Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
410 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 57 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 | #20285605 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20276646 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20276643 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20275825 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #20272732 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272640 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1350 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#13133245 | — | 2 | 1 | no | — |
| 9 | C22×D424 | C22 | 1 | 1 | yes | characteristic |
| 10 | #16811196 | — | 2 | 1 | no | — |
| 11 | C2×#13133162 | — | 2 | 1 | no | — |
| 12 | C2×#13133160 | — | 2 | 1 | no | — |
| 13 | #16810966 | — | 2 | 1 | no | — |
| 14 | #16810963 | — | 2 | 1 | no | — |
| 15 | #16810879 | — | 2 | 1 | no | — |
| 16 | #16810864 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16810780 | — | 2 | 1 | no | — |
| 18 | #16810777 | — | 2 | 1 | no | — |
| 19 | C2×#13133133 | — | 2 | 1 | no | — |
| 20 | #16810589 | C22 | 1 | 1 | yes | characteristic |
| 21 | #16810425 | — | 2 | 1 | no | — |
| 22 | #16810423 | — | 2 | 1 | no | — |
| 23 | C22⋊#11719908 | C22 | 1 | 1 | yes | characteristic |
| 24 | C53×#467 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 26 | C53×#341 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#11719945 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 29 | C22×D212 | — | 2 | 1 | no | — |
| 30 | #13133245 | — | 4 | 2 | no | — |
| 31 | #13133245 | — | 4 | 2 | no | — |
| 32 | C2×Dic212 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×#11719925 | — | 2 | 1 | no | — |
| 34 | C2×#11719913 | — | 4 | 1 | no | — |
| 35 | C2×D424 | — | 2 | 1 | no | — |
| 36 | C2×D424 | — | 2 | 1 | no | — |
| 37 | C2×D424 | — | 4 | 2 | no | — |
| 38 | C2×D424 | — | 4 | 1 | no | — |
| 39 | C2×#11719917 | D4 | 1 | 1 | yes | characteristic |
| 40 | #13133216 | — | 4 | 1 | no | — |
| 41 | #13133203 | — | 4 | 1 | no | — |
| 42 | #13133202 | — | 4 | 1 | no | — |
| 43 | #13133199 | — | 4 | 1 | no | — |
| 44 | #13133197 | — | 2 | 1 | no | — |
| 45 | #13133196 | — | 2 | 1 | no | — |
| 46 | #13133193 | — | 2 | 1 | no | — |
| 47 | #13133175 | — | 2 | 1 | no | — |
| 48 | #13133162 | — | 4 | 2 | no | — |
| 49 | #13133160 | — | 4 | 2 | no | — |
| 50 | C2×#11719908 | — | 2 | 1 | no | — |
| 51 | #13133151 | D4 | 1 | 1 | yes | characteristic |
| 52 | #13133148 | — | 2 | 1 | no | — |
| 53 | #13133142 | — | 2 | 1 | no | — |
| 54 | #13133141 | — | 2 | 1 | no | — |
| 55 | #13133140 | — | 2 | 1 | no | — |
| 56 | #13133133 | — | 4 | 2 | no | — |
| 57 | #13133129 | — | 2 | 1 | no | — |
| 58 | #13133129 | — | 2 | 1 | no | — |
| 59 | C2×Q16×C53 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×M16×C53 | — | 2 | 1 | no | — |
| 61 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 62 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 63 | C2×C16×C53 | — | 2 | 1 | no | — |
| 64 | #107×C53 | D4 | 1 | 1 | yes | characteristic |
