← #15881815
Subgroups — #15881815
Order 3328.
638 conjugacy classes of subgroups.
The subgroup lattice has 552 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | M16×Dic26 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #13123787 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#11718489 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #13115612 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #13115610 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #13115610 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #13115608 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #13115608 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #13115010 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #13115009 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #13115006 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #13114743 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #13114741 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #13114737 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C13×#1950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C2×C4×Dic26 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C13×#108 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C13×#108 | C22 | 1 | 1 | yes | characteristic |
| 19 | C13×#423 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C13×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C4×C13×M16 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#88062 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#88062 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#88062 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#88062 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#88062 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#88062 | C22 | 1 | 1 | yes | characteristic |
| 28 | #11718779 | C22 | 1 | 1 | yes | characteristic |
| 29 | #11718779 | C22 | 1 | 1 | yes | characteristic |
| 30 | #11718779 | C22 | 1 | 1 | yes | characteristic |
| 31 | #11718779 | C22 | 1 | 1 | yes | characteristic |
| 32 | M16×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 33 | M16×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 34 | M16×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 35 | M16×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#88059 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#88059 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#88055 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#88054 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#88054 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×C8×Dic13 | C22 | 1 | 1 | yes | characteristic |
| 42 | #11718585 | C22 | 1 | 1 | yes | characteristic |
| 43 | C4×#6099 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#88043 | C22 | 1 | 1 | yes | characteristic |
| 45 | #11718492 | — | 2 | 1 | no | — |
| 46 | #11718491 | — | 2 | 1 | no | — |
| 47 | #11718489 | — | 2 | 1 | no | — |
| 48 | #11718489 | — | 2 | 1 | no | — |
| 49 | #11718489 | C4 | 1 | 2 | yes | — |
| 50 | #11718489 | C4 | 1 | 2 | yes | — |
