← D53×#2843 #27590682
Subgroups — D53×#2843 #27590682
Order 13568.
1806 conjugacy classes of subgroups.
The subgroup lattice has 370 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #20282985 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #20282984 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20282983 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #20282982 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20282981 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #400×D53 | C2 | 1 | 3 | yes | maximal |
| 7 | #398×D53 | C2 | 1 | 6 | yes | maximal |
| 8 | #395×D53 | C2 | 1 | 3 | yes | maximal |
| 9 | #384×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #383×D53 | C2 | 1 | 2 | yes | maximal |
| 11 | C53×#2843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×Q8×D53 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C4⋊C4×D53 | C22 | 1 | 3 | yes | — |
| 14 | C2×C4⋊C4×D53 | C22 | 1 | 3 | yes | — |
| 15 | C2×C4⋊C4×D53 | C22 | 1 | 6 | yes | — |
| 16 | C2×C4⋊C4×D53 | C22 | 1 | 3 | yes | — |
| 17 | C2×C42×D53 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16810565 | C22 | 1 | 6 | yes | — |
| 19 | #16810564 | C22 | 1 | 6 | yes | — |
| 20 | #16810563 | C22 | 1 | 3 | yes | — |
| 21 | #16810562 | C22 | 1 | 3 | yes | — |
| 22 | #16810561 | C22 | 1 | 3 | yes | — |
| 23 | #16810557 | C22 | 1 | 6 | yes | — |
| 24 | #16810557 | C22 | 1 | 6 | yes | — |
| 25 | #16810556 | C22 | 1 | 6 | yes | — |
| 26 | #16810556 | C22 | 1 | 6 | yes | — |
| 27 | #16810555 | C22 | 1 | 6 | yes | — |
| 28 | #16810554 | C22 | 1 | 6 | yes | — |
| 29 | #16810553 | C22 | 1 | 6 | yes | — |
| 30 | #16810544 | C22 | 1 | 6 | yes | — |
| 31 | #16810544 | C22 | 1 | 3 | yes | — |
| 32 | #16810543 | C22 | 1 | 6 | yes | — |
| 33 | #16810543 | C22 | 1 | 3 | yes | — |
| 34 | #16810542 | C22 | 1 | 3 | yes | — |
| 35 | #16810493 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16810492 | C22 | 1 | 3 | yes | — |
| 37 | #16810492 | C22 | 1 | 3 | yes | — |
| 38 | #16810491 | C22 | 1 | 2 | yes | — |
| 39 | #16810490 | C22 | 1 | 6 | yes | — |
| 40 | #16810490 | C22 | 1 | 6 | yes | — |
| 41 | #95×D53 | C22 | 1 | 6 | yes | — |
| 42 | #95×D53 | C22 | 1 | 6 | yes | — |
| 43 | #95×D53 | C22 | 1 | 3 | yes | — |
| 44 | #95×D53 | C22 | 1 | 3 | yes | — |
| 45 | C53×#400 | C22 | 1 | 3 | yes | — |
| 46 | C53×#398 | C22 | 1 | 6 | yes | — |
| 47 | C53×#395 | C22 | 1 | 3 | yes | — |
| 48 | C53×#384 | C22 | 1 | 1 | yes | characteristic |
| 49 | C53×#383 | C22 | 1 | 2 | yes | — |
| 50 | C22×Dic106 | C23 | 1 | 2 | yes | — |
| 51 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×Q8×D53 | — | 4 | 6 | no | — |
