Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1186 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1186 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20276361 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #20274636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20274630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C53×#3484 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C2×#13133134 | — | 2 | 1 | no | — |
| 6 | C2×#13133134 | C22 | 1 | 2 | yes | complemented |
| 7 | C2×#13133132 | — | 2 | 1 | no | — |
| 8 | C2×#13133132 | C22 | 1 | 2 | yes | complemented |
| 9 | #16810587 | — | 2 | 1 | no | — |
| 10 | #16810479 | — | 2 | 1 | no | — |
| 11 | #16810413 | — | 2 | 4 | no | — |
| 12 | #16810410 | — | 2 | 4 | no | — |
| 13 | C2×H(5,𝔽2)×C53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | C23×D4×C53 | C22 | 1 | 1 | yes | characteristic |
| 15 | C53×#546 | — | 2 | 4 | no | — |
| 16 | D42×C53 | — | 2 | 4 | no | — |
| 17 | C53×#535 | — | 2 | 1 | no | — |
| 18 | C53×#534 | — | 2 | 1 | no | — |
| 19 | C53×#534 | C22 | 1 | 2 | yes | — |
| 20 | C53×#525 | — | 2 | 1 | no | — |
| 21 | C2×#120×C53 | — | 2 | 1 | no | — |
| 22 | C2×#120×C53 | C4 | 1 | 2 | yes | complemented |
| 23 | C53×#518 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×#11719917 | — | 2 | 2 | no | — |
| 25 | C2×C22⋊Dic53 | — | 2 | 2 | no | — |
| 26 | C2×C22⋊Dic53 | — | 4 | 2 | no | — |
| 27 | #13133134 | — | 2 | 4 | no | — |
| 28 | #13133134 | — | 4 | 2 | no | — |
| 29 | #13133132 | — | 2 | 4 | no | — |
| 30 | #13133132 | — | 4 | 2 | no | — |
| 31 | C22⋊#88322 | — | 4 | 2 | no | — |
| 32 | C25×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | C25×C53 | D4 | 1 | 1 | yes | characteristic |
| 34 | H(5,𝔽2)×C53 | — | 4 | 2 | no | — |
| 35 | H(5,𝔽2)×C53 | — | 4 | 2 | no | — |
| 36 | C2×#41×C53 | — | 2 | 1 | no | — |
| 37 | C2×#41×C53 | — | 2 | 2 | no | — |
| 38 | C22×D4×C53 | — | 2 | 1 | no | — |
| 39 | C22×D4×C53 | — | 2 | 2 | no | — |
| 40 | C22×D4×C53 | — | 2 | 2 | no | — |
| 41 | C22×D4×C53 | — | 2 | 2 | no | — |
| 42 | C22×D4×C53 | — | 2 | 4 | no | — |
| 43 | C22×D4×C53 | — | 4 | 2 | no | — |
| 44 | C22×D4×C53 | — | 4 | 2 | no | — |
| 45 | C22×D4×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C22×D4×C53 | C2×C4 | 1 | 2 | yes | — |
| 47 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 48 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 49 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 50 | C23×C4×C53 | D4 | 1 | 1 | yes | characteristic |
| 51 | #127×C53 | — | 2 | 2 | no | — |
| 52 | #124×C53 | — | 2 | 2 | no | — |
| 53 | #123×C53 | — | 2 | 2 | no | — |
| 54 | #123×C53 | — | 2 | 2 | no | — |
| 55 | #123×C53 | D4 | 1 | 4 | yes | — |
| 56 | C22⋊Q8×C53 | — | 2 | 2 | no | — |
| 57 | #121×C53 | — | 2 | 2 | no | — |
| 58 | #121×C53 | — | 2 | 4 | no | — |
| 59 | #121×C53 | — | 2 | 4 | no | — |
