Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
720 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 77 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 | #20285576 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20284117 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20276406 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20276365 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20274666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272845 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#3021 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16811187 | — | 2 | 1 | no | — |
| 9 | #16811187 | C22 | 1 | 1 | yes | characteristic |
| 10 | #16810947 | — | 2 | 1 | no | — |
| 11 | #16810944 | — | 2 | 1 | no | — |
| 12 | #16810874 | — | 2 | 1 | no | — |
| 13 | #16810857 | — | 2 | 1 | no | — |
| 14 | #16810810 | — | 2 | 2 | no | — |
| 15 | #16810810 | — | 2 | 2 | no | — |
| 16 | #16810757 | — | 2 | 1 | no | — |
| 17 | #16810756 | — | 2 | 1 | no | — |
| 18 | #16810607 | — | 2 | 1 | no | — |
| 19 | #16810607 | C22 | 1 | 1 | yes | characteristic |
| 20 | #16810597 | — | 2 | 1 | no | — |
| 21 | #16810597 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16810590 | — | 2 | 1 | no | — |
| 23 | #16810590 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16810419 | — | 2 | 2 | no | — |
| 25 | #16810410 | — | 2 | 2 | no | — |
| 26 | C53×#585 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 28 | C53×#535 | C22 | 1 | 1 | yes | characteristic |
| 29 | C53×#454 | — | 2 | 2 | no | — |
| 30 | C53×#453 | — | 2 | 2 | no | — |
| 31 | C53×#421 | — | 2 | 1 | no | — |
| 32 | C53×#413 | C22 | 1 | 1 | yes | characteristic |
| 33 | C22×D212 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×#11719922 | — | 2 | 1 | no | — |
| 35 | C2×#11719922 | — | 2 | 1 | no | — |
| 36 | C2×#11719917 | — | 2 | 1 | no | — |
| 37 | C2×#11719917 | D4 | 1 | 1 | yes | characteristic, complemented |
| 38 | C22×#88322 | D4 | 1 | 1 | yes | characteristic, complemented |
| 39 | #13133213 | — | 2 | 1 | no | — |
| 40 | #13133213 | — | 4 | 1 | no | — |
| 41 | #13133206 | — | 2 | 1 | no | — |
| 42 | #13133206 | — | 4 | 1 | no | — |
| 43 | #13133191 | — | 2 | 1 | no | — |
| 44 | #13133191 | — | 2 | 1 | no | — |
| 45 | #13133191 | — | 4 | 2 | no | — |
| 46 | #13133185 | — | 2 | 4 | no | — |
| 47 | #13133185 | — | 2 | 1 | no | — |
| 48 | #13133185 | — | 2 | 1 | no | — |
| 49 | #13133176 | — | 2 | 1 | no | — |
| 50 | #13133176 | D4 | 1 | 1 | yes | characteristic |
| 51 | #13133150 | — | 2 | 1 | no | — |
| 52 | #13133148 | — | 2 | 1 | no | — |
| 53 | #13133138 | — | 2 | 1 | no | — |
| 54 | #13133138 | — | 2 | 1 | no | — |
| 55 | #13133137 | — | 2 | 1 | no | — |
| 56 | #13133137 | — | 2 | 1 | no | — |
| 57 | #13133136 | — | 2 | 1 | no | — |
| 58 | #13133136 | — | 4 | 1 | no | — |
| 59 | #13133134 | — | 2 | 1 | no | — |
| 60 | #13133134 | — | 4 | 1 | no | — |
| 61 | #13133132 | — | 2 | 4 | no | — |
