← D53⋊#1580 #28316374
Subgroups — D53⋊#1580 #28316374
Order 13568.
894 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D4×D53⋊C8 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #20290313 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20290312 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20290311 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | D53⋊#334 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | D53⋊(D4⋊C8) | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20289909 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C4×D8×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C22×D53⋊C8 | — | 2 | 2 | no | — |
| 10 | #16811651 | C22 | 1 | 4 | yes | complemented |
| 11 | #16811650 | — | 2 | 4 | no | — |
| 12 | D4×#88324 | C22 | 1 | 4 | yes | complemented |
| 13 | D53⋊(C4⋊C8) | C22 | 1 | 2 | yes | — |
| 14 | D53⋊(C22⋊C8) | — | 2 | 2 | no | — |
| 15 | C4×D53⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×D53⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16811485 | C22 | 1 | 2 | yes | complemented |
| 18 | #16811484 | C22 | 1 | 2 | yes | complemented |
| 19 | #16811471 | C22 | 1 | 4 | yes | complemented |
| 20 | D4⋊#88324 | C22 | 1 | 4 | yes | complemented |
| 21 | #16811464 | C22 | 1 | 2 | yes | complemented |
| 22 | #16811464 | C22 | 1 | 2 | yes | complemented |
| 23 | C2×D8×D53 | C4 | 1 | 1 | yes | characteristic |
| 24 | C4×D4×D53 | C22 | 1 | 2 | yes | — |
| 25 | C4×D424 | C4 | 1 | 1 | yes | characteristic |
| 26 | D8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 27 | #16810705 | C22 | 1 | 1 | yes | characteristic |
| 28 | C4×#11719922 | C4 | 1 | 2 | yes | — |
| 29 | #16810703 | C22 | 1 | 2 | yes | — |
| 30 | #107×D53 | C4 | 1 | 1 | yes | characteristic |
| 31 | #102×D53 | C4 | 1 | 2 | yes | — |
| 32 | C4×C8×D53 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×D8×C53 | C4 | 1 | 1 | yes | characteristic |
| 34 | C2×D53⋊C8 | — | 2 | 2 | no | — |
| 35 | C2×D53⋊C8 | — | 2 | 1 | no | — |
| 36 | C2×D53⋊C8 | — | 2 | 4 | no | — |
| 37 | C2×D53⋊C8 | — | 4 | 8 | no | — |
| 38 | C2×D53⋊C8 | D4 | 1 | 2 | yes | — |
| 39 | C22×#88324 | — | 2 | 4 | no | — |
| 40 | #13133284 | — | 2 | 2 | no | — |
| 41 | C4⋊#88324 | C23 | 1 | 4 | yes | — |
| 42 | #13133274 | — | 2 | 4 | no | — |
| 43 | C22⋊#88324 | — | 2 | 4 | no | — |
| 44 | C4×#88324 | — | 2 | 1 | no | — |
| 45 | C4×#88324 | D4 | 1 | 2 | yes | — |
| 46 | C4×#88324 | C23 | 1 | 2 | yes | — |
| 47 | C4×#88324 | C23 | 1 | 2 | yes | — |
| 48 | C2×D4×D53 | C2×C4 | 1 | 2 | yes | — |
| 49 | C22×C4×D53 | — | 2 | 2 | no | — |
| 50 | C2×D424 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×#11719922 | C2×C4 | 1 | 2 | yes | — |
