← C53×#22761 #27230273
Subgroups — C53×#22761 #27230273
Order 13568.
782 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C4×Q16×C53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C53×#2356 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C53×#2351 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C53×#1935 | C2 | 1 | 2 | yes | maximal |
| 5 | C53×#1921 | C2 | 1 | 2 | yes | maximal |
| 6 | C53×#1878 | C2 | 1 | 2 | yes | maximal |
| 7 | C53×#1835 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C53×#1805 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C53×#1805 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C53×#1770 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C53×#1763 | C2 | 1 | 2 | yes | maximal |
| 12 | C22×Q16×C53 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C4×Q8×C53 | C22 | 1 | 2 | yes | — |
| 14 | C2×C4×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C4×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 16 | C4×Q16×C53 | C4 | 1 | 8 | yes | complemented |
| 17 | C2×#107×C53 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4⋊C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#103×C53 | C22 | 1 | 2 | yes | — |
| 20 | C2×#103×C53 | C22 | 1 | 2 | yes | — |
| 21 | C2×#103×C53 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#103×C53 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#97×C53 | C22 | 1 | 2 | yes | — |
| 24 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#391 | C22 | 1 | 2 | yes | — |
| 26 | C53×#389 | — | 2 | 2 | no | — |
| 27 | C53×#389 | C22 | 1 | 2 | yes | — |
| 28 | C53×#387 | — | 2 | 2 | no | — |
| 29 | C53×#383 | — | 2 | 1 | no | — |
| 30 | C53×#382 | — | 2 | 1 | no | — |
| 31 | C53×#382 | C22 | 1 | 1 | yes | characteristic |
| 32 | C53×#382 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 34 | C4×C4⋊C4×C53 | C22 | 1 | 2 | yes | — |
| 35 | C4×C4⋊C4×C53 | C22 | 1 | 1 | yes | characteristic |
| 36 | C53×#376 | — | 2 | 1 | no | — |
| 37 | C53×#340 | C22 | 1 | 2 | yes | — |
| 38 | C53×#340 | C22 | 1 | 2 | yes | — |
| 39 | C53×#340 | C22 | 1 | 2 | yes | — |
| 40 | C53×#340 | C22 | 1 | 2 | yes | — |
| 41 | C53×#336 | C22 | 1 | 2 | yes | — |
| 42 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 43 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 45 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 46 | C2×Q16×C53 | C2×C4 | 1 | 4 | yes | — |
| 47 | C22×C8×C53 | C23 | 1 | 2 | yes | — |
| 48 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 50 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 51 | C4×Q8×C53 | — | 2 | 2 | no | — |
| 52 | C4×Q8×C53 | — | 2 | 4 | no | — |
| 53 | C4×Q8×C53 | — | 4 | 2 | no | — |
| 54 | C4×Q8×C53 | C2×C4 | 1 | 4 | yes | — |
| 55 | C4×Q8×C53 | C2×C4 | 1 | 4 | yes | — |
| 56 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 57 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 58 | C2×C4⋊C4×C53 | — | 2 | 2 | no | — |
| 59 | C2×C4⋊C4×C53 | — | 2 | 2 | no | — |
| 60 | C2×C4⋊C4×C53 | D4 | 1 | 2 | yes | — |
| 61 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 62 | C2×C4⋊C4×C53 | C23 | 1 | 2 | yes | — |
