← C53×#22218 #27229730
Subgroups — C53×#22218 #27229730
Order 13568.
822 conjugacy classes of subgroups.
The subgroup lattice has 380 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C53×#487 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C4×C4⋊Q8×C53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C4×C4⋊Q8×C53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C53×#1990 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C53×#1956 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C53×#1927 | C2 | 1 | 4 | yes | maximal |
| 7 | C53×#1865 | C2 | 1 | 4 | yes | maximal |
| 8 | C53×#1844 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C53×#1744 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C2×C4⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C4⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C4×Q8×C53 | — | 2 | 1 | no | — |
| 13 | C2×C4×Q8×C53 | C22 | 1 | 2 | yes | — |
| 14 | C53×#487 | C4 | 1 | 8 | yes | complemented |
| 15 | C2×#106×C53 | C22 | 1 | 4 | yes | — |
| 16 | C2×#103×C53 | C22 | 1 | 4 | yes | — |
| 17 | C2×#103×C53 | C22 | 1 | 4 | yes | — |
| 18 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 20 | C53×#391 | — | 2 | 1 | no | — |
| 21 | C53×#391 | C22 | 1 | 2 | yes | — |
| 22 | C53×#389 | — | 2 | 1 | no | — |
| 23 | C53×#389 | — | 2 | 1 | no | — |
| 24 | C53×#389 | — | 2 | 1 | no | — |
| 25 | C53×#389 | C22 | 1 | 2 | yes | — |
| 26 | C53×#384 | C22 | 1 | 1 | yes | characteristic |
| 27 | C53×#384 | C22 | 1 | 1 | yes | characteristic |
| 28 | C4×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 29 | C4×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 30 | C4×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 31 | C4×C4⋊C4×C53 | C22 | 1 | 2 | yes | — |
| 32 | C43×C53 | C22 | 1 | 1 | yes | characteristic |
| 33 | C53×#340 | C22 | 1 | 4 | yes | — |
| 34 | C53×#336 | C22 | 1 | 2 | yes | — |
| 35 | C53×#336 | C22 | 1 | 2 | yes | — |
| 36 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 37 | C22×Q8×C53 | C23 | 1 | 2 | yes | — |
| 38 | C22×C8×C53 | C23 | 1 | 2 | yes | — |
| 39 | C22×C8×C53 | C23 | 1 | 2 | yes | — |
| 40 | C4⋊Q8×C53 | — | 2 | 2 | no | — |
| 41 | C4⋊Q8×C53 | — | 2 | 2 | no | — |
| 42 | C4⋊Q8×C53 | C2×C4 | 1 | 4 | yes | — |
| 43 | C4⋊Q8×C53 | C2×C4 | 1 | 4 | yes | — |
| 44 | C4×Q8×C53 | — | 4 | 4 | no | — |
| 45 | C4×Q8×C53 | — | 4 | 4 | no | — |
| 46 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 47 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 48 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 49 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 50 | C2×C4⋊C4×C53 | — | 2 | 2 | no | — |
| 51 | C2×C4⋊C4×C53 | — | 2 | 2 | no | — |
| 52 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 53 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 54 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 55 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 56 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 57 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 58 | C2×C42×C53 | — | 2 | 2 | no | — |