| 52 | D8×D53 | C8 | 1 | 8 | yes | complemented |
| 53 | C2×C8×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 54 | C2×C8×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C4×D212 | C2×C4 | 1 | 2 | yes | — |
| 56 | D4×Dic53 | C23 | 1 | 2 | yes | — |
| 57 | #13133179 | C23 | 1 | 2 | yes | — |
| 58 | C4×C22⋊D53 | — | 2 | 2 | no | — |
| 59 | #13133177 | — | 2 | 2 | no | — |
| 60 | C4⋊C4×D53 | C2×C4 | 1 | 2 | yes | — |
| 61 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 62 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 63 | #13133151 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | #13133150 | C2×C4 | 1 | 2 | yes | — |
| 65 | #13133139 | C2×C4 | 1 | 2 | yes | — |
| 66 | #13133138 | C2×C4 | 1 | 2 | yes | — |
| 67 | #13133137 | C2×C4 | 1 | 2 | yes | — |
| 68 | C4×#88322 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 70 | C8×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×D8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | C4×D4×C53 | C2×C4 | 1 | 2 | yes | — |
| 73 | #107×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 74 | #102×C53 | C2×C4 | 1 | 2 | yes | — |
| 75 | C4×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | C23×D53 | — | 2 | 2 | no | — |
| 77 | C2×D4×C53 | C22×C4 | 1 | 2 | yes | — |
| 78 | C22×C4×C53 | — | 2 | 2 | no | — |
| 79 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 80 | C22×Dic53 | — | 2 | 2 | no | — |
| 81 | D4×D53 | — | 2 | 4 | no | — |
| 82 | D4×D53 | C2×C8 | 1 | 8 | yes | complemented |
| 83 | C2×D212 | C22×C4 | 1 | 2 | yes | — |
| 84 | C2×C4×D53 | — | 2 | 2 | no | — |
| 85 | C2×C4×D53 | — | 2 | 2 | no | — |
| 86 | C2×C4×D53 | — | 2 | 2 | no | — |
| 87 | C2×C4×D53 | — | 4 | 4 | no | — |
| 88 | C2×C4×D53 | — | 4 | 4 | no | — |
| 89 | C2×C4×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×D53 | #41 | 1 | 1 | yes | characteristic |
| 92 | C2×#88324 | — | 2 | 4 | no | — |
| 93 | C2×#88324 | — | 2 | 2 | no | — |
| 94 | C2×#88324 | — | 4 | 8 | no | — |
| 95 | C2×#88324 | C2×D4 | 1 | 4 | yes | — |
| 96 | D53⋊C8 | — | 2 | 4 | no | — |
| 97 | D53⋊C8 | — | 4 | 8 | no | — |
| 98 | D53⋊C8 | — | 4 | 2 | no | — |
| 99 | D53⋊C8 | — | 4 | 4 | no | — |
| 100 | D8×C53 | C2×C8 | 1 | 4 | yes | complemented |
| 101 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 102 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 103 | C4⋊C4×C53 | C22×C4 | 1 | 2 | yes | — |
| 104 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 105 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 106 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 107 | #11719922 | C2×C8 | 1 | 8 | yes | complemented |
| 108 | #11719921 | — | 2 | 2 | no | — |
| 109 | #11719921 | — | 2 | 2 | no | — |