| 62 | #13133132 | — | 2 | 1 | no | — |
| 63 | #13133132 | D4 | 1 | 2 | yes | — |
| 64 | C22⋊#88322 | — | 2 | 1 | no | — |
| 65 | C22⋊#88322 | — | 2 | 1 | no | — |
| 66 | C22⋊#88322 | — | 4 | 2 | no | — |
| 67 | 2−1+4×C53 | — | 2 | 1 | no | — |
| 68 | 2−1+4×C53 | — | 4 | 1 | no | — |
| 69 | H(5,𝔽2)×C53 | — | 2 | 1 | no | — |
| 70 | H(5,𝔽2)×C53 | — | 2 | 1 | no | — |
| 71 | H(5,𝔽2)×C53 | — | 4 | 1 | no | — |
| 72 | H(5,𝔽2)×C53 | D4 | 1 | 2 | yes | — |
| 73 | C2×#41×C53 | — | 2 | 1 | no | — |
| 74 | C2×#41×C53 | — | 2 | 1 | no | — |
| 75 | C2×#41×C53 | — | 2 | 1 | no | — |
| 76 | C2×#41×C53 | — | 4 | 2 | no | — |
| 77 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×D4×C53 | D4 | 1 | 1 | yes | characteristic, complemented |
| 79 | AGL(1,ℤ/8)×C53 | — | 2 | 4 | no | — |
| 80 | AGL(1,ℤ/8)×C53 | — | 4 | 2 | no | — |
| 81 | C2×SD16×C53 | — | 4 | 1 | no | — |
| 82 | C2×D8×C53 | — | 4 | 1 | no | — |
| 83 | C2×M16×C53 | — | 2 | 1 | no | — |
| 84 | #127×C53 | — | 2 | 1 | no | — |
| 85 | #124×C53 | — | 2 | 1 | no | — |
| 86 | #121×C53 | — | 2 | 1 | no | — |
| 87 | #121×C53 | — | 2 | 1 | no | — |
| 88 | #120×C53 | — | 2 | 1 | no | — |
| 89 | #120×C53 | — | 2 | 1 | no | — |
| 90 | #117×C53 | D4 | 1 | 1 | yes | characteristic, complemented |
| 91 | #104×C53 | — | 2 | 4 | no | — |
| 92 | #101×C53 | D4 | 1 | 2 | yes | complemented |
| 93 | #100×C53 | — | 2 | 1 | no | — |
| 94 | C24×C53 | — | 2 | 1 | no | — |
| 95 | C23×D53 | — | 2 | 1 | no | — |
| 96 | #41×C53 | — | 2 | 2 | no | — |
| 97 | #41×C53 | — | 2 | 2 | no | — |
| 98 | #41×C53 | — | 4 | 1 | no | — |
| 99 | #41×C53 | — | 4 | 1 | no | — |
| 100 | #41×C53 | — | 4 | 2 | no | — |
| 101 | #41×C53 | — | 4 | 1 | no | — |
| 102 | #41×C53 | — | 4 | 1 | no | — |
| 103 | #41×C53 | — | 4 | 1 | no | — |
| 104 | #41×C53 | — | 4 | 1 | no | — |
| 105 | #41×C53 | — | 4 | 1 | no | — |
| 106 | #41×C53 | — | 4 | 2 | no | — |
| 107 | #41×C53 | — | 4 | 2 | no | — |
| 108 | #41×C53 | — | 4 | 2 | no | — |
| 109 | #41×C53 | — | 4 | 1 | no | — |
| 110 | #41×C53 | — | 4 | 1 | no | — |
| 111 | #41×C53 | — | 4 | 1 | no | — |
| 112 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 113 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 114 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 115 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 116 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×D4×C53 | — | 2 | 1 | no | — |
| 118 | C2×D4×C53 | — | 2 | 1 | no | — |
| 119 | C2×D4×C53 | — | 2 | 1 | no | — |
| 120 | C2×D4×C53 | — | 2 | 2 | no | — |
| 121 | C2×D4×C53 | — | 2 | 2 | no | — |
| 122 | C2×D4×C53 | — | 2 | 1 | no | — |
| 123 | C2×D4×C53 | — | 2 | 1 | no | — |
| 124 | C2×D4×C53 | — | 4 | 1 | no | — |
| 125 | C2×D4×C53 | — | 4 | 1 | no | — |
| 126 | C2×D4×C53 | — | 4 | 2 | no | — |
| 127 | C2×D4×C53 | — | 4 | 2 | no | — |
| 128 | C2×D4×C53 | — | 4 | 2 | no | — |
| 129 | C2×D4×C53 | — | 4 | 1 | no | — |
| 130 | C2×D4×C53 | — | 4 | 1 | no | — |
