — |
| 212 | C2×C4×C53 | — | 2 | 4 | no | — |
| 213 | C2×C4×C53 | — | 2 | 4 | no | — |
| 214 | C2×C4×C53 | — | 2 | 4 | no | — |
| 215 | C2×C4×C53 | — | 2 | 4 | no | — |
| 216 | C2×C4×C53 | — | 2 | 4 | no | — |
| 217 | C2×C4×C53 | — | 2 | 4 | no | — |
| 218 | C2×C4×C53 | — | 2 | 4 | no | — |
| 219 | C2×C4×C53 | — | 2 | 4 | no | — |
| 220 | C2×C4×C53 | — | 4 | 4 | no | — |
| 221 | C2×C4×C53 | — | 8 | 4 | no | — |
| 222 | C2×C4×C53 | C2×#41 | 1 | 4 | yes | — |
| 223 | C22⋊D53 | — | 4 | 16 | no | — |
| 224 | C2×Dic53 | — | 2 | 1 | no | — |
| 225 | C2×Dic53 | — | 2 | 1 | no | — |
| 226 | C2×Dic53 | — | 2 | 4 | no | — |
| 227 | C2×Dic53 | — | 2 | 2 | no | — |
| 228 | C2×Dic53 | — | 2 | 2 | no | — |
| 229 | C2×Dic53 | — | 2 | 4 | no | — |
| 230 | C2×Dic53 | — | 2 | 4 | no | — |
| 231 | C2×Dic53 | — | 2 | 4 | no | — |
| 232 | C2×Dic53 | — | 2 | 4 | no | — |
| 233 | C2×Dic53 | — | 2 | 4 | no | — |
| 234 | C2×Dic53 | — | 4 | 4 | no | — |
| 235 | C2×Dic53 | — | 8 | 4 | no | — |
| 236 | D212 | — | 8 | 4 | no | — |
| 237 | D212 | — | 8 | 8 | no | — |
| 238 | D212 | — | 8 | 8 | no | — |
| 239 | D212 | — | 8 | 8 | no | — |
| 240 | C4×D53 | — | 4 | 8 | no | — |
| 241 | C4×D53 | — | 4 | 8 | no | — |
| 242 | C4×D53 | — | 8 | 8 | no | — |
| 243 | #36731 | — | 53 | 1 | no | maximal, Sylow |
| 244 | C22×C53 | — | 2 | 2 | no | — |
| 245 | C22×C53 | — | 2 | 2 | no | — |
| 246 | C22×C53 | — | 2 | 4 | no | — |
| 247 | C22×C53 | — | 2 | 4 | no | — |
| 248 | C22×C53 | #540 | 1 | 4 | yes | — |
| 249 | C22×C53 | C22×#41 | 1 | 1 | yes | characteristic |
| 250 | C22×C53 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 251 | C22×C53 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 252 | C22×C53 | #585 | 1 | 1 | yes | characteristic |
| 253 | C22×C53 | #585 | 1 | 1 | yes | characteristic |
| 254 | C2×D53 | — | 2 | 4 | no | — |
| 255 | C2×D53 | — | 2 | 4 | no | — |
| 256 | C2×D53 | — | 2 | 4 | no | — |
| 257 | C2×D53 | — | 4 | 16 | no | — |
| 258 | C2×D53 | — | 4 | 2 | no | — |
| 259 | C2×D53 | — | 4 | 2 | no | — |
| 260 | C2×D53 | — | 4 | 2 | no | — |
| 261 | C2×D53 | — | 4 | 2 | no | — |
| 262 | C2×D53 | — | 4 | 4 | no | — |
| 263 | C2×D53 | — | 4 | 4 | no | — |
| 264 | C2×D53 | — | 4 | 4 | no | — |
| 265 | C2×D53 | — | 4 | 4 | no | — |
| 266 | C2×D53 | — | 4 | 4 | no | — |
| 267 | C2×D53 | — | 4 | 4 | no | — |
| 268 | C2×D53 | — | 4 | 4 | no | — |
| 269 | C4×C53 | — | 2 | 4 | no | — |
| 270 | C4×C53 | — | 4 | 4 | no | — |
| 271 | C4×C53 | — | 4 | 4 | no | — |
| 272 | C4×C53 | — | 4 | 4 | no | — |
| 273 | Dic53 | — | 4 | 4 | no | — |
| 274 | Dic53 | — | 4 | 1 | no | — |
| 275 | Dic53 | — | 4 | 1 | no | — |
| 276 | Dic53 | — | 4 | 4 | no | — |
| 277 | #2847 | — | 53 | 2 | no | — |