| 65 | #103×C53 | — | 2 | 1 | no | — |
| 66 | C23×D53 | — | 4 | 1 | no | — |
| 67 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 68 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 70 | Q8×D53 | — | 8 | 1 | no | — |
| 71 | Q8×D53 | — | 8 | 1 | no | — |
| 72 | #11719945 | — | 4 | 1 | no | — |
| 73 | #11719945 | — | 4 | 1 | no | — |
| 74 | C2×D212 | — | 2 | 2 | no | — |
| 75 | C2×D212 | — | 4 | 1 | no | — |
| 76 | C2×D212 | — | 4 | 1 | no | — |
| 77 | C2×D212 | — | 4 | 1 | no | — |
| 78 | C2×D212 | — | 4 | 1 | no | — |
| 79 | C2×D212 | — | 4 | 1 | no | — |
| 80 | C2×D212 | D8 | 1 | 1 | yes | characteristic |
| 81 | C2×C4×D53 | — | 2 | 1 | no | — |
| 82 | C2×C4×D53 | — | 4 | 1 | no | — |
| 83 | C2×Dic106 | — | 2 | 1 | no | — |
| 84 | C2×Dic106 | — | 4 | 1 | no | — |
| 85 | C2×Dic106 | D8 | 1 | 1 | yes | characteristic |
| 86 | Q16×C53 | — | 4 | 1 | no | — |
| 87 | M16×C53 | — | 2 | 2 | no | — |
| 88 | M16×C53 | — | 4 | 1 | no | — |
| 89 | C2×C8×C53 | — | 4 | 1 | no | — |
| 90 | C2×C8×C53 | — | 4 | 1 | no | — |
| 91 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 92 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 93 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 94 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 95 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 96 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 97 | #11719925 | — | 8 | 1 | no | — |
| 98 | #11719921 | — | 4 | 1 | no | — |
| 99 | #11719921 | — | 4 | 1 | no | — |
| 100 | #11719921 | — | 4 | 1 | no | — |
| 101 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 102 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 103 | #11719919 | — | 4 | 1 | no | — |
| 104 | #11719919 | — | 4 | 1 | no | — |
| 105 | C4×Dic53 | — | 4 | 1 | no | — |
| 106 | #11719917 | — | 4 | 1 | no | — |
| 107 | C2×#88322 | — | 2 | 1 | no | — |
| 108 | Dic212 | — | 4 | 1 | no | — |
| 109 | D424 | — | 2 | 2 | no | — |
| 110 | D424 | — | 2 | 2 | no | — |
| 111 | D424 | — | 4 | 1 | no | — |
| 112 | D424 | — | 4 | 1 | no | — |
| 113 | D424 | — | 4 | 4 | no | — |
| 114 | #11719913 | — | 4 | 4 | no | — |
| 115 | C16×C53 | — | 4 | 1 | no | — |
| 116 | #11719908 | — | 4 | 1 | no | — |
| 117 | C23×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 118 | C22×D53 | — | 2 | 1 | no | — |
| 119 | C22×D53 | — | 4 | 2 | no | — |
| 120 | C22×D53 | — | 8 | 1 | no | — |
| 121 | C22×D53 | — | 8 | 1 | no | — |
| 122 | C22×D53 | — | 16 | 1 | no | — |
| 123 | C22×D53 | — | 16 | 1 | no | — |
| 124 | Q8×C53 | — | 4 | 1 | no | — |
| 125 | Q8×C53 | — | 4 | 1 | no | — |
| 126 | C2×C4×C53 | — | 2 | 1 | no | — |
| 127 | C2×C4×C53 | — | 2 | 1 | no | — |
| 128 | C2×C4×C53 | — | 4 | 1 | no | — |
| 129 | C2×C4×C53 | — | 4 | 1 | no | — |
| 130 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 132 | C22⋊D53 | — | 8 | 1 | no | — |
| 133 | C2×Dic53 | — | 2 | 1 | no | — |
| 134 | C2×Dic53 | — | 4 | 1 | no | — |
| 135 | C2×Dic53 | — | 4 | 1 | no | — |
| 136 | D212 | — | 4 | 1 | no | — |
| 137 | D212 | — | 4 | 2 | no | — |
| 138 | D212 | — | 4 | 2 | no | — |
