Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1080 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #20288488 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20276400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20276364 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20274683 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C53×#2126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#13133263 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×#13133263 | C22 | 1 | 1 | yes | characteristic |
| 8 | #16811294 | — | 2 | 2 | no | — |
| 9 | D4×D212 | — | 2 | 2 | no | — |
| 10 | #16811257 | — | 2 | 4 | no | — |
| 11 | #16811191 | — | 2 | 1 | no | — |
| 12 | #16811191 | — | 2 | 1 | no | — |
| 13 | #16811187 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16811187 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16811174 | — | 2 | 1 | no | — |
| 16 | C2×#13133214 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #127×D53 | — | 2 | 1 | no | — |
| 18 | C4×#11719945 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #16810641 | — | 2 | 2 | no | — |
| 20 | #16810627 | — | 2 | 2 | no | — |
| 21 | #16810607 | C22 | 1 | 2 | yes | complemented |
| 22 | #16810422 | — | 2 | 1 | no | — |
| 23 | #16810420 | — | 2 | 1 | no | — |
| 24 | #16810409 | — | 2 | 4 | no | — |
| 25 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 26 | C53×#410 | C22 | 1 | 2 | yes | complemented |
| 27 | C53×#354 | — | 2 | 1 | no | — |
| 28 | C53×#353 | — | 2 | 1 | no | — |
| 29 | #13133263 | — | 4 | 2 | no | — |
| 30 | #13133263 | — | 4 | 2 | no | — |
| 31 | #13133263 | — | 4 | 2 | no | — |
| 32 | #13133263 | — | 4 | 2 | no | — |
| 33 | C2×#11719949 | — | 2 | 1 | no | — |
| 34 | C2×#11719949 | — | 2 | 1 | no | — |
| 35 | C2×#11719945 | — | 2 | 1 | no | — |
| 36 | C2×#11719945 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×#11719945 | D4 | 1 | 2 | yes | — |
| 38 | C22×D212 | — | 2 | 2 | no | — |
| 39 | C22×D212 | — | 2 | 1 | no | — |
| 40 | C22×D212 | C2×C4 | 1 | 1 | yes | characteristic |
| 41 | C22×D212 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C22×D212 | D4 | 1 | 2 | yes | — |
| 43 | C2×D4×D53 | — | 2 | 2 | no | — |
| 44 | C2×D4×D53 | — | 2 | 1 | no | — |
| 45 | C2×D4×D53 | — | 2 | 1 | no | — |
| 46 | C2×D4×D53 | — | 2 | 2 | no | — |
| 47 | C2×D4×D53 | — | 2 | 4 | no | — |
| 48 | C2×#11719917 | — | 2 | 2 | no | — |
| 49 | #13133214 | — | 2 | 1 | no | — |
| 50 | #13133214 | — | 2 | 1 | no | — |
| 51 | #13133214 | — | 2 | 2 | no | — |
| 52 | #13133213 | — | 2 | 4 | no | — |
| 53 | #13133213 | — | 2 | 1 | no | — |
| 54 | #13133213 | — | 2 | 1 | no | — |
| 55 | #13133206 | — | 2 | 1 | no | — |
| 56 | #13133206 | — | 2 | 1 | no | — |
| 57 | #13133192 | — | 2 | 4 | no | — |
| 58 | #13133191 | — | 2 | 2 | no | — |
| 59 | #13133191 | — | 2 | 2 | no | — |