| 278 | #2743 | — | 53 | 4 | no | — |
| 279 | #2740 | — | 53 | 4 | no | — |
| 280 | #2699 | — | 53 | 4 | no | — |
| 281 | #2688 | — | 53 | 4 | no | — |
| 282 | #2656 | — | 53 | 1 | no | — |
| 283 | #2646 | D53 | 1 | 1 | yes | characteristic, complemented |
| 284 | #2444 | — | 53 | 4 | no | — |
| 285 | #2424 | — | 53 | 4 | no | — |
| 286 | #2325 | — | 53 | 2 | no | — |
| 287 | C2×#381 | — | 53 | 1 | no | — |
| 288 | C2×C53 | — | 2 | 4 | no | — |
| 289 | C2×C53 | C2×#540 | 1 | 1 | yes | characteristic |
| 290 | C2×C53 | #3490 | 1 | 1 | yes | characteristic |
| 291 | C2×C53 | #3493 | 1 | 1 | yes | characteristic |
| 292 | C2×C53 | #3534 | 1 | 2 | yes | — |
| 293 | C2×C53 | #3534 | 1 | 2 | yes | — |
| 294 | D53 | — | 4 | 4 | no | — |
| 295 | D53 | — | 8 | 4 | no | — |
| 296 | C24×C4 | — | 53 | 1 | no | — |
| 297 | C2×#121 | — | 53 | 2 | no | — |
| 298 | C2×#121 | — | 53 | 4 | no | — |
| 299 | C2×#121 | — | 53 | 2 | no | — |
| 300 | C2×#121 | — | 53 | 2 | no | — |
| 301 | C2×#121 | — | 53 | 4 | no | — |
| 302 | C2×#120 | — | 53 | 4 | no | — |
| 303 | C2×C4×D4 | — | 53 | 4 | no | — |
| 304 | C22×C22⋊C4 | — | 53 | 2 | no | — |
| 305 | #400 | — | 53 | 4 | no | — |
| 306 | #400 | C2×D53 | 1 | 4 | yes | complemented |
| 307 | #399 | — | 53 | 4 | no | — |
| 308 | #398 | C2×D53 | 1 | 4 | yes | complemented |
| 309 | #397 | — | 53 | 4 | no | — |
| 310 | #397 | — | 53 | 4 | no | — |
| 311 | #396 | — | 53 | 4 | no | — |
| 312 | #394 | — | 53 | 4 | no | — |
| 313 | #394 | — | 53 | 4 | no | — |
| 314 | #394 | — | 53 | 4 | no | — |
| 315 | #392 | — | 53 | 4 | no | — |
| 316 | #392 | — | 53 | 4 | no | — |
| 317 | #390 | — | 53 | 4 | no | — |
| 318 | #388 | — | 53 | 4 | no | — |
| 319 | #388 | — | 53 | 4 | no | — |
| 320 | #388 | — | 53 | 4 | no | — |
| 321 | #387 | — | 53 | 4 | no | — |
| 322 | #387 | — | 53 | 4 | no | — |
| 323 | #386 | — | 53 | 4 | no | — |
| 324 | #386 | — | 53 | 4 | no | — |
| 325 | #386 | — | 53 | 4 | no | — |
| 326 | #386 | — | 53 | 4 | no | — |
| 327 | #386 | — | 53 | 4 | no | — |
| 328 | #386 | — | 53 | 4 | no | — |
| 329 | #386 | — | 53 | 4 | no | — |
| 330 | #385 | — | 53 | 4 | no | — |
| 331 | #385 | C2×D53 | 1 | 4 | yes | — |
| 332 | #381 | — | 53 | 4 | no | — |
| 333 | #381 | — | 53 | 4 | no | — |
| 334 | #381 | — | 53 | 4 | no | — |
| 335 | #380 | — | 53 | 2 | no | — |
| 336 | #380 | — | 53 | 2 | no | — |
| 337 | #380 | C2×D53 | 1 | 2 | yes | — |
| 338 | C2×#95 | — | 53 | 1 | no | — |
| 339 | C2×#95 | — | 53 | 2 | no | — |
| 340 | C2×#95 | C2×D53 | 1 | 1 | yes | characteristic |
| 341 | C53 | #36731 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 342 | C25 | — | 53 | 1 | no | — |
| 343 | C22×D4 | — | 53 | 4 | no | — |