| 51 | #11718489 | C4 | 1 | 2 | yes | — |
| 52 | #11718489 | C4 | 1 | 2 | yes | — |
| 53 | #11718362 | — | 2 | 1 | no | — |
| 54 | #11718362 | — | 2 | 1 | no | — |
| 55 | #11718340 | — | 2 | 1 | no | — |
| 56 | C8×Dic26 | — | 2 | 1 | no | — |
| 57 | C13×#341 | C22 | 1 | 1 | yes | characteristic |
| 58 | C13×#341 | C22 | 1 | 1 | yes | characteristic |
| 59 | #11718150 | C22 | 1 | 1 | yes | characteristic |
| 60 | #11718150 | C22 | 1 | 1 | yes | characteristic |
| 61 | #11718144 | C22 | 1 | 1 | yes | characteristic |
| 62 | #11718144 | C22 | 1 | 1 | yes | characteristic |
| 63 | C22×Dic26 | Q8 | 1 | 1 | yes | characteristic |
| 64 | C2×C13×M16 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C13×M16 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C13×M16 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C13×M16 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C42×C13 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C4⋊Dic13 | Q8 | 1 | 1 | yes | characteristic |
| 72 | C2×#6101 | Q8 | 1 | 1 | yes | characteristic |
| 73 | C2×#6101 | Q8 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×Dic13 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#6099 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×#1055 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×#1055 | C23 | 1 | 1 | yes | characteristic |
| 82 | C4×Dic26 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C4×Dic26 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C4×Dic26 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | C4×Dic26 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | C4×Dic26 | D4 | 1 | 1 | yes | characteristic |
| 87 | C4×Dic26 | D4 | 1 | 1 | yes | characteristic |
| 88 | C4×Dic26 | D4 | 1 | 1 | yes | characteristic |
| 89 | C4×Dic26 | D4 | 1 | 1 | yes | characteristic |
| 90 | C13×#108 | — | 4 | 1 | no | — |
| 91 | C13×#108 | — | 4 | 1 | no | — |
| 92 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 93 | C13×C4⋊C8 | — | 2 | 1 | no | — |
| 94 | C13×C4⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 95 | C13×C4⋊C8 | C2×C4 | 1 | 2 | yes | — |
| 96 | C13×#97 | — | 2 | 1 | no | — |
| 97 | C4×C8×C13 | — | 2 | 1 | no | — |
| 98 | #88062 | — | 2 | 2 | no | — |
| 99 | #88062 | — | 2 | 2 | no | — |
| 100 | #88062 | — | 2 | 2 | no | — |
| 101 | #88062 | — | 4 | 1 | no | — |
| 102 | #88062 | — | 4 | 1 | no | — |
| 103 | #88062 | Q8 | 1 | 4 | yes | complemented |
| 104 | #88059 | — | 4 | 1 | no | — |
| 105 | #88059 | — | 4 | 1 | no | — |
| 106 | #88055 | — | 2 | 1 | no | — |
| 107 | #88055 | — | 2 | 1 | no | — |
| 108 | #88055 | — | 2 | 1 | no | — |
| 109 | #88055 | — | 2 | 1 | no | — |
| 110 | #88055 | C2×C4 | 1 | 2 | yes | — |
| 111 | #88055 | C2×C4 | 1 | 2 | yes | — |
| 112 | #88054 | — | 2 | 1 | no | — |
| 113 | #88054 | — | 2 | 1 | no | — |
| 114 | #88054 | — | 2 | 1 | no | — |
| 115 | #88054 | — | 2 | 1 | no | — |
| 116 | #88054 | — | 2 | 1 | no | — |
| 117 | #88054 | — | 2 | 1 | no | — |
| 118 | #88054 | — | 2 | 1 | no | — |
| 119 | #88054 | — | 2 | 1 | no | — |
| 120 | #88054 | C2×C4 | 1 | 2 | yes | — |