| 131 | C2×D4×C53 | — | 4 | 1 | no | — |
| 132 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×D4×C53 | #41 | 1 | 1 | yes | characteristic |
| 135 | C22×C4×C53 | — | 2 | 2 | no | — |
| 136 | C22×C4×C53 | — | 2 | 2 | no | — |
| 137 | C22×C4×C53 | — | 4 | 1 | no | — |
| 138 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C2×C22⋊D53 | — | 4 | 4 | no | — |
| 142 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 143 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 144 | C2×D212 | — | 2 | 1 | no | — |
| 145 | C2×D212 | — | 2 | 1 | no | — |
| 146 | C2×D212 | — | 4 | 1 | no | — |
| 147 | C2×D212 | — | 4 | 1 | no | — |
| 148 | SD16×C53 | — | 4 | 4 | no | — |
| 149 | D8×C53 | — | 4 | 4 | no | — |
| 150 | M16×C53 | — | 2 | 2 | no | — |
| 151 | M16×C53 | — | 4 | 1 | no | — |
| 152 | C2×C8×C53 | — | 4 | 1 | no | — |
| 153 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 154 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 155 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 156 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 157 | C42×C53 | — | 2 | 1 | no | — |
| 158 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 159 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 160 | #11719922 | — | 8 | 1 | no | — |
| 161 | #11719922 | — | 8 | 1 | no | — |
| 162 | #11719921 | — | 4 | 4 | no | — |
| 163 | #11719921 | — | 4 | 1 | no | — |
| 164 | #11719921 | — | 4 | 1 | no | — |
| 165 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 166 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 167 | C4×Dic53 | — | 2 | 1 | no | — |
| 168 | C4×Dic53 | — | 4 | 1 | no | — |
| 169 | #11719917 | — | 4 | 1 | no | — |
| 170 | #11719917 | — | 4 | 1 | no | — |
| 171 | #11719917 | — | 4 | 1 | no | — |
| 172 | C2×#88322 | — | 2 | 1 | no | — |
| 173 | C2×#88322 | — | 2 | 1 | no | — |
| 174 | C2×#88322 | — | 4 | 1 | no | — |
| 175 | C2×#88322 | — | 4 | 1 | no | — |
| 176 | C23×C53 | — | 2 | 2 | no | — |
| 177 | C23×C53 | — | 2 | 2 | no | — |
| 178 | C23×C53 | — | 4 | 1 | no | — |
| 179 | C23×C53 | — | 4 | 1 | no | — |
| 180 | C23×C53 | — | 8 | 1 | no | — |
| 181 | C23×C53 | — | 16 | 1 | no | — |
| 182 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 183 | C23×C53 | #121 | 1 | 1 | yes | characteristic |
| 184 | C23×C53 | #121 | 1 | 1 | yes | characteristic |
| 185 | C22×D53 | — | 4 | 2 | no | — |
| 186 | C22×D53 | — | 4 | 1 | no | — |
| 187 | C22×D53 | — | 16 | 1 | no | — |
| 188 | Q8×C53 | — | 2 | 2 | no | — |
| 189 | Q8×C53 | — | 4 | 1 | no | — |
| 190 | Q8×C53 | — | 4 | 1 | no | — |
| 191 | Q8×C53 | — | 4 | 1 | no | — |
| 192 | Q8×C53 | — | 4 | 1 | no | — |
| 193 | D4×C53 | — | 2 | 2 | no | — |
| 194 | D4×C53 | — | 4 | 1 | no | — |
| 195 | D4×C53 | — | 4 | 1 | no | — |
| 196 | D4×C53 | — | 4 | 1 | no | — |
| 197 | D4×C53 | — | 4 | 1 | no | — |
| 198 | D4×C53 | — | 4 | 1 | no | — |
| 199 | D4×C53 | — | 4 | 2 | no | — |
| 200 | D4×C53 | — | 4 | 2 | no | — |
