← #16809640
Subgroups — #16809640
Order 3328.
11222 conjugacy classes of subgroups.
The subgroup lattice has 254 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | 2−1+4×#261 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | H(5,𝔽2)×#261 | C2 | 1 | 20 | yes | maximal, complemented |
| 3 | #13131816 | C2 | 1 | 15 | yes | maximal, complemented |
| 4 | C2×#11719631 | C2 | 1 | 15 | yes | maximal, complemented |
| 5 | D13×#585 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C13×#585 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | #11719652 | C4 | 1 | 6 | yes | complemented |
| 8 | D13×2−1+4 | C22 | 1 | 6 | yes | — |
| 9 | #11719650 | C4 | 1 | 10 | yes | complemented |
| 10 | D13×H(5,𝔽2) | C22 | 1 | 10 | yes | — |
| 11 | #11719648 | C4 | 1 | 15 | yes | complemented |
| 12 | C2×#41×D13 | C22 | 1 | 15 | yes | — |
| 13 | #11719631 | C22 | 1 | 60 | yes | complemented |
| 14 | #11719631 | C22 | 1 | 120 | yes | complemented |
| 15 | #11719631 | C22 | 1 | 20 | yes | complemented |
| 16 | #41×#261 | C22 | 1 | 120 | yes | complemented |
| 17 | #11719627 | C22 | 1 | 30 | yes | complemented |
| 18 | C2×Q8×#261 | C22 | 1 | 30 | yes | complemented |
| 19 | #11719623 | C22 | 1 | 90 | yes | complemented |
| 20 | C2×D4×#261 | C22 | 1 | 90 | yes | complemented |
| 21 | C2×#88237 | C22 | 1 | 45 | yes | complemented |
| 22 | C22×C4⋊#261 | C22 | 1 | 15 | yes | complemented |
| 23 | C23×#261 | C23 | 1 | 30 | yes | — |
| 24 | C13×2−1+4 | C2×C4 | 1 | 6 | yes | complemented |
| 25 | C13×H(5,𝔽2) | C2×C4 | 1 | 10 | yes | complemented |
| 26 | C2×C13×#41 | C2×C4 | 1 | 15 | yes | complemented |
| 27 | #88257 | C2×C4 | 1 | 60 | yes | complemented |
| 28 | #88256 | C2×C4 | 1 | 60 | yes | complemented |
| 29 | #41×D13 | C2×C4 | 1 | 60 | yes | complemented |
| 30 | #41×D13 | C2×C4 | 1 | 60 | yes | complemented |
| 31 | #41×D13 | C23 | 1 | 60 | yes | — |
| 32 | #41×D13 | C23 | 1 | 20 | yes | — |
| 33 | #88254 | C2×C4 | 1 | 30 | yes | complemented |
| 34 | C2×#6131 | C2×C4 | 1 | 15 | yes | complemented |
| 35 | C2×Q8×D13 | C23 | 1 | 15 | yes | — |
| 36 | #88251 | C2×C4 | 1 | 90 | yes | complemented |
| 37 | C2×#6129 | C2×C4 | 1 | 45 | yes | complemented |
| 38 | C2×D4×D13 | C23 | 1 | 45 | yes | — |
| 39 | C2×#6127 | C2×C4 | 1 | 45 | yes | complemented |
| 40 | C22×C4×D13 | C23 | 1 | 15 | yes | — |
| 41 | C2×C22⋊#261 | C23 | 1 | 90 | yes | — |
| 42 | Q8×#261 | C23 | 1 | 120 | yes | — |
| 43 | Q8×#261 | C23 | 1 | 40 | yes | — |
| 44 | D4×#261 | C23 | 1 | 360 | yes | — |
| 45 | D4×#261 | C23 | 1 | 120 | yes | — |
| 46 | #88237 | C23 | 1 | 60 | yes | — |
| 47 | #88237 | C23 | 1 | 180 | yes | — |
| 48 | C2×C4⋊#261 | C23 | 1 | 45 | yes | — |
| 49 | C2×C4⋊#261 | C23 | 1 | 90 | yes | — |
| 50 | C2×C4⋊#261 | C23 | 1 | 15 | yes | — |
| 51 | C2×C4×#261 | C23 | 1 | 90 | yes | — |
| 52 | #62654 | — | 13 | 1 | no | maximal, Sylow |
| 53 | C23×D13 | C24 | 1 | 15 | yes | — |