| 121 | #88054 | C2×C4 | 1 | 2 | yes | — |
| 122 | #88054 | C2×C4 | 1 | 2 | yes | — |
| 123 | #88054 | C2×C4 | 1 | 2 | yes | — |
| 124 | C8×Dic13 | — | 2 | 1 | no | — |
| 125 | C8×Dic13 | — | 2 | 1 | no | — |
| 126 | C8×Dic13 | — | 2 | 1 | no | — |
| 127 | C8×Dic13 | — | 2 | 1 | no | — |
| 128 | C8×Dic13 | C2×C4 | 1 | 2 | yes | — |
| 129 | C8×Dic13 | C2×C4 | 1 | 2 | yes | — |
| 130 | C4⋊#1055 | — | 2 | 1 | no | — |
| 131 | C4⋊#1055 | — | 2 | 1 | no | — |
| 132 | #88043 | — | 2 | 1 | no | — |
| 133 | #88043 | C2×C4 | 1 | 2 | yes | — |
| 134 | #88043 | C2×C4 | 1 | 2 | yes | — |
| 135 | C4×#1055 | — | 2 | 1 | no | — |
| 136 | #22733 | — | 13 | 1 | no | maximal, Sylow |
| 137 | C22×C4×C13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 138 | C22×C4×C13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 139 | C22×C4×C13 | C24 | 1 | 1 | yes | characteristic |
| 140 | C22×Dic13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 141 | C22×Dic13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 142 | C22×Dic13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 143 | C22×Dic13 | C2×Q8 | 1 | 1 | yes | characteristic |
| 144 | C2×Dic26 | — | 4 | 2 | no | — |
| 145 | C2×Dic26 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 146 | C2×Dic26 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 147 | C2×Dic26 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 148 | C2×Dic26 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C13×M16 | — | 2 | 1 | no | — |
| 150 | C13×M16 | — | 2 | 1 | no | — |
| 151 | C13×M16 | — | 2 | 1 | no | — |
| 152 | C13×M16 | — | 2 | 1 | no | — |
| 153 | C13×M16 | — | 2 | 1 | no | — |
| 154 | C13×M16 | — | 2 | 1 | no | — |
| 155 | C13×M16 | — | 2 | 1 | no | — |
| 156 | C13×M16 | C2×Q8 | 1 | 2 | yes | — |
| 157 | C2×C8×C13 | — | 2 | 1 | no | — |
| 158 | C2×C8×C13 | — | 2 | 1 | no | — |
| 159 | C2×C8×C13 | — | 2 | 1 | no | — |
| 160 | C2×C8×C13 | — | 2 | 1 | no | — |
| 161 | C2×C8×C13 | — | 2 | 1 | no | — |
| 162 | C2×C8×C13 | — | 2 | 1 | no | — |
| 163 | C2×C8×C13 | — | 2 | 1 | no | — |
| 164 | C2×C8×C13 | — | 2 | 1 | no | — |
| 165 | C2×C8×C13 | C22×C4 | 1 | 2 | yes | — |
| 166 | C2×C8×C13 | C22×C4 | 1 | 2 | yes | — |
| 167 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 168 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 169 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C42×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C4⋊Dic13 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 172 | C4⋊Dic13 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 173 | C4⋊Dic13 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 174 | C4⋊Dic13 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 175 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 176 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 177 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 178 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 179 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 180 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 181 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 182 | #6101 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 183 | C4×Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 184 | C4×Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 185 | C4×Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 186 | C4×Dic13 | C22×C4 | 1 | 1 | yes | characteristic |