| 201 | D4×C53 | — | 4 | 2 | no | — |
| 202 | D4×C53 | — | 4 | 2 | no | — |
| 203 | D4×C53 | — | 4 | 2 | no | — |
| 204 | D4×C53 | — | 4 | 1 | no | — |
| 205 | D4×C53 | — | 4 | 1 | no | — |
| 206 | D4×C53 | — | 4 | 1 | no | — |
| 207 | D4×C53 | — | 16 | 1 | no | — |
| 208 | D4×C53 | — | 16 | 1 | no | — |
| 209 | C2×C4×C53 | — | 2 | 1 | no | — |
| 210 | C2×C4×C53 | — | 2 | 1 | no | — |
| 211 | C2×C4×C53 | — | 2 | 1 | no | — |
| 212 | C2×C4×C53 | — | 2 | 1 | no | — |
| 213 | C2×C4×C53 | — | 2 | 1 | no | — |
| 214 | C2×C4×C53 | — | 2 | 1 | no | — |
| 215 | C2×C4×C53 | — | 2 | 2 | no | — |
| 216 | C2×C4×C53 | — | 2 | 2 | no | — |
| 217 | C2×C4×C53 | — | 4 | 2 | no | — |
| 218 | C2×C4×C53 | — | 4 | 2 | no | — |
| 219 | C2×C4×C53 | — | 4 | 2 | no | — |
| 220 | C2×C4×C53 | — | 4 | 1 | no | — |
| 221 | C2×C4×C53 | — | 4 | 2 | no | — |
| 222 | C2×C4×C53 | — | 4 | 1 | no | — |
| 223 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 225 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 226 | C2×C4×C53 | #127 | 1 | 1 | yes | characteristic |
| 227 | C22⋊D53 | — | 16 | 1 | no | — |
| 228 | C22⋊D53 | — | 16 | 1 | no | — |
| 229 | C22⋊D53 | — | 16 | 4 | no | — |
| 230 | C2×Dic53 | — | 4 | 2 | no | — |
| 231 | C2×Dic53 | — | 4 | 1 | no | — |
| 232 | D212 | — | 4 | 1 | no | — |
| 233 | D212 | — | 4 | 1 | no | — |
| 234 | D212 | — | 8 | 1 | no | — |
| 235 | C8×C53 | — | 4 | 2 | no | — |
| 236 | #88322 | — | 4 | 1 | no | — |
| 237 | #88322 | — | 4 | 1 | no | — |
| 238 | #88322 | — | 8 | 1 | no | — |
| 239 | #13353 | — | 53 | 1 | no | maximal, Sylow |
| 240 | C22×C53 | — | 2 | 1 | no | — |
| 241 | C22×C53 | — | 2 | 1 | no | — |
| 242 | C22×C53 | — | 2 | 1 | no | — |
| 243 | C22×C53 | — | 4 | 1 | no | — |
| 244 | C22×C53 | — | 4 | 1 | no | — |
| 245 | C22×C53 | — | 4 | 1 | no | — |
| 246 | C22×C53 | — | 4 | 2 | no | — |
| 247 | C22×C53 | — | 8 | 1 | no | — |
| 248 | C22×C53 | — | 8 | 1 | no | — |
| 249 | C22×C53 | — | 8 | 2 | no | — |
| 250 | C22×C53 | — | 8 | 2 | no | — |
| 251 | C22×C53 | — | 8 | 1 | no | — |
| 252 | C22×C53 | — | 16 | 1 | no | — |
| 253 | C22×C53 | — | 16 | 2 | no | — |
| 254 | C22×C53 | #392 | 1 | 1 | yes | characteristic |
| 255 | C2×D53 | — | 8 | 1 | no | — |
| 256 | C2×D53 | — | 8 | 1 | no | — |
| 257 | C2×D53 | — | 8 | 4 | no | — |
| 258 | C2×D53 | — | 8 | 1 | no | — |
| 259 | C4×C53 | — | 2 | 1 | no | — |
| 260 | C4×C53 | — | 2 | 1 | no | — |
| 261 | C4×C53 | — | 2 | 1 | no | — |
| 262 | C4×C53 | — | 4 | 2 | no | — |
| 263 | C4×C53 | — | 8 | 1 | no | — |
| 264 | C4×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 265 | C4×C53 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 266 | Dic53 | — | 8 | 1 | no | — |
| 267 | Dic53 | — | 8 | 2 | no | — |
| 268 | #3199 | — | 53 | 1 | no | — |
| 269 | #3027 | — | 53 | 1 | no | — |
| 270 | #3021 | D53 | 1 | 1 | yes | characteristic, complemented |
| 271 | #2134 | — | 53 | 1 | no | — |
| 272 | #2122 | — | 53 | 1 | no | — |
