← #16735431
Subgroups — #16735431
Order 3328.
1666 conjugacy classes of subgroups.
The subgroup lattice has 664 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13128655 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13126098 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #13125991 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13125991 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13125984 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13125977 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13125383 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13125346 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13125216 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#11718742 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #13124799 | C2 | 1 | 4 | yes | maximal |
| 12 | #13124678 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #13123480 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | C13×#3509 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C13×#557 | — | 2 | 1 | no | — |
| 16 | C13×#557 | — | 2 | 1 | no | — |
| 17 | C13×#556 | — | 2 | 1 | no | — |
| 18 | C13×#556 | — | 2 | 1 | no | — |
| 19 | C13×#552 | — | 2 | 2 | no | — |
| 20 | C13×#552 | — | 2 | 2 | no | — |
| 21 | C13×#541 | C22 | 1 | 4 | yes | — |
| 22 | C13×#536 | C22 | 1 | 2 | yes | — |
| 23 | C13×#533 | C22 | 1 | 2 | yes | — |
| 24 | C13×#533 | C22 | 1 | 2 | yes | — |
| 25 | C13×#533 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C13×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 27 | C13×#519 | C22 | 1 | 2 | yes | — |
| 28 | C4×C13×#41 | C22 | 1 | 1 | yes | characteristic |
| 29 | #11719532 | C22 | 1 | 2 | yes | — |
| 30 | #11719275 | — | 2 | 1 | no | — |
| 31 | Q8×Dic26 | — | 2 | 1 | no | — |
| 32 | #11719248 | — | 2 | 2 | no | — |
| 33 | #11719248 | — | 2 | 1 | no | — |
| 34 | D4×Dic26 | — | 2 | 2 | no | — |
| 35 | D4×Dic26 | — | 2 | 1 | no | — |
| 36 | #11719224 | C22 | 1 | 2 | yes | — |
| 37 | #11719224 | C22 | 1 | 4 | yes | — |
| 38 | #11719175 | C22 | 1 | 1 | yes | characteristic |
| 39 | #11719175 | C22 | 1 | 2 | yes | — |
| 40 | C2×#88123 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#88123 | C22 | 1 | 2 | yes | — |
| 42 | #11718895 | C22 | 1 | 2 | yes | — |
| 43 | #11718886 | C22 | 1 | 4 | yes | — |
| 44 | C2×#88075 | C22 | 1 | 4 | yes | — |
| 45 | #11718743 | C22 | 1 | 4 | yes | — |
| 46 | #11718742 | C22 | 1 | 2 | yes | — |
| 47 | #11718742 | C22 | 1 | 2 | yes | — |
| 48 | #11718742 | C22 | 1 | 4 | yes | — |
| 49 | #11718742 | C22 | 1 | 2 | yes | — |
| 50 | #11718742 | C22 | 1 | 2 | yes | — |
| 51 | #11718740 | C22 | 1 | 2 | yes | — |
| 52 | #11718740 | C22 | 1 | 1 | yes | characteristic |
| 53 | #11718740 | C22 | 1 | 1 | yes | characteristic |
| 54 | #11718739 | C22 | 1 | 2 | yes | — |
| 55 | #11718739 | C22 | 1 | 1 | yes | characteristic |
| 56 | #11718739 | C22 | 1 | 1 | yes | characteristic |
| 57 | #11718726 | C22 | 1 | 4 | yes | — |
| 58 | #11718725 | C22 | 1 | 4 | yes | — |
| 59 | #11718706 | C22 | 1 | 8 | yes | — |
| 60 | #11718706 | C22 | 1 | 8 | yes | — |
| 61 | #11718705 | C22 | 1 | 8 | yes | — |
| 62 | #11718704 | C22 | 1 | 8 | yes | — |
| 63 | #11718683 | C22 | 1 | 8 | yes | — |
| 64 | #11718683 | C22 | 1 | 8 | yes | — |
| 65 | #11718682 | C22 | 1 | 8 | yes | — |
| 66 | #11718681 | C22 | 1 | 8 | yes | — |
| 67 | #11718661 | C22 | 1 | 4 | yes | — |
| 68 | #11718660 | C22 | 1 | 2 | yes | — |
| 69 | #11718659 | C22 | 1 | 4 | yes | — |
| 70 | #11718656 | C22 | 1 | 4 | yes | — |
| 71 | #11718586 | C22 | 1 | 2 | yes | — |
| 72 | #11718586 | C22 | 1 | 2 | yes | — |