| 110 | C4⋊Dic53 | C22×C4 | 1 | 2 | yes | — |
| 111 | #11719919 | — | 2 | 2 | no | — |
| 112 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | C4×Dic53 | #41 | 1 | 1 | yes | characteristic |
| 114 | C4×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 115 | C2×#88322 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | C2×#88322 | C22×C4 | 1 | 1 | yes | characteristic |
| 117 | D424 | C2×C8 | 1 | 4 | yes | complemented |
| 118 | C8×D53 | — | 2 | 2 | no | — |
| 119 | C8×D53 | C2×C8 | 1 | 4 | yes | complemented |
| 120 | C23×C53 | — | 2 | 2 | no | — |
| 121 | C22×D53 | — | 2 | 2 | no | — |
| 122 | C22×D53 | — | 2 | 8 | no | — |
| 123 | C22×D53 | — | 4 | 4 | no | — |
| 124 | C22×D53 | — | 4 | 4 | no | — |
| 125 | C22×D53 | C4×D4 | 1 | 1 | yes | characteristic |
| 126 | D4×C53 | — | 2 | 2 | no | — |
| 127 | D4×C53 | C22×C8 | 1 | 4 | yes | complemented |
| 128 | C2×C4×C53 | — | 2 | 2 | no | — |
| 129 | C2×C4×C53 | — | 4 | 4 | no | — |
| 130 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 133 | C22⋊D53 | — | 2 | 8 | no | — |
| 134 | C2×Dic53 | — | 2 | 2 | no | — |
| 135 | C2×Dic53 | — | 4 | 2 | no | — |
| 136 | C2×Dic53 | — | 4 | 2 | no | — |
| 137 | C2×Dic53 | C4×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic53 | C2×#41 | 1 | 1 | yes | characteristic |
| 140 | D212 | — | 2 | 2 | no | — |
| 141 | D212 | C22×C8 | 1 | 4 | yes | complemented |
| 142 | C4×D53 | — | 2 | 2 | no | — |
| 143 | C4×D53 | — | 4 | 4 | no | — |
| 144 | C4×D53 | — | 4 | 4 | no | — |
| 145 | C4×D53 | — | 4 | 2 | no | — |
| 146 | C4×D53 | — | 4 | 2 | no | — |
| 147 | C4×D53 | C22×C8 | 1 | 2 | yes | — |
| 148 | C4×D53 | #131 | 1 | 2 | yes | — |
| 149 | C4×D53 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 150 | #88324 | — | 2 | 4 | no | — |
| 151 | #88324 | — | 4 | 2 | no | — |
| 152 | #88324 | — | 4 | 4 | no | — |
| 153 | C8×C53 | — | 2 | 1 | no | — |
| 154 | C8×C53 | C22×C8 | 1 | 2 | yes | complemented |
| 155 | #88322 | — | 2 | 1 | no | — |
| 156 | #88322 | C22×C8 | 1 | 2 | yes | complemented |
| 157 | C2×#1580 | — | 53 | 1 | no | maximal, Sylow |
| 158 | C22×C53 | — | 2 | 4 | no | — |
| 159 | C22×C53 | — | 4 | 2 | no | — |
| 160 | C22×C53 | — | 4 | 2 | no | — |
| 161 | C22×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 162 | C2×D53 | — | 2 | 4 | no | — |
| 163 | C2×D53 | — | 4 | 2 | no | — |
| 164 | C2×D53 | — | 4 | 2 | no | — |
| 165 | C2×D53 | — | 4 | 16 | no | — |
| 166 | C2×D53 | C8×D4 | 1 | 2 | yes | — |
| 167 | C2×D53 | #442 | 1 | 2 | yes | — |
| 168 | C2×D53 | #444 | 1 | 2 | yes | — |
| 169 | C4×C53 | — | 2 | 1 | no | — |
| 170 | C4×C53 | — | 4 | 2 | no | — |
| 171 | C4×C53 | #442 | 1 | 2 | yes | — |