| 344 | C22×D4 | — | 53 | 4 | no | — |
| 345 | C22×D4 | — | 53 | 4 | no | — |
| 346 | C22×D4 | — | 53 | 2 | no | — |
| 347 | C22×D4 | — | 53 | 4 | no | — |
| 348 | C23×C4 | — | 53 | 2 | no | — |
| 349 | C23×C4 | — | 53 | 1 | no | — |
| 350 | C23×C4 | — | 53 | 2 | no | — |
| 351 | C23×C4 | — | 53 | 2 | no | — |
| 352 | C23×C4 | — | 53 | 4 | no | — |
| 353 | C23×C4 | — | 106 | 4 | no | — |
| 354 | C23×C4 | — | 212 | 4 | no | — |
| 355 | C23×C4 | C22×D53 | 1 | 2 | yes | — |
| 356 | C23×C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 357 | #121 | — | 106 | 8 | no | — |
| 358 | #121 | — | 212 | 8 | no | — |
| 359 | #121 | — | 212 | 4 | no | — |
| 360 | #121 | — | 212 | 4 | no | — |
| 361 | #121 | — | 212 | 8 | no | — |
| 362 | #120 | — | 212 | 8 | no | — |
| 363 | C4×D4 | — | 212 | 8 | no | — |
| 364 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 365 | C2×C4⋊C4 | — | 53 | 4 | no | — |
| 366 | C2×C4⋊C4 | — | 53 | 4 | no | — |
| 367 | C2×C4⋊C4 | C22×D53 | 1 | 2 | yes | — |
| 368 | C2×C4⋊C4 | C22×D53 | 1 | 2 | yes | — |
| 369 | C2×C4⋊C4 | C22×D53 | 1 | 4 | yes | — |
| 370 | C2×C4⋊C4 | C22×D53 | 1 | 4 | yes | — |
| 371 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 372 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 373 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 374 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 375 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 376 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 377 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 378 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 379 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 380 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 381 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 382 | C2×C22⋊C4 | — | 53 | 4 | no | — |
| 383 | C2×C22⋊C4 | — | 212 | 4 | no | — |
| 384 | C2×C22⋊C4 | C22×D53 | 1 | 4 | yes | — |
| 385 | C2×C42 | — | 53 | 4 | no | — |
| 386 | #95 | — | 53 | 4 | no | — |
| 387 | #95 | — | 53 | 4 | no | — |
| 388 | #95 | — | 53 | 4 | no | — |
| 389 | #95 | — | 53 | 4 | no | — |
| 390 | #95 | — | 53 | 4 | no | — |
| 391 | #95 | — | 53 | 4 | no | — |
| 392 | #95 | — | 53 | 4 | no | — |
| 393 | #95 | C22×D53 | 1 | 4 | yes | — |
| 394 | #95 | C22×D53 | 1 | 4 | yes | — |
| 395 | #95 | C22×D53 | 1 | 4 | yes | — |
| 396 | #95 | C22×D53 | 1 | 4 | yes | — |
| 397 | C24 | — | 53 | 2 | no | — |
| 398 | C24 | — | 53 | 4 | no | — |
| 399 | C24 | — | 106 | 4 | no | — |
| 400 | C24 | — | 106 | 2 | no | — |
| 401 | C24 | — | 106 | 4 | no | — |
| 402 | C24 | — | 212 | 1 | no | — |
| 403 | C24 | — | 212 | 1 | no | — |
| 404 | C24 | C23×D53 | 1 | 1 | yes | characteristic |