| 54 | C22×#261 | — | 8 | 30 | no | — |
| 55 | C22×#261 | C24 | 1 | 30 | yes | — |
| 56 | C22×#261 | C24 | 1 | 90 | yes | — |
| 57 | C13×#41 | C22×C4 | 1 | 20 | yes | complemented |
| 58 | C13×#41 | C22×C4 | 1 | 60 | yes | complemented |
| 59 | C2×Q8×C13 | C22×C4 | 1 | 15 | yes | complemented |
| 60 | C2×D4×C13 | C22×C4 | 1 | 45 | yes | complemented |
| 61 | C22×C4×C13 | C22×C4 | 1 | 15 | yes | complemented |
| 62 | C2×C22⋊D13 | C22×C4 | 1 | 90 | yes | complemented |
| 63 | C22×Dic13 | C22×C4 | 1 | 15 | yes | complemented |
| 64 | #6131 | C22×C4 | 1 | 20 | yes | complemented |
| 65 | #6131 | C22×C4 | 1 | 60 | yes | complemented |
| 66 | Q8×D13 | C22×C4 | 1 | 60 | yes | complemented |
| 67 | Q8×D13 | C24 | 1 | 20 | yes | — |
| 68 | #6129 | C22×C4 | 1 | 60 | yes | complemented |
| 69 | #6129 | C22×C4 | 1 | 180 | yes | complemented |
| 70 | D4×D13 | C22×C4 | 1 | 180 | yes | complemented |
| 71 | D4×D13 | C24 | 1 | 60 | yes | — |
| 72 | #6127 | C22×C4 | 1 | 60 | yes | complemented |
| 73 | #6127 | C22×C4 | 1 | 180 | yes | complemented |
| 74 | C2×D52 | C22×C4 | 1 | 45 | yes | complemented |
| 75 | C2×C4×D13 | C22×C4 | 1 | 45 | yes | complemented |
| 76 | C2×C4×D13 | C22×C4 | 1 | 45 | yes | complemented |
| 77 | C2×C4×D13 | C24 | 1 | 45 | yes | — |
| 78 | C2×C4×D13 | C24 | 1 | 15 | yes | — |
| 79 | C2×Dic26 | C22×C4 | 1 | 45 | yes | complemented |
| 80 | C22⋊#261 | C24 | 1 | 120 | yes | — |
| 81 | C4⋊#261 | C24 | 1 | 10 | yes | — |
| 82 | C4⋊#261 | C24 | 1 | 6 | yes | — |
| 83 | C4⋊#261 | C24 | 1 | 90 | yes | — |
| 84 | C4⋊#261 | C24 | 1 | 30 | yes | — |
| 85 | C4×#261 | C24 | 1 | 120 | yes | — |
| 86 | C2×#585 | — | 13 | 1 | no | — |
| 87 | C4×2−1+4 | — | 13 | 12 | no | — |
| 88 | C4×H(5,𝔽2) | — | 13 | 20 | no | — |
| 89 | #3428 | — | 13 | 15 | no | — |
| 90 | C2×#520 | — | 13 | 15 | no | — |
| 91 | C23×C13 | C23×C4 | 1 | 15 | yes | — |
| 92 | C22×D13 | — | 4 | 15 | no | — |
| 93 | C22×D13 | — | 4 | 15 | no | — |
| 94 | C22×D13 | C23×C4 | 1 | 45 | yes | — |
| 95 | C22×D13 | C25 | 1 | 15 | yes | — |
| 96 | C2×#261 | — | 4 | 90 | no | — |
| 97 | C2×#261 | — | 4 | 30 | no | — |
| 98 | C2×#261 | C25 | 1 | 12 | yes | — |
| 99 | C2×#261 | C25 | 1 | 20 | yes | — |
| 100 | Q8×C13 | C23×C4 | 1 | 20 | yes | — |
| 101 | D4×C13 | C23×C4 | 1 | 60 | yes | — |
| 102 | C2×C4×C13 | C23×C4 | 1 | 45 | yes | — |
| 103 | C2×C4×C13 | C23×C4 | 1 | 15 | yes | — |
| 104 | C22⋊D13 | C23×C4 | 1 | 120 | yes | — |
| 105 | C2×Dic13 | C23×C4 | 1 | 45 | yes | — |
| 106 | C2×Dic13 | C23×C4 | 1 | 15 | yes | — |
| 107 | D52 | C23×C4 | 1 | 60 | yes | — |
| 108 | C4×D13 | C23×C4 | 1 | 15 | yes | — |
| 109 | C4×D13 | C23×C4 | 1 | 15 | yes | — |
| 110 | C4×D13 | C23×C4 | 1 | 90 | yes | — |
| 111 | C4×D13 | C25 | 1 | 15 | yes | — |
| 112 | C4×D13 | C25 | 1 | 1 | yes | characteristic |
| 113 | Dic26 | C23×C4 | 1 | 60 | yes | — |
| 114 | #585 | — | 13 | 6 | no | — |