| 172 | C4×C53 | C23×C8 | 1 | 1 | yes | characteristic |
| 173 | C4×C53 | C2×#131 | 1 | 1 | yes | characteristic |
| 174 | Dic53 | — | 2 | 1 | no | — |
| 175 | Dic53 | — | 4 | 2 | no | — |
| 176 | Dic53 | C8×D4 | 1 | 2 | yes | — |
| 177 | Dic53 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 178 | C2×C4×D8 | — | 53 | 1 | no | — |
| 179 | C2×C8×D4 | — | 53 | 2 | no | — |
| 180 | #1580 | — | 53 | 2 | no | — |
| 181 | #1580 | — | 53 | 4 | no | — |
| 182 | #1580 | — | 53 | 2 | no | — |
| 183 | C2×#334 | — | 53 | 1 | no | — |
| 184 | C2×D4⋊C8 | — | 53 | 2 | no | — |
| 185 | C2×#322 | — | 53 | 1 | no | — |
| 186 | C2×C53 | — | 4 | 4 | no | — |
| 187 | C2×C53 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C53 | C2×#442 | 1 | 1 | yes | characteristic |
| 189 | C2×C53 | C2×#444 | 1 | 1 | yes | characteristic |
| 190 | D53 | — | 4 | 4 | no | — |
| 191 | D53 | #1580 | 1 | 4 | yes | complemented |
| 192 | C22×D8 | — | 53 | 1 | no | — |
| 193 | C23×C8 | — | 106 | 2 | no | — |
| 194 | C2×C4×D4 | — | 53 | 2 | no | — |
| 195 | C4×D8 | — | 53 | 1 | no | — |
| 196 | C4×D8 | — | 53 | 2 | no | — |
| 197 | C4×D8 | — | 53 | 1 | no | — |
| 198 | C4×D8 | — | 53 | 2 | no | — |
| 199 | C4×D8 | — | 53 | 1 | no | — |
| 200 | C4×D8 | #6157 | 1 | 1 | yes | characteristic |
| 201 | C8×D4 | — | 53 | 4 | no | — |
| 202 | C8×D4 | — | 53 | 4 | no | — |
| 203 | C8×D4 | — | 106 | 4 | no | — |
| 204 | C2×#107 | — | 53 | 1 | no | — |
| 205 | C2×C4⋊C8 | — | 53 | 2 | no | — |
| 206 | C2×#102 | — | 53 | 2 | no | — |
| 207 | C2×C22⋊C8 | — | 106 | 2 | no | — |
| 208 | C2×C4×C8 | — | 53 | 1 | no | — |
| 209 | C2×C4×C8 | — | 53 | 1 | no | — |
| 210 | C2×C4×C8 | — | 53 | 1 | no | — |
| 211 | #334 | — | 53 | 2 | no | — |
| 212 | #334 | — | 53 | 2 | no | — |
| 213 | D4⋊C8 | — | 53 | 4 | no | — |
| 214 | D4⋊C8 | — | 53 | 4 | no | — |
| 215 | #322 | — | 53 | 2 | no | — |
| 216 | #322 | — | 53 | 2 | no | — |
| 217 | C53 | C2×#1580 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 218 | C22×D4 | — | 53 | 2 | no | — |
| 219 | C23×C4 | — | 106 | 2 | no | — |
| 220 | C2×D8 | — | 53 | 2 | no | — |
| 221 | C2×D8 | — | 53 | 8 | no | — |
| 222 | C2×D8 | — | 53 | 1 | no | — |
| 223 | C2×D8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 224 | C22×C8 | — | 53 | 1 | no | — |
| 225 | C22×C8 | — | 53 | 2 | no | — |
| 226 | C22×C8 | — | 53 | 1 | no | — |
| 227 | C22×C8 | — | 106 | 4 | no | — |
| 228 | C22×C8 | — | 106 | 4 | no | — |
| 229 | C22×C8 | — | 106 | 2 | no | — |
| 230 | C22×C8 | — | 106 | 1 | no | — |
| 231 | C22×C8 | — | 212 | 8 | no | — |
| 232 | C4×D4 | — | 53 | 2 | no | — |
| 233 | C4×D4 | — | 53 | 2 | no | — |
| 234 | C4×D4 | — | 53 | 2 | no | — |
| 235 | C4×D4 | — | 106 | 2 | no | — |