| 187 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C4×Dic13 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | #6099 | — | 2 | 1 | no | — |
| 192 | #6099 | — | 2 | 1 | no | — |
| 193 | #6099 | — | 2 | 1 | no | — |
| 194 | #6099 | — | 2 | 1 | no | — |
| 195 | #6099 | — | 2 | 1 | no | — |
| 196 | #6099 | — | 2 | 1 | no | — |
| 197 | #6099 | — | 2 | 1 | no | — |
| 198 | #6099 | C2×Q8 | 1 | 2 | yes | — |
| 199 | C2×#1055 | — | 2 | 1 | no | — |
| 200 | C2×#1055 | — | 2 | 1 | no | — |
| 201 | C2×#1055 | — | 2 | 1 | no | — |
| 202 | C2×#1055 | — | 2 | 1 | no | — |
| 203 | C2×#1055 | — | 2 | 1 | no | — |
| 204 | C2×#1055 | — | 2 | 1 | no | — |
| 205 | C2×#1055 | C22×C4 | 1 | 2 | yes | — |
| 206 | C2×#1055 | C22×C4 | 1 | 2 | yes | — |
| 207 | C2×#1055 | C2×Q8 | 1 | 2 | yes | — |
| 208 | C2×#1055 | #41 | 1 | 2 | yes | — |
| 209 | Q8×M16 | — | 13 | 1 | no | — |
| 210 | Q8×M16 | — | 13 | 1 | no | — |
| 211 | C2×#446 | — | 13 | 1 | no | — |
| 212 | #1950 | — | 13 | 1 | no | — |
| 213 | #1950 | — | 13 | 1 | no | — |
| 214 | #1950 | — | 13 | 1 | no | — |
| 215 | #1950 | — | 13 | 1 | no | — |
| 216 | #1950 | — | 13 | 1 | no | — |
| 217 | #1950 | D13 | 1 | 1 | yes | characteristic |
| 218 | #1849 | — | 13 | 1 | no | — |
| 219 | #1849 | — | 13 | 1 | no | — |
| 220 | #1848 | — | 13 | 1 | no | — |
| 221 | #1778 | — | 13 | 1 | no | — |
| 222 | #1778 | — | 13 | 1 | no | — |
| 223 | C4×#108 | — | 13 | 1 | no | — |
| 224 | C23×C13 | C22×Q8 | 1 | 1 | yes | characteristic |
| 225 | C2×C4×C13 | — | 4 | 1 | no | — |
| 226 | C2×C4×C13 | — | 4 | 1 | no | — |
| 227 | C2×C4×C13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 229 | C2×C4×C13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×C13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×C13 | C22×Q8 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×C13 | C2×#41 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C13 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 236 | C2×C4×C13 | 2−1+4 | 1 | 1 | yes | characteristic |
| 237 | C2×Dic13 | — | 2 | 2 | no | — |
| 238 | C2×Dic13 | — | 4 | 1 | no | — |
| 239 | C2×Dic13 | — | 4 | 1 | no | — |
| 240 | C2×Dic13 | — | 4 | 1 | no | — |
| 241 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 242 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 243 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 244 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 245 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 246 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 247 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 248 | C2×Dic13 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 249 | Dic26 | — | 2 | 2 | no | — |
| 250 | Dic26 | — | 2 | 2 | no | — |
| 251 | Dic26 | — | 4 | 1 | no | — |
