← #14471905
Subgroups — #14471905
Order 1920.
784 conjugacy classes of subgroups.
The subgroup lattice has 308 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×C5×#550 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×Dic30 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11751176 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #11751171 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | Q8×C3⋊#168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C4×#6716 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #11751109 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #10615317 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C3×C5×#41 | — | 2 | 1 | no | — |
| 10 | C3×C5×#127 | C22 | 1 | 3 | yes | — |
| 11 | C3×C5×#121 | — | 2 | 3 | no | — |
| 12 | C3×C4×C5×Q8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×C4×C5×D4 | C22 | 1 | 3 | yes | — |
| 14 | Q8×Dic15 | — | 2 | 1 | no | — |
| 15 | C2×#6716 | C22 | 1 | 3 | yes | — |
| 16 | #91777 | — | 2 | 3 | no | — |
| 17 | #91758 | C22 | 1 | 3 | yes | — |
| 18 | C4×Dic30 | C22 | 1 | 3 | yes | — |
| 19 | #91116 | C22 | 1 | 3 | yes | — |
| 20 | #91116 | C22 | 1 | 6 | yes | — |
| 21 | #91094 | C22 | 1 | 1 | yes | characteristic |
| 22 | #91092 | C22 | 1 | 3 | yes | — |
| 23 | C4⋊(C3⋊#168) | C22 | 1 | 3 | yes | — |
| 24 | C4×C3⋊#168 | C22 | 1 | 3 | yes | — |
| 25 | #83586 | — | 5 | 1 | no | maximal, Hall |
| 26 | C5×#550 | D3 | 1 | 1 | yes | characteristic |
| 27 | Q8×Dic10 | — | 3 | 1 | no | — |
| 28 | #65364 | — | 3 | 3 | no | — |
| 29 | #65359 | — | 3 | 3 | no | — |
| 30 | Q8×#168 | — | 3 | 1 | no | — |
| 31 | C4×#687 | — | 3 | 3 | no | — |
| 32 | #65297 | — | 3 | 3 | no | — |
| 33 | C3×C5×#41 | — | 4 | 4 | no | — |
| 34 | C2×C3×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×C3×C5×D4 | — | 2 | 3 | no | — |
| 36 | C2×C3×C5×D4 | — | 2 | 3 | no | — |
| 37 | C2×C3×C5×D4 | C23 | 1 | 3 | yes | — |
| 38 | C22×C3×C4×C5 | — | 2 | 3 | no | — |
| 39 | C2×Dic30 | — | 2 | 3 | no | — |
| 40 | C2×Dic30 | C23 | 1 | 1 | yes | characteristic |
| 41 | C3×C5×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 42 | C3×C5×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 43 | C3×C5×C22⋊C4 | — | 2 | 3 | no | — |
| 44 | C3×C42×C5 | C23 | 1 | 3 | yes | — |
| 45 | #6716 | — | 2 | 6 | no | — |
| 46 | C4⋊Dic15 | — | 2 | 3 | no | — |
| 47 | C4⋊Dic15 | C23 | 1 | 3 | yes | — |
| 48 | #6712 | — | 2 | 3 | no | — |
| 49 | C4×Dic15 | — | 2 | 3 | no | — |
| 50 | C2×C3⋊#168 | C23 | 1 | 3 | yes | — |
| 51 | C2×C3⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 52 | C3×#550 | D5 | 1 | 1 | yes | characteristic |
| 53 | Q8×Dic6 | — | 5 | 1 | no | — |
| 54 | #5075 | — | 5 | 3 | no | — |