| 73 | C4×#6099 | C22 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×#1055 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×C13×#41 | C23 | 1 | 1 | yes | characteristic |
| 76 | C22×Q8×C13 | C23 | 1 | 2 | yes | — |
| 77 | C22×Dic26 | — | 2 | 1 | no | — |
| 78 | C22×Dic26 | — | 2 | 2 | no | — |
| 79 | C13×C4⋊Q8 | — | 2 | 2 | no | — |
| 80 | C13×C4⋊Q8 | — | 2 | 1 | no | — |
| 81 | C13×C4⋊Q8 | — | 2 | 1 | no | — |
| 82 | C13×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 83 | C13×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 84 | C13×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 85 | C13×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 86 | C13×#126 | — | 2 | 4 | no | — |
| 87 | C13×#126 | — | 2 | 4 | no | — |
| 88 | C13×#125 | — | 2 | 4 | no | — |
| 89 | C13×#125 | — | 2 | 4 | no | — |
| 90 | C13×#125 | — | 2 | 2 | no | — |
| 91 | C13×#125 | — | 2 | 2 | no | — |
| 92 | C13×#125 | C23 | 1 | 2 | yes | — |
| 93 | C13×#124 | — | 2 | 2 | no | — |
| 94 | C13×#123 | — | 2 | 4 | no | — |
| 95 | C13×C22⋊Q8 | — | 2 | 1 | no | — |
| 96 | C13×C22⋊Q8 | — | 2 | 1 | no | — |
| 97 | C13×C22⋊Q8 | — | 2 | 2 | no | — |
| 98 | C13×C22⋊Q8 | — | 2 | 2 | no | — |
| 99 | C13×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 100 | C13×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 101 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 102 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 103 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 104 | C4×Q8×C13 | — | 2 | 2 | no | — |
| 105 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 106 | C4×Q8×C13 | — | 2 | 1 | no | — |
| 107 | C4×Q8×C13 | D4 | 1 | 1 | yes | characteristic |
| 108 | C4×Q8×C13 | D4 | 1 | 1 | yes | characteristic |
| 109 | C4×Q8×C13 | C23 | 1 | 4 | yes | — |
| 110 | C4×Q8×C13 | C23 | 1 | 4 | yes | — |
| 111 | C4×D4×C13 | D4 | 1 | 2 | yes | — |
| 112 | C4×D4×C13 | D4 | 1 | 1 | yes | characteristic |
| 113 | C4×D4×C13 | D4 | 1 | 2 | yes | — |
| 114 | C4×D4×C13 | D4 | 1 | 1 | yes | characteristic |
| 115 | C13×#117 | — | 2 | 2 | no | — |
| 116 | C13×#117 | — | 2 | 2 | no | — |
| 117 | C13×#117 | — | 2 | 4 | no | — |
| 118 | C13×#117 | C23 | 1 | 2 | yes | — |
| 119 | C13×#117 | C23 | 1 | 1 | yes | characteristic |
| 120 | C13×#117 | C23 | 1 | 2 | yes | — |
| 121 | C2×C13×C4⋊C4 | — | 2 | 1 | no | — |
| 122 | C2×C13×C4⋊C4 | — | 2 | 1 | no | — |
| 123 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 124 | C2×C42×C13 | C23 | 1 | 2 | yes | — |
| 125 | Q8×Dic13 | — | 2 | 2 | no | — |
| 126 | D4×Dic13 | — | 2 | 4 | no | — |
| 127 | D4×Dic13 | — | 2 | 2 | no | — |
| 128 | #88180 | C23 | 1 | 2 | yes | — |
| 129 | #88180 | C23 | 1 | 4 | yes | — |
| 130 | C2×C4⋊Dic13 | — | 2 | 1 | no | — |
| 131 | C2×C4⋊Dic13 | — | 2 | 2 | no | — |
| 132 | C2×C4⋊Dic13 | C23 | 1 | 2 | yes | — |
| 133 | C2×C4⋊Dic13 | C23 | 1 | 4 | yes | — |
| 134 | #88178 | — | 2 | 1 | no | — |
| 135 | #88178 | — | 2 | 2 | no | — |
| 136 | #88178 | — | 2 | 1 | no | — |
| 137 | #88178 | — | 2 | 2 | no | — |
| 138 | C2×#6099 | C23 | 1 | 2 | yes | — |
| 139 | C22×#1055 | C23 | 1 | 2 | yes | — |
| 140 | #88144 | — | 2 | 2 | no | — |
| 141 | #88144 | — | 2 | 4 | no | — |
| 142 | #88142 | — | 2 | 2 | no | — |
| 143 | #88142 | — | 2 | 4 | no | — |
| 144 | #88132 | — | 2 | 4 | no | — |
| 145 | #88132 | — | 2 | 4 | no | — |
| 146 | #88132 | — | 2 | 4 | no | — |
| 147 | #88124 | C23 | 1 | 4 | yes | — |
| 148 | #88124 | C23 | 1 | 2 | yes | — |
| 149 | #88123 | — | 2 | 2 | no | — |
| 150 | #88123 | — | 2 | 1 | no | — |
| 151 | #88123 | — | 2 | 2 | no | — |
| 152 | #88123 | — | 2 | 1 | no | — |