| 139 | D212 | — | 8 | 1 | no | — |
| 140 | D212 | — | 8 | 1 | no | — |
| 141 | C4×D53 | — | 4 | 1 | no | — |
| 142 | C4×D53 | — | 4 | 1 | no | — |
| 143 | C4×D53 | — | 8 | 2 | no | — |
| 144 | Dic106 | — | 4 | 1 | no | — |
| 145 | Dic106 | — | 4 | 1 | no | — |
| 146 | Dic106 | — | 4 | 1 | no | — |
| 147 | Dic106 | — | 8 | 2 | no | — |
| 148 | C8×C53 | — | 2 | 1 | no | — |
| 149 | C8×C53 | — | 2 | 1 | no | — |
| 150 | C8×C53 | — | 4 | 2 | no | — |
| 151 | #88322 | — | 4 | 1 | no | — |
| 152 | #12109 | — | 53 | 1 | no | maximal, Sylow |
| 153 | C22×C53 | — | 2 | 1 | no | — |
| 154 | C22×C53 | — | 2 | 1 | no | — |
| 155 | C22×C53 | — | 2 | 1 | no | — |
| 156 | C22×C53 | #447 | 1 | 1 | yes | characteristic |
| 157 | C2×D53 | — | 4 | 1 | no | — |
| 158 | C2×D53 | — | 4 | 1 | no | — |
| 159 | C2×D53 | — | 4 | 1 | no | — |
| 160 | C2×D53 | — | 8 | 2 | no | — |
| 161 | C2×D53 | — | 16 | 2 | no | — |
| 162 | C2×D53 | — | 16 | 1 | no | — |
| 163 | C2×D53 | — | 16 | 1 | no | — |
| 164 | C2×D53 | — | 16 | 2 | no | — |
| 165 | C4×C53 | — | 2 | 1 | no | — |
| 166 | C4×C53 | — | 8 | 1 | no | — |
| 167 | C4×C53 | — | 8 | 1 | no | — |
| 168 | C4×C53 | #453 | 1 | 1 | yes | characteristic |
| 169 | C4×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 170 | Dic53 | — | 4 | 1 | no | — |
| 171 | Dic53 | — | 8 | 1 | no | — |
| 172 | Dic53 | — | 8 | 1 | no | — |
| 173 | #3202 | — | 53 | 1 | no | — |
| 174 | #2187 | — | 53 | 1 | no | — |
| 175 | #2187 | — | 53 | 1 | no | — |
| 176 | #2018 | — | 53 | 1 | no | — |
| 177 | #1350 | — | 53 | 1 | no | — |
| 178 | #1350 | D53 | 1 | 1 | yes | characteristic, complemented |
| 179 | #1315 | — | 53 | 1 | no | — |
| 180 | C2×C53 | — | 4 | 1 | no | — |
| 181 | C2×C53 | #1595 | 1 | 1 | yes | characteristic |
| 182 | C2×C53 | #2193 | 1 | 1 | yes | characteristic |
| 183 | C2×C53 | #2193 | 1 | 1 | yes | characteristic |
| 184 | D53 | — | 8 | 1 | no | — |
| 185 | D53 | — | 16 | 2 | no | — |
| 186 | C2×AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 187 | C22×D8 | — | 53 | 1 | no | — |
| 188 | #536 | — | 106 | 1 | no | — |
| 189 | C2×SD32 | — | 106 | 1 | no | — |
| 190 | C2×SD32 | — | 106 | 1 | no | — |
| 191 | #485 | — | 106 | 1 | no | — |
| 192 | #485 | — | 106 | 1 | no | — |
| 193 | #470 | — | 106 | 1 | no | — |
| 194 | #467 | — | 53 | 1 | no | — |
| 195 | #467 | C2×D53 | 1 | 1 | yes | characteristic |
| 196 | #451 | — | 106 | 1 | no | — |
| 197 | #451 | — | 106 | 1 | no | — |
| 198 | C2×#100 | — | 106 | 1 | no | — |
| 199 | #408 | — | 53 | 1 | no | — |
| 200 | #357 | — | 106 | 1 | no | — |
| 201 | #357 | — | 106 | 1 | no | — |
| 202 | C22⋊C16 | — | 53 | 1 | no | — |
| 203 | C22⋊C16 | C2×D53 | 1 | 1 | yes | characteristic |
| 204 | #341 | C2×D53 | 1 | 1 | yes | characteristic |
| 205 | C53 | #12109 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 206 | C2×#41 | — | 53 | 1 | no | — |
| 207 | C22×Q8 | — | 106 | 1 | no | — |
| 208 | C22×D4 | — | 106 | 1 | no | — |
| 209 | AGL(1,ℤ/8) | — | 212 | 2 | no | — |
| 210 | AGL(1,ℤ/8) | — | 212 | 2 | no | — |
| 211 | C2×Q16 | — | 53 | 1 | no | — |
| 212 | C2×Q16 | — | 106 | 1 | no | — |