| 60 | #13133190 | — | 2 | 4 | no | — |
| 61 | #13133190 | — | 2 | 4 | no | — |
| 62 | #13133187 | — | 2 | 4 | no | — |
| 63 | #13133187 | — | 2 | 4 | no | — |
| 64 | #13133185 | — | 2 | 2 | no | — |
| 65 | #13133185 | D4 | 1 | 4 | yes | — |
| 66 | C4×Dic106 | — | 2 | 1 | no | — |
| 67 | C4×D212 | — | 2 | 1 | no | — |
| 68 | #13133179 | — | 2 | 4 | no | — |
| 69 | C4×C22⋊D53 | — | 2 | 2 | no | — |
| 70 | #13133176 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | #13133174 | — | 2 | 1 | no | — |
| 72 | C42×D53 | — | 2 | 1 | no | — |
| 73 | #13133145 | — | 4 | 4 | no | — |
| 74 | #13133137 | — | 4 | 4 | no | — |
| 75 | #13133136 | — | 2 | 2 | no | — |
| 76 | #13133134 | — | 2 | 2 | no | — |
| 77 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 79 | C4⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 80 | #127×C53 | D4 | 1 | 1 | yes | characteristic |
| 81 | #124×C53 | D4 | 1 | 1 | yes | characteristic |
| 82 | #124×C53 | D4 | 1 | 1 | yes | characteristic |
| 83 | #121×C53 | — | 2 | 2 | no | — |
| 84 | C4×D4×C53 | — | 2 | 2 | no | — |
| 85 | #117×C53 | — | 2 | 2 | no | — |
| 86 | C2×C42×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #99×C53 | — | 2 | 2 | no | — |
| 88 | #99×C53 | — | 2 | 2 | no | — |
| 89 | C23×D53 | — | 2 | 2 | no | — |
| 90 | C23×D53 | — | 2 | 1 | no | — |
| 91 | C23×D53 | — | 2 | 2 | no | — |
| 92 | C23×D53 | C22⋊C4 | 1 | 2 | yes | — |
| 93 | #41×C53 | — | 4 | 1 | no | — |
| 94 | #41×C53 | — | 4 | 1 | no | — |
| 95 | #41×C53 | — | 4 | 1 | no | — |
| 96 | #41×C53 | — | 4 | 1 | no | — |
| 97 | C2×Q8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 98 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | C2×D4×C53 | — | 2 | 1 | no | — |
| 100 | C2×D4×C53 | — | 2 | 2 | no | — |
| 101 | C2×D4×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 102 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 104 | C22×C4×C53 | — | 2 | 1 | no | — |
| 105 | C22×C4×C53 | — | 2 | 1 | no | — |
| 106 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 107 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 108 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 109 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 110 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 111 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 112 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 113 | #11719949 | — | 4 | 4 | no | — |
| 114 | #11719949 | — | 4 | 4 | no | — |
| 115 | D4×D53 | — | 4 | 4 | no | — |
| 116 | D4×D53 | — | 4 | 4 | no | — |
| 117 | D4×D53 | — | 4 | 8 | no | — |
| 118 | D4×D53 | — | 4 | 8 | no | — |
| 119 | D4×D53 | — | 8 | 8 | no | — |
| 120 | #11719945 | — | 2 | 2 | no | — |
| 121 | #11719945 | — | 2 | 2 | no | — |
| 122 | #11719945 | — | 2 | 4 | no | — |
| 123 | #11719945 | — | 4 | 2 | no | — |
| 124 | #11719945 | — | 4 | 2 | no | — |