| 273 | #1791 | — | 53 | 1 | no | — |
| 274 | #1395 | — | 53 | 1 | no | — |
| 275 | C2×C53 | — | 2 | 1 | no | — |
| 276 | C2×C53 | — | 4 | 1 | no | — |
| 277 | C2×C53 | — | 4 | 1 | no | — |
| 278 | C2×C53 | — | 4 | 1 | no | — |
| 279 | C2×C53 | — | 8 | 2 | no | — |
| 280 | C2×C53 | — | 16 | 1 | no | — |
| 281 | C2×C53 | #2021 | 1 | 1 | yes | characteristic |
| 282 | D53 | — | 16 | 1 | no | — |
| 283 | #585 | C2×D53 | 1 | 1 | yes | characteristic |
| 284 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 285 | #535 | — | 53 | 1 | no | — |
| 286 | #535 | — | 106 | 1 | no | — |
| 287 | #535 | C2×D53 | 1 | 1 | yes | characteristic |
| 288 | #482 | — | 106 | 1 | no | — |
| 289 | #482 | — | 106 | 1 | no | — |
| 290 | #469 | — | 106 | 1 | no | — |
| 291 | #466 | — | 106 | 1 | no | — |
| 292 | B(4,𝔽2) | — | 106 | 2 | no | — |
| 293 | B(4,𝔽2) | — | 106 | 2 | no | — |
| 294 | #454 | — | 2 | 2 | no | — |
| 295 | #453 | — | 2 | 2 | no | — |
| 296 | #447 | — | 106 | 1 | no | — |
| 297 | #447 | — | 106 | 1 | no | — |
| 298 | #421 | — | 2 | 1 | no | — |
| 299 | #413 | — | 53 | 1 | no | — |
| 300 | #413 | — | 106 | 1 | no | — |
| 301 | #413 | C2×D53 | 1 | 1 | yes | characteristic |
| 302 | #410 | — | 53 | 1 | no | — |
| 303 | #410 | — | 106 | 1 | no | — |
| 304 | #408 | — | 53 | 1 | no | — |
| 305 | #408 | — | 106 | 1 | no | — |
| 306 | #355 | — | 106 | 2 | no | — |
| 307 | AΣL(1,𝔽16) | — | 106 | 2 | no | — |
| 308 | C53 | #13353 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 309 | 2−1+4 | — | 2 | 1 | no | — |
| 310 | 2−1+4 | — | 4 | 1 | no | — |
| 311 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 312 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 313 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 314 | H(5,𝔽2) | C22⋊D53 | 1 | 2 | yes | — |
| 315 | C2×#41 | — | 2 | 1 | no | — |
| 316 | C2×#41 | — | 2 | 1 | no | — |
| 317 | C2×#41 | — | 2 | 1 | no | — |
| 318 | C2×#41 | — | 4 | 2 | no | — |
| 319 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 320 | C22×D4 | — | 53 | 1 | no | — |
| 321 | C22×D4 | C22⋊D53 | 1 | 1 | yes | characteristic, complemented |
| 322 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 323 | AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 324 | C2×SD16 | — | 4 | 1 | no | — |
| 325 | C2×D8 | — | 4 | 1 | no | — |
| 326 | C2×D8 | — | 106 | 1 | no | — |
| 327 | C2×D8 | — | 106 | 1 | no | — |
| 328 | C2×M16 | — | 2 | 1 | no | — |
| 329 | C2×M16 | — | 53 | 1 | no | — |
| 330 | C2×M16 | — | 106 | 1 | no | — |
| 331 | C22×C8 | — | 53 | 1 | no | — |
| 332 | #127 | — | 2 | 1 | no | — |
| 333 | #127 | — | 106 | 1 | no | — |
| 334 | #127 | — | 212 | 1 | no | — |
| 335 | #124 | — | 2 | 1 | no | — |
| 336 | #124 | — | 106 | 1 | no | — |
| 337 | #124 | — | 212 | 1 | no | — |
| 338 | #121 | — | 2 | 1 | no | — |
| 339 | #121 | — | 2 | 1 | no | — |
| 340 | #121 | — | 106 | 1 | no | — |
| 341 | #121 | — | 106 | 1 | no | — |