| 60 | #121×C53 | — | 2 | 4 | no | — |
| 61 | #120×C53 | — | 2 | 4 | no | — |
| 62 | #120×C53 | — | 2 | 2 | no | — |
| 63 | #120×C53 | — | 2 | 4 | no | — |
| 64 | #120×C53 | — | 2 | 2 | no | — |
| 65 | #120×C53 | — | 2 | 2 | no | — |
| 66 | #120×C53 | — | 2 | 2 | no | — |
| 67 | #120×C53 | D4 | 1 | 4 | yes | — |
| 68 | C4×D4×C53 | — | 2 | 4 | no | — |
| 69 | C4×D4×C53 | — | 2 | 4 | no | — |
| 70 | #117×C53 | — | 2 | 1 | no | — |
| 71 | C2×C22⋊C4×C53 | — | 2 | 2 | no | — |
| 72 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 73 | C2×C22⋊C4×C53 | — | 2 | 2 | no | — |
| 74 | C2×C22⋊C4×C53 | C2×C4 | 1 | 2 | yes | — |
| 75 | C24×C53 | — | 2 | 1 | no | — |
| 76 | C24×C53 | — | 2 | 2 | no | — |
| 77 | C24×C53 | — | 2 | 2 | no | — |
| 78 | C24×C53 | — | 2 | 2 | no | — |
| 79 | C24×C53 | — | 4 | 1 | no | — |
| 80 | C24×C53 | — | 4 | 1 | no | — |
| 81 | C24×C53 | — | 4 | 1 | no | — |
| 82 | C24×C53 | — | 8 | 2 | no | — |
| 83 | C24×C53 | — | 8 | 2 | no | — |
| 84 | C24×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 85 | C24×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 86 | C24×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 87 | C24×C53 | C22⋊C4 | 1 | 2 | yes | complemented |
| 88 | C24×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C24×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | #41×C53 | — | 4 | 2 | no | — |
| 91 | #41×C53 | — | 4 | 8 | no | — |
| 92 | #41×C53 | — | 4 | 2 | no | — |
| 93 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 94 | C2×D4×C53 | — | 2 | 2 | no | — |
| 95 | C2×D4×C53 | — | 2 | 2 | no | — |
| 96 | C2×D4×C53 | — | 2 | 4 | no | — |
| 97 | C2×D4×C53 | — | 2 | 2 | no | — |
| 98 | C2×D4×C53 | — | 2 | 1 | no | — |
| 99 | C2×D4×C53 | — | 2 | 2 | no | — |
| 100 | C2×D4×C53 | — | 2 | 2 | no | — |
| 101 | C2×D4×C53 | — | 2 | 2 | no | — |
| 102 | C2×D4×C53 | — | 2 | 2 | no | — |
| 103 | C2×D4×C53 | — | 2 | 4 | no | — |
| 104 | C2×D4×C53 | — | 2 | 4 | no | — |
| 105 | C2×D4×C53 | — | 2 | 2 | no | — |
| 106 | C2×D4×C53 | — | 2 | 2 | no | — |
| 107 | C2×D4×C53 | — | 2 | 2 | no | — |
| 108 | C2×D4×C53 | — | 4 | 1 | no | — |
| 109 | C2×D4×C53 | — | 4 | 1 | no | — |
| 110 | C2×D4×C53 | — | 4 | 1 | no | — |
| 111 | C2×D4×C53 | — | 4 | 1 | no | — |
| 112 | C2×D4×C53 | — | 4 | 16 | no | — |
| 113 | C2×D4×C53 | — | 4 | 8 | no | — |
| 114 | C2×D4×C53 | — | 4 | 2 | no | — |
| 115 | C2×D4×C53 | — | 4 | 2 | no | — |
| 116 | C2×D4×C53 | — | 4 | 2 | no | — |
| 117 | C2×D4×C53 | — | 4 | 2 | no | — |
| 118 | C2×D4×C53 | — | 8 | 4 | no | — |
| 119 | C2×D4×C53 | — | 8 | 4 | no | — |
| 120 | C2×D4×C53 | C2×D4 | 1 | 4 | yes | — |
| 121 | C22×C4×C53 | — | 2 | 1 | no | — |
| 122 | C22×C4×C53 | — | 2 | 2 | no | — |
| 123 | C22×C4×C53 | — | 2 | 2 | no | — |
| 124 | C22×C4×C53 | — | 2 | 2 | no | — |
| 125 | C22×C4×C53 | — | 2 | 2 | no | — |
| 126 | C22×C4×C53 | — | 2 | 2 | no | — |