| 252 | Dic26 | — | 4 | 1 | no | — |
| 253 | C8×C13 | — | 2 | 2 | no | — |
| 254 | C8×C13 | — | 2 | 2 | no | — |
| 255 | C8×C13 | — | 2 | 2 | no | — |
| 256 | C8×C13 | — | 4 | 1 | no | — |
| 257 | C8×C13 | — | 4 | 1 | no | — |
| 258 | C8×C13 | — | 4 | 1 | no | — |
| 259 | #1055 | — | 2 | 2 | no | — |
| 260 | #1055 | — | 2 | 2 | no | — |
| 261 | #1055 | — | 4 | 1 | no | — |
| 262 | #1055 | — | 4 | 1 | no | — |
| 263 | #1055 | — | 4 | 1 | no | — |
| 264 | #1055 | C4×Q8 | 1 | 4 | yes | — |
| 265 | C2×C4×Q8 | — | 13 | 1 | no | — |
| 266 | #446 | — | 13 | 2 | no | — |
| 267 | #446 | — | 13 | 2 | no | — |
| 268 | #446 | — | 13 | 2 | no | — |
| 269 | #446 | — | 13 | 2 | no | — |
| 270 | #446 | — | 26 | 1 | no | — |
| 271 | #446 | — | 26 | 1 | no | — |
| 272 | #446 | — | 26 | 1 | no | — |
| 273 | #446 | — | 26 | 1 | no | — |
| 274 | #446 | — | 26 | 1 | no | — |
| 275 | #446 | — | 26 | 1 | no | — |
| 276 | C8×Q8 | — | 26 | 1 | no | — |
| 277 | C8×Q8 | — | 26 | 1 | no | — |
| 278 | C2×#108 | — | 13 | 1 | no | — |
| 279 | C2×#108 | — | 13 | 1 | no | — |
| 280 | C2×#108 | — | 13 | 1 | no | — |
| 281 | C2×#108 | — | 13 | 1 | no | — |
| 282 | C2×#108 | — | 13 | 1 | no | — |
| 283 | C2×#108 | — | 13 | 1 | no | — |
| 284 | C2×#108 | — | 13 | 1 | no | — |
| 285 | C2×#108 | — | 13 | 1 | no | — |
| 286 | C2×#108 | C2×D13 | 1 | 1 | yes | characteristic |
| 287 | C2×#108 | C2×D13 | 1 | 1 | yes | characteristic |
| 288 | #423 | — | 13 | 1 | no | — |
| 289 | #423 | — | 13 | 1 | no | — |
| 290 | #423 | — | 13 | 1 | no | — |
| 291 | #423 | — | 13 | 1 | no | — |
| 292 | #423 | — | 13 | 1 | no | — |
| 293 | #423 | C2×D13 | 1 | 1 | yes | characteristic |
| 294 | C2×C4⋊C8 | — | 13 | 1 | no | — |
| 295 | C2×C4⋊C8 | — | 13 | 1 | no | — |
| 296 | C2×C4⋊C8 | C2×D13 | 1 | 1 | yes | characteristic |
| 297 | C4×M16 | — | 13 | 1 | no | — |
| 298 | C4×M16 | — | 13 | 1 | no | — |
| 299 | C4×M16 | — | 13 | 1 | no | — |
| 300 | C4×M16 | — | 13 | 1 | no | — |
| 301 | C4×M16 | — | 13 | 1 | no | — |
| 302 | C4×M16 | C2×D13 | 1 | 1 | yes | characteristic |
| 303 | C2×#97 | — | 13 | 1 | no | — |
| 304 | C2×#97 | — | 13 | 1 | no | — |
| 305 | C2×C4×C8 | — | 13 | 1 | no | — |
| 306 | #341 | — | 13 | 1 | no | — |
| 307 | #341 | — | 13 | 1 | no | — |
| 308 | #341 | — | 13 | 1 | no | — |
| 309 | #341 | — | 13 | 1 | no | — |
| 310 | #341 | C2×D13 | 1 | 1 | yes | characteristic |
| 311 | #341 | C2×D13 | 1 | 1 | yes | characteristic |
| 312 | C22×C13 | — | 2 | 1 | no | — |
| 313 | C22×C13 | — | 2 | 1 | no | — |
| 314 | C22×C13 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 315 | C22×C13 | #557 | 1 | 1 | yes | characteristic |
| 316 | C22×C13 | Q82 | 1 | 1 | yes | characteristic |
| 317 | C4×C13 | — | 2 | 1 | no | — |
| 318 | C4×C13 | — | 2 | 1 | no | — |
| 319 | C4×C13 | — | 2 | 1 | no | — |
| 320 | C4×C13 | — | 2 | 1 | no | — |
| 321 | C4×C13 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 322 | C4×C13 | #520 | 1 | 1 | yes | characteristic |
| 323 | C4×C13 | D4×Q8 | 1 | 1 | yes | characteristic |
| 324 | C4×C13 | #550 | 1 | 1 | yes | characteristic |