| 59 | C2×C42×C53 | — | 2 | 2 | no | — |
| 60 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 62 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×C42×C53 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 67 | #106×C53 | — | 4 | 4 | no | — |
| 68 | #103×C53 | — | 4 | 4 | no | — |
| 69 | #103×C53 | C2×C4 | 1 | 16 | yes | — |
| 70 | C4×C8×C53 | — | 2 | 2 | no | — |
| 71 | C4×C8×C53 | C2×C4 | 1 | 4 | yes | — |
| 72 | #95×C53 | — | 2 | 2 | no | — |
| 73 | #95×C53 | — | 2 | 2 | no | — |
| 74 | #95×C53 | — | 2 | 2 | no | — |
| 75 | #95×C53 | — | 2 | 2 | no | — |
| 76 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 77 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 78 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 79 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 80 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 81 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 82 | C2×Q8×C53 | C22×C4 | 1 | 4 | yes | — |
| 83 | C22×C4×C53 | — | 2 | 2 | no | — |
| 84 | C22×C4×C53 | — | 2 | 2 | no | — |
| 85 | C22×C4×C53 | — | 2 | 2 | no | — |
| 86 | C22×C4×C53 | — | 2 | 2 | no | — |
| 87 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 88 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 90 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 94 | C2×C8×C53 | — | 2 | 2 | no | — |
| 95 | C2×C8×C53 | — | 2 | 2 | no | — |
| 96 | C2×C8×C53 | — | 2 | 2 | no | — |
| 97 | C2×C8×C53 | — | 2 | 2 | no | — |
| 98 | C2×C8×C53 | — | 2 | 2 | no | — |
| 99 | C2×C8×C53 | C22×C4 | 1 | 4 | yes | — |
| 100 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 101 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 102 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 103 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 104 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 105 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 106 | C4⋊C4×C53 | — | 4 | 4 | no | — |
| 107 | C4⋊C4×C53 | — | 4 | 4 | no | — |
| 108 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 109 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 110 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 111 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 112 | C4⋊C4×C53 | C22×C4 | 1 | 4 | yes | — |
| 113 | C42×C53 | — | 2 | 2 | no | — |
| 114 | C42×C53 | — | 2 | 2 | no | — |
| 115 | C42×C53 | — | 2 | 2 | no | — |
| 116 | C42×C53 | — | 2 | 2 | no | — |
| 117 | C42×C53 | — | 2 | 2 | no | — |
| 118 | C42×C53 | — | 4 | 4 | no | — |
| 119 | C42×C53 | — | 4 | 4 | no | — |
| 120 | C42×C53 | SD16 | 1 | 4 | yes | — |
| 121 | C42×C53 | C22×C4 | 1 | 2 | yes | — |
| 122 | C42×C53 | #41 | 1 | 2 | yes | — |