| 115 | #585 | — | 13 | 10 | no | — |
| 116 | #585 | — | 13 | 15 | no | — |
| 117 | #585 | #261 | 1 | 1 | yes | characteristic, complemented |
| 118 | C2×2−1+4 | — | 13 | 6 | no | — |
| 119 | C2×H(5,𝔽2) | — | 13 | 10 | no | — |
| 120 | C22×#41 | — | 13 | 15 | no | — |
| 121 | #520 | — | 13 | 60 | no | — |
| 122 | #520 | — | 13 | 120 | no | — |
| 123 | #520 | — | 13 | 20 | no | — |
| 124 | #519 | — | 13 | 30 | no | — |
| 125 | #518 | — | 13 | 90 | no | — |
| 126 | C4×#41 | — | 13 | 120 | no | — |
| 127 | C2×C4×Q8 | — | 13 | 30 | no | — |
| 128 | C2×C4×D4 | — | 13 | 90 | no | — |
| 129 | C2×#117 | — | 13 | 45 | no | — |
| 130 | C22×C4⋊C4 | — | 13 | 15 | no | — |
| 131 | C22×C13 | — | 4 | 15 | no | — |
| 132 | C22×C13 | C24×C4 | 1 | 15 | yes | — |
| 133 | C2×D13 | — | 2 | 15 | no | — |
| 134 | C2×D13 | — | 2 | 15 | no | — |
| 135 | C2×D13 | — | 4 | 45 | no | — |
| 136 | C2×D13 | C24×C4 | 1 | 15 | yes | — |
| 137 | C2×D13 | C26 | 1 | 1 | yes | characteristic |
| 138 | #261 | — | 2 | 20 | no | — |
| 139 | #261 | — | 2 | 12 | no | — |
| 140 | C4×C13 | C24×C4 | 1 | 15 | yes | — |
| 141 | C4×C13 | C24×C4 | 1 | 1 | yes | characteristic |
| 142 | Dic13 | C24×C4 | 1 | 15 | yes | — |
| 143 | Dic13 | C24×C4 | 1 | 1 | yes | characteristic |
| 144 | 2−1+4 | — | 13 | 60 | no | — |
| 145 | 2−1+4 | — | 13 | 30 | no | — |
| 146 | 2−1+4 | C2×#261 | 1 | 6 | yes | complemented |
| 147 | H(5,𝔽2) | — | 13 | 60 | no | — |
| 148 | H(5,𝔽2) | — | 13 | 90 | no | — |
| 149 | H(5,𝔽2) | C2×#261 | 1 | 10 | yes | complemented |
| 150 | C2×#41 | — | 13 | 60 | no | — |
| 151 | C2×#41 | — | 13 | 20 | no | — |
| 152 | C2×#41 | — | 13 | 60 | no | — |
| 153 | C2×#41 | — | 13 | 60 | no | — |
| 154 | C2×#41 | — | 13 | 15 | no | — |
| 155 | C2×#41 | — | 13 | 45 | no | — |
| 156 | C2×#41 | — | 13 | 45 | no | — |
| 157 | C2×#41 | C2×#261 | 1 | 15 | yes | complemented |
| 158 | C22×Q8 | — | 13 | 15 | no | — |
| 159 | C22×D4 | — | 13 | 45 | no | — |
| 160 | C23×C4 | — | 13 | 15 | no | — |
| 161 | C23×C4 | — | 13 | 30 | no | — |
| 162 | C4×Q8 | — | 13 | 120 | no | — |
| 163 | C4×Q8 | — | 13 | 40 | no | — |
| 164 | C4×D4 | — | 13 | 360 | no | — |
| 165 | C4×D4 | — | 13 | 120 | no | — |
| 166 | #117 | — | 13 | 60 | no | — |
| 167 | #117 | — | 13 | 180 | no | — |
| 168 | C2×C4⋊C4 | — | 13 | 45 | no | — |
| 169 | C2×C4⋊C4 | — | 13 | 90 | no | — |
| 170 | C2×C4⋊C4 | — | 13 | 15 | no | — |
| 171 | C2×C22⋊C4 | — | 13 | 90 | no | — |
| 172 | C2×C42 | — | 13 | 90 | no | — |
| 173 | C2×C13 | — | 2 | 15 | no | — |
| 174 | C2×C13 | C25×C4 | 1 | 1 | yes | characteristic |
| 175 | D13 | — | 2 | 15 | no | — |
| 176 | D13 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 177 | D13 | 2−1+6 | 1 | 1 | yes | characteristic |
| 178 | C24 | — | 13 | 15 | no | — |
| 179 | #41 | — | 13 | 20 | no | — |
| 180 | #41 | — | 13 | 60 | no | — |
| 181 | #41 | — | 13 | 60 | no | — |
| 182 | #41 | — | 13 | 180 | no | — |