| 127 | C22×C4×C53 | — | 4 | 1 | no | — |
| 128 | C22×C4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C22×C4×C53 | C22⋊C4 | 1 | 2 | yes | complemented |
| 130 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C22×Dic53 | — | 4 | 2 | no | — |
| 132 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 133 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 134 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 135 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 136 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 137 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 138 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 139 | C22⋊C4×C53 | — | 2 | 4 | no | — |
| 140 | C22⋊C4×C53 | C22⋊C4 | 1 | 4 | yes | complemented |
| 141 | C42×C53 | — | 2 | 2 | no | — |
| 142 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 143 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 144 | C22⋊Dic53 | — | 8 | 4 | no | — |
| 145 | #11719917 | — | 4 | 2 | no | — |
| 146 | #11719917 | — | 4 | 2 | no | — |
| 147 | C2×#88322 | — | 4 | 2 | no | — |
| 148 | C23×C53 | — | 2 | 1 | no | — |
| 149 | C23×C53 | — | 2 | 1 | no | — |
| 150 | C23×C53 | — | 2 | 1 | no | — |
| 151 | C23×C53 | — | 2 | 1 | no | — |
| 152 | C23×C53 | — | 2 | 1 | no | — |
| 153 | C23×C53 | — | 2 | 1 | no | — |
| 154 | C23×C53 | — | 2 | 1 | no | — |
| 155 | C23×C53 | — | 2 | 1 | no | — |
| 156 | C23×C53 | — | 2 | 1 | no | — |
| 157 | C23×C53 | — | 2 | 2 | no | — |
| 158 | C23×C53 | — | 2 | 1 | no | — |
| 159 | C23×C53 | — | 2 | 1 | no | — |
| 160 | C23×C53 | — | 2 | 1 | no | — |
| 161 | C23×C53 | — | 4 | 2 | no | — |
| 162 | C23×C53 | — | 4 | 4 | no | — |
| 163 | C23×C53 | — | 4 | 4 | no | — |
| 164 | C23×C53 | — | 4 | 4 | no | — |
| 165 | C23×C53 | — | 4 | 4 | no | — |
| 166 | C23×C53 | — | 4 | 4 | no | — |
| 167 | C23×C53 | — | 4 | 2 | no | — |
| 168 | C23×C53 | — | 4 | 2 | no | — |
| 169 | C23×C53 | — | 8 | 2 | no | — |
| 170 | C23×C53 | — | 8 | 2 | no | — |
| 171 | C23×C53 | — | 8 | 2 | no | — |
| 172 | C23×C53 | — | 8 | 1 | no | — |
| 173 | C23×C53 | — | 8 | 1 | no | — |
| 174 | C23×C53 | — | 8 | 1 | no | — |
| 175 | C23×C53 | — | 8 | 1 | no | — |
| 176 | C23×C53 | — | 8 | 2 | no | — |
| 177 | C23×C53 | — | 8 | 2 | no | — |
| 178 | C23×C53 | — | 8 | 2 | no | — |
| 179 | C23×C53 | — | 8 | 2 | no | — |
| 180 | C23×C53 | — | 8 | 2 | no | — |
| 181 | C23×C53 | — | 8 | 2 | no | — |
| 182 | C23×C53 | — | 8 | 2 | no | — |
| 183 | C23×C53 | — | 8 | 2 | no | — |
| 184 | C23×C53 | #99 | 1 | 2 | yes | — |
| 185 | C23×C53 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 186 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 187 | C23×C53 | #120 | 1 | 2 | yes | — |
| 188 | Q8×C53 | — | 4 | 2 | no | — |
| 189 | D4×C53 | — | 2 | 8 | no | — |
| 190 | D4×C53 | — | 4 | 4 | no | — |
| 191 | D4×C53 | — | 4 | 4 | no | — |
| 192 | D4×C53 | — | 4 | 4 | no | — |