| 125 | #11719945 | — | 4 | 2 | no | — |
| 126 | C2×D212 | — | 2 | 4 | no | — |
| 127 | C2×D212 | — | 2 | 4 | no | — |
| 128 | C2×D212 | — | 2 | 2 | no | — |
| 129 | C2×D212 | — | 2 | 1 | no | — |
| 130 | C2×D212 | — | 2 | 1 | no | — |
| 131 | C2×D212 | — | 2 | 1 | no | — |
| 132 | C2×D212 | — | 2 | 2 | no | — |
| 133 | C2×D212 | — | 2 | 4 | no | — |
| 134 | C2×D212 | — | 4 | 1 | no | — |
| 135 | C2×D212 | — | 4 | 1 | no | — |
| 136 | C2×D212 | — | 4 | 2 | no | — |
| 137 | C2×D212 | — | 4 | 2 | no | — |
| 138 | C2×D212 | — | 4 | 2 | no | — |
| 139 | C2×D212 | — | 4 | 1 | no | — |
| 140 | C2×D212 | — | 4 | 1 | no | — |
| 141 | C2×D212 | — | 8 | 4 | no | — |
| 142 | C2×D212 | C22⋊C4 | 1 | 2 | yes | — |
| 143 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 144 | C2×C4×D53 | — | 2 | 1 | no | — |
| 145 | C2×C4×D53 | — | 2 | 2 | no | — |
| 146 | C2×C4×D53 | — | 2 | 2 | no | — |
| 147 | C2×C4×D53 | — | 2 | 2 | no | — |
| 148 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 150 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 151 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 152 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 153 | C22⋊C4×C53 | — | 4 | 2 | no | — |
| 154 | C42×C53 | — | 2 | 1 | no | — |
| 155 | C42×C53 | — | 4 | 2 | no | — |
| 156 | C42×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 157 | C42×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C22⋊Dic53 | C22⋊C4 | 1 | 2 | yes | — |
| 159 | #11719921 | — | 2 | 2 | no | — |
| 160 | #11719921 | — | 2 | 4 | no | — |
| 161 | #11719921 | — | 2 | 4 | no | — |
| 162 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 163 | #11719919 | — | 2 | 2 | no | — |
| 164 | C4×Dic53 | — | 2 | 2 | no | — |
| 165 | C4×Dic53 | — | 2 | 1 | no | — |
| 166 | #11719917 | — | 4 | 2 | no | — |
| 167 | #11719917 | — | 4 | 2 | no | — |
| 168 | C2×#88322 | — | 4 | 2 | no | — |
| 169 | C23×C53 | — | 2 | 1 | no | — |
| 170 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 171 | C23×C53 | #120 | 1 | 2 | yes | — |
| 172 | C22×D53 | — | 2 | 1 | no | — |
| 173 | C22×D53 | — | 2 | 2 | no | — |
| 174 | C22×D53 | — | 2 | 2 | no | — |
| 175 | C22×D53 | — | 4 | 4 | no | — |
| 176 | C22×D53 | — | 4 | 4 | no | — |
| 177 | C22×D53 | — | 4 | 2 | no | — |
| 178 | C22×D53 | — | 4 | 2 | no | — |
| 179 | C22×D53 | — | 8 | 2 | no | — |
| 180 | C22×D53 | — | 8 | 4 | no | — |
| 181 | C22×D53 | — | 8 | 4 | no | — |
| 182 | C22×D53 | — | 8 | 2 | no | — |
| 183 | Q8×C53 | — | 4 | 1 | no | — |
| 184 | Q8×C53 | — | 4 | 1 | no | — |
| 185 | D4×C53 | — | 4 | 2 | no | — |
| 186 | D4×C53 | — | 4 | 1 | no | — |
| 187 | D4×C53 | — | 4 | 1 | no | — |
| 188 | D4×C53 | — | 4 | 4 | no | — |
| 189 | D4×C53 | — | 4 | 2 | no | — |
| 190 | C2×C4×C53 | — | 2 | 1 | no | — |
| 191 | C2×C4×C53 | — | 2 | 2 | no | — |
| 192 | C2×C4×C53 | — | 2 | 1 | no | — |