| 213 | C2×Q16 | D212 | 1 | 1 | yes | characteristic |
| 214 | C2×SD16 | — | 212 | 1 | no | — |
| 215 | C2×D8 | — | 106 | 1 | no | — |
| 216 | C2×D8 | — | 106 | 1 | no | — |
| 217 | C2×D8 | — | 212 | 2 | no | — |
| 218 | C2×D8 | — | 212 | 1 | no | — |
| 219 | C2×M16 | — | 2 | 1 | no | — |
| 220 | C2×M16 | — | 53 | 1 | no | — |
| 221 | C22×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 222 | C4⋊Q8 | — | 212 | 1 | no | — |
| 223 | #124 | — | 212 | 1 | no | — |
| 224 | #123 | — | 212 | 1 | no | — |
| 225 | #123 | — | 212 | 1 | no | — |
| 226 | C22⋊Q8 | — | 2 | 1 | no | — |
| 227 | C22⋊Q8 | — | 106 | 1 | no | — |
| 228 | C22⋊Q8 | — | 106 | 1 | no | — |
| 229 | C22⋊Q8 | — | 106 | 1 | no | — |
| 230 | #117 | — | 106 | 1 | no | — |
| 231 | SD32 | — | 212 | 2 | no | — |
| 232 | SD32 | — | 212 | 2 | no | — |
| 233 | C2×C16 | — | 2 | 1 | no | — |
| 234 | C2×C16 | — | 106 | 1 | no | — |
| 235 | #107 | — | 53 | 1 | no | — |
| 236 | #107 | D212 | 1 | 1 | yes | characteristic |
| 237 | #106 | — | 106 | 1 | no | — |
| 238 | #103 | — | 2 | 1 | no | — |
| 239 | #103 | — | 106 | 1 | no | — |
| 240 | #103 | — | 106 | 1 | no | — |
| 241 | #103 | — | 106 | 1 | no | — |
| 242 | #100 | — | 212 | 2 | no | — |
| 243 | C22⋊C8 | — | 106 | 1 | no | — |
| 244 | C22⋊C8 | — | 106 | 1 | no | — |
| 245 | C24 | — | 212 | 1 | no | — |
| 246 | #41 | — | 212 | 1 | no | — |
| 247 | #41 | — | 212 | 1 | no | — |
| 248 | C2×Q8 | — | 2 | 1 | no | — |
| 249 | C2×Q8 | — | 53 | 1 | no | — |
| 250 | C2×Q8 | — | 106 | 1 | no | — |
| 251 | C2×Q8 | — | 424 | 1 | no | — |
| 252 | C2×Q8 | — | 424 | 1 | no | — |
| 253 | C2×Q8 | — | 212 | 1 | no | — |
| 254 | C2×D4 | — | 53 | 1 | no | — |
| 255 | C2×D4 | — | 106 | 2 | no | — |
| 256 | C2×D4 | — | 106 | 1 | no | — |
| 257 | C2×D4 | — | 212 | 1 | no | — |
| 258 | C2×D4 | — | 212 | 1 | no | — |
| 259 | C2×D4 | — | 212 | 1 | no | — |
| 260 | C2×D4 | — | 212 | 1 | no | — |
| 261 | C2×D4 | — | 212 | 1 | no | — |
| 262 | C22×C4 | — | 106 | 1 | no | — |
| 263 | C22×C4 | — | 212 | 1 | no | — |
| 264 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 265 | Q16 | — | 4 | 1 | no | — |
| 266 | Q16 | — | 424 | 1 | no | — |
| 267 | Q16 | — | 212 | 1 | no | — |
| 268 | SD16 | — | 212 | 4 | no | — |
| 269 | D8 | — | 106 | 2 | no | — |
| 270 | D8 | — | 106 | 2 | no | — |
| 271 | D8 | — | 212 | 1 | no | — |
| 272 | D8 | — | 212 | 1 | no | — |
| 273 | D8 | — | 212 | 4 | no | — |
| 274 | M16 | — | 2 | 2 | no | — |
| 275 | M16 | — | 4 | 1 | no | — |
| 276 | M16 | — | 212 | 1 | no | — |
| 277 | C2×C8 | — | 4 | 1 | no | — |
| 278 | C2×C8 | — | 4 | 1 | no | — |
| 279 | C2×C8 | — | 106 | 1 | no | — |
| 280 | C2×C8 | C2×D212 | 1 | 1 | yes | characteristic |
| 281 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 282 | C4⋊C4 | — | 2 | 1 | no | — |
| 283 | C4⋊C4 | — | 4 | 1 | no | — |
| 284 | C4⋊C4 | — | 106 | 1 | no | — |
| 285 | C4⋊C4 | — | 212 | 1 | no | — |
| 286 | C4⋊C4 | — | 212 | 1 | no | — |
| 287 | C4⋊C4 | — | 212 | 1 | no | — |
| 288 | C22⋊C4 | — | 4 | 1 | no | — |
| 289 | C22⋊C4 | — | 212 | 1 | no | — |