| 405 | C2×D4 | — | 106 | 8 | no | — |
| 406 | C2×D4 | — | 106 | 8 | no | — |
| 407 | C2×D4 | — | 106 | 8 | no | — |
| 408 | C2×D4 | — | 106 | 8 | no | — |
| 409 | C2×D4 | — | 106 | 8 | no | — |
| 410 | C2×D4 | — | 106 | 4 | no | — |
| 411 | C2×D4 | — | 212 | 4 | no | — |
| 412 | C2×D4 | — | 212 | 4 | no | — |
| 413 | C2×D4 | — | 212 | 2 | no | — |
| 414 | C2×D4 | — | 212 | 2 | no | — |
| 415 | C2×D4 | — | 212 | 4 | no | — |
| 416 | C2×D4 | — | 212 | 4 | no | — |
| 417 | C2×D4 | — | 212 | 4 | no | — |
| 418 | C2×D4 | — | 212 | 4 | no | — |
| 419 | C2×D4 | — | 212 | 4 | no | — |
| 420 | C22×C4 | — | 2 | 4 | no | — |
| 421 | C22×C4 | — | 4 | 2 | no | — |
| 422 | C22×C4 | — | 4 | 2 | no | — |
| 423 | C22×C4 | — | 4 | 2 | no | — |
| 424 | C22×C4 | — | 53 | 1 | no | — |
| 425 | C22×C4 | — | 53 | 1 | no | — |
| 426 | C22×C4 | — | 53 | 4 | no | — |
| 427 | C22×C4 | — | 53 | 4 | no | — |
| 428 | C22×C4 | — | 106 | 4 | no | — |
| 429 | C22×C4 | — | 106 | 4 | no | — |
| 430 | C22×C4 | — | 106 | 4 | no | — |
| 431 | C22×C4 | — | 106 | 2 | no | — |
| 432 | C22×C4 | — | 106 | 4 | no | — |
| 433 | C22×C4 | — | 106 | 4 | no | — |
| 434 | C22×C4 | — | 212 | 4 | no | — |
| 435 | C22×C4 | — | 212 | 4 | no | — |
| 436 | C22×C4 | — | 212 | 4 | no | — |
| 437 | C22×C4 | — | 212 | 2 | no | — |
| 438 | C22×C4 | — | 212 | 2 | no | — |
| 439 | C22×C4 | — | 212 | 16 | no | — |
| 440 | C22×C4 | — | 212 | 2 | no | — |
| 441 | C22×C4 | — | 212 | 2 | no | — |
| 442 | C22×C4 | — | 212 | 2 | no | — |
| 443 | C22×C4 | #11719949 | 1 | 4 | yes | — |
| 444 | C22×C4 | C23×D53 | 1 | 4 | yes | — |
| 445 | C22×C4 | C23×D53 | 1 | 4 | yes | — |
| 446 | C22×C4 | C23×D53 | 1 | 4 | yes | — |
| 447 | C22×C4 | C23×D53 | 1 | 2 | yes | — |
| 448 | C4⋊C4 | — | 4 | 2 | no | — |
| 449 | C4⋊C4 | — | 4 | 2 | no | — |
| 450 | C4⋊C4 | — | 4 | 4 | no | — |
| 451 | C4⋊C4 | — | 4 | 4 | no | — |
| 452 | C4⋊C4 | — | 106 | 4 | no | — |
| 453 | C4⋊C4 | — | 212 | 4 | no | — |
| 454 | C4⋊C4 | — | 212 | 4 | no | — |
| 455 | C22⋊C4 | — | 2 | 8 | no | — |
| 456 | C22⋊C4 | — | 106 | 8 | no | — |
| 457 | C22⋊C4 | — | 106 | 8 | no | — |
| 458 | C22⋊C4 | — | 212 | 4 | no | — |
| 459 | C22⋊C4 | — | 212 | 4 | no | — |
| 460 | C22⋊C4 | — | 212 | 4 | no | — |
| 461 | C22⋊C4 | — | 212 | 4 | no | — |
| 462 | C22⋊C4 | — | 212 | 4 | no | — |
| 463 | C22⋊C4 | — | 212 | 4 | no | — |
| 464 | C22⋊C4 | — | 212 | 4 | no | — |
| 465 | C22⋊C4 | — | 212 | 4 | no | — |
| 466 | C22⋊C4 | — | 212 | 4 | no | — |
| 467 | C22⋊C4 | — | 212 | 4 | no | — |
| 468 | C42 | — | 212 | 4 | no | — |
| 469 | C23 | — | 2 | 2 | no | — |
| 470 | C23 | — | 2 | 1 | no | — |
| 471 | C23 | — | 2 | 1 | no | — |
| 472 | C23 | — | 53 | 4 | no | — |
| 473 | C23 | — | 106 | 8 | no | — |