| 53 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 54 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×C4×D53 | C23 | 1 | 2 | yes | — |
| 56 | C22×C4×D53 | C23 | 1 | 6 | yes | — |
| 57 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 58 | C2×C4⋊Dic53 | C23 | 1 | 6 | yes | — |
| 59 | C2×C4⋊Dic53 | C23 | 1 | 3 | yes | — |
| 60 | C2×C4⋊Dic53 | C23 | 1 | 3 | yes | — |
| 61 | C2×C4⋊Dic53 | C23 | 1 | 3 | yes | — |
| 62 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 63 | C2×#11719919 | C23 | 1 | 3 | yes | — |
| 64 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 65 | C2×#11719919 | C23 | 1 | 3 | yes | — |
| 66 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 67 | C2×#11719919 | C23 | 1 | 6 | yes | — |
| 68 | C4⋊C4×D53 | — | 4 | 6 | no | — |
| 69 | C4⋊C4×D53 | — | 4 | 6 | no | — |
| 70 | C4⋊C4×D53 | — | 4 | 6 | no | — |
| 71 | C4⋊C4×D53 | — | 4 | 12 | no | — |
| 72 | C2×C4×Dic53 | C23 | 1 | 3 | yes | — |
| 73 | C42×D53 | Q8 | 1 | 8 | yes | complemented |
| 74 | #13133124 | C23 | 1 | 6 | yes | — |
| 75 | #13133124 | C23 | 1 | 3 | yes | — |
| 76 | #13133124 | C23 | 1 | 6 | yes | — |
| 77 | #13133124 | C23 | 1 | 6 | yes | — |
| 78 | #13133124 | C23 | 1 | 6 | yes | — |
| 79 | #13133124 | C23 | 1 | 6 | yes | — |
| 80 | #13133124 | C23 | 1 | 6 | yes | — |
| 81 | #13133124 | C23 | 1 | 3 | yes | — |
| 82 | #13133124 | C23 | 1 | 6 | yes | — |
| 83 | #13133124 | C23 | 1 | 6 | yes | — |
| 84 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C4⋊C4×C53 | C23 | 1 | 6 | yes | — |
| 86 | C2×C4⋊C4×C53 | C23 | 1 | 3 | yes | — |
| 87 | C2×C4⋊C4×C53 | C23 | 1 | 3 | yes | — |
| 88 | C2×C4⋊C4×C53 | C23 | 1 | 3 | yes | — |
| 89 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 90 | #95×C53 | C23 | 1 | 6 | yes | — |
| 91 | #95×C53 | C23 | 1 | 3 | yes | — |
| 92 | #95×C53 | C23 | 1 | 6 | yes | — |
| 93 | #95×C53 | C23 | 1 | 3 | yes | — |
| 94 | C23×D53 | C24 | 1 | 1 | yes | characteristic |
| 95 | C2×Q8×C53 | — | 4 | 3 | no | — |
| 96 | C22×C4×C53 | C24 | 1 | 6 | yes | — |
| 97 | C22×C4×C53 | C24 | 1 | 2 | yes | — |
| 98 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 99 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 100 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 101 | C22×Dic53 | C24 | 1 | 6 | yes | — |
| 102 | C22×Dic53 | C24 | 1 | 2 | yes | — |
| 103 | C22×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 104 | C22×Dic53 | C24 | 1 | 3 | yes | — |
| 105 | C22×Dic53 | C24 | 1 | 3 | yes | — |
| 106 | Q8×D53 | — | 4 | 16 | no | — |
| 107 | C2×C4×D53 | — | 2 | 6 | no | — |
| 108 | C2×C4×D53 | — | 2 | 6 | no | — |
| 109 | C2×C4×D53 | — | 2 | 6 | no | — |
| 110 | C2×C4×D53 | — | 2 | 12 | no | — |