| 153 | #88123 | C23 | 1 | 2 | yes | — |
| 154 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 155 | #88123 | C23 | 1 | 4 | yes | — |
| 156 | #88123 | C23 | 1 | 2 | yes | — |
| 157 | #88123 | C23 | 1 | 1 | yes | characteristic |
| 158 | C4×Dic26 | — | 2 | 2 | no | — |
| 159 | C4×Dic26 | — | 2 | 1 | no | — |
| 160 | C4×Dic26 | — | 2 | 2 | no | — |
| 161 | C4×Dic26 | — | 2 | 1 | no | — |
| 162 | #88075 | C23 | 1 | 8 | yes | — |
| 163 | #88075 | C23 | 1 | 8 | yes | — |
| 164 | #88075 | C23 | 1 | 8 | yes | — |
| 165 | #88075 | C23 | 1 | 8 | yes | — |
| 166 | C22⋊#1055 | C23 | 1 | 4 | yes | — |
| 167 | C22⋊#1055 | C23 | 1 | 4 | yes | — |
| 168 | #88048 | C23 | 1 | 8 | yes | — |
| 169 | #88048 | C23 | 1 | 4 | yes | — |
| 170 | #88048 | C23 | 1 | 4 | yes | — |
| 171 | #88047 | C23 | 1 | 8 | yes | — |
| 172 | #88047 | C23 | 1 | 4 | yes | — |
| 173 | #88047 | C23 | 1 | 4 | yes | — |
| 174 | C4⋊#1055 | C23 | 1 | 4 | yes | — |
| 175 | C4⋊#1055 | C23 | 1 | 4 | yes | — |
| 176 | #88043 | C23 | 1 | 2 | yes | — |
| 177 | C4×#1055 | C23 | 1 | 2 | yes | — |
| 178 | C4×#1055 | C23 | 1 | 1 | yes | characteristic |
| 179 | C4×#1055 | C23 | 1 | 2 | yes | — |
| 180 | C4×#1055 | C23 | 1 | 1 | yes | characteristic |
| 181 | #60878 | — | 13 | 1 | no | maximal, Sylow |
| 182 | C13×#41 | — | 2 | 4 | no | — |
| 183 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 184 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 185 | C2×Q8×C13 | — | 2 | 2 | no | — |
| 186 | C2×Q8×C13 | — | 2 | 8 | no | — |
| 187 | C2×Q8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×Q8×C13 | C24 | 1 | 4 | yes | — |
| 189 | C2×D4×C13 | C2×D4 | 1 | 2 | yes | — |
| 190 | C2×D4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C22×C4×C13 | — | 2 | 2 | no | — |
| 192 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 194 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C22×C4×C13 | C2×D4 | 1 | 2 | yes | — |
| 196 | C22×C4×C13 | C24 | 1 | 2 | yes | — |
| 197 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 198 | C22×Dic13 | — | 2 | 4 | no | — |
| 199 | C22×Dic13 | — | 2 | 2 | no | — |
| 200 | C2×Dic26 | — | 2 | 1 | no | — |
| 201 | C2×Dic26 | — | 2 | 2 | no | — |
| 202 | C2×Dic26 | — | 2 | 1 | no | — |
| 203 | C2×Dic26 | — | 2 | 4 | no | — |
| 204 | C2×Dic26 | — | 2 | 2 | no | — |
| 205 | C2×Dic26 | — | 8 | 2 | no | — |
| 206 | C2×Dic26 | — | 8 | 4 | no | — |
| 207 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 208 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 209 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 210 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 211 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 212 | C13×C4⋊C4 | — | 2 | 1 | no | — |
| 213 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 214 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 215 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 216 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 217 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 218 | C13×C4⋊C4 | — | 2 | 4 | no | — |
| 219 | C13×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C13×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 221 | C13×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C13×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 223 | C13×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 224 | C13×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 225 | C13×C22⋊C4 | — | 2 | 2 | no | — |
| 226 | C13×C22⋊C4 | — | 2 | 4 | no | — |
| 227 | C13×C22⋊C4 | — | 2 | 4 | no | — |