| 342 | #121 | — | 212 | 2 | no | — |
| 343 | #120 | — | 2 | 1 | no | — |
| 344 | #120 | — | 2 | 1 | no | — |
| 345 | #120 | — | 106 | 4 | no | — |
| 346 | #120 | — | 106 | 1 | no | — |
| 347 | #120 | — | 106 | 1 | no | — |
| 348 | #117 | — | 53 | 1 | no | — |
| 349 | #117 | — | 106 | 1 | no | — |
| 350 | #117 | C22⋊D53 | 1 | 1 | yes | characteristic, complemented |
| 351 | #107 | — | 106 | 1 | no | — |
| 352 | #106 | — | 106 | 1 | no | — |
| 353 | #104 | — | 2 | 4 | no | — |
| 354 | #102 | — | 106 | 1 | no | — |
| 355 | #102 | — | 106 | 1 | no | — |
| 356 | #102 | — | 106 | 1 | no | — |
| 357 | #102 | — | 106 | 1 | no | — |
| 358 | #101 | — | 106 | 1 | no | — |
| 359 | #101 | — | 212 | 1 | no | — |
| 360 | #101 | C22⋊D53 | 1 | 2 | yes | complemented |
| 361 | #100 | — | 2 | 1 | no | — |
| 362 | #100 | — | 106 | 1 | no | — |
| 363 | #100 | — | 212 | 1 | no | — |
| 364 | #99 | — | 53 | 2 | no | — |
| 365 | #99 | — | 106 | 4 | no | — |
| 366 | #99 | — | 106 | 1 | no | — |
| 367 | C22⋊C8 | — | 106 | 1 | no | — |
| 368 | C22⋊C8 | — | 106 | 1 | no | — |
| 369 | C22⋊C8 | — | 212 | 2 | no | — |
| 370 | C24 | — | 2 | 1 | no | — |
| 371 | C24 | — | 106 | 1 | no | — |
| 372 | #41 | — | 2 | 2 | no | — |
| 373 | #41 | — | 2 | 2 | no | — |
| 374 | #41 | — | 4 | 1 | no | — |
| 375 | #41 | — | 4 | 1 | no | — |
| 376 | #41 | — | 4 | 2 | no | — |
| 377 | #41 | — | 4 | 1 | no | — |
| 378 | #41 | — | 4 | 1 | no | — |
| 379 | #41 | — | 4 | 1 | no | — |
| 380 | #41 | — | 4 | 1 | no | — |
| 381 | #41 | — | 4 | 1 | no | — |
| 382 | #41 | — | 4 | 2 | no | — |
| 383 | #41 | — | 4 | 2 | no | — |
| 384 | #41 | — | 4 | 2 | no | — |
| 385 | #41 | — | 4 | 1 | no | — |
| 386 | #41 | — | 4 | 1 | no | — |
| 387 | #41 | — | 4 | 1 | no | — |
| 388 | C2×Q8 | — | 2 | 1 | no | — |
| 389 | C2×Q8 | — | 2 | 1 | no | — |
| 390 | C2×Q8 | — | 2 | 1 | no | — |
| 391 | C2×Q8 | — | 4 | 2 | no | — |
| 392 | C2×Q8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 393 | C2×D4 | — | 2 | 1 | no | — |
| 394 | C2×D4 | — | 2 | 1 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 2 | 2 | no | — |
| 397 | C2×D4 | — | 2 | 2 | no | — |
| 398 | C2×D4 | — | 2 | 1 | no | — |
| 399 | C2×D4 | — | 2 | 1 | no | — |
| 400 | C2×D4 | — | 4 | 1 | no | — |
| 401 | C2×D4 | — | 4 | 1 | no | — |
| 402 | C2×D4 | — | 4 | 2 | no | — |
| 403 | C2×D4 | — | 4 | 2 | no | — |
| 404 | C2×D4 | — | 4 | 2 | no | — |
| 405 | C2×D4 | — | 4 | 1 | no | — |
| 406 | C2×D4 | — | 4 | 1 | no | — |
| 407 | C2×D4 | — | 4 | 1 | no | — |
| 408 | C2×D4 | — | 106 | 1 | no | — |
| 409 | C2×D4 | — | 106 | 1 | no | — |
| 410 | C2×D4 | — | 212 | 1 | no | — |
| 411 | C2×D4 | — | 212 | 1 | no | — |
| 412 | C2×D4 | — | 212 | 4 | no | — |
| 413 | C2×D4 | — | 212 | 1 | no | — |
| 414 | C2×D4 | — | 212 | 1 | no | — |
| 415 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 416 | C2×D4 | #11719947 | 1 | 1 | yes | characteristic |
| 417 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 418 | C22×C4 | — | 2 | 2 | no | — |