| 193 | D4×C53 | — | 4 | 2 | no | — |
| 194 | D4×C53 | — | 4 | 4 | no | — |
| 195 | D4×C53 | — | 4 | 4 | no | — |
| 196 | D4×C53 | — | 4 | 8 | no | — |
| 197 | D4×C53 | — | 4 | 2 | no | — |
| 198 | D4×C53 | — | 4 | 2 | no | — |
| 199 | D4×C53 | — | 8 | 4 | no | — |
| 200 | D4×C53 | — | 8 | 4 | no | — |
| 201 | C2×C4×C53 | — | 2 | 1 | no | — |
| 202 | C2×C4×C53 | — | 2 | 1 | no | — |
| 203 | C2×C4×C53 | — | 2 | 1 | no | — |
| 204 | C2×C4×C53 | — | 2 | 1 | no | — |
| 205 | C2×C4×C53 | — | 2 | 2 | no | — |
| 206 | C2×C4×C53 | — | 2 | 4 | no | — |
| 207 | C2×C4×C53 | — | 4 | 4 | no | — |
| 208 | C2×C4×C53 | — | 4 | 4 | no | — |
| 209 | C2×C4×C53 | — | 4 | 2 | no | — |
| 210 | C2×C4×C53 | — | 4 | 2 | no | — |
| 211 | C2×C4×C53 | — | 8 | 2 | no | — |
| 212 | C2×C4×C53 | — | 8 | 2 | no | — |
| 213 | C2×C4×C53 | #99 | 1 | 2 | yes | — |
| 214 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 215 | C2×Dic53 | — | 8 | 2 | no | — |
| 216 | C2×Dic53 | — | 8 | 4 | no | — |
| 217 | #88322 | — | 8 | 2 | no | — |
| 218 | #12705 | — | 53 | 1 | no | maximal, Sylow |
| 219 | C22×C53 | — | 2 | 2 | no | — |
| 220 | C22×C53 | — | 2 | 2 | no | — |
| 221 | C22×C53 | — | 2 | 2 | no | — |
| 222 | C22×C53 | — | 2 | 2 | no | — |
| 223 | C22×C53 | — | 2 | 2 | no | — |
| 224 | C22×C53 | — | 2 | 2 | no | — |
| 225 | C22×C53 | — | 4 | 1 | no | — |
| 226 | C22×C53 | — | 4 | 2 | no | — |
| 227 | C22×C53 | — | 4 | 2 | no | — |
| 228 | C22×C53 | — | 4 | 2 | no | — |
| 229 | C22×C53 | — | 4 | 2 | no | — |
| 230 | C22×C53 | — | 4 | 2 | no | — |
| 231 | C22×C53 | — | 4 | 1 | no | — |
| 232 | C22×C53 | — | 4 | 1 | no | — |
| 233 | C22×C53 | — | 4 | 1 | no | — |
| 234 | C22×C53 | — | 4 | 4 | no | — |
| 235 | C22×C53 | — | 4 | 2 | no | — |
| 236 | C22×C53 | — | 4 | 1 | no | — |
| 237 | C22×C53 | — | 4 | 2 | no | — |
| 238 | C22×C53 | — | 4 | 1 | no | — |
| 239 | C22×C53 | — | 8 | 1 | no | — |
| 240 | C22×C53 | — | 8 | 1 | no | — |
| 241 | C22×C53 | — | 8 | 1 | no | — |
| 242 | C22×C53 | — | 8 | 1 | no | — |
| 243 | C22×C53 | — | 8 | 1 | no | — |
| 244 | C22×C53 | — | 8 | 1 | no | — |
| 245 | C22×C53 | — | 8 | 8 | no | — |
| 246 | C22×C53 | — | 8 | 8 | no | — |
| 247 | C22×C53 | — | 16 | 2 | no | — |
| 248 | C22×C53 | — | 16 | 2 | no | — |
| 249 | C22×C53 | #379 | 1 | 1 | yes | characteristic |
| 250 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 251 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 252 | C4×C53 | — | 2 | 2 | no | — |
| 253 | C4×C53 | — | 2 | 2 | no | — |
| 254 | C4×C53 | — | 4 | 4 | no | — |
| 255 | C4×C53 | — | 4 | 2 | no | — |
| 256 | Dic53 | — | 16 | 2 | no | — |
| 257 | #3484 | D53 | 1 | 1 | yes | characteristic |
| 258 | #2121 | — | 53 | 4 | no | — |
| 259 | #1783 | — | 53 | 1 | no | — |
| 260 | #1781 | — | 53 | 1 | no | — |
| 261 | C2×C53 | — | 2 | 1 | no | — |
| 262 | C2×C53 | — | 2 | 1 | no | — |
| 263 | C2×C53 | — | 2 | 1 | no | — |