| 63 | C2×C4⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 64 | C2×C4⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C42×C53 | — | 2 | 1 | no | — |
| 66 | C2×C42×C53 | — | 2 | 1 | no | — |
| 67 | C2×C42×C53 | — | 2 | 2 | no | — |
| 68 | C2×C42×C53 | — | 2 | 2 | no | — |
| 69 | C2×C42×C53 | C23 | 1 | 2 | yes | — |
| 70 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 71 | #107×C53 | C2×C4 | 1 | 4 | yes | — |
| 72 | C4⋊C8×C53 | — | 2 | 2 | no | — |
| 73 | #103×C53 | — | 2 | 4 | no | — |
| 74 | #103×C53 | — | 4 | 2 | no | — |
| 75 | #103×C53 | C2×C4 | 1 | 4 | yes | — |
| 76 | #103×C53 | C2×C4 | 1 | 4 | yes | — |
| 77 | #97×C53 | — | 4 | 2 | no | — |
| 78 | C4×C8×C53 | C2×C4 | 1 | 4 | yes | — |
| 79 | #95×C53 | — | 2 | 1 | no | — |
| 80 | #95×C53 | — | 2 | 2 | no | — |
| 81 | #95×C53 | — | 2 | 1 | no | — |
| 82 | #95×C53 | — | 2 | 2 | no | — |
| 83 | #95×C53 | — | 2 | 2 | no | — |
| 84 | #95×C53 | — | 2 | 1 | no | — |
| 85 | #95×C53 | — | 2 | 1 | no | — |
| 86 | #95×C53 | — | 2 | 2 | no | — |
| 87 | #95×C53 | D4 | 1 | 1 | yes | characteristic |
| 88 | #95×C53 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 90 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 91 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 92 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 93 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 94 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 95 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 96 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 97 | C2×Q8×C53 | C22×C4 | 1 | 2 | yes | — |
| 98 | C2×Q8×C53 | C22×C4 | 1 | 2 | yes | — |
| 99 | C2×Q8×C53 | #41 | 1 | 2 | yes | — |
| 100 | C2×Q8×C53 | #41 | 1 | 2 | yes | — |
| 101 | C22×C4×C53 | — | 2 | 1 | no | — |
| 102 | C22×C4×C53 | — | 2 | 1 | no | — |
| 103 | C22×C4×C53 | — | 2 | 1 | no | — |
| 104 | C22×C4×C53 | — | 2 | 1 | no | — |
| 105 | C22×C4×C53 | — | 2 | 2 | no | — |
| 106 | C22×C4×C53 | — | 2 | 2 | no | — |
| 107 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 108 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 109 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 110 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 112 | Q16×C53 | — | 2 | 8 | no | — |
| 113 | C2×C8×C53 | — | 2 | 1 | no | — |
| 114 | C2×C8×C53 | — | 2 | 1 | no | — |
| 115 | C2×C8×C53 | — | 2 | 1 | no | — |
| 116 | C2×C8×C53 | — | 2 | 1 | no | — |
| 117 | C2×C8×C53 | — | 2 | 2 | no | — |
| 118 | C2×C8×C53 | — | 2 | 2 | no | — |
| 119 | C2×C8×C53 | — | 2 | 2 | no | — |
| 120 | C2×C8×C53 | C22×C4 | 1 | 2 | yes | — |
| 121 | C2×C8×C53 | C22×C4 | 1 | 2 | yes | — |
| 122 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 123 | C4⋊C4×C53 | — | 2 | 4 | no | — |
| 124 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 125 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 126 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 127 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 128 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 129 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 130 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 131 | C4⋊C4×C53 | — | 4 | 4 | no | — |
| 132 | C4⋊C4×C53 | — | 4 | 4 | no | — |
| 133 | C4⋊C4×C53 | C22×C4 | 1 | 2 | yes | — |