| 111 | C2×C4×D53 | — | 2 | 12 | no | — |
| 112 | C2×C4×D53 | — | 2 | 6 | no | — |
| 113 | C2×C4×D53 | — | 2 | 12 | no | — |
| 114 | C2×C4×D53 | — | 2 | 24 | no | — |
| 115 | C2×C4×D53 | C2×Q8 | 1 | 12 | yes | — |
| 116 | C2×Dic106 | — | 4 | 6 | no | — |
| 117 | C2×Dic106 | — | 4 | 3 | no | — |
| 118 | C4⋊C4×C53 | — | 4 | 3 | no | — |
| 119 | C4⋊C4×C53 | — | 4 | 3 | no | — |
| 120 | C4⋊C4×C53 | — | 4 | 6 | no | — |
| 121 | C4⋊C4×C53 | — | 4 | 3 | no | — |
| 122 | C42×C53 | C2×Q8 | 1 | 4 | yes | complemented |
| 123 | C4⋊Dic53 | — | 4 | 3 | no | — |
| 124 | C4⋊Dic53 | — | 4 | 6 | no | — |
| 125 | C4⋊Dic53 | — | 4 | 3 | no | — |
| 126 | C4⋊Dic53 | — | 4 | 3 | no | — |
| 127 | #11719919 | — | 4 | 3 | no | — |
| 128 | #11719919 | — | 4 | 3 | no | — |
| 129 | #11719919 | — | 4 | 6 | no | — |
| 130 | #11719919 | — | 4 | 6 | no | — |
| 131 | #11719919 | — | 4 | 6 | no | — |
| 132 | #11719919 | — | 4 | 6 | no | — |
| 133 | C4×Dic53 | C2×Q8 | 1 | 12 | yes | complemented |
| 134 | C23×C53 | C25 | 1 | 1 | yes | characteristic |
| 135 | C22×D53 | C22×Q8 | 1 | 2 | yes | — |
| 136 | C22×D53 | H(5,𝔽2) | 1 | 6 | yes | — |
| 137 | C22×D53 | 2−1+4 | 1 | 6 | yes | — |
| 138 | Q8×C53 | — | 4 | 4 | no | — |
| 139 | C2×C4×C53 | — | 2 | 3 | no | — |
| 140 | C2×C4×C53 | — | 2 | 3 | no | — |
| 141 | C2×C4×C53 | — | 2 | 6 | no | — |
| 142 | C2×C4×C53 | — | 2 | 3 | no | — |
| 143 | C2×C4×C53 | — | 2 | 6 | no | — |
| 144 | C2×C4×C53 | — | 2 | 3 | no | — |
| 145 | C2×C4×C53 | — | 2 | 6 | no | — |
| 146 | C2×C4×C53 | — | 2 | 12 | no | — |
| 147 | C2×C4×C53 | C22×Q8 | 1 | 6 | yes | — |
| 148 | C2×Dic53 | — | 2 | 3 | no | — |
| 149 | C2×Dic53 | — | 2 | 3 | no | — |
| 150 | C2×Dic53 | — | 2 | 6 | no | — |
| 151 | C2×Dic53 | — | 2 | 3 | no | — |
| 152 | C2×Dic53 | — | 2 | 3 | no | — |
| 153 | C2×Dic53 | — | 2 | 6 | no | — |
| 154 | C2×Dic53 | — | 2 | 6 | no | — |
| 155 | C2×Dic53 | — | 2 | 12 | no | — |
| 156 | C2×Dic53 | C22×Q8 | 1 | 6 | yes | — |
| 157 | C4×D53 | — | 2 | 24 | no | — |
| 158 | C4×D53 | — | 4 | 12 | no | — |
| 159 | C4×D53 | — | 4 | 4 | no | — |
| 160 | C4×D53 | — | 4 | 8 | no | — |
| 161 | C4×D53 | — | 4 | 24 | no | — |
| 162 | Dic106 | — | 4 | 8 | no | — |
| 163 | Dic106 | — | 4 | 4 | no | — |
| 164 | C2×#2843 | — | 53 | 1 | no | maximal, Sylow |
| 165 | C22×C53 | C23×Q8 | 1 | 1 | yes | characteristic |
| 166 | C22×C53 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 167 | C22×C53 | C2×2−1+4 | 1 | 3 | yes | — |
| 168 | C2×D53 | #544 | 1 | 12 | yes | — |
| 169 | C2×D53 | #560 | 1 | 4 | yes | — |
| 170 | C2×D53 | #563 | 1 | 12 | yes | — |
| 171 | C4×C53 | — | 2 | 6 | no | — |
| 172 | C4×C53 | — | 4 | 2 | no | — |
| 173 | C4×C53 | — | 4 | 1 | no | — |