| 264 | C2×C53 | — | 4 | 2 | no | — |
| 265 | C2×C53 | — | 4 | 2 | no | — |
| 266 | C2×C53 | — | 4 | 2 | no | — |
| 267 | C2×C53 | — | 4 | 2 | no | — |
| 268 | C2×C53 | — | 8 | 1 | no | — |
| 269 | C2×C53 | — | 8 | 2 | no | — |
| 270 | C2×C53 | #1781 | 1 | 1 | yes | characteristic |
| 271 | C2×H(5,𝔽2) | Dic53 | 1 | 1 | yes | characteristic, complemented |
| 272 | C23×D4 | C2×D53 | 1 | 1 | yes | characteristic |
| 273 | #546 | — | 2 | 4 | no | — |
| 274 | D42 | — | 2 | 4 | no | — |
| 275 | #535 | — | 2 | 1 | no | — |
| 276 | #534 | — | 2 | 1 | no | — |
| 277 | #534 | C2×D53 | 1 | 2 | yes | — |
| 278 | #525 | — | 2 | 1 | no | — |
| 279 | C2×#120 | — | 2 | 1 | no | — |
| 280 | C2×#120 | Dic53 | 1 | 2 | yes | complemented |
| 281 | #518 | Dic53 | 1 | 1 | yes | characteristic, complemented |
| 282 | C2×#100 | — | 53 | 2 | no | — |
| 283 | C2×#100 | — | 106 | 1 | no | — |
| 284 | C2×#99 | — | 53 | 2 | no | — |
| 285 | C2×#99 | — | 106 | 1 | no | — |
| 286 | #407 | — | 106 | 1 | no | — |
| 287 | #379 | — | 106 | 1 | no | — |
| 288 | #352 | — | 106 | 4 | no | — |
| 289 | AΣL(1,𝔽16) | — | 106 | 4 | no | — |
| 290 | C53 | #12705 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 291 | C25 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 292 | C25 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 293 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 294 | H(5,𝔽2) | — | 4 | 2 | no | — |
| 295 | C2×#41 | — | 2 | 1 | no | — |
| 296 | C2×#41 | — | 2 | 2 | no | — |
| 297 | C22×D4 | — | 2 | 1 | no | — |
| 298 | C22×D4 | — | 2 | 2 | no | — |
| 299 | C22×D4 | — | 2 | 2 | no | — |
| 300 | C22×D4 | — | 2 | 2 | no | — |
| 301 | C22×D4 | — | 2 | 4 | no | — |
| 302 | C22×D4 | — | 4 | 2 | no | — |
| 303 | C22×D4 | — | 4 | 2 | no | — |
| 304 | C22×D4 | C2×Dic53 | 1 | 1 | yes | characteristic |
| 305 | C22×D4 | C2×Dic53 | 1 | 2 | yes | — |
| 306 | C22×D4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 307 | C22×D4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 308 | C22×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 309 | C23×C4 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 310 | C2×M16 | — | 106 | 2 | no | — |
| 311 | #127 | — | 2 | 2 | no | — |
| 312 | #124 | — | 2 | 2 | no | — |
| 313 | #123 | — | 2 | 2 | no | — |
| 314 | #123 | — | 2 | 2 | no | — |
| 315 | #123 | C22⋊D53 | 1 | 4 | yes | — |
| 316 | C22⋊Q8 | — | 2 | 2 | no | — |
| 317 | #121 | — | 2 | 2 | no | — |
| 318 | #121 | — | 2 | 4 | no | — |
| 319 | #121 | — | 2 | 4 | no | — |
| 320 | #121 | — | 2 | 4 | no | — |
| 321 | #120 | — | 2 | 4 | no | — |
| 322 | #120 | — | 2 | 2 | no | — |
| 323 | #120 | — | 2 | 2 | no | — |
| 324 | #120 | — | 2 | 2 | no | — |
| 325 | #120 | — | 2 | 2 | no | — |
| 326 | #120 | — | 2 | 4 | no | — |
| 327 | #120 | C22⋊D53 | 1 | 4 | yes | — |
| 328 | C4×D4 | — | 2 | 4 | no | — |
| 329 | C4×D4 | — | 2 | 4 | no | — |