| 419 | C22×C4 | — | 2 | 2 | no | — |
| 420 | C22×C4 | — | 4 | 1 | no | — |
| 421 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 422 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 423 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 424 | SD16 | — | 4 | 4 | no | — |
| 425 | D8 | — | 4 | 4 | no | — |
| 426 | D8 | — | 424 | 1 | no | — |
| 427 | D8 | — | 424 | 1 | no | — |
| 428 | M16 | — | 2 | 2 | no | — |
| 429 | M16 | — | 4 | 1 | no | — |
| 430 | M16 | — | 212 | 1 | no | — |
| 431 | M16 | — | 212 | 1 | no | — |
| 432 | M16 | — | 212 | 1 | no | — |
| 433 | C2×C8 | — | 4 | 1 | no | — |
| 434 | C2×C8 | — | 106 | 1 | no | — |
| 435 | C2×C8 | — | 106 | 1 | no | — |
| 436 | C2×C8 | — | 212 | 1 | no | — |
| 437 | C2×C8 | — | 212 | 1 | no | — |
| 438 | C4⋊C4 | — | 2 | 1 | no | — |
| 439 | C4⋊C4 | — | 106 | 1 | no | — |
| 440 | C4⋊C4 | — | 212 | 1 | no | — |
| 441 | C22⋊C4 | — | 2 | 1 | no | — |
| 442 | C22⋊C4 | — | 4 | 1 | no | — |
| 443 | C22⋊C4 | — | 4 | 1 | no | — |
| 444 | C22⋊C4 | — | 106 | 2 | no | — |
| 445 | C22⋊C4 | — | 106 | 1 | no | — |
| 446 | C22⋊C4 | — | 212 | 4 | no | — |
| 447 | C22⋊C4 | — | 212 | 1 | no | — |
| 448 | C22⋊C4 | — | 212 | 1 | no | — |
| 449 | C42 | — | 2 | 1 | no | — |
| 450 | C42 | — | 106 | 1 | no | — |
| 451 | C42 | — | 212 | 1 | no | — |
| 452 | C23 | — | 2 | 2 | no | — |
| 453 | C23 | — | 2 | 2 | no | — |
| 454 | C23 | — | 4 | 1 | no | — |
| 455 | C23 | — | 4 | 1 | no | — |
| 456 | C23 | — | 8 | 1 | no | — |
| 457 | C23 | — | 16 | 1 | no | — |
| 458 | C23 | — | 848 | 1 | no | — |
| 459 | C23 | — | 212 | 2 | no | — |
| 460 | C23 | — | 212 | 1 | no | — |
| 461 | C23 | #13133185 | 1 | 1 | yes | characteristic |
| 462 | C23 | #13133189 | 1 | 1 | yes | characteristic |
| 463 | C23 | #13133189 | 1 | 1 | yes | characteristic |
| 464 | Q8 | — | 2 | 2 | no | — |
| 465 | Q8 | — | 4 | 1 | no | — |
| 466 | Q8 | — | 4 | 1 | no | — |
| 467 | Q8 | — | 4 | 1 | no | — |
| 468 | Q8 | — | 4 | 1 | no | — |
| 469 | D4 | — | 2 | 2 | no | — |
| 470 | D4 | — | 4 | 1 | no | — |
| 471 | D4 | — | 4 | 1 | no | — |
| 472 | D4 | — | 4 | 1 | no | — |
| 473 | D4 | — | 4 | 1 | no | — |
| 474 | D4 | — | 4 | 1 | no | — |
| 475 | D4 | — | 4 | 2 | no | — |
| 476 | D4 | — | 4 | 2 | no | — |
| 477 | D4 | — | 4 | 2 | no | — |
| 478 | D4 | — | 4 | 2 | no | — |
| 479 | D4 | — | 4 | 2 | no | — |
| 480 | D4 | — | 4 | 1 | no | — |
| 481 | D4 | — | 4 | 1 | no | — |
| 482 | D4 | — | 4 | 1 | no | — |
| 483 | D4 | — | 16 | 1 | no | — |
| 484 | D4 | — | 16 | 1 | no | — |
| 485 | D4 | — | 848 | 1 | no | — |
| 486 | D4 | — | 848 | 1 | no | — |
| 487 | D4 | — | 848 | 4 | no | — |
| 488 | D4 | — | 424 | 1 | no | — |
| 489 | D4 | — | 212 | 1 | no | — |
| 490 | D4 | — | 212 | 1 | no | — |
| 491 | C2×C4 | — | 2 | 1 | no | — |
| 492 | C2×C4 | — | 2 | 1 | no | — |
| 493 | C2×C4 | — | 2 | 1 | no | — |
| 494 | C2×C4 | — | 2 | 1 | no | — |
| 495 | C2×C4 | — | 2 | 1 | no | — |