| 55 | #5070 | — | 5 | 3 | no | — |
| 56 | Q8×C3⋊C8 | — | 5 | 1 | no | — |
| 57 | C4×#214 | — | 5 | 3 | no | — |
| 58 | #5008 | — | 5 | 3 | no | — |
| 59 | C2×C5×#41 | — | 2 | 1 | no | — |
| 60 | C5×#127 | C2×D3 | 1 | 3 | yes | — |
| 61 | C5×#121 | — | 2 | 3 | no | — |
| 62 | C4×C5×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 63 | C4×C5×D4 | C2×D3 | 1 | 3 | yes | — |
| 64 | Q8×Dic5 | — | 6 | 1 | no | — |
| 65 | C2×#687 | — | 3 | 3 | no | — |
| 66 | #4034 | — | 6 | 3 | no | — |
| 67 | #4015 | — | 3 | 3 | no | — |
| 68 | C4×Dic10 | — | 3 | 3 | no | — |
| 69 | #3964 | — | 3 | 6 | no | — |
| 70 | #3964 | — | 3 | 3 | no | — |
| 71 | #3942 | — | 3 | 1 | no | — |
| 72 | #3940 | — | 3 | 3 | no | — |
| 73 | C4⋊#168 | — | 3 | 3 | no | — |
| 74 | C4×#168 | — | 3 | 3 | no | — |
| 75 | #3362 | — | 15 | 1 | no | Sylow |
| 76 | C23×C3×C5 | — | 2 | 3 | no | — |
| 77 | C3×C5×Q8 | SD16 | 1 | 4 | yes | complemented |
| 78 | C3×C5×D4 | — | 2 | 3 | no | — |
| 79 | C3×C5×D4 | — | 2 | 3 | no | — |
| 80 | C3×C5×D4 | — | 4 | 6 | no | — |
| 81 | C3×C5×D4 | — | 8 | 3 | no | — |
| 82 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 83 | C2×C3×C4×C5 | — | 4 | 6 | no | — |
| 84 | C2×C3×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 85 | C2×C3×C4×C5 | C2×D4 | 1 | 3 | yes | — |
| 86 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 87 | C2×Dic15 | — | 2 | 1 | no | — |
| 88 | C2×Dic15 | — | 2 | 3 | no | — |
| 89 | Dic30 | — | 2 | 1 | no | — |
| 90 | Dic30 | — | 8 | 3 | no | — |
| 91 | Dic30 | #41 | 1 | 2 | yes | complemented |
| 92 | C3⋊#168 | — | 2 | 3 | no | — |
| 93 | C3⋊#168 | — | 2 | 1 | no | — |
| 94 | C2×C3×#41 | — | 2 | 1 | no | — |
| 95 | C3×#127 | C2×D5 | 1 | 3 | yes | — |
| 96 | C3×#121 | — | 2 | 3 | no | — |
| 97 | C3×C4×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 98 | C3×C4×D4 | C2×D5 | 1 | 3 | yes | — |
| 99 | Q8×Dic3 | — | 10 | 1 | no | — |
| 100 | C2×#214 | — | 5 | 3 | no | — |
| 101 | #888 | — | 10 | 3 | no | — |
| 102 | #869 | — | 5 | 3 | no | — |
| 103 | C4×Dic6 | — | 5 | 3 | no | — |
| 104 | #832 | — | 5 | 6 | no | — |
| 105 | #832 | — | 5 | 3 | no | — |
| 106 | #810 | — | 5 | 1 | no | — |
| 107 | #808 | — | 5 | 3 | no | — |
| 108 | C4⋊(C3⋊C8) | — | 5 | 3 | no | — |
| 109 | C4×C3⋊C8 | — | 5 | 3 | no | — |
| 110 | C5×#41 | — | 4 | 4 | no | — |
| 111 | C2×C5×Q8 | #67 | 1 | 1 | yes | characteristic |
| 112 | C2×C5×D4 | — | 2 | 3 | no | — |
| 113 | C2×C5×D4 | — | 2 | 3 | no | — |
| 114 | C2×C5×D4 | C22×D3 | 1 | 3 | yes | — |
| 115 | C22×C4×C5 | — | 2 | 3 | no | — |
| 116 | C2×Dic10 | — | 3 | 1 | no | — |
| 117 | C2×Dic10 | — | 6 | 3 | no | — |
| 118 | C5×C4⋊C4 | #67 | 1 | 3 | yes | — |