| 330 | #117 | — | 2 | 1 | no | — |
| 331 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 332 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 333 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 334 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 335 | C2×C22⋊C4 | — | 212 | 2 | no | — |
| 336 | C2×C22⋊C4 | C2×Dic53 | 1 | 2 | yes | — |
| 337 | #100 | — | 106 | 4 | no | — |
| 338 | #100 | — | 212 | 2 | no | — |
| 339 | #99 | — | 106 | 4 | no | — |
| 340 | #99 | — | 212 | 2 | no | — |
| 341 | C22⋊C8 | — | 212 | 2 | no | — |
| 342 | C24 | — | 2 | 1 | no | — |
| 343 | C24 | — | 2 | 2 | no | — |
| 344 | C24 | — | 2 | 2 | no | — |
| 345 | C24 | — | 2 | 2 | no | — |
| 346 | C24 | — | 4 | 1 | no | — |
| 347 | C24 | — | 4 | 1 | no | — |
| 348 | C24 | — | 4 | 1 | no | — |
| 349 | C24 | — | 8 | 2 | no | — |
| 350 | C24 | — | 8 | 2 | no | — |
| 351 | C24 | C22⋊Dic53 | 1 | 1 | yes | characteristic |
| 352 | C24 | C22⋊Dic53 | 1 | 1 | yes | characteristic |
| 353 | C24 | C22⋊Dic53 | 1 | 1 | yes | characteristic |
| 354 | C24 | C22⋊Dic53 | 1 | 2 | yes | complemented |
| 355 | C24 | C22×Dic53 | 1 | 1 | yes | characteristic |
| 356 | C24 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 357 | #41 | — | 4 | 2 | no | — |
| 358 | #41 | — | 4 | 8 | no | — |
| 359 | #41 | — | 4 | 2 | no | — |
| 360 | C2×Q8 | — | 2 | 1 | no | — |
| 361 | C2×D4 | — | 2 | 2 | no | — |
| 362 | C2×D4 | — | 2 | 2 | no | — |
| 363 | C2×D4 | — | 2 | 4 | no | — |
| 364 | C2×D4 | — | 2 | 2 | no | — |
| 365 | C2×D4 | — | 2 | 1 | no | — |
| 366 | C2×D4 | — | 2 | 2 | no | — |
| 367 | C2×D4 | — | 2 | 2 | no | — |
| 368 | C2×D4 | — | 2 | 2 | no | — |
| 369 | C2×D4 | — | 2 | 2 | no | — |
| 370 | C2×D4 | — | 2 | 4 | no | — |
| 371 | C2×D4 | — | 2 | 4 | no | — |
| 372 | C2×D4 | — | 2 | 2 | no | — |
| 373 | C2×D4 | — | 2 | 2 | no | — |
| 374 | C2×D4 | — | 2 | 2 | no | — |
| 375 | C2×D4 | — | 4 | 1 | no | — |
| 376 | C2×D4 | — | 4 | 1 | no | — |
| 377 | C2×D4 | — | 4 | 1 | no | — |
| 378 | C2×D4 | — | 4 | 1 | no | — |
| 379 | C2×D4 | — | 4 | 16 | no | — |
| 380 | C2×D4 | — | 4 | 8 | no | — |
| 381 | C2×D4 | — | 4 | 2 | no | — |
| 382 | C2×D4 | — | 4 | 2 | no | — |
| 383 | C2×D4 | — | 4 | 2 | no | — |
| 384 | C2×D4 | — | 4 | 2 | no | — |
| 385 | C2×D4 | — | 8 | 4 | no | — |
| 386 | C2×D4 | — | 8 | 4 | no | — |
| 387 | C2×D4 | C2×C22⋊D53 | 1 | 4 | yes | — |
| 388 | C22×C4 | — | 2 | 1 | no | — |
| 389 | C22×C4 | — | 2 | 2 | no | — |
| 390 | C22×C4 | — | 2 | 2 | no | — |
| 391 | C22×C4 | — | 2 | 2 | no | — |
| 392 | C22×C4 | — | 2 | 2 | no | — |
| 393 | C22×C4 | — | 2 | 2 | no | — |
| 394 | C22×C4 | — | 4 | 1 | no | — |
| 395 | C22×C4 | — | 212 | 2 | no | — |
| 396 | C22×C4 | C22⋊Dic53 | 1 | 1 | yes | characteristic |
| 397 | C22×C4 | C22⋊Dic53 | 1 | 2 | yes | complemented |
| 398 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 399 | M16 | — | 212 | 2 | no | — |