| 193 | C2×C4×C53 | — | 2 | 1 | no | — |
| 194 | C2×C4×C53 | — | 2 | 2 | no | — |
| 195 | C2×C4×C53 | — | 2 | 1 | no | — |
| 196 | C2×C4×C53 | — | 2 | 1 | no | — |
| 197 | C2×C4×C53 | — | 4 | 2 | no | — |
| 198 | C2×C4×C53 | — | 4 | 1 | no | — |
| 199 | C2×C4×C53 | — | 4 | 1 | no | — |
| 200 | C2×C4×C53 | — | 8 | 2 | no | — |
| 201 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 202 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 203 | C2×C4×C53 | #120 | 1 | 2 | yes | — |
| 204 | C22⋊D53 | — | 2 | 4 | no | — |
| 205 | C22⋊D53 | — | 4 | 4 | no | — |
| 206 | C22⋊D53 | — | 4 | 4 | no | — |
| 207 | C22⋊D53 | — | 8 | 4 | no | — |
| 208 | C22⋊D53 | — | 8 | 4 | no | — |
| 209 | C2×Dic53 | — | 2 | 1 | no | — |
| 210 | C2×Dic53 | — | 2 | 2 | no | — |
| 211 | D212 | — | 2 | 1 | no | — |
| 212 | D212 | — | 2 | 2 | no | — |
| 213 | D212 | — | 2 | 2 | no | — |
| 214 | D212 | — | 4 | 4 | no | — |
| 215 | D212 | — | 4 | 2 | no | — |
| 216 | D212 | — | 4 | 2 | no | — |
| 217 | D212 | — | 4 | 8 | no | — |
| 218 | D212 | — | 4 | 4 | no | — |
| 219 | D212 | — | 4 | 1 | no | — |
| 220 | D212 | — | 4 | 1 | no | — |
| 221 | D212 | — | 8 | 4 | no | — |
| 222 | D212 | #99 | 1 | 2 | yes | — |
| 223 | C4×D53 | — | 2 | 4 | no | — |
| 224 | C4×D53 | — | 4 | 4 | no | — |
| 225 | C4×D53 | — | 4 | 4 | no | — |
| 226 | C4×D53 | — | 4 | 4 | no | — |
| 227 | Dic106 | — | 2 | 1 | no | — |
| 228 | Dic106 | #99 | 1 | 2 | yes | — |
| 229 | #88322 | — | 8 | 2 | no | — |
| 230 | #12718 | — | 53 | 1 | no | maximal, Sylow |
| 231 | C22×C53 | — | 2 | 1 | no | — |
| 232 | C22×C53 | — | 2 | 2 | no | — |
| 233 | C22×C53 | — | 4 | 2 | no | — |
| 234 | C22×C53 | — | 4 | 1 | no | — |
| 235 | C22×C53 | — | 4 | 2 | no | — |
| 236 | C22×C53 | — | 4 | 1 | no | — |
| 237 | C22×C53 | #379 | 1 | 1 | yes | characteristic |
| 238 | C2×D53 | — | 2 | 2 | no | — |
| 239 | C2×D53 | — | 4 | 2 | no | — |
| 240 | C2×D53 | — | 4 | 4 | no | — |
| 241 | C2×D53 | — | 4 | 4 | no | — |
| 242 | C2×D53 | — | 4 | 2 | no | — |
| 243 | C2×D53 | — | 4 | 2 | no | — |
| 244 | C2×D53 | — | 16 | 4 | no | — |
| 245 | C2×D53 | — | 16 | 4 | no | — |
| 246 | C2×D53 | — | 16 | 2 | no | — |
| 247 | C2×D53 | — | 16 | 2 | no | — |
| 248 | C4×C53 | — | 2 | 2 | no | — |
| 249 | C4×C53 | — | 2 | 2 | no | — |
| 250 | C4×C53 | — | 2 | 1 | no | — |
| 251 | C4×C53 | — | 4 | 1 | no | — |
| 252 | C4×C53 | — | 4 | 1 | no | — |
| 253 | C4×C53 | — | 16 | 2 | no | — |
| 254 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 255 | C4×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 256 | Dic53 | — | 2 | 2 | no | — |
| 257 | Dic53 | — | 4 | 2 | no | — |
| 258 | #3498 | — | 53 | 1 | no | — |
| 259 | #2132 | — | 53 | 1 | no | — |
| 260 | #2126 | D53 | 1 | 1 | yes | characteristic, complemented |
| 261 | #2122 | — | 53 | 2 | no | — |
| 262 | #1795 | — | 53 | 2 | no | — |