| 496 | C2×C4 | — | 2 | 1 | no | — |
| 497 | C2×C4 | — | 2 | 2 | no | — |
| 498 | C2×C4 | — | 2 | 2 | no | — |
| 499 | C2×C4 | — | 4 | 2 | no | — |
| 500 | C2×C4 | — | 4 | 2 | no | — |
| 501 | C2×C4 | — | 4 | 2 | no | — |
| 502 | C2×C4 | — | 4 | 1 | no | — |
| 503 | C2×C4 | — | 4 | 2 | no | — |
| 504 | C2×C4 | — | 4 | 1 | no | — |
| 505 | C2×C4 | — | 212 | 2 | no | — |
| 506 | C2×C4 | — | 212 | 1 | no | — |
| 507 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | #13133186 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | #13133188 | 1 | 1 | yes | characteristic |
| 510 | C2×C4 | #13133213 | 1 | 1 | yes | characteristic |
| 511 | C8 | — | 4 | 2 | no | — |
| 512 | C8 | — | 424 | 1 | no | — |
| 513 | C8 | — | 212 | 1 | no | — |
| 514 | C8 | — | 212 | 1 | no | — |
| 515 | C22 | — | 2 | 1 | no | — |
| 516 | C22 | — | 2 | 1 | no | — |
| 517 | C22 | — | 2 | 1 | no | — |
| 518 | C22 | — | 4 | 1 | no | — |
| 519 | C22 | — | 4 | 1 | no | — |
| 520 | C22 | — | 4 | 1 | no | — |
| 521 | C22 | — | 4 | 2 | no | — |
| 522 | C22 | — | 8 | 1 | no | — |
| 523 | C22 | — | 8 | 1 | no | — |
| 524 | C22 | — | 8 | 2 | no | — |
| 525 | C22 | — | 8 | 2 | no | — |
| 526 | C22 | — | 8 | 1 | no | — |
| 527 | C22 | — | 16 | 1 | no | — |
| 528 | C22 | — | 16 | 2 | no | — |
| 529 | C22 | — | 424 | 1 | no | — |
| 530 | C22 | — | 424 | 1 | no | — |
| 531 | C22 | — | 424 | 4 | no | — |
| 532 | C22 | — | 424 | 1 | no | — |
| 533 | C22 | #16810531 | 1 | 1 | yes | characteristic |
| 534 | C4 | — | 2 | 1 | no | — |
| 535 | C4 | — | 2 | 1 | no | — |
| 536 | C4 | — | 2 | 1 | no | — |
| 537 | C4 | — | 4 | 2 | no | — |
| 538 | C4 | — | 8 | 1 | no | — |
| 539 | C4 | — | 424 | 1 | no | — |
| 540 | C4 | — | 424 | 2 | no | — |
| 541 | C4 | #16810809 | 1 | 1 | yes | characteristic |
| 542 | C4 | #16810809 | 1 | 1 | yes | characteristic |
| 543 | C2 | — | 2 | 1 | no | — |
| 544 | C2 | — | 4 | 1 | no | — |
| 545 | C2 | — | 4 | 1 | no | — |
| 546 | C2 | — | 4 | 1 | no | — |
| 547 | C2 | — | 8 | 2 | no | — |
| 548 | C2 | — | 16 | 1 | no | — |
| 549 | C2 | — | 848 | 1 | no | — |
| 550 | C2 | #20275838 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20285576 | C2 | semidirect |
| 2. #20284117 | C2 | semidirect |
| 3. #20276406 | C2 | semidirect |
| 4. #20276365 | C2 | semidirect |
| 5. #20274666 | C2 | semidirect |
| 6. #20272845 | C2 | semidirect |
| 7. C53×#3021 | C2 | semidirect |
| 37. C2×#11719917 | D4 | semidirect |
| 38. C22×#88322 | D4 | semidirect |
| 78. C22×D4×C53 | D4 | semidirect |
| 90. #117×C53 | D4 | semidirect |
| 92. #101×C53 | D4 | semidirect |
| 270. #3021 | D53 | semidirect |
| 308. C53 | #13353 | semidirect |
| 321. C22×D4 | C22⋊D53 | semidirect |
| 350. #117 | C22⋊D53 | semidirect |
| 360. #101 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285576 | 2 |
| #20284117 | 2 |
| #20276406 | 2 |
| #20276365 | 2 |
| #20274666 | 2 |
| #20272845 | 2 |
| C53×#3021 | 2 |
| #13353 | 53 |