| 123 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 124 | Q8×C53 | — | 2 | 8 | no | — |
| 125 | Q8×C53 | — | 4 | 4 | no | — |
| 126 | Q8×C53 | — | 4 | 8 | no | — |
| 127 | C2×C4×C53 | — | 2 | 1 | no | — |
| 128 | C2×C4×C53 | — | 2 | 1 | no | — |
| 129 | C2×C4×C53 | — | 2 | 1 | no | — |
| 130 | C2×C4×C53 | — | 2 | 1 | no | — |
| 131 | C2×C4×C53 | — | 2 | 4 | no | — |
| 132 | C2×C4×C53 | — | 2 | 4 | no | — |
| 133 | C2×C4×C53 | — | 2 | 1 | no | — |
| 134 | C2×C4×C53 | — | 2 | 1 | no | — |
| 135 | C2×C4×C53 | — | 2 | 1 | no | — |
| 136 | C2×C4×C53 | — | 2 | 1 | no | — |
| 137 | C2×C4×C53 | — | 2 | 1 | no | — |
| 138 | C2×C4×C53 | — | 2 | 1 | no | — |
| 139 | C2×C4×C53 | — | 4 | 2 | no | — |
| 140 | C2×C4×C53 | — | 4 | 2 | no | — |
| 141 | C2×C4×C53 | — | 4 | 2 | no | — |
| 142 | C2×C4×C53 | — | 4 | 2 | no | — |
| 143 | C2×C4×C53 | — | 4 | 2 | no | — |
| 144 | C2×C4×C53 | — | 4 | 2 | no | — |
| 145 | C2×C4×C53 | — | 4 | 2 | no | — |
| 146 | C2×C4×C53 | — | 4 | 2 | no | — |
| 147 | C2×C4×C53 | — | 4 | 2 | no | — |
| 148 | C2×C4×C53 | — | 4 | 2 | no | — |
| 149 | C2×C4×C53 | C4×D4 | 1 | 2 | yes | — |
| 150 | C2×C4×C53 | C4×D4 | 1 | 2 | yes | — |
| 151 | C2×C4×C53 | C2×SD16 | 1 | 2 | yes | — |
| 152 | C2×C4×C53 | C2×SD16 | 1 | 2 | yes | — |
| 153 | C2×C4×C53 | C2×SD16 | 1 | 2 | yes | — |
| 154 | C2×C4×C53 | #135 | 1 | 2 | yes | — |
| 155 | C2×C4×C53 | #137 | 1 | 2 | yes | — |
| 156 | C2×C4×C53 | #137 | 1 | 2 | yes | — |
| 157 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 159 | C2×C4×C53 | H(5,𝔽2) | 1 | 2 | yes | — |
| 160 | C2×C4×C53 | 2−1+4 | 1 | 2 | yes | — |
| 161 | C8×C53 | — | 2 | 4 | no | — |
| 162 | C8×C53 | — | 4 | 2 | no | — |
| 163 | #22218 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 164 | C22×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 165 | C22×C53 | #535 | 1 | 1 | yes | characteristic |
| 166 | C22×C53 | #536 | 1 | 1 | yes | characteristic |
| 167 | C22×C53 | C22×SD16 | 1 | 1 | yes | characteristic |
| 168 | C22×C53 | C2×#135 | 1 | 1 | yes | characteristic |
| 169 | C22×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 170 | C22×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 171 | C4×C53 | — | 2 | 2 | no | — |
| 172 | C4×C53 | — | 2 | 2 | no | — |
| 173 | C4×C53 | — | 4 | 4 | no | — |
| 174 | C4×C53 | — | 4 | 4 | no | — |
| 175 | C4×C53 | — | 4 | 1 | no | — |
| 176 | C4×C53 | — | 4 | 1 | no | — |
| 177 | C4×C53 | — | 8 | 2 | no | — |
| 178 | C4×C53 | — | 8 | 2 | no | — |
| 179 | C4×C53 | C4×SD16 | 1 | 4 | yes | — |
| 180 | C4×C53 | #441 | 1 | 4 | yes | — |
| 181 | C4×C53 | #520 | 1 | 2 | yes | — |
| 182 | C4×C53 | #542 | 1 | 2 | yes | — |
| 183 | C2×#487 | C2×C53 | 1 | 1 | yes | characteristic |
| 184 | C4×C4⋊Q8 | C2×C53 | 1 | 1 | yes | characteristic |
| 185 | C4×C4⋊Q8 | C2×C53 | 1 | 1 | yes | characteristic |
| 186 | #1990 | C2×C53 | 1 | 1 | yes | characteristic |
| 187 | #1956 | C2×C53 | 1 | 1 | yes | characteristic |