| 263 | C2×C53 | — | 2 | 1 | no | — |
| 264 | C2×C53 | — | 4 | 2 | no | — |
| 265 | C2×C53 | — | 4 | 1 | no | — |
| 266 | C2×C53 | — | 8 | 1 | no | — |
| 267 | C2×C53 | #1781 | 1 | 1 | yes | characteristic |
| 268 | D53 | — | 4 | 2 | no | — |
| 269 | D53 | — | 8 | 2 | no | — |
| 270 | D53 | — | 8 | 2 | no | — |
| 271 | C2×H(5,𝔽2) | — | 53 | 1 | no | — |
| 272 | C2×H(5,𝔽2) | — | 53 | 1 | no | — |
| 273 | #550 | — | 106 | 2 | no | — |
| 274 | D42 | — | 106 | 2 | no | — |
| 275 | D42 | — | 106 | 4 | no | — |
| 276 | #535 | — | 53 | 1 | no | — |
| 277 | #535 | — | 53 | 1 | no | — |
| 278 | #535 | — | 106 | 1 | no | — |
| 279 | #535 | — | 106 | 1 | no | — |
| 280 | #532 | — | 106 | 1 | no | — |
| 281 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 282 | C2×#127 | — | 53 | 1 | no | — |
| 283 | C2×#127 | — | 106 | 1 | no | — |
| 284 | C4×#41 | — | 53 | 1 | no | — |
| 285 | #421 | — | 106 | 2 | no | — |
| 286 | #418 | — | 106 | 2 | no | — |
| 287 | #413 | — | 53 | 2 | no | — |
| 288 | #410 | C2×D53 | 1 | 2 | yes | complemented |
| 289 | #356 | — | 106 | 1 | no | — |
| 290 | #355 | — | 106 | 1 | no | — |
| 291 | #354 | — | 2 | 1 | no | — |
| 292 | #353 | — | 2 | 1 | no | — |
| 293 | AΣL(1,𝔽16) | — | 106 | 4 | no | — |
| 294 | C53 | #12718 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 295 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 296 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 297 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 298 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 299 | C2×#41 | — | 53 | 1 | no | — |
| 300 | C2×#41 | — | 53 | 2 | no | — |
| 301 | C2×#41 | — | 106 | 1 | no | — |
| 302 | C2×#41 | — | 106 | 1 | no | — |
| 303 | C2×#41 | — | 106 | 1 | no | — |
| 304 | C2×#41 | C4×D53 | 1 | 1 | yes | characteristic |
| 305 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 306 | C22×D4 | — | 53 | 1 | no | — |
| 307 | C22×D4 | — | 53 | 1 | no | — |
| 308 | C22×D4 | — | 53 | 2 | no | — |
| 309 | C22×D4 | — | 106 | 1 | no | — |
| 310 | C22×D4 | — | 106 | 2 | no | — |
| 311 | C22×D4 | — | 106 | 4 | no | — |
| 312 | C22×D4 | — | 106 | 2 | no | — |
| 313 | C22×D4 | — | 106 | 2 | no | — |
| 314 | C22×D4 | — | 106 | 1 | no | — |
| 315 | C22×D4 | — | 106 | 1 | no | — |
| 316 | C2×M16 | — | 106 | 2 | no | — |
| 317 | C4⋊Q8 | D212 | 1 | 1 | yes | characteristic |
| 318 | #127 | — | 106 | 2 | no | — |
| 319 | #127 | — | 106 | 4 | no | — |
| 320 | #127 | — | 106 | 1 | no | — |
| 321 | #127 | — | 106 | 1 | no | — |
| 322 | #127 | — | 106 | 1 | no | — |
| 323 | #127 | — | 106 | 1 | no | — |
| 324 | #127 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 325 | #124 | — | 106 | 1 | no | — |
| 326 | #124 | — | 106 | 1 | no | — |
| 327 | #124 | D212 | 1 | 1 | yes | characteristic |
| 328 | #124 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 329 | #121 | — | 2 | 2 | no | — |