| 119 | C5×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 120 | C5×C22⋊C4 | — | 2 | 3 | no | — |
| 121 | C42×C5 | C22×D3 | 1 | 3 | yes | — |
| 122 | #687 | — | 6 | 6 | no | — |
| 123 | C4⋊Dic5 | — | 3 | 3 | no | — |
| 124 | C4⋊Dic5 | — | 6 | 3 | no | — |
| 125 | #683 | — | 6 | 3 | no | — |
| 126 | C4×Dic5 | — | 6 | 3 | no | — |
| 127 | C2×#168 | — | 3 | 1 | no | — |
| 128 | C2×#168 | — | 3 | 3 | no | — |
| 129 | Q82 | — | 15 | 1 | no | — |
| 130 | #550 | D15 | 1 | 1 | yes | characteristic |
| 131 | #486 | — | 15 | 3 | no | — |
| 132 | #476 | — | 15 | 3 | no | — |
| 133 | #460 | — | 15 | 3 | no | — |
| 134 | C8×Q8 | — | 15 | 1 | no | — |
| 135 | C4×SD16 | — | 15 | 3 | no | — |
| 136 | C22×C3×C5 | — | 4 | 3 | no | — |
| 137 | C22×C3×C5 | — | 4 | 3 | no | — |
| 138 | C22×C3×C5 | — | 4 | 3 | no | — |
| 139 | C22×C3×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 140 | C3×C4×C5 | — | 2 | 3 | no | — |
| 141 | C3×C4×C5 | — | 4 | 1 | no | — |
| 142 | C3×C4×C5 | C2×SD16 | 1 | 6 | yes | — |
| 143 | C3×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 144 | C3×C4×C5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 145 | Dic15 | — | 2 | 2 | no | — |
| 146 | Dic15 | — | 4 | 3 | no | — |
| 147 | C3×#41 | — | 4 | 4 | no | — |
| 148 | C2×C3×Q8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 149 | C2×C3×D4 | — | 2 | 3 | no | — |
| 150 | C2×C3×D4 | — | 2 | 3 | no | — |
| 151 | C2×C3×D4 | C22×D5 | 1 | 3 | yes | — |
| 152 | C22×C3×C4 | — | 2 | 3 | no | — |
| 153 | C2×Dic6 | — | 5 | 1 | no | — |
| 154 | C2×Dic6 | — | 10 | 3 | no | — |
| 155 | C3×C4⋊C4 | C22⋊D5 | 1 | 3 | yes | — |
| 156 | C3×C4⋊C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 157 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 158 | C3×C42 | C22×D5 | 1 | 3 | yes | — |
| 159 | #214 | — | 10 | 6 | no | — |
| 160 | C4⋊Dic3 | — | 5 | 3 | no | — |
| 161 | C4⋊Dic3 | — | 10 | 3 | no | — |
| 162 | Dic3⋊C4 | — | 10 | 3 | no | — |
| 163 | C4×Dic3 | — | 10 | 3 | no | — |
| 164 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 165 | C2×C3⋊C8 | — | 5 | 3 | no | — |
| 166 | C23×C5 | — | 2 | 3 | no | — |
| 167 | C5×Q8 | #214 | 1 | 4 | yes | complemented |
| 168 | C5×D4 | — | 2 | 3 | no | — |
| 169 | C5×D4 | — | 2 | 3 | no | — |
| 170 | C5×D4 | — | 4 | 6 | no | — |
| 171 | C5×D4 | — | 8 | 3 | no | — |
| 172 | C2×C4×C5 | — | 2 | 1 | no | — |
| 173 | C2×C4×C5 | — | 4 | 6 | no | — |
| 174 | C2×C4×C5 | C2×#67 | 1 | 3 | yes | — |
| 175 | C2×C4×C5 | C2×#67 | 1 | 3 | yes | — |
| 176 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 177 | C2×Dic5 | — | 6 | 1 | no | — |
| 178 | C2×Dic5 | — | 6 | 3 | no | — |
| 179 | Dic10 | — | 3 | 2 | no | — |
| 180 | Dic10 | — | 6 | 1 | no | — |
| 181 | Dic10 | — | 24 | 3 | no | — |
