Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 76 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 | C3×#66017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11751159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11747036 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C5×#4540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11745846 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10599143 | — | 3 | 1 | no | maximal, Hall |
| 7 | C3×C5×#124 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×#6717 | — | 2 | 1 | no | — |
| 9 | C2×#6715 | — | 2 | 1 | no | — |
| 10 | #91763 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C3×#4093 | — | 2 | 1 | no | — |
| 12 | C3×#4083 | — | 2 | 1 | no | — |
| 13 | C3×#4031 | — | 2 | 2 | no | — |
| 14 | C3×#4028 | — | 2 | 2 | no | — |
| 15 | C3×#4021 | C22 | 1 | 2 | yes | — |
| 16 | C2×#6658 | — | 2 | 2 | no | — |
| 17 | C2×#6653 | — | 2 | 2 | no | — |
| 18 | #91087 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C5×#803 | C22 | 1 | 2 | yes | complemented |
| 20 | #71948 | — | 5 | 1 | no | maximal, Hall |
| 21 | #66017 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #65347 | — | 3 | 1 | no | — |
| 23 | #65001 | — | 3 | 2 | no | — |
| 24 | C5×#329 | — | 3 | 1 | no | — |
| 25 | #64684 | — | 3 | 2 | no | — |
| 26 | C23×C3×D5 | — | 2 | 1 | no | — |
| 27 | C2×C3×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×C3×C5×D4 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×D60 | — | 2 | 2 | no | — |
| 30 | C2×D60 | — | 2 | 1 | no | — |
| 31 | C2×C3×C22⋊D5 | — | 2 | 2 | no | — |
| 32 | C2×C3×D20 | — | 2 | 1 | no | — |
| 33 | C2×C3×D20 | D4 | 1 | 2 | yes | — |
| 34 | C2×C3×Dic10 | D4 | 1 | 2 | yes | — |
| 35 | C3×C5×C22⋊C4 | — | 2 | 2 | no | — |
| 36 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 37 | #6717 | — | 4 | 2 | no | — |
| 38 | #6715 | — | 4 | 2 | no | — |
| 39 | C2×C3⋊#168 | — | 2 | 1 | no | — |
| 40 | C2×C5×C3⋊C8 | — | 2 | 2 | no | — |
| 41 | C3×C22⋊Dic5 | — | 2 | 1 | no | — |
| 42 | C3×#685 | — | 2 | 2 | no | — |
| 43 | C3×#685 | — | 2 | 2 | no | — |
| 44 | C3×#685 | — | 2 | 2 | no | — |
| 45 | C3×C4×Dic5 | — | 2 | 1 | no | — |
| 46 | #6658 | — | 4 | 4 | no | — |
| 47 | #6653 | — | 4 | 4 | no | — |
| 48 | C3×H(3,𝔽4) | — | 5 | 1 | no | — |
| 49 | #5058 | — | 5 | 1 | no | — |
| 50 | #5058 | — | 5 | 2 | no | — |
| 51 | #4540 | — | 5 | 2 | no | — |
| 52 | #4540 | D5 | 1 | 1 | yes | characteristic, complemented |
| 53 | C5×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | #4093 | — | 2 | 1 | no | — |
| 55 | C2×#688 | — | 6 | 1 | no | — |
| 56 | #4083 | — | 2 | 1 | no | — |
| 57 | C2×#686 | — | 6 | 1 | no | — |
| 58 | C2×D40 | — | 6 | 2 | no | — |
| 59 | C2×#677 | — | 6 | 2 | no | — |
| 60 | #4031 | — | 2 | 2 | no | — |
| 61 | #4028 | — | 2 | 2 | no | — |
| 62 | #4021 | C2×D3 | 1 | 2 | yes | — |
| 63 | #4020 | — | 3 | 1 | no | — |
| 64 | C5×#97 | — | 3 | 2 | no | — |
| 65 | #3935 | — | 3 | 1 | no | — |
| 66 | #1655 | — | 15 | 1 | no | Sylow |
| 67 | C23×C3×C5 | — | 2 | 1 | no | — |
| 68 | C22×D15 | — | 4 | 1 | no | — |
| 69 | C22×C3×D5 | — | 2 | 2 | no | — |
| 70 | C22×C3×D5 | — | 8 | 2 | no | — |
| 71 | C22×C3×D5 | — | 8 | 1 | no | — |
| 72 | C3×C5×Q8 | — | 4 | 1 | no | — |
| 73 | C3×C5×D4 | — | 4 | 1 | no | — |
| 74 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 75 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C3×C4×C5 | C2×D4 | 1 | 2 | yes | — |
| 77 | D60 | — | 4 | 2 | no | — |
| 78 | D60 | — | 4 | 1 | no | — |
| 79 | D60 | — | 4 | 1 | no | — |
| 80 | D60 | — | 4 | 2 | no | — |
| 81 | C3×C22⋊D5 | — | 8 | 2 | no | — |
| 82 | C2×C3×Dic5 | — | 2 | 2 | no | — |