| 188 | #1927 | C2×C53 | 1 | 4 | yes | — |
| 189 | #1865 | C2×C53 | 1 | 4 | yes | — |
| 190 | #1844 | C2×C53 | 1 | 1 | yes | characteristic |
| 191 | #1744 | C2×C53 | 1 | 1 | yes | characteristic |
| 192 | C2×C53 | #2326 | 1 | 1 | yes | characteristic |
| 193 | C2×C53 | C2×C4×SD16 | 1 | 1 | yes | characteristic |
| 194 | C2×C53 | C2×#441 | 1 | 1 | yes | characteristic |
| 195 | C2×C53 | #3206 | 1 | 1 | yes | characteristic |
| 196 | C2×C53 | #3210 | 1 | 1 | yes | characteristic |
| 197 | C2×C53 | #3229 | 1 | 1 | yes | characteristic |
| 198 | C2×C53 | #3231 | 1 | 1 | yes | characteristic |
| 199 | C2×C4⋊Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 200 | C2×C4⋊Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 201 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 202 | C2×C4×Q8 | C22×C53 | 1 | 2 | yes | — |
| 203 | #487 | C4×C53 | 1 | 8 | yes | complemented |
| 204 | C2×#106 | C22×C53 | 1 | 4 | yes | — |
| 205 | C2×#103 | C22×C53 | 1 | 4 | yes | — |
| 206 | C2×#103 | C22×C53 | 1 | 4 | yes | — |
| 207 | C2×C4×C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 209 | #391 | — | 2 | 1 | no | — |
| 210 | #391 | C22×C53 | 1 | 2 | yes | — |
| 211 | #389 | — | 2 | 1 | no | — |
| 212 | #389 | — | 2 | 1 | no | — |
| 213 | #389 | — | 2 | 1 | no | — |
| 214 | #389 | C22×C53 | 1 | 2 | yes | — |
| 215 | #384 | C22×C53 | 1 | 1 | yes | characteristic |
| 216 | #384 | C22×C53 | 1 | 1 | yes | characteristic |
| 217 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 218 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 219 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 220 | C4×C4⋊C4 | C22×C53 | 1 | 2 | yes | — |
| 221 | C43 | C22×C53 | 1 | 1 | yes | characteristic |
| 222 | #340 | C22×C53 | 1 | 4 | yes | — |
| 223 | #336 | C22×C53 | 1 | 2 | yes | — |
| 224 | #336 | C22×C53 | 1 | 2 | yes | — |
| 225 | C53 | #22218 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 226 | C22×Q8 | — | 2 | 1 | no | — |
| 227 | C22×Q8 | C23×C53 | 1 | 2 | yes | — |
| 228 | C22×C8 | C23×C53 | 1 | 2 | yes | — |
| 229 | C22×C8 | C23×C53 | 1 | 2 | yes | — |
| 230 | C4⋊Q8 | — | 2 | 2 | no | — |
| 231 | C4⋊Q8 | — | 2 | 2 | no | — |
| 232 | C4⋊Q8 | C2×C4×C53 | 1 | 4 | yes | — |
| 233 | C4⋊Q8 | C2×C4×C53 | 1 | 4 | yes | — |
| 234 | C4×Q8 | — | 4 | 4 | no | — |
| 235 | C4×Q8 | — | 4 | 4 | no | — |
| 236 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 237 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 238 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 239 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 240 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 241 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 242 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 243 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 244 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 245 | C2×C4⋊C4 | C23×C53 | 1 | 2 | yes | — |