| 134 | C4⋊C4×C53 | C22×C4 | 1 | 2 | yes | — |
| 135 | C42×C53 | — | 2 | 4 | no | — |
| 136 | C42×C53 | — | 2 | 4 | no | — |
| 137 | C42×C53 | — | 2 | 2 | no | — |
| 138 | C42×C53 | — | 2 | 2 | no | — |
| 139 | C42×C53 | — | 4 | 4 | no | — |
| 140 | C42×C53 | — | 4 | 4 | no | — |
| 141 | C42×C53 | C22×C4 | 1 | 2 | yes | — |
| 142 | C42×C53 | #41 | 1 | 2 | yes | — |
| 143 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 144 | Q8×C53 | — | 2 | 2 | no | — |
| 145 | Q8×C53 | — | 2 | 2 | no | — |
| 146 | Q8×C53 | — | 2 | 2 | no | — |
| 147 | Q8×C53 | — | 2 | 2 | no | — |
| 148 | Q8×C53 | — | 2 | 2 | no | — |
| 149 | Q8×C53 | — | 4 | 1 | no | — |
| 150 | Q8×C53 | — | 4 | 1 | no | — |
| 151 | Q8×C53 | #117 | 1 | 4 | yes | — |
| 152 | C2×C4×C53 | — | 2 | 2 | no | — |
| 153 | C2×C4×C53 | — | 2 | 2 | no | — |
| 154 | C2×C4×C53 | — | 2 | 2 | no | — |
| 155 | C2×C4×C53 | — | 2 | 2 | no | — |
| 156 | C2×C4×C53 | — | 2 | 2 | no | — |
| 157 | C2×C4×C53 | — | 2 | 2 | no | — |
| 158 | C2×C4×C53 | — | 2 | 2 | no | — |
| 159 | C2×C4×C53 | — | 2 | 2 | no | — |
| 160 | C2×C4×C53 | — | 2 | 2 | no | — |
| 161 | C2×C4×C53 | — | 2 | 2 | no | — |
| 162 | C2×C4×C53 | — | 2 | 2 | no | — |
| 163 | C2×C4×C53 | — | 2 | 2 | no | — |
| 164 | C2×C4×C53 | — | 2 | 2 | no | — |
| 165 | C2×C4×C53 | — | 2 | 2 | no | — |
| 166 | C2×C4×C53 | — | 4 | 1 | no | — |
| 167 | C2×C4×C53 | — | 4 | 1 | no | — |
| 168 | C2×C4×C53 | — | 4 | 2 | no | — |
| 169 | C2×C4×C53 | — | 4 | 2 | no | — |
| 170 | C2×C4×C53 | — | 4 | 2 | no | — |
| 171 | C2×C4×C53 | — | 4 | 2 | no | — |
| 172 | C2×C4×C53 | — | 4 | 2 | no | — |
| 173 | C2×C4×C53 | — | 4 | 2 | no | — |
| 174 | C2×C4×C53 | — | 4 | 2 | no | — |
| 175 | C2×C4×C53 | — | 4 | 2 | no | — |
| 176 | C2×C4×C53 | C4×D4 | 1 | 2 | yes | — |
| 177 | C2×C4×C53 | C4×D4 | 1 | 2 | yes | — |
| 178 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 179 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 180 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 181 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 183 | C2×C4×C53 | 2−1+4 | 1 | 1 | yes | characteristic |
| 184 | C8×C53 | — | 2 | 2 | no | — |
| 185 | C8×C53 | — | 2 | 2 | no | — |
| 186 | C8×C53 | — | 4 | 2 | no | — |
| 187 | #22761 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 188 | C22×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 189 | C22×C53 | #546 | 1 | 1 | yes | characteristic |
| 190 | C22×C53 | #548 | 1 | 1 | yes | characteristic |
| 191 | C22×C53 | #575 | 1 | 2 | yes | — |
| 192 | C22×C53 | #578 | 1 | 2 | yes | — |
| 193 | C4×C53 | — | 2 | 4 | no | — |
| 194 | C4×C53 | — | 2 | 2 | no | — |
| 195 | C4×C53 | — | 2 | 2 | no | — |
| 196 | C4×C53 | — | 4 | 2 | no | — |
| 197 | C4×C53 | — | 4 | 2 | no | — |
| 198 | C4×C53 | — | 4 | 2 | no | — |
| 199 | C4×C53 | — | 4 | 2 | no | — |
| 200 | C4×C53 | — | 4 | 2 | no | — |
| 201 | C4×C53 | — | 8 | 2 | no | — |
| 202 | C4×C53 | — | 8 | 2 | no | — |
| 203 | C4×C53 | C2×#117 | 1 | 1 | yes | characteristic |
| 204 | C4×C53 | #520 | 1 | 1 | yes | characteristic |
| 205 | C4×C53 | #552 | 1 | 1 | yes | characteristic |
| 206 | C4×C53 | #553 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×Q16 | C2×C53 | 1 | 1 | yes | characteristic |