| 183 | #41 | — | 13 | 60 | no | — |
| 184 | #41 | — | 13 | 180 | no | — |
| 185 | #41 | C22×#261 | 1 | 20 | yes | complemented |
| 186 | #41 | C22×#261 | 1 | 60 | yes | complemented |
| 187 | C2×Q8 | — | 13 | 20 | no | — |
| 188 | C2×Q8 | — | 13 | 60 | no | — |
| 189 | C2×Q8 | — | 13 | 45 | no | — |
| 190 | C2×Q8 | C22×#261 | 1 | 15 | yes | complemented |
| 191 | C2×D4 | — | 13 | 90 | no | — |
| 192 | C2×D4 | — | 13 | 60 | no | — |
| 193 | C2×D4 | — | 13 | 180 | no | — |
| 194 | C2×D4 | — | 13 | 45 | no | — |
| 195 | C2×D4 | C22×#261 | 1 | 45 | yes | complemented |
| 196 | C22×C4 | — | 13 | 15 | no | — |
| 197 | C22×C4 | — | 13 | 45 | no | — |
| 198 | C22×C4 | — | 13 | 15 | no | — |
| 199 | C22×C4 | — | 13 | 45 | no | — |
| 200 | C22×C4 | — | 13 | 45 | no | — |
| 201 | C22×C4 | — | 13 | 30 | no | — |
| 202 | C22×C4 | — | 13 | 90 | no | — |
| 203 | C22×C4 | — | 104 | 30 | no | — |
| 204 | C22×C4 | C22×#261 | 1 | 15 | yes | complemented |
| 205 | C4⋊C4 | — | 13 | 10 | no | — |
| 206 | C4⋊C4 | — | 13 | 6 | no | — |
| 207 | C4⋊C4 | — | 13 | 90 | no | — |
| 208 | C4⋊C4 | — | 13 | 30 | no | — |
| 209 | C22⋊C4 | — | 13 | 120 | no | — |
| 210 | C42 | — | 13 | 120 | no | — |
| 211 | C13 | #62654 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 212 | C23 | — | 13 | 15 | no | — |
| 213 | C23 | — | 13 | 45 | no | — |
| 214 | C23 | — | 52 | 15 | no | — |
| 215 | C23 | — | 52 | 15 | no | — |
| 216 | C23 | C23×#261 | 1 | 15 | yes | — |
| 217 | Q8 | — | 13 | 60 | no | — |
| 218 | Q8 | C23×#261 | 1 | 20 | yes | — |
| 219 | D4 | — | 13 | 120 | no | — |
| 220 | D4 | — | 13 | 60 | no | — |
| 221 | D4 | C23×#261 | 1 | 60 | yes | — |
| 222 | C2×C4 | — | 13 | 15 | no | — |
| 223 | C2×C4 | — | 13 | 45 | no | — |
| 224 | C2×C4 | — | 13 | 15 | no | — |
| 225 | C2×C4 | — | 13 | 1 | no | — |
| 226 | C2×C4 | — | 13 | 15 | no | — |
| 227 | C2×C4 | — | 13 | 15 | no | — |
| 228 | C2×C4 | — | 13 | 90 | no | — |
| 229 | C2×C4 | — | 13 | 12 | no | — |
| 230 | C2×C4 | — | 13 | 20 | no | — |
| 231 | C2×C4 | — | 52 | 90 | no | — |
| 232 | C2×C4 | — | 52 | 30 | no | — |
| 233 | C2×C4 | C23×#261 | 1 | 15 | yes | — |
| 234 | C2×C4 | C23×#261 | 1 | 45 | yes | — |
| 235 | C22 | — | 4 | 15 | no | — |
| 236 | C22 | — | 13 | 1 | no | — |
| 237 | C22 | — | 13 | 15 | no | — |
| 238 | C22 | — | 26 | 15 | no | — |
| 239 | C22 | — | 26 | 15 | no | — |
| 240 | C22 | — | 52 | 45 | no | — |
| 241 | C22 | C24×#261 | 1 | 15 | yes | — |
| 242 | C4 | — | 13 | 1 | no | — |
| 243 | C4 | — | 13 | 15 | no | — |
| 244 | C4 | — | 26 | 12 | no | — |
| 245 | C4 | — | 26 | 20 | no | — |
| 246 | C4 | C24×#261 | 1 | 1 | yes | characteristic |
| 247 | C4 | C24×#261 | 1 | 15 | yes | — |
| 248 | C2 | — | 2 | 15 | no | — |
| 249 | C2 | — | 13 | 1 | no | — |
| 250 | C2 | — | 13 | 1 | no | — |
| 251 | C2 | — | 26 | 15 | no | — |
| 252 | C2 | C25×#261 | 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