| 246 | C2×C4⋊C4 | C23×C53 | 1 | 2 | yes | — |
| 247 | C2×C4⋊C4 | C23×C53 | 1 | 2 | yes | — |
| 248 | C2×C42 | — | 2 | 2 | no | — |
| 249 | C2×C42 | — | 2 | 2 | no | — |
| 250 | C2×C42 | D4×C53 | 1 | 1 | yes | characteristic |
| 251 | C2×C42 | D4×C53 | 1 | 1 | yes | characteristic |
| 252 | C2×C42 | D4×C53 | 1 | 1 | yes | characteristic |
| 253 | C2×C42 | D4×C53 | 1 | 1 | yes | characteristic |
| 254 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 255 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 256 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 257 | #106 | — | 4 | 4 | no | — |
| 258 | #103 | — | 4 | 4 | no | — |
| 259 | #103 | C2×C4×C53 | 1 | 16 | yes | — |
| 260 | C4×C8 | — | 2 | 2 | no | — |
| 261 | C4×C8 | C2×C4×C53 | 1 | 4 | yes | — |
| 262 | #95 | — | 2 | 2 | no | — |
| 263 | #95 | — | 2 | 2 | no | — |
| 264 | #95 | — | 2 | 2 | no | — |
| 265 | #95 | — | 2 | 2 | no | — |
| 266 | C2×Q8 | — | 2 | 4 | no | — |
| 267 | C2×Q8 | — | 2 | 2 | no | — |
| 268 | C2×Q8 | — | 2 | 4 | no | — |
| 269 | C2×Q8 | — | 2 | 4 | no | — |
| 270 | C2×Q8 | — | 4 | 2 | no | — |
| 271 | C2×Q8 | — | 4 | 2 | no | — |
| 272 | C2×Q8 | C22×C4×C53 | 1 | 4 | yes | — |
| 273 | C22×C4 | — | 2 | 2 | no | — |
| 274 | C22×C4 | — | 2 | 2 | no | — |
| 275 | C22×C4 | — | 2 | 2 | no | — |
| 276 | C22×C4 | — | 2 | 2 | no | — |
| 277 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 278 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 279 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 280 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 281 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 282 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 283 | C22×C4 | C24×C53 | 1 | 1 | yes | characteristic |
| 284 | C2×C8 | — | 2 | 2 | no | — |
| 285 | C2×C8 | — | 2 | 2 | no | — |
| 286 | C2×C8 | — | 2 | 2 | no | — |
| 287 | C2×C8 | — | 2 | 2 | no | — |
| 288 | C2×C8 | — | 2 | 2 | no | — |
| 289 | C2×C8 | C22×C4×C53 | 1 | 4 | yes | — |
| 290 | C4⋊C4 | — | 2 | 4 | no | — |
| 291 | C4⋊C4 | — | 2 | 4 | no | — |
| 292 | C4⋊C4 | — | 2 | 4 | no | — |
| 293 | C4⋊C4 | — | 2 | 2 | no | — |
| 294 | C4⋊C4 | — | 2 | 4 | no | — |
| 295 | C4⋊C4 | — | 2 | 4 | no | — |
| 296 | C4⋊C4 | — | 4 | 4 | no | — |
| 297 | C4⋊C4 | — | 4 | 4 | no | — |
| 298 | C4⋊C4 | — | 4 | 2 | no | — |
| 299 | C4⋊C4 | — | 4 | 2 | no | — |
| 300 | C4⋊C4 | — | 4 | 2 | no | — |
| 301 | C4⋊C4 | — | 4 | 2 | no | — |
| 302 | C4⋊C4 | C22×C4×C53 | 1 | 4 | yes | — |
| 303 | C42 | — | 2 | 2 | no | — |
| 304 | C42 | — | 2 | 2 | no | — |
| 305 | C42 | — | 2 | 2 | no | — |
| 306 | C42 | — | 2 | 2 | no | — |
| 307 | C42 | — | 2 | 2 | no | — |
| 308 | C42 | — | 4 | 4 | no | — |
| 309 | C42 | — | 4 | 4 | no | — |
| 310 | C42 | SD16×C53 | 1 | 4 | yes | — |
| 311 | C42 | C22×C4×C53 | 1 | 2 | yes | — |
| 312 | C42 | #41×C53 | 1 | 2 | yes | — |