| 228 | C13×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 229 | C13×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 230 | C13×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 231 | C42×C13 | — | 2 | 4 | no | — |
| 232 | C42×C13 | — | 2 | 4 | no | — |
| 233 | C42×C13 | — | 2 | 2 | no | — |
| 234 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 235 | C42×C13 | C2×D4 | 1 | 2 | yes | — |
| 236 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 239 | C42×C13 | C24 | 1 | 2 | yes | — |
| 240 | C42×C13 | C24 | 1 | 1 | yes | characteristic |
| 241 | C22⋊Dic13 | — | 2 | 4 | no | — |
| 242 | C22⋊Dic13 | — | 2 | 2 | no | — |
| 243 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 244 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 245 | C4⋊Dic13 | — | 2 | 1 | no | — |
| 246 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 247 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 248 | C4⋊Dic13 | — | 2 | 4 | no | — |
| 249 | C4⋊Dic13 | — | 2 | 2 | no | — |
| 250 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 251 | C4⋊Dic13 | C24 | 1 | 4 | yes | — |
| 252 | C4⋊Dic13 | C24 | 1 | 2 | yes | — |
| 253 | #6101 | — | 2 | 4 | no | — |
| 254 | #6101 | — | 2 | 2 | no | — |
| 255 | #6101 | — | 2 | 4 | no | — |
| 256 | #6101 | — | 2 | 2 | no | — |
| 257 | C4×Dic13 | — | 2 | 4 | no | — |
| 258 | C4×Dic13 | — | 2 | 2 | no | — |
| 259 | #6099 | — | 2 | 4 | no | — |
| 260 | C2×#1055 | — | 2 | 4 | no | — |
| 261 | C2×#1055 | C24 | 1 | 2 | yes | — |
| 262 | C2×#1055 | C24 | 1 | 2 | yes | — |
| 263 | C2×#1055 | C24 | 1 | 4 | yes | — |
| 264 | #3509 | D13 | 1 | 1 | yes | characteristic |
| 265 | #3503 | — | 13 | 1 | no | — |
| 266 | #3242 | — | 13 | 8 | no | — |
| 267 | #3231 | — | 13 | 2 | no | — |
| 268 | #3231 | — | 13 | 2 | no | — |
| 269 | #3230 | — | 13 | 2 | no | — |
| 270 | #3229 | — | 13 | 2 | no | — |
| 271 | #3165 | — | 13 | 1 | no | — |
| 272 | #3160 | — | 13 | 1 | no | — |
| 273 | #3139 | — | 13 | 1 | no | — |
| 274 | C2×#487 | — | 13 | 1 | no | — |
| 275 | #3097 | — | 13 | 4 | no | — |
| 276 | #3082 | — | 13 | 4 | no | — |
| 277 | #2922 | — | 13 | 1 | no | — |
| 278 | C23×C13 | C22×D4 | 1 | 2 | yes | — |
| 279 | C23×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 280 | Q8×C13 | — | 2 | 2 | no | — |
| 281 | Q8×C13 | — | 2 | 8 | no | — |
| 282 | Q8×C13 | — | 4 | 4 | no | — |
| 283 | Q8×C13 | — | 4 | 2 | no | — |
| 284 | Q8×C13 | — | 4 | 2 | no | — |
| 285 | D4×C13 | — | 2 | 4 | no | — |
| 286 | D4×C13 | — | 2 | 2 | no | — |
| 287 | C2×C4×C13 | — | 2 | 2 | no | — |
| 288 | C2×C4×C13 | — | 2 | 4 | no | — |
| 289 | C2×C4×C13 | — | 2 | 2 | no | — |
| 290 | C2×C4×C13 | — | 2 | 4 | no | — |
| 291 | C2×C4×C13 | — | 2 | 4 | no | — |
| 292 | C2×C4×C13 | — | 2 | 2 | no | — |
| 293 | C2×C4×C13 | — | 2 | 2 | no | — |
| 294 | C2×C4×C13 | — | 2 | 4 | no | — |
| 295 | C2×C4×C13 | — | 4 | 4 | no | — |
| 296 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 297 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 298 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×C13 | C22×D4 | 1 | 2 | yes | — |
| 300 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 301 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 302 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 303 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 304 | C2×C4×C13 | 2−1+4 | 1 | 4 | yes | — |
| 305 | C2×C4×C13 | C25 | 1 | 1 | yes | characteristic |
| 306 | C2×Dic13 | — | 2 | 2 | no | — |
| 307 | C2×Dic13 | — | 2 | 4 | no | — |
| 308 | C2×Dic13 | — | 2 | 2 | no | — |
| 309 | C2×Dic13 | — | 8 | 2 | no | — |
| 310 | C2×Dic13 | — | 8 | 4 | no | — |
| 311 | Dic26 | — | 4 | 4 | no | — |
| 312 | Dic26 | — | 4 | 2 | no | — |
| 313 | Dic26 | — | 4 | 2 | no | — |