| 330 | #121 | — | 106 | 4 | no | — |
| 331 | #121 | — | 106 | 4 | no | — |
| 332 | #121 | — | 106 | 4 | no | — |
| 333 | #121 | — | 106 | 2 | no | — |
| 334 | #121 | — | 106 | 2 | no | — |
| 335 | #120 | — | 53 | 4 | no | — |
| 336 | #120 | — | 106 | 4 | no | — |
| 337 | #120 | — | 106 | 4 | no | — |
| 338 | #120 | — | 106 | 2 | no | — |
| 339 | C4×Q8 | — | 106 | 1 | no | — |
| 340 | C4×D4 | — | 2 | 2 | no | — |
| 341 | C4×D4 | — | 106 | 1 | no | — |
| 342 | C4×D4 | — | 106 | 2 | no | — |
| 343 | C4×D4 | — | 106 | 4 | no | — |
| 344 | #117 | — | 2 | 2 | no | — |
| 345 | #117 | — | 53 | 1 | no | — |
| 346 | #117 | — | 106 | 1 | no | — |
| 347 | C2×C42 | — | 106 | 1 | no | — |
| 348 | C2×C42 | C4×D53 | 1 | 1 | yes | characteristic |
| 349 | #104 | — | 212 | 4 | no | — |
| 350 | #102 | — | 212 | 4 | no | — |
| 351 | #101 | — | 106 | 2 | no | — |
| 352 | #100 | — | 106 | 2 | no | — |
| 353 | #99 | — | 2 | 2 | no | — |
| 354 | #99 | — | 2 | 2 | no | — |
| 355 | C24 | — | 53 | 2 | no | — |
| 356 | C24 | — | 106 | 2 | no | — |
| 357 | C24 | — | 106 | 1 | no | — |
| 358 | C24 | — | 106 | 2 | no | — |
| 359 | #41 | — | 4 | 1 | no | — |
| 360 | #41 | — | 4 | 1 | no | — |
| 361 | #41 | — | 4 | 1 | no | — |
| 362 | #41 | — | 4 | 1 | no | — |
| 363 | #41 | — | 106 | 2 | no | — |
| 364 | #41 | — | 106 | 2 | no | — |
| 365 | #41 | — | 106 | 4 | no | — |
| 366 | #41 | — | 212 | 2 | no | — |
| 367 | #41 | — | 212 | 2 | no | — |
| 368 | #41 | — | 212 | 2 | no | — |
| 369 | #41 | — | 212 | 4 | no | — |
| 370 | #41 | — | 212 | 4 | no | — |
| 371 | C2×Q8 | — | 53 | 1 | no | — |
| 372 | C2×Q8 | #11719921 | 1 | 1 | yes | characteristic |
| 373 | C2×Q8 | C2×D212 | 1 | 1 | yes | characteristic |
| 374 | C2×D4 | — | 2 | 1 | no | — |
| 375 | C2×D4 | — | 2 | 2 | no | — |
| 376 | C2×D4 | — | 53 | 1 | no | — |
| 377 | C2×D4 | — | 53 | 2 | no | — |
| 378 | C2×D4 | — | 106 | 4 | no | — |
| 379 | C2×D4 | — | 106 | 4 | no | — |
| 380 | C2×D4 | — | 106 | 4 | no | — |
| 381 | C2×D4 | — | 106 | 2 | no | — |
| 382 | C2×D4 | — | 106 | 1 | no | — |
| 383 | C2×D4 | — | 106 | 4 | no | — |
| 384 | C2×D4 | — | 106 | 4 | no | — |
| 385 | C2×D4 | — | 106 | 2 | no | — |
| 386 | C2×D4 | — | 106 | 2 | no | — |
| 387 | C2×D4 | — | 106 | 1 | no | — |
| 388 | C2×D4 | — | 106 | 1 | no | — |
| 389 | C2×D4 | — | 106 | 1 | no | — |
| 390 | C2×D4 | — | 106 | 2 | no | — |
| 391 | C2×D4 | — | 424 | 4 | no | — |
| 392 | C2×D4 | — | 424 | 8 | no | — |
| 393 | C2×D4 | — | 212 | 2 | no | — |
| 394 | C2×D4 | — | 212 | 1 | no | — |
| 395 | C2×D4 | — | 212 | 1 | no | — |
| 396 | C2×D4 | — | 212 | 1 | no | — |
| 397 | C2×D4 | — | 212 | 1 | no | — |
| 398 | C2×D4 | — | 212 | 2 | no | — |
| 399 | C2×D4 | — | 212 | 2 | no | — |
| 400 | C2×D4 | — | 212 | 4 | no | — |
| 401 | C2×D4 | — | 212 | 4 | no | — |