| 400 | M16 | — | 212 | 2 | no | — |
| 401 | C2×C8 | — | 212 | 2 | no | — |
| 402 | C4⋊C4 | — | 2 | 2 | no | — |
| 403 | C4⋊C4 | — | 2 | 4 | no | — |
| 404 | C22⋊C4 | — | 2 | 4 | no | — |
| 405 | C22⋊C4 | — | 2 | 2 | no | — |
| 406 | C22⋊C4 | — | 2 | 4 | no | — |
| 407 | C22⋊C4 | — | 2 | 2 | no | — |
| 408 | C22⋊C4 | — | 2 | 4 | no | — |
| 409 | C22⋊C4 | — | 2 | 4 | no | — |
| 410 | C22⋊C4 | — | 424 | 4 | no | — |
| 411 | C22⋊C4 | — | 212 | 2 | no | — |
| 412 | C22⋊C4 | — | 212 | 2 | no | — |
| 413 | C22⋊C4 | C22⋊Dic53 | 1 | 4 | yes | complemented |
| 414 | C42 | — | 2 | 2 | no | — |
| 415 | C23 | — | 2 | 1 | no | — |
| 416 | C23 | — | 2 | 1 | no | — |
| 417 | C23 | — | 2 | 1 | no | — |
| 418 | C23 | — | 2 | 1 | no | — |
| 419 | C23 | — | 2 | 1 | no | — |
| 420 | C23 | — | 2 | 1 | no | — |
| 421 | C23 | — | 2 | 1 | no | — |
| 422 | C23 | — | 2 | 1 | no | — |
| 423 | C23 | — | 2 | 1 | no | — |
| 424 | C23 | — | 2 | 1 | no | — |
| 425 | C23 | — | 2 | 2 | no | — |
| 426 | C23 | — | 2 | 1 | no | — |
| 427 | C23 | — | 2 | 1 | no | — |
| 428 | C23 | — | 4 | 2 | no | — |
| 429 | C23 | — | 4 | 4 | no | — |
| 430 | C23 | — | 4 | 4 | no | — |
| 431 | C23 | — | 4 | 4 | no | — |
| 432 | C23 | — | 4 | 4 | no | — |
| 433 | C23 | — | 4 | 4 | no | — |
| 434 | C23 | — | 4 | 2 | no | — |
| 435 | C23 | — | 4 | 2 | no | — |
| 436 | C23 | — | 8 | 2 | no | — |
| 437 | C23 | — | 8 | 2 | no | — |
| 438 | C23 | — | 8 | 2 | no | — |
| 439 | C23 | — | 8 | 1 | no | — |
| 440 | C23 | — | 8 | 1 | no | — |
| 441 | C23 | — | 8 | 1 | no | — |
| 442 | C23 | — | 8 | 1 | no | — |
| 443 | C23 | — | 8 | 2 | no | — |
| 444 | C23 | — | 8 | 2 | no | — |
| 445 | C23 | — | 8 | 2 | no | — |
| 446 | C23 | — | 8 | 2 | no | — |
| 447 | C23 | — | 8 | 2 | no | — |
| 448 | C23 | — | 8 | 2 | no | — |
| 449 | C23 | — | 8 | 2 | no | — |
| 450 | C23 | — | 8 | 2 | no | — |
| 451 | C23 | #13133132 | 1 | 2 | yes | — |
| 452 | C23 | C2×C22⋊Dic53 | 1 | 2 | yes | — |
| 453 | C23 | C2×C22⋊Dic53 | 1 | 1 | yes | characteristic |
| 454 | C23 | #13133186 | 1 | 2 | yes | — |
| 455 | Q8 | — | 4 | 2 | no | — |
| 456 | D4 | — | 2 | 8 | no | — |
| 457 | D4 | — | 4 | 4 | no | — |
| 458 | D4 | — | 4 | 4 | no | — |
| 459 | D4 | — | 4 | 4 | no | — |
| 460 | D4 | — | 4 | 2 | no | — |
| 461 | D4 | — | 4 | 4 | no | — |
| 462 | D4 | — | 4 | 4 | no | — |
| 463 | D4 | — | 4 | 8 | no | — |
| 464 | D4 | — | 4 | 2 | no | — |
| 465 | D4 | — | 4 | 2 | no | — |
| 466 | D4 | — | 8 | 4 | no | — |
| 467 | D4 | — | 8 | 4 | no | — |
| 468 | C2×C4 | — | 2 | 1 | no | — |
| 469 | C2×C4 | — | 2 | 1 | no | — |
| 470 | C2×C4 | — | 2 | 1 | no | — |
| 471 | C2×C4 | — | 2 | 1 | no | — |
| 472 | C2×C4 | — | 2 | 4 | no | — |
| 473 | C2×C4 | — | 2 | 2 | no | — |
| 474 | C2×C4 | — | 4 | 4 | no | — |
| 475 | C2×C4 | — | 4 | 4 | no | — |
| 476 | C2×C4 | — | 4 | 2 | no | — |
| 477 | C2×C4 | — | 4 | 2 | no | — |