| 236 | C4×D4 | — | 106 | 2 | no | — |
| 237 | C4×D4 | C2×#6157 | 1 | 2 | yes | — |
| 238 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 239 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 240 | C2×C42 | — | 53 | 1 | no | — |
| 241 | #107 | — | 53 | 1 | no | — |
| 242 | #107 | — | 53 | 2 | no | — |
| 243 | #107 | C2×#6157 | 1 | 1 | yes | characteristic |
| 244 | C4⋊C8 | — | 53 | 4 | no | — |
| 245 | C4⋊C8 | — | 106 | 2 | no | — |
| 246 | #102 | — | 53 | 2 | no | — |
| 247 | #102 | — | 53 | 2 | no | — |
| 248 | #102 | — | 53 | 2 | no | — |
| 249 | #102 | C2×#6157 | 1 | 2 | yes | — |
| 250 | C22⋊C8 | — | 106 | 4 | no | — |
| 251 | C22⋊C8 | — | 106 | 4 | no | — |
| 252 | C4×C8 | — | 53 | 2 | no | — |
| 253 | C4×C8 | — | 53 | 2 | no | — |
| 254 | C4×C8 | — | 53 | 1 | no | — |
| 255 | C4×C8 | — | 53 | 1 | no | — |
| 256 | C4×C8 | — | 53 | 2 | no | — |
| 257 | C4×C8 | — | 53 | 1 | no | — |
| 258 | C4×C8 | — | 106 | 1 | no | — |
| 259 | C4×C8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 260 | C24 | — | 106 | 2 | no | — |
| 261 | C2×D4 | — | 53 | 8 | no | — |
| 262 | C2×D4 | — | 53 | 2 | no | — |
| 263 | C2×D4 | — | 106 | 4 | no | — |
| 264 | C2×D4 | — | 106 | 2 | no | — |
| 265 | C2×D4 | C22×#6157 | 1 | 2 | yes | — |
| 266 | C22×C4 | — | 2 | 2 | no | — |
| 267 | C22×C4 | — | 53 | 1 | no | — |
| 268 | C22×C4 | — | 53 | 1 | no | — |
| 269 | C22×C4 | — | 53 | 1 | no | — |
| 270 | C22×C4 | — | 106 | 2 | no | — |
| 271 | C22×C4 | — | 106 | 2 | no | — |
| 272 | C22×C4 | — | 106 | 2 | no | — |
| 273 | C22×C4 | — | 106 | 2 | no | — |
| 274 | C22×C4 | — | 212 | 4 | no | — |
| 275 | C22×C4 | — | 212 | 4 | no | — |
| 276 | D8 | — | 53 | 8 | no | — |
| 277 | D8 | — | 53 | 4 | no | — |
| 278 | D8 | D53⋊C8 | 1 | 4 | yes | complemented |
| 279 | C2×C8 | — | 53 | 1 | no | — |
| 280 | C2×C8 | — | 53 | 4 | no | — |
| 281 | C2×C8 | — | 53 | 4 | no | — |
| 282 | C2×C8 | — | 53 | 1 | no | — |
| 283 | C2×C8 | — | 106 | 2 | no | — |
| 284 | C2×C8 | — | 106 | 4 | no | — |
| 285 | C2×C8 | — | 106 | 2 | no | — |
| 286 | C2×C8 | — | 106 | 4 | no | — |
| 287 | C2×C8 | — | 212 | 8 | no | — |
| 288 | C2×C8 | — | 212 | 8 | no | — |
| 289 | C2×C8 | — | 212 | 4 | no | — |
| 290 | C2×C8 | — | 212 | 2 | no | — |
| 291 | C2×C8 | C22×#6157 | 1 | 1 | yes | characteristic |
| 292 | C2×C8 | C22×#6157 | 1 | 1 | yes | characteristic |
| 293 | C4⋊C4 | — | 53 | 2 | no | — |
| 294 | C4⋊C4 | — | 106 | 2 | no | — |
| 295 | C4⋊C4 | C22×#6157 | 1 | 2 | yes | — |
| 296 | C22⋊C4 | — | 2 | 2 | no | — |
| 297 | C22⋊C4 | — | 106 | 2 | no | — |
| 298 | C22⋊C4 | — | 106 | 2 | no | — |
| 299 | C22⋊C4 | — | 106 | 2 | no | — |
| 300 | C42 | — | 53 | 1 | no | — |