| 313 | C23 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 314 | Q8 | — | 2 | 8 | no | — |
| 315 | Q8 | — | 4 | 4 | no | — |
| 316 | Q8 | — | 4 | 8 | no | — |
| 317 | C2×C4 | — | 2 | 1 | no | — |
| 318 | C2×C4 | — | 2 | 1 | no | — |
| 319 | C2×C4 | — | 2 | 1 | no | — |
| 320 | C2×C4 | — | 2 | 1 | no | — |
| 321 | C2×C4 | — | 2 | 4 | no | — |
| 322 | C2×C4 | — | 2 | 4 | no | — |
| 323 | C2×C4 | — | 2 | 1 | no | — |
| 324 | C2×C4 | — | 2 | 1 | no | — |
| 325 | C2×C4 | — | 2 | 1 | no | — |
| 326 | C2×C4 | — | 2 | 1 | no | — |
| 327 | C2×C4 | — | 2 | 1 | no | — |
| 328 | C2×C4 | — | 2 | 1 | no | — |
| 329 | C2×C4 | — | 4 | 2 | no | — |
| 330 | C2×C4 | — | 4 | 2 | no | — |
| 331 | C2×C4 | — | 4 | 2 | no | — |
| 332 | C2×C4 | — | 4 | 2 | no | — |
| 333 | C2×C4 | — | 4 | 2 | no | — |
| 334 | C2×C4 | — | 4 | 2 | no | — |
| 335 | C2×C4 | — | 4 | 2 | no | — |
| 336 | C2×C4 | — | 4 | 2 | no | — |
| 337 | C2×C4 | — | 4 | 2 | no | — |
| 338 | C2×C4 | — | 4 | 2 | no | — |
| 339 | C2×C4 | C4×D4×C53 | 1 | 2 | yes | — |
| 340 | C2×C4 | C4×D4×C53 | 1 | 2 | yes | — |
| 341 | C2×C4 | C2×SD16×C53 | 1 | 2 | yes | — |
| 342 | C2×C4 | C2×SD16×C53 | 1 | 2 | yes | — |
| 343 | C2×C4 | C2×SD16×C53 | 1 | 2 | yes | — |
| 344 | C2×C4 | #135×C53 | 1 | 2 | yes | — |
| 345 | C2×C4 | #137×C53 | 1 | 2 | yes | — |
| 346 | C2×C4 | #137×C53 | 1 | 2 | yes | — |
| 347 | C2×C4 | C23×C4×C53 | 1 | 1 | yes | characteristic |
| 348 | C2×C4 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 349 | C2×C4 | H(5,𝔽2)×C53 | 1 | 2 | yes | — |
| 350 | C2×C4 | 2−1+4×C53 | 1 | 2 | yes | — |
| 351 | C8 | — | 2 | 4 | no | — |
| 352 | C8 | — | 4 | 2 | no | — |
| 353 | C22 | C2×C4×D4×C53 | 1 | 1 | yes | characteristic |
| 354 | C22 | C53×#535 | 1 | 1 | yes | characteristic |
| 355 | C22 | C53×#536 | 1 | 1 | yes | characteristic |
| 356 | C22 | C22×SD16×C53 | 1 | 1 | yes | characteristic |
| 357 | C22 | C2×#135×C53 | 1 | 1 | yes | characteristic |
| 358 | C22 | C2×#137×C53 | 1 | 1 | yes | characteristic |
| 359 | C22 | C2×#137×C53 | 1 | 1 | yes | characteristic |
| 360 | C4 | — | 2 | 2 | no | — |
| 361 | C4 | — | 2 | 2 | no | — |
| 362 | C4 | — | 4 | 4 | no | — |
| 363 | C4 | — | 4 | 1 | no | — |
| 364 | C4 | — | 4 | 1 | no | — |
| 365 | C4 | — | 4 | 4 | no | — |
| 366 | C4 | — | 8 | 2 | no | — |
| 367 | C4 | — | 8 | 2 | no | — |
| 368 | C4 | C4×SD16×C53 | 1 | 4 | yes | — |
| 369 | C4 | C53×#441 | 1 | 4 | yes | — |
| 370 | C4 | C53×#520 | 1 | 2 | yes | — |
| 371 | C4 | C53×#542 | 1 | 2 | yes | — |
| 372 | C2 | C53×#2326 | 1 | 1 | yes | characteristic |
| 373 | C2 | C2×C4×SD16×C53 | 1 | 1 | yes | characteristic |
| 374 | C2 | C2×C53×#441 | 1 | 1 | yes | characteristic |
| 375 | C2 | C53×#3206 | 1 | 1 | yes | characteristic |
| 376 | C2 | C53×#3210 | 1 | 1 | yes | characteristic |
| 377 | C2 | C53×#3229 | 1 | 1 | yes | characteristic |
| 378 | C2 | C53×#3231 | 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