| 325 | Dic13 | — | 2 | 1 | no | — |
| 326 | Dic13 | — | 2 | 1 | no | — |
| 327 | Dic13 | — | 2 | 1 | no | — |
| 328 | Dic13 | — | 2 | 1 | no | — |
| 329 | Dic13 | — | 2 | 1 | no | — |
| 330 | Dic13 | — | 2 | 1 | no | — |
| 331 | Dic13 | — | 2 | 1 | no | — |
| 332 | Dic13 | #430 | 1 | 2 | yes | — |
| 333 | C22×Q8 | — | 13 | 1 | no | — |
| 334 | C2×M16 | — | 13 | 1 | no | — |
| 335 | C2×M16 | — | 13 | 1 | no | — |
| 336 | C2×M16 | — | 13 | 1 | no | — |
| 337 | C2×M16 | — | 13 | 1 | no | — |
| 338 | C2×M16 | C22×D13 | 1 | 1 | yes | characteristic |
| 339 | C2×M16 | C22×D13 | 1 | 1 | yes | characteristic |
| 340 | C2×M16 | C22×D13 | 1 | 1 | yes | characteristic |
| 341 | C2×M16 | C22×D13 | 1 | 1 | yes | characteristic |
| 342 | C22×C8 | — | 13 | 1 | no | — |
| 343 | C22×C8 | — | 13 | 1 | no | — |
| 344 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 345 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 346 | C4×Q8 | — | 13 | 1 | no | — |
| 347 | C4×Q8 | — | 13 | 1 | no | — |
| 348 | C4×Q8 | — | 13 | 1 | no | — |
| 349 | C4×Q8 | — | 13 | 1 | no | — |
| 350 | C4×Q8 | — | 13 | 1 | no | — |
| 351 | C4×Q8 | — | 13 | 1 | no | — |
| 352 | C4×Q8 | — | 13 | 1 | no | — |
| 353 | C4×Q8 | — | 13 | 1 | no | — |
| 354 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 355 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 356 | C2×C4⋊C4 | — | 13 | 1 | no | — |
| 357 | C2×C42 | — | 13 | 1 | no | — |
| 358 | C2×C42 | — | 13 | 1 | no | — |
| 359 | C2×C42 | C22×D13 | 1 | 1 | yes | characteristic |
| 360 | #108 | — | 4 | 1 | no | — |
| 361 | #108 | — | 4 | 1 | no | — |
| 362 | #108 | — | 13 | 4 | no | — |
| 363 | #108 | — | 26 | 2 | no | — |
| 364 | #108 | — | 26 | 2 | no | — |
| 365 | #108 | — | 26 | 2 | no | — |
| 366 | #108 | — | 52 | 1 | no | — |
| 367 | #108 | — | 52 | 1 | no | — |
| 368 | #108 | — | 52 | 1 | no | — |
| 369 | #108 | — | 52 | 1 | no | — |
| 370 | C4⋊C8 | — | 2 | 1 | no | — |
| 371 | C4⋊C8 | — | 2 | 1 | no | — |
| 372 | C4⋊C8 | — | 13 | 2 | no | — |
| 373 | C4⋊C8 | — | 13 | 2 | no | — |
| 374 | C4⋊C8 | — | 13 | 2 | no | — |
| 375 | C4⋊C8 | — | 13 | 2 | no | — |
| 376 | C4⋊C8 | — | 26 | 1 | no | — |
| 377 | C4⋊C8 | — | 26 | 1 | no | — |
| 378 | C4⋊C8 | — | 26 | 1 | no | — |
| 379 | C4⋊C8 | — | 26 | 1 | no | — |
| 380 | C4⋊C8 | — | 26 | 1 | no | — |
| 381 | C4⋊C8 | — | 26 | 1 | no | — |
| 382 | C4⋊C8 | — | 26 | 1 | no | — |
| 383 | C4⋊C8 | — | 26 | 1 | no | — |
| 384 | C4⋊C8 | — | 26 | 1 | no | — |
| 385 | C4⋊C8 | — | 26 | 1 | no | — |
| 386 | C4⋊C8 | C4×D13 | 1 | 2 | yes | — |
| 387 | C4⋊C8 | C4×D13 | 1 | 2 | yes | — |
| 388 | #97 | — | 2 | 1 | no | — |
| 389 | #97 | — | 13 | 2 | no | — |
| 390 | #97 | — | 13 | 2 | no | — |
| 391 | #97 | — | 13 | 2 | no | — |
| 392 | #97 | — | 13 | 2 | no | — |
| 393 | #97 | — | 26 | 1 | no | — |
| 394 | #97 | — | 26 | 1 | no | — |
| 395 | #97 | — | 26 | 1 | no | — |
| 396 | #97 | — | 26 | 1 | no | — |
| 397 | #97 | — | 26 | 1 | no | — |
| 398 | C4×C8 | — | 2 | 1 | no | — |
| 399 | C4×C8 | — | 13 | 2 | no | — |
| 400 | C4×C8 | — | 13 | 2 | no | — |