| 208 | #2356 | C2×C53 | 1 | 1 | yes | characteristic |
| 209 | #2351 | C2×C53 | 1 | 1 | yes | characteristic |
| 210 | #1935 | C2×C53 | 1 | 2 | yes | — |
| 211 | #1921 | C2×C53 | 1 | 2 | yes | — |
| 212 | #1878 | C2×C53 | 1 | 2 | yes | — |
| 213 | #1835 | C2×C53 | 1 | 1 | yes | characteristic |
| 214 | #1805 | C2×C53 | 1 | 1 | yes | characteristic |
| 215 | #1805 | C2×C53 | 1 | 1 | yes | characteristic |
| 216 | #1770 | C2×C53 | 1 | 1 | yes | characteristic |
| 217 | #1763 | C2×C53 | 1 | 2 | yes | — |
| 218 | C2×C53 | #2352 | 1 | 1 | yes | characteristic |
| 219 | C2×C53 | #2943 | 1 | 1 | yes | characteristic |
| 220 | C2×C53 | #2950 | 1 | 1 | yes | characteristic |
| 221 | C2×C53 | #3327 | 1 | 2 | yes | — |
| 222 | C2×C53 | #3377 | 1 | 2 | yes | — |
| 223 | C22×Q16 | C22×C53 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×Q8 | C22×C53 | 1 | 2 | yes | — |
| 225 | C2×C4×Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 226 | C2×C4×Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 227 | C4×Q16 | C4×C53 | 1 | 8 | yes | complemented |
| 228 | C2×#107 | C22×C53 | 1 | 1 | yes | characteristic |
| 229 | C2×C4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 230 | C2×#103 | C22×C53 | 1 | 2 | yes | — |
| 231 | C2×#103 | C22×C53 | 1 | 2 | yes | — |
| 232 | C2×#103 | C22×C53 | 1 | 1 | yes | characteristic |
| 233 | C2×#103 | C22×C53 | 1 | 1 | yes | characteristic |
| 234 | C2×#97 | C22×C53 | 1 | 2 | yes | — |
| 235 | C2×C4×C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 236 | #391 | C22×C53 | 1 | 2 | yes | — |
| 237 | #389 | — | 2 | 2 | no | — |
| 238 | #389 | C22×C53 | 1 | 2 | yes | — |
| 239 | #387 | — | 2 | 2 | no | — |
| 240 | #383 | — | 2 | 1 | no | — |
| 241 | #382 | — | 2 | 1 | no | — |
| 242 | #382 | C22×C53 | 1 | 1 | yes | characteristic |
| 243 | #382 | C22×C53 | 1 | 1 | yes | characteristic |
| 244 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 245 | C4×C4⋊C4 | C22×C53 | 1 | 2 | yes | — |
| 246 | C4×C4⋊C4 | C22×C53 | 1 | 1 | yes | characteristic |
| 247 | #376 | — | 2 | 1 | no | — |
| 248 | #340 | C22×C53 | 1 | 2 | yes | — |
| 249 | #340 | C22×C53 | 1 | 2 | yes | — |
| 250 | #340 | C22×C53 | 1 | 2 | yes | — |
| 251 | #340 | C22×C53 | 1 | 2 | yes | — |
| 252 | #336 | C22×C53 | 1 | 2 | yes | — |
| 253 | C53 | #22761 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 254 | C22×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 255 | C22×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 256 | C2×Q16 | — | 2 | 2 | no | — |
| 257 | C2×Q16 | — | 2 | 2 | no | — |
| 258 | C2×Q16 | C2×C4×C53 | 1 | 4 | yes | — |
| 259 | C22×C8 | C23×C53 | 1 | 2 | yes | — |
| 260 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 261 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 262 | C4×Q8 | — | 2 | 2 | no | — |
| 263 | C4×Q8 | — | 2 | 2 | no | — |
| 264 | C4×Q8 | — | 2 | 4 | no | — |
| 265 | C4×Q8 | — | 4 | 2 | no | — |
| 266 | C4×Q8 | C2×C4×C53 | 1 | 4 | yes | — |
| 267 | C4×Q8 | C2×C4×C53 | 1 | 4 | yes | — |