| 174 | C4×C53 | — | 4 | 3 | no | — |
| 175 | C4×C53 | — | 4 | 6 | no | — |
| 176 | Dic53 | — | 2 | 6 | no | — |
| 177 | Dic53 | — | 4 | 2 | no | — |
| 178 | Dic53 | — | 4 | 1 | no | — |
| 179 | Dic53 | — | 4 | 3 | no | — |
| 180 | Dic53 | — | 4 | 6 | no | — |
| 181 | #2843 | — | 53 | 3 | no | — |
| 182 | #2843 | — | 53 | 6 | no | — |
| 183 | #2843 | — | 53 | 3 | no | — |
| 184 | #2843 | — | 53 | 1 | no | — |
| 185 | #2843 | — | 53 | 2 | no | — |
| 186 | #2843 | D53 | 1 | 1 | yes | characteristic, direct product factor |
| 187 | C2×#400 | — | 53 | 3 | no | — |
| 188 | C2×#398 | — | 53 | 6 | no | — |
| 189 | C2×#395 | — | 53 | 3 | no | — |
| 190 | C2×#384 | — | 53 | 1 | no | — |
| 191 | C2×#383 | — | 53 | 2 | no | — |
| 192 | C2×C53 | C2×#544 | 1 | 3 | yes | — |
| 193 | C2×C53 | C2×#560 | 1 | 1 | yes | characteristic |
| 194 | C2×C53 | C2×#563 | 1 | 3 | yes | — |
| 195 | D53 | #2843 | 1 | 8 | yes | direct product factor |
| 196 | C23×Q8 | — | 53 | 1 | no | — |
| 197 | C22×C4⋊C4 | — | 53 | 6 | no | — |
| 198 | C22×C4⋊C4 | — | 53 | 3 | no | — |
| 199 | C22×C4⋊C4 | — | 53 | 3 | no | — |
| 200 | C22×C4⋊C4 | — | 53 | 3 | no | — |
| 201 | C22×C42 | — | 53 | 1 | no | — |
| 202 | #400 | — | 53 | 3 | no | — |
| 203 | #400 | — | 53 | 3 | no | — |
| 204 | #400 | — | 53 | 3 | no | — |
| 205 | #400 | — | 53 | 6 | no | — |
| 206 | #400 | — | 53 | 6 | no | — |
| 207 | #400 | C2×D53 | 1 | 3 | yes | — |
| 208 | #398 | — | 53 | 6 | no | — |
| 209 | #398 | — | 53 | 6 | no | — |
| 210 | #398 | — | 53 | 6 | no | — |
| 211 | #398 | — | 53 | 6 | no | — |
| 212 | #398 | — | 53 | 6 | no | — |
| 213 | #398 | — | 53 | 6 | no | — |
| 214 | #398 | — | 53 | 6 | no | — |
| 215 | #398 | C2×D53 | 1 | 6 | yes | — |
| 216 | #395 | — | 53 | 3 | no | — |
| 217 | #395 | — | 53 | 6 | no | — |
| 218 | #395 | — | 53 | 3 | no | — |
| 219 | #395 | — | 53 | 3 | no | — |
| 220 | #395 | — | 53 | 6 | no | — |
| 221 | #395 | C2×D53 | 1 | 3 | yes | — |
| 222 | #384 | — | 53 | 3 | no | — |
| 223 | #384 | — | 53 | 3 | no | — |
| 224 | #384 | — | 53 | 1 | no | — |
| 225 | #384 | C2×D53 | 1 | 1 | yes | characteristic |
| 226 | #383 | — | 53 | 2 | no | — |
| 227 | #383 | — | 53 | 6 | no | — |
| 228 | #383 | — | 53 | 6 | no | — |
| 229 | #383 | C2×D53 | 1 | 2 | yes | — |
| 230 | C2×#95 | — | 53 | 6 | no | — |
| 231 | C2×#95 | — | 53 | 3 | no | — |
| 232 | C2×#95 | — | 53 | 3 | no | — |
| 233 | C2×#95 | — | 53 | 6 | no | — |
| 234 | C53 | C2×#2843 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 235 | C22×Q8 | — | 53 | 1 | no | — |
| 236 | C22×Q8 | — | 53 | 2 | no | — |
| 237 | C22×Q8 | — | 212 | 6 | no | — |
| 238 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 239 | C23×C4 | — | 53 | 3 | no | — |