| 474 | C23 | — | 106 | 2 | no | — |
| 475 | C23 | — | 106 | 2 | no | — |
| 476 | C23 | — | 106 | 2 | no | — |
| 477 | C23 | — | 106 | 2 | no | — |
| 478 | C23 | — | 106 | 2 | no | — |
| 479 | C23 | — | 106 | 2 | no | — |
| 480 | C23 | — | 106 | 4 | no | — |
| 481 | C23 | — | 106 | 4 | no | — |
| 482 | C23 | — | 106 | 4 | no | — |
| 483 | C23 | — | 106 | 4 | no | — |
| 484 | C23 | — | 106 | 4 | no | — |
| 485 | C23 | — | 106 | 4 | no | — |
| 486 | C23 | — | 106 | 4 | no | — |
| 487 | C23 | — | 212 | 8 | no | — |
| 488 | C23 | — | 212 | 8 | no | — |
| 489 | C23 | — | 212 | 4 | no | — |
| 490 | C23 | — | 212 | 4 | no | — |
| 491 | C23 | C2×#11719949 | 1 | 2 | yes | — |
| 492 | C23 | #13133263 | 1 | 4 | yes | — |
| 493 | C23 | C24×D53 | 1 | 1 | yes | characteristic |
| 494 | D4 | — | 424 | 4 | no | — |
| 495 | D4 | — | 424 | 8 | no | — |
| 496 | D4 | — | 424 | 8 | no | — |
| 497 | D4 | — | 424 | 8 | no | — |
| 498 | D4 | — | 212 | 16 | no | — |
| 499 | C2×C4 | — | 2 | 2 | no | — |
| 500 | C2×C4 | — | 2 | 2 | no | — |
| 501 | C2×C4 | — | 2 | 4 | no | — |
| 502 | C2×C4 | — | 2 | 4 | no | — |
| 503 | C2×C4 | — | 2 | 4 | no | — |
| 504 | C2×C4 | — | 2 | 4 | no | — |
| 505 | C2×C4 | — | 2 | 4 | no | — |
| 506 | C2×C4 | — | 2 | 4 | no | — |
| 507 | C2×C4 | — | 2 | 4 | no | — |
| 508 | C2×C4 | — | 2 | 4 | no | — |
| 509 | C2×C4 | — | 2 | 4 | no | — |
| 510 | C2×C4 | — | 4 | 4 | no | — |
| 511 | C2×C4 | — | 8 | 4 | no | — |
| 512 | C2×C4 | — | 106 | 4 | no | — |
| 513 | C2×C4 | — | 106 | 1 | no | — |
| 514 | C2×C4 | — | 106 | 1 | no | — |
| 515 | C2×C4 | — | 106 | 4 | no | — |
| 516 | C2×C4 | — | 106 | 2 | no | — |
| 517 | C2×C4 | — | 106 | 2 | no | — |
| 518 | C2×C4 | — | 106 | 4 | no | — |
| 519 | C2×C4 | — | 106 | 4 | no | — |
| 520 | C2×C4 | — | 106 | 4 | no | — |
| 521 | C2×C4 | — | 106 | 4 | no | — |
| 522 | C2×C4 | — | 424 | 8 | no | — |
| 523 | C2×C4 | — | 424 | 4 | no | — |
| 524 | C2×C4 | — | 212 | 8 | no | — |
| 525 | C2×C4 | — | 212 | 8 | no | — |
| 526 | C2×C4 | — | 212 | 4 | no | — |
| 527 | C2×C4 | C2×#11719949 | 1 | 4 | yes | — |
| 528 | C22 | — | 2 | 4 | no | — |
| 529 | C22 | — | 2 | 4 | no | — |
| 530 | C22 | — | 2 | 2 | no | — |
| 531 | C22 | — | 2 | 2 | no | — |
| 532 | C22 | — | 106 | 4 | no | — |
| 533 | C22 | — | 106 | 4 | no | — |
| 534 | C22 | — | 106 | 4 | no | — |
| 535 | C22 | — | 212 | 16 | no | — |
| 536 | C22 | — | 212 | 4 | no | — |
| 537 | C22 | — | 212 | 4 | no | — |
| 538 | C22 | — | 212 | 4 | no | — |
| 539 | C22 | — | 212 | 4 | no | — |
| 540 | C22 | — | 212 | 4 | no | — |
| 541 | C22 | — | 212 | 4 | no | — |
| 542 | C22 | — | 212 | 4 | no | — |
| 543 | C22 | — | 212 | 2 | no | — |
| 544 | C22 | — | 212 | 2 | no | — |