| 268 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 269 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 270 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 271 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 272 | C2×C4⋊C4 | D4×C53 | 1 | 2 | yes | — |
| 273 | C2×C4⋊C4 | C23×C53 | 1 | 2 | yes | — |
| 274 | C2×C4⋊C4 | C23×C53 | 1 | 2 | yes | — |
| 275 | C2×C4⋊C4 | C23×C53 | 1 | 1 | yes | characteristic |
| 276 | C2×C4⋊C4 | C23×C53 | 1 | 1 | yes | characteristic |
| 277 | C2×C42 | — | 2 | 1 | no | — |
| 278 | C2×C42 | — | 2 | 1 | no | — |
| 279 | C2×C42 | — | 2 | 2 | no | — |
| 280 | C2×C42 | — | 2 | 2 | no | — |
| 281 | C2×C42 | C23×C53 | 1 | 2 | yes | — |
| 282 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 283 | #107 | C2×C4×C53 | 1 | 4 | yes | — |
| 284 | C4⋊C8 | — | 2 | 2 | no | — |
| 285 | #103 | — | 2 | 4 | no | — |
| 286 | #103 | — | 4 | 2 | no | — |
| 287 | #103 | C2×C4×C53 | 1 | 4 | yes | — |
| 288 | #103 | C2×C4×C53 | 1 | 4 | yes | — |
| 289 | #97 | — | 4 | 2 | no | — |
| 290 | C4×C8 | C2×C4×C53 | 1 | 4 | yes | — |
| 291 | #95 | — | 2 | 1 | no | — |
| 292 | #95 | — | 2 | 2 | no | — |
| 293 | #95 | — | 2 | 1 | no | — |
| 294 | #95 | — | 2 | 2 | no | — |
| 295 | #95 | — | 2 | 2 | no | — |
| 296 | #95 | — | 2 | 1 | no | — |
| 297 | #95 | — | 2 | 1 | no | — |
| 298 | #95 | — | 2 | 2 | no | — |
| 299 | #95 | D4×C53 | 1 | 1 | yes | characteristic |
| 300 | #95 | D4×C53 | 1 | 1 | yes | characteristic |
| 301 | C2×Q8 | — | 2 | 1 | no | — |
| 302 | C2×Q8 | — | 2 | 1 | no | — |
| 303 | C2×Q8 | — | 2 | 1 | no | — |
| 304 | C2×Q8 | — | 2 | 1 | no | — |
| 305 | C2×Q8 | — | 2 | 1 | no | — |
| 306 | C2×Q8 | — | 2 | 1 | no | — |
| 307 | C2×Q8 | — | 2 | 1 | no | — |
| 308 | C2×Q8 | — | 2 | 1 | no | — |
| 309 | C2×Q8 | C22×C4×C53 | 1 | 2 | yes | — |
| 310 | C2×Q8 | C22×C4×C53 | 1 | 2 | yes | — |
| 311 | C2×Q8 | #41×C53 | 1 | 2 | yes | — |
| 312 | C2×Q8 | #41×C53 | 1 | 2 | yes | — |
| 313 | C22×C4 | — | 2 | 1 | no | — |
| 314 | C22×C4 | — | 2 | 1 | no | — |
| 315 | C22×C4 | — | 2 | 1 | no | — |
| 316 | C22×C4 | — | 2 | 1 | no | — |
| 317 | C22×C4 | — | 2 | 2 | no | — |
| 318 | C22×C4 | — | 2 | 2 | no | — |
| 319 | C22×C4 | C2×D4×C53 | 1 | 2 | yes | — |
| 320 | C22×C4 | C2×D4×C53 | 1 | 2 | yes | — |
| 321 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 322 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 323 | C22×C4 | C24×C53 | 1 | 1 | yes | characteristic |
| 324 | Q16 | — | 2 | 8 | no | — |
| 325 | C2×C8 | — | 2 | 1 | no | — |
| 326 | C2×C8 | — | 2 | 1 | no | — |
| 327 | C2×C8 | — | 2 | 1 | no | — |
| 328 | C2×C8 | — | 2 | 1 | no | — |
| 329 | C2×C8 | — | 2 | 2 | no | — |
| 330 | C2×C8 | — | 2 | 2 | no | — |
| 331 | C2×C8 | — | 2 | 2 | no | — |
| 332 | C2×C8 | C22×C4×C53 | 1 | 2 | yes | — |
| 333 | C2×C8 | C22×C4×C53 | 1 | 2 | yes | — |
| 334 | C4⋊C4 | — | 2 | 4 | no | — |
| 335 | C4⋊C4 | — | 2 | 4 | no | — |
| 336 | C4⋊C4 | — | 2 | 1 | no | — |
| 337 | C4⋊C4 | — | 2 | 1 | no | — |
| 338 | C4⋊C4 | — | 2 | 2 | no | — |
| 339 | C4⋊C4 | — | 2 | 2 | no | — |
| 340 | C4⋊C4 | — | 2 | 2 | no | — |
| 341 | C4⋊C4 | — | 2 | 2 | no | — |
| 342 | C4⋊C4 | — | 4 | 2 | no | — |
| 343 | C4⋊C4 | — | 4 | 4 | no | — |
| 344 | C4⋊C4 | — | 4 | 4 | no | — |
| 345 | C4⋊C4 | C22×C4×C53 | 1 | 2 | yes | — |
| 346 | C4⋊C4 | C22×C4×C53 | 1 | 2 | yes | — |