| 401 | C4×C8 | — | 26 | 1 | no | — |
| 402 | C4×C8 | — | 26 | 1 | no | — |
| 403 | C4×C8 | — | 26 | 1 | no | — |
| 404 | C4×C8 | — | 26 | 1 | no | — |
| 405 | C4×C8 | — | 26 | 1 | no | — |
| 406 | C2×C13 | — | 2 | 1 | no | — |
| 407 | C2×C13 | — | 2 | 1 | no | — |
| 408 | C2×C13 | Q8×C4⋊C4 | 1 | 1 | yes | characteristic |
| 409 | C2×C13 | C2×#430 | 1 | 1 | yes | characteristic |
| 410 | C2×C13 | #2916 | 1 | 1 | yes | characteristic |
| 411 | C2×Q8 | — | 13 | 1 | no | — |
| 412 | C2×Q8 | — | 13 | 1 | no | — |
| 413 | C2×Q8 | — | 13 | 1 | no | — |
| 414 | C2×Q8 | — | 13 | 1 | no | — |
| 415 | C2×Q8 | — | 52 | 2 | no | — |
| 416 | C22×C4 | — | 13 | 1 | no | — |
| 417 | C22×C4 | — | 13 | 1 | no | — |
| 418 | C22×C4 | — | 13 | 1 | no | — |
| 419 | C22×C4 | — | 13 | 1 | no | — |
| 420 | C22×C4 | Q8×D13 | 1 | 1 | yes | characteristic |
| 421 | C22×C4 | Q8×D13 | 1 | 1 | yes | characteristic |
| 422 | C22×C4 | C23×D13 | 1 | 1 | yes | characteristic |
| 423 | M16 | — | 2 | 1 | no | — |
| 424 | M16 | — | 2 | 1 | no | — |
| 425 | M16 | — | 2 | 1 | no | — |
| 426 | M16 | — | 2 | 1 | no | — |
| 427 | M16 | — | 2 | 1 | no | — |
| 428 | M16 | — | 2 | 1 | no | — |
| 429 | M16 | — | 2 | 1 | no | — |
| 430 | M16 | — | 13 | 2 | no | — |
| 431 | M16 | — | 26 | 1 | no | — |
| 432 | M16 | — | 26 | 1 | no | — |
| 433 | M16 | — | 26 | 1 | no | — |
| 434 | M16 | — | 26 | 1 | no | — |
| 435 | M16 | — | 26 | 1 | no | — |
| 436 | M16 | — | 26 | 1 | no | — |
| 437 | M16 | — | 26 | 1 | no | — |
| 438 | M16 | Q8×D13 | 1 | 2 | yes | — |
| 439 | C2×C8 | — | 2 | 1 | no | — |
| 440 | C2×C8 | — | 2 | 1 | no | — |
| 441 | C2×C8 | — | 2 | 1 | no | — |
| 442 | C2×C8 | — | 2 | 1 | no | — |
| 443 | C2×C8 | — | 2 | 1 | no | — |
| 444 | C2×C8 | — | 2 | 1 | no | — |
| 445 | C2×C8 | — | 2 | 1 | no | — |
| 446 | C2×C8 | — | 2 | 1 | no | — |
| 447 | C2×C8 | — | 13 | 2 | no | — |
| 448 | C2×C8 | — | 13 | 2 | no | — |
| 449 | C2×C8 | — | 13 | 2 | no | — |
| 450 | C2×C8 | — | 13 | 2 | no | — |
| 451 | C2×C8 | — | 26 | 1 | no | — |
| 452 | C2×C8 | — | 26 | 1 | no | — |
| 453 | C2×C8 | — | 26 | 1 | no | — |
| 454 | C2×C8 | — | 26 | 1 | no | — |
| 455 | C2×C8 | — | 26 | 1 | no | — |
| 456 | C2×C8 | — | 26 | 1 | no | — |
| 457 | C2×C8 | C2×C4×D13 | 1 | 2 | yes | — |
| 458 | C2×C8 | C2×C4×D13 | 1 | 2 | yes | — |
| 459 | C4⋊C4 | — | 13 | 1 | no | — |
| 460 | C4⋊C4 | — | 13 | 1 | no | — |
| 461 | C4⋊C4 | — | 13 | 1 | no | — |
| 462 | C4⋊C4 | — | 13 | 1 | no | — |
| 463 | C4⋊C4 | — | 13 | 1 | no | — |
| 464 | C4⋊C4 | — | 13 | 1 | no | — |
| 465 | C4⋊C4 | — | 13 | 1 | no | — |
| 466 | C4⋊C4 | — | 13 | 1 | no | — |
| 467 | C4⋊C4 | — | 13 | 1 | no | — |
| 468 | C4⋊C4 | — | 13 | 1 | no | — |
| 469 | C4⋊C4 | — | 13 | 1 | no | — |
| 470 | C4⋊C4 | — | 13 | 1 | no | — |
| 471 | C42 | — | 13 | 1 | no | — |
| 472 | C42 | — | 13 | 1 | no | — |
| 473 | C42 | — | 13 | 1 | no | — |
| 474 | C42 | — | 13 | 1 | no | — |
| 475 | C42 | — | 13 | 1 | no | — |
| 476 | C42 | — | 13 | 1 | no | — |
| 477 | C42 | — | 13 | 1 | no | — |
| 478 | C42 | — | 13 | 1 | no | — |