| 402 | C2×D4 | — | 212 | 8 | no | — |
| 403 | C2×D4 | — | 212 | 8 | no | — |
| 404 | C2×D4 | #11719921 | 1 | 1 | yes | characteristic |
| 405 | C2×D4 | D4×D53 | 1 | 2 | yes | — |
| 406 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 407 | C22×C4 | — | 2 | 1 | no | — |
| 408 | C22×C4 | — | 2 | 1 | no | — |
| 409 | C22×C4 | — | 106 | 2 | no | — |
| 410 | C22×C4 | — | 106 | 2 | no | — |
| 411 | C22×C4 | — | 106 | 1 | no | — |
| 412 | C22×C4 | — | 106 | 2 | no | — |
| 413 | C22×C4 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 414 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 415 | M16 | — | 212 | 2 | no | — |
| 416 | M16 | — | 212 | 2 | no | — |
| 417 | C2×C8 | — | 212 | 2 | no | — |
| 418 | C4⋊C4 | — | 2 | 2 | no | — |
| 419 | C4⋊C4 | — | 4 | 2 | no | — |
| 420 | C4⋊C4 | — | 106 | 2 | no | — |
| 421 | C4⋊C4 | — | 106 | 1 | no | — |
| 422 | C22⋊C4 | — | 2 | 2 | no | — |
| 423 | C22⋊C4 | — | 2 | 2 | no | — |
| 424 | C22⋊C4 | — | 4 | 2 | no | — |
| 425 | C22⋊C4 | — | 53 | 2 | no | — |
| 426 | C22⋊C4 | — | 106 | 2 | no | — |
| 427 | C22⋊C4 | — | 106 | 4 | no | — |
| 428 | C22⋊C4 | — | 106 | 4 | no | — |
| 429 | C42 | — | 2 | 1 | no | — |
| 430 | C42 | — | 4 | 2 | no | — |
| 431 | C42 | — | 106 | 2 | no | — |
| 432 | C42 | — | 106 | 1 | no | — |
| 433 | C42 | #11719921 | 1 | 1 | yes | characteristic |
| 434 | C42 | #11719921 | 1 | 1 | yes | characteristic |
| 435 | C23 | — | 2 | 1 | no | — |
| 436 | C23 | — | 106 | 1 | no | — |
| 437 | C23 | — | 106 | 2 | no | — |
| 438 | C23 | — | 106 | 2 | no | — |
| 439 | C23 | — | 424 | 2 | no | — |
| 440 | C23 | — | 424 | 4 | no | — |
| 441 | C23 | — | 424 | 4 | no | — |
| 442 | C23 | — | 424 | 2 | no | — |
| 443 | C23 | — | 212 | 4 | no | — |
| 444 | C23 | — | 212 | 2 | no | — |
| 445 | C23 | — | 212 | 2 | no | — |
| 446 | C23 | — | 212 | 4 | no | — |
| 447 | C23 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 448 | C23 | #13133185 | 1 | 2 | yes | — |
| 449 | Q8 | — | 4 | 1 | no | — |
| 450 | Q8 | — | 4 | 1 | no | — |
| 451 | Q8 | — | 53 | 2 | no | — |
| 452 | Q8 | — | 106 | 1 | no | — |
| 453 | D4 | — | 4 | 2 | no | — |
| 454 | D4 | — | 4 | 1 | no | — |
| 455 | D4 | — | 4 | 1 | no | — |
| 456 | D4 | — | 4 | 4 | no | — |
| 457 | D4 | — | 4 | 2 | no | — |
| 458 | D4 | — | 53 | 2 | no | — |
| 459 | D4 | — | 106 | 4 | no | — |
| 460 | D4 | — | 106 | 1 | no | — |
| 461 | D4 | — | 106 | 2 | no | — |
| 462 | D4 | — | 106 | 2 | no | — |
| 463 | D4 | — | 424 | 4 | no | — |
| 464 | D4 | — | 424 | 4 | no | — |
| 465 | D4 | — | 424 | 4 | no | — |
| 466 | D4 | — | 212 | 4 | no | — |
| 467 | D4 | — | 212 | 8 | no | — |
| 468 | D4 | — | 212 | 2 | no | — |
| 469 | D4 | — | 212 | 2 | no | — |
| 470 | D4 | — | 212 | 4 | no | — |
| 471 | D4 | — | 212 | 4 | no | — |
| 472 | D4 | — | 212 | 4 | no | — |
| 473 | D4 | — | 212 | 1 | no | — |