| 347 | C42 | — | 2 | 4 | no | — |
| 348 | C42 | — | 2 | 4 | no | — |
| 349 | C42 | — | 2 | 2 | no | — |
| 350 | C42 | — | 2 | 2 | no | — |
| 351 | C42 | — | 4 | 4 | no | — |
| 352 | C42 | — | 4 | 4 | no | — |
| 353 | C42 | C22×C4×C53 | 1 | 2 | yes | — |
| 354 | C42 | #41×C53 | 1 | 2 | yes | — |
| 355 | C23 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 356 | Q8 | — | 2 | 2 | no | — |
| 357 | Q8 | — | 2 | 2 | no | — |
| 358 | Q8 | — | 2 | 2 | no | — |
| 359 | Q8 | — | 2 | 2 | no | — |
| 360 | Q8 | — | 2 | 2 | no | — |
| 361 | Q8 | — | 4 | 1 | no | — |
| 362 | Q8 | — | 4 | 1 | no | — |
| 363 | Q8 | #117×C53 | 1 | 4 | yes | — |
| 364 | C2×C4 | — | 2 | 2 | no | — |
| 365 | C2×C4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 2 | 2 | no | — |
| 367 | C2×C4 | — | 2 | 2 | no | — |
| 368 | C2×C4 | — | 2 | 2 | no | — |
| 369 | C2×C4 | — | 2 | 2 | no | — |
| 370 | C2×C4 | — | 2 | 2 | no | — |
| 371 | C2×C4 | — | 2 | 2 | no | — |
| 372 | C2×C4 | — | 2 | 2 | no | — |
| 373 | C2×C4 | — | 2 | 2 | no | — |
| 374 | C2×C4 | — | 2 | 2 | no | — |
| 375 | C2×C4 | — | 2 | 2 | no | — |
| 376 | C2×C4 | — | 2 | 2 | no | — |
| 377 | C2×C4 | — | 2 | 2 | no | — |
| 378 | C2×C4 | — | 4 | 1 | no | — |
| 379 | C2×C4 | — | 4 | 1 | no | — |
| 380 | C2×C4 | — | 4 | 2 | no | — |
| 381 | C2×C4 | — | 4 | 2 | no | — |
| 382 | C2×C4 | — | 4 | 2 | no | — |
| 383 | C2×C4 | — | 4 | 2 | no | — |
| 384 | C2×C4 | — | 4 | 2 | no | — |
| 385 | C2×C4 | — | 4 | 2 | no | — |
| 386 | C2×C4 | — | 4 | 2 | no | — |
| 387 | C2×C4 | — | 4 | 2 | no | — |
| 388 | C2×C4 | C4×D4×C53 | 1 | 2 | yes | — |
| 389 | C2×C4 | C4×D4×C53 | 1 | 2 | yes | — |
| 390 | C2×C4 | C23×C4×C53 | 1 | 1 | yes | characteristic |
| 391 | C2×C4 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 392 | C2×C4 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 394 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 395 | C2×C4 | 2−1+4×C53 | 1 | 1 | yes | characteristic |
| 396 | C8 | — | 2 | 2 | no | — |
| 397 | C8 | — | 2 | 2 | no | — |
| 398 | C8 | — | 4 | 2 | no | — |
| 399 | C22 | C2×C4×D4×C53 | 1 | 1 | yes | characteristic |
| 400 | C22 | C53×#546 | 1 | 1 | yes | characteristic |
| 401 | C22 | C53×#548 | 1 | 1 | yes | characteristic |
| 402 | C22 | C53×#575 | 1 | 2 | yes | — |
| 403 | C22 | C53×#578 | 1 | 2 | yes | — |
| 404 | C4 | — | 2 | 2 | no | — |
| 405 | C4 | — | 2 | 2 | no | — |
| 406 | C4 | — | 2 | 4 | no | — |
| 407 | C4 | — | 4 | 2 | no | — |
| 408 | C4 | — | 4 | 2 | no | — |
| 409 | C4 | — | 4 | 2 | no | — |
| 410 | C4 | — | 4 | 2 | no | — |
| 411 | C4 | — | 4 | 2 | no | — |
| 412 | C4 | — | 8 | 2 | no | — |
| 413 | C4 | — | 8 | 2 | no | — |
| 414 | C4 | C2×#117×C53 | 1 | 1 | yes | characteristic |
| 415 | C4 | C53×#520 | 1 | 1 | yes | characteristic |
| 416 | C4 | C53×#552 | 1 | 1 | yes | characteristic |
| 417 | C4 | C53×#553 | 1 | 1 | yes | characteristic |
| 418 | C2 | C53×#2352 | 1 | 1 | yes | characteristic |
| 419 | C2 | C53×#2943 | 1 | 1 | yes | characteristic |
| 420 | C2 | C53×#2950 | 1 | 1 | yes | characteristic |
| 421 | C2 | C53×#3327 | 1 | 2 | yes | — |
| 422 | C2 | C53×#3377 | 1 | 2 | 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