| 479 | C42 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 480 | C42 | C2×C4×D13 | 1 | 1 | yes | characteristic |
| 481 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 482 | C42 | D4×D13 | 1 | 1 | yes | characteristic |
| 483 | C13 | #22733 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 484 | C23 | C2×Q8×D13 | 1 | 1 | yes | characteristic |
| 485 | Q8 | — | 26 | 2 | no | — |
| 486 | Q8 | — | 26 | 2 | no | — |
| 487 | Q8 | — | 52 | 1 | no | — |
| 488 | Q8 | — | 52 | 1 | no | — |
| 489 | C2×C4 | — | 4 | 1 | no | — |
| 490 | C2×C4 | — | 4 | 1 | no | — |
| 491 | C2×C4 | — | 13 | 1 | no | — |
| 492 | C2×C4 | — | 13 | 1 | no | — |
| 493 | C2×C4 | — | 13 | 1 | no | — |
| 494 | C2×C4 | — | 13 | 1 | no | — |
| 495 | C2×C4 | — | 13 | 1 | no | — |
| 496 | C2×C4 | — | 13 | 1 | no | — |
| 497 | C2×C4 | — | 13 | 1 | no | — |
| 498 | C2×C4 | — | 13 | 1 | no | — |
| 499 | C2×C4 | — | 26 | 2 | no | — |
| 500 | C2×C4 | — | 52 | 1 | no | — |
| 501 | C2×C4 | — | 52 | 1 | no | — |
| 502 | C2×C4 | — | 52 | 1 | no | — |
| 503 | C2×C4 | C4⋊C4×D13 | 1 | 1 | yes | characteristic |
| 504 | C2×C4 | C4⋊C4×D13 | 1 | 1 | yes | characteristic |
| 505 | C2×C4 | C4⋊C4×D13 | 1 | 1 | yes | characteristic |
| 506 | C2×C4 | C4⋊C4×D13 | 1 | 1 | yes | characteristic |
| 507 | C2×C4 | C22×C4×D13 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | #88251 | 1 | 1 | yes | characteristic |
| 510 | C2×C4 | C2×Q8×D13 | 1 | 1 | yes | characteristic |
| 511 | C2×C4 | #41×D13 | 1 | 1 | yes | characteristic |
| 512 | C2×C4 | #88257 | 1 | 1 | yes | characteristic |
| 513 | C8 | — | 2 | 2 | no | — |
| 514 | C8 | — | 2 | 2 | no | — |
| 515 | C8 | — | 2 | 2 | no | — |
| 516 | C8 | — | 4 | 1 | no | — |
| 517 | C8 | — | 4 | 1 | no | — |
| 518 | C8 | — | 4 | 1 | no | — |
| 519 | C8 | — | 13 | 4 | no | — |
| 520 | C8 | — | 26 | 2 | no | — |
| 521 | C8 | — | 26 | 2 | no | — |
| 522 | C8 | — | 52 | 1 | no | — |
| 523 | C8 | — | 52 | 1 | no | — |
| 524 | C8 | — | 52 | 1 | no | — |
| 525 | C22 | — | 2 | 1 | no | — |
| 526 | C22 | — | 2 | 1 | no | — |
| 527 | C22 | C2×C4⋊C4×D13 | 1 | 1 | yes | characteristic |
| 528 | C22 | #11719390 | 1 | 1 | yes | characteristic |
| 529 | C22 | #11719427 | 1 | 1 | yes | characteristic |
| 530 | C4 | — | 2 | 1 | no | — |
| 531 | C4 | — | 2 | 1 | no | — |
| 532 | C4 | — | 2 | 1 | no | — |
| 533 | C4 | — | 2 | 1 | no | — |
| 534 | C4 | — | 13 | 2 | no | — |
| 535 | C4 | — | 26 | 1 | no | — |
| 536 | C4 | — | 26 | 1 | no | — |
| 537 | C4 | — | 26 | 1 | no | — |
| 538 | C4 | — | 26 | 1 | no | — |
| 539 | C4 | — | 26 | 1 | no | — |
| 540 | C4 | — | 26 | 1 | no | — |
| 541 | C4 | — | 26 | 1 | no | — |
| 542 | C4 | #11719251 | 1 | 1 | yes | characteristic |
| 543 | C4 | C4×Q8×D13 | 1 | 1 | yes | characteristic |
| 544 | C4 | #11719304 | 1 | 1 | yes | characteristic |
| 545 | C4 | #11719337 | 1 | 1 | yes | characteristic |
| 546 | C2 | — | 2 | 1 | no | — |
| 547 | C2 | — | 2 | 1 | no | — |
| 548 | C2 | #13117750 | 1 | 1 | yes | characteristic |
| 549 | C2 | D13×#430 | 1 | 1 | yes | characteristic |
| 550 | C2 | #13123444 | 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