| 314 | Dic26 | — | 8 | 4 | no | — |
| 315 | Dic26 | — | 8 | 2 | no | — |
| 316 | #1055 | — | 2 | 2 | no | — |
| 317 | #1055 | — | 2 | 2 | no | — |
| 318 | #1055 | — | 2 | 4 | no | — |
| 319 | Q82 | — | 26 | 1 | no | — |
| 320 | #557 | — | 2 | 1 | no | — |
| 321 | #557 | — | 2 | 1 | no | — |
| 322 | #557 | — | 26 | 1 | no | — |
| 323 | #556 | — | 2 | 1 | no | — |
| 324 | #556 | — | 2 | 1 | no | — |
| 325 | #554 | — | 26 | 2 | no | — |
| 326 | #554 | — | 26 | 1 | no | — |
| 327 | #552 | — | 2 | 2 | no | — |
| 328 | #552 | — | 2 | 2 | no | — |
| 329 | D4×Q8 | — | 26 | 2 | no | — |
| 330 | D4×Q8 | — | 26 | 1 | no | — |
| 331 | #544 | — | 13 | 2 | no | — |
| 332 | #544 | — | 13 | 4 | no | — |
| 333 | #541 | C2×D13 | 1 | 4 | yes | — |
| 334 | #536 | C2×D13 | 1 | 2 | yes | — |
| 335 | #533 | — | 13 | 1 | no | — |
| 336 | #533 | — | 13 | 2 | no | — |
| 337 | #533 | C2×D13 | 1 | 2 | yes | — |
| 338 | #533 | C2×D13 | 1 | 2 | yes | — |
| 339 | #533 | C2×D13 | 1 | 1 | yes | characteristic |
| 340 | C2×C4⋊Q8 | — | 13 | 1 | no | — |
| 341 | C2×C4⋊Q8 | — | 13 | 2 | no | — |
| 342 | C2×C4⋊Q8 | C2×D13 | 1 | 1 | yes | characteristic |
| 343 | #520 | — | 13 | 2 | no | — |
| 344 | #519 | C2×D13 | 1 | 2 | yes | — |
| 345 | C4×#41 | C2×D13 | 1 | 1 | yes | characteristic |
| 346 | #501 | — | 13 | 4 | no | — |
| 347 | #500 | — | 13 | 1 | no | — |
| 348 | #500 | — | 13 | 1 | no | — |
| 349 | #500 | — | 13 | 2 | no | — |
| 350 | #499 | — | 13 | 4 | no | — |
| 351 | #498 | — | 13 | 1 | no | — |
| 352 | #498 | — | 13 | 1 | no | — |
| 353 | #498 | — | 13 | 2 | no | — |
| 354 | #491 | — | 13 | 4 | no | — |
| 355 | #487 | — | 13 | 2 | no | — |
| 356 | #487 | — | 13 | 2 | no | — |
| 357 | #487 | — | 13 | 4 | no | — |
| 358 | #487 | — | 13 | 2 | no | — |
| 359 | #487 | — | 13 | 2 | no | — |
| 360 | #485 | — | 13 | 8 | no | — |
| 361 | #485 | — | 13 | 8 | no | — |
| 362 | #484 | — | 13 | 8 | no | — |
| 363 | #483 | — | 13 | 8 | no | — |
| 364 | #479 | — | 13 | 8 | no | — |
| 365 | #479 | — | 13 | 8 | no | — |
| 366 | #477 | — | 13 | 8 | no | — |
| 367 | #475 | — | 13 | 8 | no | — |
| 368 | #433 | — | 13 | 4 | no | — |
| 369 | #431 | — | 13 | 2 | no | — |
| 370 | #431 | — | 13 | 2 | no | — |
| 371 | #428 | — | 13 | 4 | no | — |
| 372 | #427 | — | 13 | 4 | no | — |
| 373 | #424 | — | 13 | 2 | no | — |
| 374 | #419 | — | 13 | 4 | no | — |
| 375 | C2×#103 | — | 13 | 4 | no | — |
| 376 | #408 | — | 13 | 2 | no | — |
| 377 | C4×M16 | — | 13 | 1 | no | — |
| 378 | C2×C4×C8 | — | 13 | 1 | no | — |
| 379 | C22×C13 | — | 2 | 1 | no | — |
| 380 | C22×C13 | — | 2 | 1 | no | — |
| 381 | C22×C13 | — | 2 | 2 | no | — |
| 382 | C22×C13 | — | 2 | 2 | no | — |
| 383 | C22×C13 | — | 2 | 2 | no | — |
| 384 | C22×C13 | #536 | 1 | 2 | yes | — |
| 385 | C22×C13 | C23×D4 | 1 | 1 | yes | characteristic |
| 386 | C4×C13 | — | 2 | 2 | no | — |
| 387 | C4×C13 | — | 2 | 2 | no | — |
| 388 | C4×C13 | — | 2 | 1 | no | — |
| 389 | C4×C13 | — | 2 | 2 | no | — |
| 390 | C4×C13 | — | 2 | 1 | no | — |
| 391 | C4×C13 | — | 4 | 4 | no | — |
| 392 | C4×C13 | — | 4 | 2 | no | — |
| 393 | C4×C13 | — | 4 | 2 | no | — |
| 394 | C4×C13 | #536 | 1 | 2 | yes | — |
| 395 | C4×C13 | #577 | 1 | 2 | yes | — |
| 396 | C4×C13 | #578 | 1 | 2 | yes | — |
| 397 | C4×C13 | C2×2−1+4 | 1 | 2 | yes | — |
| 398 | Dic13 | — | 4 | 4 | no | — |
| 399 | Dic13 | — | 4 | 2 | no | — |
| 400 | Dic13 | — | 4 | 2 | no | — |
| 401 | C2×#41 | C22×D13 | 1 | 1 | yes | characteristic |
| 402 | C22×Q8 | — | 26 | 1 | no | — |
| 403 | C22×Q8 | — | 26 | 2 | no | — |
| 404 | C22×Q8 | C22×D13 | 1 | 2 | yes | — |
| 405 | C2×M16 | — | 13 | 2 | no | — |