| 240 | C23×C4 | — | 53 | 3 | no | — |
| 241 | C23×C4 | — | 53 | 2 | no | — |
| 242 | C23×C4 | — | 53 | 1 | no | — |
| 243 | C23×C4 | — | 53 | 6 | no | — |
| 244 | C2×C4⋊C4 | — | 53 | 3 | no | — |
| 245 | C2×C4⋊C4 | — | 53 | 3 | no | — |
| 246 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 247 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 248 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 249 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 250 | C2×C4⋊C4 | — | 53 | 3 | no | — |
| 251 | C2×C4⋊C4 | — | 53 | 3 | no | — |
| 252 | C2×C4⋊C4 | — | 53 | 6 | no | — |
| 253 | C2×C4⋊C4 | — | 53 | 3 | no | — |
| 254 | C2×C4⋊C4 | — | 212 | 6 | no | — |
| 255 | C2×C4⋊C4 | — | 212 | 6 | no | — |
| 256 | C2×C4⋊C4 | — | 212 | 6 | no | — |
| 257 | C2×C4⋊C4 | — | 212 | 12 | no | — |
| 258 | C2×C4⋊C4 | C22×D53 | 1 | 3 | yes | — |
| 259 | C2×C4⋊C4 | C22×D53 | 1 | 3 | yes | — |
| 260 | C2×C4⋊C4 | C22×D53 | 1 | 6 | yes | — |
| 261 | C2×C4⋊C4 | C22×D53 | 1 | 3 | yes | — |
| 262 | C2×C42 | — | 53 | 3 | no | — |
| 263 | C2×C42 | — | 53 | 8 | no | — |
| 264 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 265 | #95 | — | 53 | 6 | no | — |
| 266 | #95 | — | 53 | 6 | no | — |
| 267 | #95 | — | 53 | 6 | no | — |
| 268 | #95 | — | 53 | 6 | no | — |
| 269 | #95 | — | 53 | 6 | no | — |
| 270 | #95 | — | 53 | 6 | no | — |
| 271 | #95 | — | 53 | 3 | no | — |
| 272 | #95 | — | 53 | 6 | no | — |
| 273 | #95 | — | 53 | 3 | no | — |
| 274 | #95 | — | 53 | 6 | no | — |
| 275 | #95 | C22×D53 | 1 | 6 | yes | — |
| 276 | #95 | C22×D53 | 1 | 6 | yes | — |
| 277 | #95 | C22×D53 | 1 | 3 | yes | — |
| 278 | #95 | C22×D53 | 1 | 3 | yes | — |
| 279 | C24 | — | 53 | 1 | no | — |
| 280 | C2×Q8 | — | 4 | 3 | no | — |
| 281 | C2×Q8 | — | 212 | 3 | no | — |
| 282 | C2×Q8 | — | 212 | 6 | no | — |
| 283 | C2×Q8 | — | 212 | 16 | no | — |
| 284 | C22×C4 | — | 53 | 3 | no | — |
| 285 | C22×C4 | — | 53 | 12 | no | — |
| 286 | C22×C4 | — | 53 | 6 | no | — |
| 287 | C22×C4 | — | 53 | 2 | no | — |
| 288 | C22×C4 | — | 53 | 1 | no | — |
| 289 | C22×C4 | — | 53 | 3 | no | — |
| 290 | C22×C4 | — | 106 | 6 | no | — |
| 291 | C22×C4 | — | 106 | 6 | no | — |
| 292 | C22×C4 | — | 106 | 12 | no | — |
| 293 | C22×C4 | — | 106 | 6 | no | — |
| 294 | C22×C4 | — | 106 | 12 | no | — |
| 295 | C22×C4 | — | 106 | 6 | no | — |
| 296 | C22×C4 | — | 106 | 12 | no | — |
| 297 | C22×C4 | — | 106 | 24 | no | — |
| 298 | C22×C4 | C23×D53 | 1 | 6 | yes | — |
| 299 | C22×C4 | C23×D53 | 1 | 2 | yes | — |
| 300 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 301 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 302 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 303 | C4⋊C4 | — | 4 | 3 | no | — |