| 301 | C42 | — | 53 | 1 | no | — |
| 302 | C42 | — | 53 | 1 | no | — |
| 303 | C42 | C22×#6157 | 1 | 1 | yes | characteristic |
| 304 | C23 | — | 2 | 2 | no | — |
| 305 | C23 | — | 53 | 1 | no | — |
| 306 | C23 | — | 106 | 8 | no | — |
| 307 | C23 | — | 106 | 2 | no | — |
| 308 | C23 | — | 212 | 4 | no | — |
| 309 | C23 | — | 212 | 4 | no | — |
| 310 | D4 | — | 2 | 2 | no | — |
| 311 | D4 | — | 53 | 4 | no | — |
| 312 | D4 | — | 106 | 8 | no | — |
| 313 | D4 | — | 106 | 2 | no | — |
| 314 | D4 | C2×D53⋊C8 | 1 | 4 | yes | complemented |
| 315 | C2×C4 | — | 2 | 2 | no | — |
| 316 | C2×C4 | — | 4 | 4 | no | — |
| 317 | C2×C4 | — | 53 | 1 | no | — |
| 318 | C2×C4 | — | 53 | 1 | no | — |
| 319 | C2×C4 | — | 53 | 4 | no | — |
| 320 | C2×C4 | — | 53 | 2 | no | — |
| 321 | C2×C4 | — | 53 | 2 | no | — |
| 322 | C2×C4 | — | 53 | 1 | no | — |
| 323 | C2×C4 | — | 106 | 2 | no | — |
| 324 | C2×C4 | — | 106 | 2 | no | — |
| 325 | C2×C4 | — | 212 | 2 | no | — |
| 326 | C2×C4 | — | 212 | 2 | no | — |
| 327 | C2×C4 | — | 212 | 4 | no | — |
| 328 | C2×C4 | — | 212 | 2 | no | — |
| 329 | C2×C4 | — | 212 | 2 | no | — |
| 330 | C2×C4 | — | 212 | 4 | no | — |
| 331 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 332 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | C23×#6157 | 1 | 1 | yes | characteristic |
| 334 | C8 | — | 2 | 1 | no | — |
| 335 | C8 | — | 53 | 2 | no | — |
| 336 | C8 | — | 106 | 4 | no | — |
| 337 | C8 | — | 106 | 1 | no | — |
| 338 | C8 | — | 212 | 4 | no | — |
| 339 | C8 | — | 212 | 2 | no | — |
| 340 | C8 | C2×D53⋊C8 | 1 | 2 | yes | complemented |
| 341 | C22 | — | 2 | 4 | no | — |
| 342 | C22 | — | 4 | 2 | no | — |
| 343 | C22 | — | 4 | 2 | no | — |
| 344 | C22 | — | 53 | 2 | no | — |
| 345 | C22 | — | 53 | 2 | no | — |
| 346 | C22 | — | 53 | 2 | no | — |
| 347 | C22 | — | 106 | 4 | no | — |
| 348 | C22 | — | 212 | 16 | no | — |
| 349 | C22 | — | 212 | 2 | no | — |
| 350 | C22 | — | 212 | 2 | no | — |
| 351 | C22 | C2×D4×#6157 | 1 | 1 | yes | characteristic |
| 352 | C4 | — | 2 | 1 | no | — |
| 353 | C4 | — | 4 | 2 | no | — |
| 354 | C4 | — | 53 | 2 | no | — |
| 355 | C4 | — | 53 | 2 | no | — |
| 356 | C4 | — | 106 | 1 | no | — |
| 357 | C4 | — | 212 | 2 | no | — |
| 358 | C4 | #16811664 | 1 | 2 | yes | — |
| 359 | C4 | C22×D53⋊C8 | 1 | 1 | yes | characteristic |
| 360 | C4 | D53⋊#131 | 1 | 1 | yes | characteristic |
| 361 | C2 | — | 4 | 4 | no | — |
| 362 | C2 | — | 53 | 4 | no | — |
| 363 | C2 | — | 212 | 4 | no | — |
| 364 | C2 | D4×D53⋊C8 | 1 | 1 | yes | characteristic |
| 365 | C2 | C2×#16811664 | 1 | 1 | yes | characteristic |
| 366 | C2 | D53⋊#444 | 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