| 478 | C2×C4 | — | 8 | 2 | no | — |
| 479 | C2×C4 | — | 8 | 2 | no | — |
| 480 | C2×C4 | — | 424 | 2 | no | — |
| 481 | C2×C4 | — | 424 | 4 | no | — |
| 482 | C2×C4 | #13133132 | 1 | 2 | yes | — |
| 483 | C2×C4 | #13133186 | 1 | 2 | yes | — |
| 484 | C8 | — | 424 | 2 | no | — |
| 485 | C22 | — | 2 | 2 | no | — |
| 486 | C22 | — | 2 | 2 | no | — |
| 487 | C22 | — | 2 | 2 | no | — |
| 488 | C22 | — | 2 | 2 | no | — |
| 489 | C22 | — | 2 | 2 | no | — |
| 490 | C22 | — | 2 | 2 | no | — |
| 491 | C22 | — | 4 | 1 | no | — |
| 492 | C22 | — | 4 | 2 | no | — |
| 493 | C22 | — | 4 | 2 | no | — |
| 494 | C22 | — | 4 | 2 | no | — |
| 495 | C22 | — | 4 | 2 | no | — |
| 496 | C22 | — | 4 | 2 | no | — |
| 497 | C22 | — | 4 | 1 | no | — |
| 498 | C22 | — | 4 | 1 | no | — |
| 499 | C22 | — | 4 | 1 | no | — |
| 500 | C22 | — | 4 | 4 | no | — |
| 501 | C22 | — | 4 | 2 | no | — |
| 502 | C22 | — | 4 | 1 | no | — |
| 503 | C22 | — | 4 | 2 | no | — |
| 504 | C22 | — | 4 | 1 | no | — |
| 505 | C22 | — | 8 | 1 | no | — |
| 506 | C22 | — | 8 | 1 | no | — |
| 507 | C22 | — | 8 | 1 | no | — |
| 508 | C22 | — | 8 | 1 | no | — |
| 509 | C22 | — | 8 | 1 | no | — |
| 510 | C22 | — | 8 | 1 | no | — |
| 511 | C22 | — | 8 | 8 | no | — |
| 512 | C22 | — | 8 | 8 | no | — |
| 513 | C22 | — | 16 | 2 | no | — |
| 514 | C22 | — | 16 | 2 | no | — |
| 515 | C22 | #16810479 | 1 | 1 | yes | characteristic |
| 516 | C22 | C2×#13133132 | 1 | 1 | yes | characteristic |
| 517 | C22 | C2×#13133132 | 1 | 1 | yes | characteristic |
| 518 | C4 | — | 2 | 2 | no | — |
| 519 | C4 | — | 2 | 2 | no | — |
| 520 | C4 | — | 4 | 4 | no | — |
| 521 | C4 | — | 4 | 2 | no | — |
| 522 | C4 | — | 848 | 2 | no | — |
| 523 | C2 | — | 2 | 1 | no | — |
| 524 | C2 | — | 2 | 1 | no | — |
| 525 | C2 | — | 2 | 1 | no | — |
| 526 | C2 | — | 4 | 2 | no | — |
| 527 | C2 | — | 4 | 2 | no | — |
| 528 | C2 | — | 4 | 2 | no | — |
| 529 | C2 | — | 4 | 2 | no | — |
| 530 | C2 | — | 8 | 1 | no | — |
| 531 | C2 | — | 8 | 2 | no | — |
| 532 | C2 | #20274630 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20276361 | C2 | semidirect |
| 2. #20274636 | C2 | semidirect |
| 3. #20274630 | C2 | semidirect |
| 6. C2×#13133134 | C22 | semidirect |
| 8. C2×#13133132 | C22 | semidirect |
| 13. C2×H(5,𝔽2)×C53 | C4 | semidirect |
| 22. C2×#120×C53 | C4 | semidirect |
| 23. C53×#518 | C4 | semidirect |
| 87. C24×C53 | C22⋊C4 | semidirect |
| 129. C22×C4×C53 | C22⋊C4 | semidirect |
| 140. C22⋊C4×C53 | C22⋊C4 | semidirect |
| 271. C2×H(5,𝔽2) | Dic53 | semidirect |
| 280. C2×#120 | Dic53 | semidirect |
| 281. #518 | Dic53 | semidirect |
| 290. C53 | #12705 | semidirect |
| 354. C24 | C22⋊Dic53 | semidirect |
| 397. C22×C4 | C22⋊Dic53 | semidirect |
| 413. C22⋊C4 | C22⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276361 | 2 |
| #20274636 | 2 |
| #20274630 | 2 |
| C53×#3484 | 2 |
| #12705 | 53 |