| 304 | C4⋊C4 | — | 4 | 3 | no | — |
| 305 | C4⋊C4 | — | 4 | 3 | no | — |
| 306 | C4⋊C4 | — | 4 | 6 | no | — |
| 307 | C4⋊C4 | — | 212 | 6 | no | — |
| 308 | C4⋊C4 | — | 212 | 3 | no | — |
| 309 | C4⋊C4 | — | 212 | 6 | no | — |
| 310 | C4⋊C4 | — | 212 | 6 | no | — |
| 311 | C4⋊C4 | — | 212 | 3 | no | — |
| 312 | C4⋊C4 | — | 212 | 6 | no | — |
| 313 | C4⋊C4 | — | 212 | 3 | no | — |
| 314 | C4⋊C4 | — | 212 | 3 | no | — |
| 315 | C4⋊C4 | — | 212 | 3 | no | — |
| 316 | C4⋊C4 | — | 212 | 6 | no | — |
| 317 | C42 | — | 53 | 12 | no | — |
| 318 | C42 | Q8×D53 | 1 | 4 | yes | complemented |
| 319 | C23 | — | 53 | 2 | no | — |
| 320 | C23 | — | 53 | 6 | no | — |
| 321 | C23 | — | 53 | 6 | no | — |
| 322 | C23 | C24×D53 | 1 | 1 | yes | characteristic |
| 323 | Q8 | — | 4 | 4 | no | — |
| 324 | Q8 | — | 212 | 4 | no | — |
| 325 | Q8 | — | 212 | 8 | no | — |
| 326 | C2×C4 | — | 2 | 3 | no | — |
| 327 | C2×C4 | — | 2 | 3 | no | — |
| 328 | C2×C4 | — | 2 | 6 | no | — |
| 329 | C2×C4 | — | 2 | 3 | no | — |
| 330 | C2×C4 | — | 2 | 6 | no | — |
| 331 | C2×C4 | — | 2 | 3 | no | — |
| 332 | C2×C4 | — | 2 | 6 | no | — |
| 333 | C2×C4 | — | 2 | 12 | no | — |
| 334 | C2×C4 | — | 53 | 6 | no | — |
| 335 | C2×C4 | — | 106 | 24 | no | — |
| 336 | C2×C4 | — | 106 | 3 | no | — |
| 337 | C2×C4 | — | 106 | 3 | no | — |
| 338 | C2×C4 | — | 106 | 3 | no | — |
| 339 | C2×C4 | — | 106 | 6 | no | — |
| 340 | C2×C4 | — | 106 | 6 | no | — |
| 341 | C2×C4 | — | 106 | 3 | no | — |
| 342 | C2×C4 | — | 106 | 6 | no | — |
| 343 | C2×C4 | — | 106 | 12 | no | — |
| 344 | C2×C4 | — | 212 | 12 | no | — |
| 345 | C2×C4 | — | 212 | 24 | no | — |
| 346 | C2×C4 | — | 212 | 4 | no | — |
| 347 | C2×C4 | — | 212 | 8 | no | — |
| 348 | C2×C4 | C2×Q8×D53 | 1 | 6 | yes | — |
| 349 | C22 | — | 53 | 4 | no | — |
| 350 | C22 | — | 53 | 12 | no | — |
| 351 | C22 | — | 53 | 12 | no | — |
| 352 | C22 | C22×Q8×D53 | 1 | 1 | yes | characteristic |
| 353 | C22 | H(5,𝔽2)×D53 | 1 | 3 | yes | — |
| 354 | C22 | 2−1+4×D53 | 1 | 3 | yes | — |
| 355 | C4 | — | 2 | 6 | no | — |
| 356 | C4 | — | 4 | 3 | no | — |
| 357 | C4 | — | 4 | 1 | no | — |
| 358 | C4 | — | 4 | 2 | no | — |
| 359 | C4 | — | 4 | 6 | no | — |
| 360 | C4 | — | 106 | 6 | no | — |
| 361 | C4 | — | 212 | 3 | no | — |
| 362 | C4 | — | 212 | 1 | no | — |
| 363 | C4 | — | 212 | 2 | no | — |
| 364 | C4 | — | 212 | 6 | no | — |
| 365 | C2 | — | 53 | 8 | no | — |
| 366 | C2 | #544×D53 | 1 | 3 | yes | — |
| 367 | C2 | #560×D53 | 1 | 1 | yes | characteristic |
| 368 | C2 | #563×D53 | 1 | 3 | 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