| 406 | C22×C8 | — | 13 | 2 | no | — |
| 407 | C4⋊Q8 | — | 2 | 2 | no | — |
| 408 | C4⋊Q8 | — | 2 | 1 | no | — |
| 409 | C4⋊Q8 | — | 2 | 1 | no | — |
| 410 | C4⋊Q8 | — | 13 | 2 | no | — |
| 411 | C4⋊Q8 | — | 13 | 1 | no | — |
| 412 | C4⋊Q8 | — | 13 | 4 | no | — |
| 413 | C4⋊Q8 | — | 13 | 2 | no | — |
| 414 | C4⋊Q8 | — | 13 | 1 | no | — |
| 415 | C4⋊Q8 | — | 26 | 2 | no | — |
| 416 | C4⋊Q8 | — | 26 | 4 | no | — |
| 417 | C4⋊Q8 | — | 26 | 2 | no | — |
| 418 | C4⋊Q8 | — | 26 | 1 | no | — |
| 419 | C4⋊Q8 | — | 26 | 2 | no | — |
| 420 | C4⋊Q8 | — | 26 | 1 | no | — |
| 421 | C4⋊Q8 | C22×D13 | 1 | 2 | yes | — |
| 422 | C4⋊Q8 | C22×D13 | 1 | 2 | yes | — |
| 423 | C4⋊Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 424 | C4⋊Q8 | C22×D13 | 1 | 1 | yes | characteristic |
| 425 | #126 | — | 2 | 4 | no | — |
| 426 | #126 | — | 2 | 4 | no | — |
| 427 | #125 | — | 2 | 4 | no | — |
| 428 | #125 | — | 2 | 4 | no | — |
| 429 | #125 | — | 2 | 2 | no | — |
| 430 | #125 | — | 2 | 2 | no | — |
| 431 | #125 | — | 13 | 4 | no | — |
| 432 | #125 | — | 13 | 2 | no | — |
| 433 | #125 | — | 26 | 2 | no | — |
| 434 | #125 | — | 26 | 4 | no | — |
| 435 | #125 | C22×D13 | 1 | 2 | yes | — |
| 436 | #124 | — | 2 | 2 | no | — |
| 437 | #123 | — | 2 | 4 | no | — |
| 438 | C22⋊Q8 | — | 2 | 1 | no | — |
| 439 | C22⋊Q8 | — | 2 | 1 | no | — |
| 440 | C22⋊Q8 | — | 2 | 2 | no | — |
| 441 | C22⋊Q8 | — | 2 | 2 | no | — |
| 442 | C22⋊Q8 | — | 26 | 1 | no | — |
| 443 | C22⋊Q8 | — | 26 | 2 | no | — |
| 444 | C22⋊Q8 | — | 26 | 1 | no | — |
| 445 | C22⋊Q8 | — | 26 | 2 | no | — |
| 446 | C22⋊Q8 | — | 26 | 4 | no | — |
| 447 | C22⋊Q8 | — | 26 | 4 | no | — |
| 448 | C22⋊Q8 | — | 26 | 4 | no | — |
| 449 | C22⋊Q8 | C22×D13 | 1 | 4 | yes | — |
| 450 | C22⋊Q8 | C22×D13 | 1 | 4 | yes | — |
| 451 | C4×Q8 | — | 2 | 2 | no | — |
| 452 | C4×Q8 | — | 2 | 2 | no | — |
| 453 | C4×Q8 | — | 2 | 2 | no | — |
| 454 | C4×Q8 | — | 2 | 2 | no | — |
| 455 | C4×Q8 | — | 2 | 1 | no | — |
| 456 | C4×Q8 | — | 2 | 1 | no | — |
| 457 | C4×Q8 | — | 26 | 2 | no | — |
| 458 | C4×Q8 | — | 26 | 2 | no | — |
| 459 | C4×Q8 | — | 26 | 1 | no | — |
| 460 | C4×Q8 | — | 26 | 2 | no | — |
| 461 | C4×Q8 | — | 26 | 1 | no | — |
| 462 | C4×Q8 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 463 | C4×Q8 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 464 | C4×Q8 | C22×D13 | 1 | 4 | yes | — |
| 465 | C4×Q8 | C22×D13 | 1 | 4 | yes | — |
| 466 | C4×D4 | — | 26 | 4 | no | — |
| 467 | C4×D4 | — | 26 | 2 | no | — |
| 468 | C4×D4 | C22⋊D13 | 1 | 2 | yes | — |
| 469 | C4×D4 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 470 | C4×D4 | C22⋊D13 | 1 | 2 | yes | — |
| 471 | C4×D4 | C22⋊D13 | 1 | 1 | yes | characteristic |
| 472 | #117 | — | 2 | 2 | no | — |
| 473 | #117 | — | 2 | 2 | no | — |
| 474 | #117 | — | 2 | 4 | no | — |
| 475 | #117 | — | 13 | 2 | no | — |
| 476 | #117 | — | 13 | 4 | no | — |
| 477 | #117 | C22×D13 | 1 | 2 | yes | — |
| 478 | #117 | C22×D13 | 1 | 1 | yes | characteristic |
| 479 | #117 | C22×D13 | 1 | 2 | yes | — |
| 480 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 481 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 482 | C2×C4⋊C4 | — | 13 | 2 | no | — |
| 483 | C2×C4⋊C4 | — | 13 | 4 | no | — |
| 484 | C2×C4⋊C4 | — | 26 | 1 | no | — |
| 485 | C2×C4⋊C4 | — | 26 | 2 | no | — |
| 486 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 487 | C2×C42 | C22×D13 | 1 | 2 | yes | — |
| 488 | #107 | — | 13 | 4 | no | — |
| 489 | #107 | — | 13 | 4 | no | — |
| 490 | #107 | — | 13 | 8 | no | — |
| 491 | #106 | — | 13 | 4 | no | — |
| 492 | #106 | — | 13 | 4 | no | — |
| 493 | #106 | — | 13 | 8 | no | — |