| 182 | #168 | — | 6 | 3 | no | — |
| 183 | #168 | — | 6 | 1 | no | — |
| 184 | C2×#41 | — | 2 | 1 | no | — |
| 185 | C2×SD16 | — | 15 | 3 | no | — |
| 186 | C4⋊Q8 | — | 15 | 3 | no | — |
| 187 | C4⋊Q8 | — | 30 | 3 | no | — |
| 188 | #127 | C2×D15 | 1 | 3 | yes | — |
| 189 | #121 | — | 2 | 3 | no | — |
| 190 | C4×Q8 | — | 15 | 3 | no | — |
| 191 | C4×Q8 | — | 30 | 1 | no | — |
| 192 | C4×Q8 | C2×D15 | 1 | 1 | yes | characteristic |
| 193 | C4×D4 | C2×D15 | 1 | 3 | yes | — |
| 194 | #106 | — | 15 | 3 | no | — |
| 195 | C4⋊C8 | — | 15 | 3 | no | — |
| 196 | #103 | — | 15 | 1 | no | — |
| 197 | #102 | — | 15 | 3 | no | — |
| 198 | #102 | — | 15 | 6 | no | — |
| 199 | C4×C8 | — | 15 | 3 | no | — |
| 200 | C2×C3×C5 | — | 8 | 3 | no | — |
| 201 | C2×C3×C5 | #548 | 1 | 1 | yes | characteristic |
| 202 | C2×C3×C5 | C22×SD16 | 1 | 1 | yes | characteristic |
| 203 | C2×C3×C5 | #576 | 1 | 1 | yes | characteristic |
| 204 | C23×C3 | — | 2 | 3 | no | — |
| 205 | C3×Q8 | #687 | 1 | 4 | yes | complemented |
| 206 | C3×D4 | — | 2 | 3 | no | — |
| 207 | C3×D4 | — | 2 | 3 | no | — |
| 208 | C3×D4 | — | 4 | 6 | no | — |
| 209 | C3×D4 | — | 8 | 3 | no | — |
| 210 | C2×C3×C4 | — | 2 | 1 | no | — |
| 211 | C2×C3×C4 | — | 4 | 6 | no | — |
| 212 | C2×C3×C4 | C2×C22⋊D5 | 1 | 3 | yes | — |
| 213 | C2×C3×C4 | C2×C22⋊D5 | 1 | 3 | yes | — |
| 214 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 215 | C2×Dic3 | — | 10 | 1 | no | — |
| 216 | C2×Dic3 | — | 10 | 3 | no | — |
| 217 | Dic6 | — | 5 | 2 | no | — |
| 218 | Dic6 | — | 10 | 1 | no | — |
| 219 | Dic6 | — | 40 | 3 | no | — |
| 220 | C3⋊C8 | — | 10 | 3 | no | — |
| 221 | C3⋊C8 | — | 10 | 1 | no | — |
| 222 | C22×C5 | — | 4 | 3 | no | — |
| 223 | C22×C5 | — | 4 | 3 | no | — |
| 224 | C22×C5 | — | 4 | 3 | no | — |
| 225 | C22×C5 | C22×#67 | 1 | 1 | yes | characteristic |
| 226 | C4×C5 | — | 2 | 3 | no | — |
| 227 | C4×C5 | — | 4 | 1 | no | — |
| 228 | C4×C5 | C2×#214 | 1 | 6 | yes | — |
| 229 | C4×C5 | D3×#41 | 1 | 1 | yes | characteristic |
| 230 | C4×C5 | #1010 | 1 | 1 | yes | characteristic |
| 231 | Dic5 | — | 6 | 2 | no | — |
| 232 | Dic5 | — | 12 | 3 | no | — |
| 233 | #41 | — | 4 | 4 | no | — |
| 234 | C2×Q8 | — | 15 | 1 | no | — |
| 235 | C2×Q8 | — | 30 | 3 | no | — |
| 236 | C2×Q8 | #1220 | 1 | 1 | yes | characteristic |
| 237 | C2×D4 | — | 2 | 3 | no | — |
| 238 | C2×D4 | — | 2 | 3 | no | — |
| 239 | C2×D4 | C22×D15 | 1 | 3 | yes | — |
| 240 | C22×C4 | — | 2 | 3 | no | — |
| 241 | SD16 | — | 30 | 6 | no | — |
| 242 | C2×C8 | — | 15 | 1 | no | — |
| 243 | C2×C8 | — | 15 | 3 | no | — |
| 244 | C4⋊C4 | — | 15 | 3 | no | — |
| 245 | C4⋊C4 | — | 30 | 3 | no | — |
| 246 | C4⋊C4 | — | 30 | 3 | no | — |