| 474 | D4 | — | 212 | 1 | no | — |
| 475 | C2×C4 | — | 2 | 1 | no | — |
| 476 | C2×C4 | — | 2 | 2 | no | — |
| 477 | C2×C4 | — | 2 | 2 | no | — |
| 478 | C2×C4 | — | 2 | 1 | no | — |
| 479 | C2×C4 | — | 2 | 1 | no | — |
| 480 | C2×C4 | — | 2 | 1 | no | — |
| 481 | C2×C4 | — | 2 | 1 | no | — |
| 482 | C2×C4 | — | 4 | 2 | no | — |
| 483 | C2×C4 | — | 4 | 1 | no | — |
| 484 | C2×C4 | — | 4 | 1 | no | — |
| 485 | C2×C4 | — | 8 | 2 | no | — |
| 486 | C2×C4 | — | 106 | 4 | no | — |
| 487 | C2×C4 | — | 106 | 1 | no | — |
| 488 | C2×C4 | — | 106 | 2 | no | — |
| 489 | C2×C4 | — | 212 | 4 | no | — |
| 490 | C2×C4 | — | 212 | 4 | no | — |
| 491 | C2×C4 | — | 212 | 4 | no | — |
| 492 | C2×C4 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 493 | C2×C4 | C2×#11719921 | 1 | 1 | yes | characteristic |
| 494 | C2×C4 | #13133187 | 1 | 2 | yes | — |
| 495 | C8 | — | 424 | 2 | no | — |
| 496 | C22 | — | 2 | 2 | no | — |
| 497 | C22 | — | 2 | 1 | no | — |
| 498 | C22 | — | 4 | 1 | no | — |
| 499 | C22 | — | 4 | 2 | no | — |
| 500 | C22 | — | 4 | 2 | no | — |
| 501 | C22 | — | 4 | 1 | no | — |
| 502 | C22 | — | 848 | 2 | no | — |
| 503 | C22 | — | 848 | 2 | no | — |
| 504 | C22 | — | 848 | 4 | no | — |
| 505 | C22 | — | 848 | 4 | no | — |
| 506 | C22 | — | 106 | 2 | no | — |
| 507 | C22 | — | 212 | 4 | no | — |
| 508 | C22 | — | 212 | 4 | no | — |
| 509 | C22 | — | 212 | 2 | no | — |
| 510 | C22 | — | 212 | 2 | no | — |
| 511 | C22 | — | 212 | 2 | no | — |
| 512 | C22 | #16810478 | 1 | 1 | yes | characteristic |
| 513 | C4 | — | 2 | 2 | no | — |
| 514 | C4 | — | 2 | 2 | no | — |
| 515 | C4 | — | 2 | 1 | no | — |
| 516 | C4 | — | 4 | 1 | no | — |
| 517 | C4 | — | 4 | 1 | no | — |
| 518 | C4 | — | 16 | 2 | no | — |
| 519 | C4 | — | 106 | 2 | no | — |
| 520 | C4 | — | 212 | 2 | no | — |
| 521 | C4 | #99×D53 | 1 | 1 | yes | characteristic |
| 522 | C4 | #99×D53 | 1 | 1 | yes | characteristic |
| 523 | C2 | — | 2 | 1 | no | — |
| 524 | C2 | — | 4 | 2 | no | — |
| 525 | C2 | — | 4 | 1 | no | — |
| 526 | C2 | — | 8 | 1 | no | — |
| 527 | C2 | — | 424 | 2 | no | — |
| 528 | C2 | — | 424 | 2 | no | — |
| 529 | C2 | — | 212 | 2 | no | — |
| 530 | C2 | #20274628 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20276400 | C2 | semidirect |
| 3. #20276364 | C2 | semidirect |
| 4. #20274683 | C2 | semidirect |
| 5. C53×#2126 | C2 | semidirect |
| 6. C2×#13133263 | C4 | semidirect |
| 13. #16811187 | C4 | semidirect |
| 16. C2×#13133214 | C4 | semidirect |
| 18. C4×#11719945 | C4 | semidirect |
| 21. #16810607 | C22 | semidirect |
| 26. C53×#410 | C22 | semidirect |
| 260. #2126 | D53 | semidirect |
| 288. #410 | C2×D53 | semidirect |
| 294. C53 | #12718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288488 | 2 |
| #20276400 | 2 |
| #20276364 | 2 |
| #20274683 | 2 |
| C53×#2126 | 2 |
| #12718 | 53 |