| 494 | C4⋊C8 | — | 13 | 4 | no | — |
| 495 | C4⋊C8 | — | 13 | 4 | no | — |
| 496 | #103 | — | 13 | 8 | no | — |
| 497 | #103 | — | 13 | 8 | no | — |
| 498 | #103 | — | 13 | 8 | no | — |
| 499 | #103 | — | 13 | 8 | no | — |
| 500 | C22⋊C8 | — | 13 | 4 | no | — |
| 501 | C22⋊C8 | — | 13 | 4 | no | — |
| 502 | #97 | — | 13 | 2 | no | — |
| 503 | C4×C8 | — | 13 | 1 | no | — |
| 504 | C4×C8 | — | 13 | 1 | no | — |
| 505 | C4×C8 | — | 13 | 2 | no | — |
| 506 | C4×C8 | — | 13 | 2 | no | — |
| 507 | C2×C13 | — | 2 | 2 | no | — |
| 508 | C2×C13 | — | 4 | 2 | no | — |
| 509 | C2×C13 | C2×#536 | 1 | 1 | yes | characteristic |
| 510 | C2×C13 | C2×#577 | 1 | 1 | yes | characteristic |
| 511 | C2×C13 | C2×#578 | 1 | 1 | yes | characteristic |
| 512 | #41 | — | 2 | 4 | no | — |
| 513 | C2×Q8 | — | 2 | 1 | no | — |
| 514 | C2×Q8 | — | 2 | 1 | no | — |
| 515 | C2×Q8 | — | 2 | 2 | no | — |
| 516 | C2×Q8 | — | 2 | 8 | no | — |
| 517 | C2×Q8 | — | 26 | 1 | no | — |
| 518 | C2×Q8 | — | 26 | 2 | no | — |
| 519 | C2×Q8 | — | 26 | 1 | no | — |
| 520 | C2×Q8 | — | 26 | 4 | no | — |
| 521 | C2×Q8 | — | 26 | 2 | no | — |
| 522 | C2×Q8 | — | 104 | 2 | no | — |
| 523 | C2×Q8 | — | 104 | 4 | no | — |
| 524 | C2×Q8 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 525 | C2×Q8 | C23×D13 | 1 | 4 | yes | — |
| 526 | C2×D4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 527 | C2×D4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 528 | C22×C4 | — | 2 | 2 | no | — |
| 529 | C22×C4 | — | 26 | 4 | no | — |
| 530 | C22×C4 | — | 26 | 2 | no | — |
| 531 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 532 | C22×C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 533 | C22×C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 534 | C22×C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 535 | C22×C4 | C23×D13 | 1 | 2 | yes | — |
| 536 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 537 | M16 | — | 26 | 4 | no | — |
| 538 | C2×C8 | — | 13 | 2 | no | — |
| 539 | C2×C8 | — | 13 | 2 | no | — |
| 540 | C2×C8 | — | 13 | 4 | no | — |
| 541 | C2×C8 | — | 26 | 4 | no | — |
| 542 | C4⋊C4 | — | 2 | 2 | no | — |
| 543 | C4⋊C4 | — | 2 | 2 | no | — |
| 544 | C4⋊C4 | — | 2 | 2 | no | — |
| 545 | C4⋊C4 | — | 2 | 2 | no | — |
| 546 | C4⋊C4 | — | 2 | 1 | no | — |
| 547 | C4⋊C4 | — | 2 | 1 | no | — |
| 548 | C4⋊C4 | — | 2 | 4 | no | — |
| 549 | C4⋊C4 | — | 2 | 4 | no | — |
| 550 | C4⋊C4 | — | 2 | 2 | no | — |
| 551 | C4⋊C4 | — | 2 | 2 | no | — |
| 552 | C4⋊C4 | — | 2 | 4 | no | — |
| 553 | C4⋊C4 | — | 2 | 4 | no | — |
| 554 | C4⋊C4 | — | 13 | 4 | no | — |
| 555 | C4⋊C4 | — | 13 | 2 | no | — |
| 556 | C4⋊C4 | — | 13 | 2 | no | — |
| 557 | C4⋊C4 | — | 26 | 4 | no | — |
| 558 | C4⋊C4 | — | 26 | 2 | no | — |
| 559 | C4⋊C4 | — | 26 | 2 | no | — |
| 560 | C4⋊C4 | — | 26 | 1 | no | — |
| 561 | C4⋊C4 | — | 26 | 4 | no | — |
| 562 | C4⋊C4 | — | 26 | 2 | no | — |
| 563 | C4⋊C4 | — | 26 | 1 | no | — |
| 564 | C4⋊C4 | — | 26 | 4 | no | — |
| 565 | C4⋊C4 | — | 26 | 2 | no | — |
| 566 | C4⋊C4 | — | 26 | 4 | no | — |
| 567 | C4⋊C4 | — | 26 | 2 | no | — |
| 568 | C4⋊C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 569 | C4⋊C4 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 570 | C4⋊C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 571 | C4⋊C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 572 | C4⋊C4 | C23×D13 | 1 | 2 | yes | — |
| 573 | C4⋊C4 | C23×D13 | 1 | 2 | yes | — |
| 574 | C22⋊C4 | — | 2 | 2 | no | — |
| 575 | C22⋊C4 | — | 2 | 4 | no | — |
| 576 | C22⋊C4 | — | 2 | 4 | no | — |
| 577 | C22⋊C4 | — | 26 | 4 | no | — |
| 578 | C22⋊C4 | — | 26 | 2 | no | — |