| 247 | C4⋊C4 | #1220 | 1 | 3 | yes | — |
| 248 | C4⋊C4 | C22×D15 | 1 | 1 | yes | characteristic |
| 249 | C22⋊C4 | — | 2 | 3 | no | — |
| 250 | C42 | — | 30 | 3 | no | — |
| 251 | C42 | C22×D15 | 1 | 3 | yes | — |
| 252 | C3×C5 | #3362 | 1 | 1 | yes | characteristic, complemented, Hall |
| 253 | C22×C3 | — | 4 | 3 | no | — |
| 254 | C22×C3 | — | 4 | 3 | no | — |
| 255 | C22×C3 | — | 4 | 3 | no | — |
| 256 | C22×C3 | C22×C22⋊D5 | 1 | 1 | yes | characteristic |
| 257 | C3×C4 | — | 2 | 3 | no | — |
| 258 | C3×C4 | — | 4 | 1 | no | — |
| 259 | C3×C4 | C2×#687 | 1 | 6 | yes | — |
| 260 | C3×C4 | D5×#41 | 1 | 1 | yes | characteristic |
| 261 | C3×C4 | #4150 | 1 | 1 | yes | characteristic |
| 262 | Dic3 | — | 10 | 2 | no | — |
| 263 | Dic3 | — | 20 | 3 | no | — |
| 264 | C2×C5 | — | 8 | 3 | no | — |
| 265 | C2×C5 | C22×#214 | 1 | 1 | yes | characteristic |
| 266 | C2×C5 | #5831 | 1 | 1 | yes | characteristic |
| 267 | C2×C5 | #5835 | 1 | 1 | yes | characteristic |
| 268 | C23 | — | 2 | 3 | no | — |
| 269 | Q8 | — | 15 | 2 | no | — |
| 270 | Q8 | — | 30 | 1 | no | — |
| 271 | Q8 | — | 120 | 3 | no | — |
| 272 | Q8 | #6716 | 1 | 4 | yes | complemented |
| 273 | D4 | — | 2 | 3 | no | — |
| 274 | D4 | — | 2 | 3 | no | — |
| 275 | D4 | — | 4 | 6 | no | — |
| 276 | D4 | — | 8 | 3 | no | — |
| 277 | C2×C4 | — | 2 | 1 | no | — |
| 278 | C2×C4 | — | 4 | 6 | no | — |
| 279 | C2×C4 | — | 30 | 1 | no | — |
| 280 | C2×C4 | — | 30 | 3 | no | — |
| 281 | C2×C4 | C2×#1220 | 1 | 3 | yes | — |
| 282 | C2×C4 | C2×#1220 | 1 | 3 | yes | — |
| 283 | C2×C4 | C23×D15 | 1 | 1 | yes | characteristic |
| 284 | C8 | — | 30 | 3 | no | — |
| 285 | C8 | — | 30 | 1 | no | — |
| 286 | C2×C3 | — | 8 | 3 | no | — |
| 287 | C2×C3 | C22×#687 | 1 | 1 | yes | characteristic |
| 288 | C2×C3 | #66165 | 1 | 1 | yes | characteristic |
| 289 | C2×C3 | #66169 | 1 | 1 | yes | characteristic |
| 290 | C5 | #83586 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 291 | C22 | — | 4 | 3 | no | — |
| 292 | C22 | — | 4 | 3 | no | — |
| 293 | C22 | — | 4 | 3 | no | — |
| 294 | C22 | C22×#1220 | 1 | 1 | yes | characteristic |
| 295 | C4 | — | 2 | 3 | no | — |
| 296 | C4 | — | 4 | 1 | no | — |
| 297 | C4 | — | 30 | 2 | no | — |
| 298 | C4 | — | 60 | 3 | no | — |
| 299 | C4 | C2×#6716 | 1 | 6 | yes | — |
| 300 | C4 | #41×D15 | 1 | 1 | yes | characteristic |
| 301 | C4 | #92101 | 1 | 1 | yes | characteristic |
| 302 | C3 | #10615317 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 303 | C2 | — | 8 | 3 | no | — |
| 304 | C2 | C22×#6716 | 1 | 1 | yes | characteristic |
| 305 | C2 | #11756590 | 1 | 1 | yes | characteristic |
| 306 | C2 | #11756594 | 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