| 545 | C22 | — | 212 | 2 | no | — |
| 546 | C22 | — | 212 | 2 | no | — |
| 547 | C22 | #16811229 | 1 | 4 | yes | — |
| 548 | C22 | C22×#11719949 | 1 | 1 | yes | characteristic |
| 549 | C22 | H(5,𝔽2)×D53 | 1 | 2 | yes | — |
| 550 | C22 | C2×#13133263 | 1 | 2 | yes | — |
| 551 | C22 | #16811458 | 1 | 1 | yes | characteristic |
| 552 | C22 | #16811460 | 1 | 1 | yes | characteristic |
| 553 | C4 | — | 2 | 4 | no | — |
| 554 | C4 | — | 4 | 4 | no | — |
| 555 | C4 | — | 4 | 4 | no | — |
| 556 | C4 | — | 4 | 4 | no | — |
| 557 | C4 | — | 212 | 4 | no | — |
| 558 | C4 | — | 212 | 4 | no | — |
| 559 | C4 | — | 212 | 1 | no | — |
| 560 | C4 | — | 212 | 1 | no | — |
| 561 | C2 | — | 2 | 4 | no | — |
| 562 | C2 | — | 424 | 4 | no | — |
| 563 | C2 | — | 212 | 4 | no | — |
| 564 | C2 | C2×#16811229 | 1 | 1 | yes | characteristic |
| 565 | C2 | #20288405 | 1 | 1 | yes | characteristic |
| 566 | C2 | #20288436 | 1 | 1 | yes | characteristic |
| 567 | C2 | #20288906 | 1 | 2 | yes | — |
| 568 | C2 | #20288910 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D53 |
| commutator, socle, cosocle | C23×C53 | C25 |
| Fitting | C53×#2646 | C2 |
| hypercenter | #2646 | D53 |
| hypocenter | C53 | #36731 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #2646 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20282998 | C2 | semidirect |
| 2. #20281853 | C2 | semidirect |
| 3. #20281822 | C2 | semidirect |
| 4. #20281301 | C2 | semidirect |
| 5. #20281158 | C2 | semidirect |
| 6. #20280817 | C2 | semidirect |
| 7. #20278469 | C2 | semidirect |
| 8. #20278249 | C2 | semidirect |
| 9. #20277415 | C2 | semidirect |
| 10. C2×#16810485 | C2 | semidirect |
| 11. C53×#2646 | C2 | semidirect |
| 21. #16810565 | C22 | semidirect |
| 22. #16810560 | C22 | semidirect |
| 23. #16810552 | C22 | semidirect |
| 24. #16810549 | C22 | semidirect |
| 28. #16810540 | C22 | semidirect |
| 30. #16810533 | C22 | semidirect |
| 33. #16810513 | C22 | semidirect |
| 34. #16810513 | C22 | semidirect |
| 35. #16810509 | C22 | semidirect |
| 36. #16810506 | C22 | semidirect |
| 40. #16810501 | C22 | semidirect |
| 41. #16810501 | C22 | semidirect |
| 44. #16810494 | C22 | semidirect |
| 47. #16810485 | C22 | semidirect |
| 52. C53×#400 | C22 | semidirect |
| 53. C53×#398 | C22 | semidirect |
| 283. #2646 | D53 | semidirect |
| 306. #400 | C2×D53 | semidirect |
| 308. #398 | C2×D53 | semidirect |
| 341. C53 | #36731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282998 | 2 |
| #20281853 | 2 |
| #20281822 | 2 |
| #20281301 | 2 |
| #20281158 | 2 |
| #20280817 | 2 |
| #20278469 | 2 |
| #20278249 | 2 |
| #20277415 | 2 |
| C2×#16810485 | 2 |
| C53×#2646 | 2 |
| #36731 | 53 |