| 579 | C22⋊C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 580 | C22⋊C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 581 | C22⋊C4 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 582 | C42 | — | 2 | 4 | no | — |
| 583 | C42 | — | 2 | 4 | no | — |
| 584 | C42 | — | 2 | 2 | no | — |
| 585 | C42 | — | 26 | 4 | no | — |
| 586 | C42 | — | 26 | 2 | no | — |
| 587 | C42 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 588 | C42 | C2×C22⋊D13 | 1 | 2 | yes | — |
| 589 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 590 | C42 | C2×C22⋊D13 | 1 | 1 | yes | characteristic |
| 591 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 592 | C42 | C23×D13 | 1 | 1 | yes | characteristic |
| 593 | C42 | C23×D13 | 1 | 2 | yes | — |
| 594 | C13 | #60878 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 595 | C23 | C22×C22⋊D13 | 1 | 2 | yes | — |
| 596 | C23 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 597 | Q8 | — | 2 | 2 | no | — |
| 598 | Q8 | — | 2 | 8 | no | — |
| 599 | Q8 | — | 4 | 4 | no | — |
| 600 | Q8 | — | 4 | 2 | no | — |
| 601 | Q8 | — | 4 | 2 | no | — |
| 602 | Q8 | — | 52 | 4 | no | — |
| 603 | Q8 | — | 52 | 2 | no | — |
| 604 | Q8 | — | 52 | 2 | no | — |
| 605 | Q8 | — | 104 | 4 | no | — |
| 606 | Q8 | — | 104 | 2 | no | — |
| 607 | D4 | — | 2 | 4 | no | — |
| 608 | D4 | — | 2 | 2 | no | — |
| 609 | C2×C4 | — | 2 | 2 | no | — |
| 610 | C2×C4 | — | 2 | 4 | no | — |
| 611 | C2×C4 | — | 2 | 2 | no | — |
| 612 | C2×C4 | — | 2 | 4 | no | — |
| 613 | C2×C4 | — | 2 | 4 | no | — |
| 614 | C2×C4 | — | 2 | 2 | no | — |
| 615 | C2×C4 | — | 2 | 2 | no | — |
| 616 | C2×C4 | — | 2 | 4 | no | — |
| 617 | C2×C4 | — | 4 | 4 | no | — |
| 618 | C2×C4 | — | 26 | 2 | no | — |
| 619 | C2×C4 | — | 26 | 4 | no | — |
| 620 | C2×C4 | — | 26 | 2 | no | — |
| 621 | C2×C4 | — | 104 | 2 | no | — |
| 622 | C2×C4 | — | 104 | 4 | no | — |
| 623 | C2×C4 | #88257 | 1 | 4 | yes | — |
| 624 | C2×C4 | C22×C22⋊D13 | 1 | 2 | yes | — |
| 625 | C2×C4 | C22×C22⋊D13 | 1 | 2 | yes | — |
| 626 | C2×C4 | C22×C22⋊D13 | 1 | 2 | yes | — |
| 627 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 628 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 629 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 630 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 631 | C2×C4 | C22×C22⋊D13 | 1 | 1 | yes | characteristic |
| 632 | C2×C4 | C24×D13 | 1 | 1 | yes | characteristic |
| 633 | C8 | — | 26 | 2 | no | — |
| 634 | C8 | — | 26 | 2 | no | — |
| 635 | C8 | — | 26 | 4 | no | — |
| 636 | C22 | — | 2 | 1 | no | — |
| 637 | C22 | — | 2 | 1 | no | — |
| 638 | C22 | — | 2 | 2 | no | — |
| 639 | C22 | — | 2 | 2 | no | — |
| 640 | C22 | — | 2 | 2 | no | — |
| 641 | C22 | #11719530 | 1 | 2 | yes | — |
| 642 | C22 | C23×C22⋊D13 | 1 | 1 | yes | characteristic |
| 643 | C4 | — | 2 | 2 | no | — |
| 644 | C4 | — | 2 | 1 | no | — |
| 645 | C4 | — | 2 | 2 | no | — |
| 646 | C4 | — | 2 | 1 | no | — |
| 647 | C4 | — | 2 | 2 | no | — |
| 648 | C4 | — | 4 | 2 | no | — |
| 649 | C4 | — | 4 | 2 | no | — |
| 650 | C4 | — | 4 | 4 | no | — |
| 651 | C4 | — | 52 | 4 | no | — |
| 652 | C4 | — | 52 | 2 | no | — |
| 653 | C4 | — | 52 | 2 | no | — |
| 654 | C4 | #11719530 | 1 | 2 | yes | — |
| 655 | C4 | #11719542 | 1 | 2 | yes | — |
| 656 | C4 | #11719543 | 1 | 2 | yes | — |
| 657 | C4 | C2×#88257 | 1 | 2 | yes | — |
| 658 | C2 | — | 2 | 2 | no | — |
| 659 | C2 | — | 4 | 2 | no | — |
| 660 | C2 | C2×#11719530 | 1 | 1 | yes | characteristic |
| 661 | C2 | C2×#11719542 | 1 | 1 | yes | characteristic |
| 662 | C2 | C2×#11719543 | 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