| 290 | C22⋊C4 | — | 212 | 1 | no | — |
| 291 | C22⋊C4 | — | 212 | 1 | no | — |
| 292 | C22⋊C4 | — | 212 | 1 | no | — |
| 293 | C42 | — | 212 | 1 | no | — |
| 294 | C16 | — | 4 | 1 | no | — |
| 295 | C16 | — | 212 | 1 | no | — |
| 296 | C23 | — | 848 | 1 | no | — |
| 297 | C23 | — | 848 | 1 | no | — |
| 298 | C23 | — | 106 | 1 | no | — |
| 299 | C23 | — | 424 | 1 | no | — |
| 300 | C23 | — | 424 | 1 | no | — |
| 301 | C23 | — | 212 | 2 | no | — |
| 302 | C23 | #13133244 | 1 | 1 | yes | characteristic |
| 303 | Q8 | — | 4 | 1 | no | — |
| 304 | Q8 | — | 4 | 1 | no | — |
| 305 | Q8 | — | 424 | 2 | no | — |
| 306 | Q8 | — | 212 | 1 | no | — |
| 307 | Q8 | — | 212 | 1 | no | — |
| 308 | Q8 | — | 212 | 1 | no | — |
| 309 | D4 | — | 424 | 1 | no | — |
| 310 | D4 | — | 424 | 1 | no | — |
| 311 | D4 | — | 424 | 1 | no | — |
| 312 | D4 | — | 212 | 2 | no | — |
| 313 | D4 | — | 212 | 1 | no | — |
| 314 | D4 | — | 212 | 2 | no | — |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 2 | 1 | no | — |
| 317 | C2×C4 | — | 4 | 1 | no | — |
| 318 | C2×C4 | — | 4 | 1 | no | — |
| 319 | C2×C4 | — | 106 | 1 | no | — |
| 320 | C2×C4 | — | 424 | 2 | no | — |
| 321 | C2×C4 | — | 212 | 1 | no | — |
| 322 | C2×C4 | — | 212 | 1 | no | — |
| 323 | C2×C4 | — | 212 | 1 | no | — |
| 324 | C2×C4 | — | 212 | 1 | no | — |
| 325 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 326 | C2×C4 | D8×D53 | 1 | 1 | yes | characteristic |
| 327 | C8 | — | 2 | 1 | no | — |
| 328 | C8 | — | 2 | 1 | no | — |
| 329 | C8 | — | 4 | 2 | no | — |
| 330 | C8 | — | 212 | 1 | no | — |
| 331 | C22 | — | 2 | 1 | no | — |
| 332 | C22 | — | 2 | 1 | no | — |
| 333 | C22 | — | 2 | 1 | no | — |
| 334 | C22 | — | 848 | 2 | no | — |
| 335 | C22 | — | 848 | 2 | no | — |
| 336 | C22 | — | 848 | 1 | no | — |
| 337 | C22 | — | 848 | 1 | no | — |
| 338 | C22 | — | 424 | 2 | no | — |
| 339 | C22 | — | 212 | 1 | no | — |
| 340 | C22 | — | 212 | 1 | no | — |
| 341 | C22 | — | 212 | 1 | no | — |
| 342 | C22 | #16810758 | 1 | 1 | yes | characteristic |
| 343 | C4 | — | 2 | 1 | no | — |
| 344 | C4 | — | 8 | 1 | no | — |
| 345 | C4 | — | 8 | 1 | no | — |
| 346 | C4 | — | 424 | 1 | no | — |
| 347 | C4 | — | 424 | 1 | no | — |
| 348 | C4 | — | 212 | 1 | no | — |
| 349 | C4 | #16810792 | 1 | 1 | yes | characteristic |
| 350 | C4 | #16810811 | 1 | 1 | yes | characteristic |
| 351 | C2 | — | 4 | 1 | no | — |
| 352 | C2 | — | 848 | 2 | no | — |
| 353 | C2 | — | 424 | 1 | no | — |
| 354 | C2 | #20273634 | 1 | 1 | yes | characteristic |
| 355 | C2 | #20276680 | 1 | 1 | yes | characteristic |
| 356 | C2 | #20276682 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20285605 | C2 | semidirect |
| 2. #20276646 | C2 | semidirect |
| 3. #20276643 | C2 | semidirect |
| 5. #20272732 | C2 | semidirect |
| 6. #20272640 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 178. #1350 | D53 | semidirect |
| 205. C53 | #12109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285605 | 2 |
| #20276646 | 2 |
| #20276643 | 2 |
| #20275825 | 2 |
| #20272732 | 2 |
| #20272640 | 2 |
| C53×#1350 | 2 |
| #12109 | 53 |