| 83 | C3×D20 | — | 4 | 2 | no | — |
| 84 | C3×D20 | — | 8 | 1 | no | — |
| 85 | C3×Dic10 | — | 4 | 2 | no | — |
| 86 | C3⋊#168 | — | 2 | 2 | no | — |
| 87 | C5×C3⋊C8 | — | 2 | 4 | no | — |
| 88 | C3×#124 | — | 5 | 2 | no | — |
| 89 | C3×#124 | — | 10 | 2 | no | — |
| 90 | C3×#124 | — | 10 | 1 | no | — |
| 91 | C3×#124 | C2×D5 | 1 | 1 | yes | characteristic |
| 92 | C3×#120 | — | 10 | 2 | no | — |
| 93 | C3×#120 | — | 10 | 1 | no | — |
| 94 | C2×#215 | — | 10 | 2 | no | — |
| 95 | C2×#215 | — | 10 | 1 | no | — |
| 96 | C2×#213 | — | 10 | 2 | no | — |
| 97 | C2×#213 | — | 10 | 1 | no | — |
| 98 | #874 | — | 5 | 1 | no | — |
| 99 | #803 | — | 5 | 1 | no | — |
| 100 | #803 | C2×D5 | 1 | 2 | yes | complemented |
| 101 | C23×D5 | — | 2 | 1 | no | — |
| 102 | C2×C5×Q8 | #67 | 1 | 1 | yes | characteristic |
| 103 | C2×C5×D4 | #67 | 1 | 1 | yes | characteristic |
| 104 | C2×C22⋊D5 | — | 2 | 2 | no | — |
| 105 | C2×D20 | — | 2 | 1 | no | — |
| 106 | C2×D20 | — | 6 | 2 | no | — |
| 107 | C2×D20 | — | 6 | 1 | no | — |
| 108 | C2×D20 | #67 | 1 | 2 | yes | — |
| 109 | C2×Dic10 | #67 | 1 | 2 | yes | — |
| 110 | C2×C5×C8 | — | 6 | 2 | no | — |
| 111 | C5×C22⋊C4 | — | 2 | 2 | no | — |
| 112 | C42×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 113 | C22⋊Dic5 | — | 2 | 1 | no | — |
| 114 | #688 | — | 12 | 2 | no | — |
| 115 | #686 | — | 12 | 2 | no | — |
| 116 | #685 | — | 2 | 2 | no | — |
| 117 | #685 | — | 2 | 2 | no | — |
| 118 | #685 | — | 2 | 2 | no | — |
| 119 | C4×Dic5 | — | 2 | 1 | no | — |
| 120 | C2×#168 | — | 6 | 1 | no | — |
| 121 | D40 | — | 12 | 4 | no | — |
| 122 | #677 | — | 12 | 4 | no | — |
| 123 | H(3,𝔽4) | — | 5 | 1 | no | — |
| 124 | #496 | — | 15 | 2 | no | — |
| 125 | #496 | — | 15 | 1 | no | — |
| 126 | #329 | — | 3 | 1 | no | — |
| 127 | #329 | — | 15 | 2 | no | — |
| 128 | C22×C3×C5 | — | 4 | 2 | no | — |
| 129 | C22×C3×C5 | — | 4 | 1 | no | — |
| 130 | C22×C3×C5 | #120 | 1 | 1 | yes | characteristic |
| 131 | C2×D15 | — | 8 | 1 | no | — |
| 132 | C2×D15 | — | 8 | 2 | no | — |
| 133 | C2×C3×D5 | — | 4 | 2 | no | — |
| 134 | C2×C3×D5 | — | 4 | 2 | no | — |
| 135 | C2×C3×D5 | — | 4 | 2 | no | — |
| 136 | C2×C3×D5 | — | 8 | 4 | no | — |
| 137 | C3×C4×C5 | — | 2 | 2 | no | — |
| 138 | C3×C4×C5 | — | 2 | 1 | no | — |
| 139 | C3×C4×C5 | — | 4 | 1 | no | — |
| 140 | C3×Dic5 | — | 4 | 2 | no | — |
| 141 | C24×C3 | — | 10 | 1 | no | — |
| 142 | C2×C3×Q8 | — | 5 | 2 | no | — |
| 143 | C2×C3×Q8 | D20 | 1 | 1 | yes | characteristic |
| 144 | C2×C3×D4 | — | 5 | 2 | no | — |
| 145 | C2×C3×D4 | — | 10 | 1 | no | — |
| 146 | C2×C3×D4 | — | 10 | 2 | no | — |
| 147 | C2×C3×D4 | D20 | 1 | 1 | yes | characteristic |
| 148 | C2×D12 | — | 10 | 1 | no | — |
| 149 | C2×D12 | — | 10 | 2 | no | — |
| 150 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 151 | C3×C22⋊C4 | — | 10 | 2 | no | — |
| 152 | C3×C22⋊C4 | — | 10 | 1 | no | — |
| 153 | C3×C22⋊C4 | — | 10 | 2 | no | — |
| 154 | C3×C22⋊C4 | — | 10 | 2 | no | — |
| 155 | C3×C42 | — | 10 | 1 | no | — |
| 156 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 157 | #215 | — | 20 | 4 | no | — |
| 158 | #215 | — | 20 | 2 | no | — |
| 159 | #213 | — | 20 | 4 | no | — |
| 160 | #213 | — | 20 | 2 | no | — |
| 161 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 162 | C2×C3⋊C8 | — | 10 | 1 | no | — |
| 163 | C23×C5 | — | 2 | 1 | no | — |
| 164 | C22×D5 | — | 2 | 2 | no | — |
| 165 | C22×D5 | — | 8 | 2 | no | — |
| 166 | C22×D5 | — | 8 | 1 | no | — |
| 167 | C22×D5 | — | 12 | 1 | no | — |
| 168 | C5×Q8 | — | 4 | 1 | no | — |
| 169 | C5×D4 | — | 4 | 1 | no | — |
| 170 | C2×C4×C5 | — | 2 | 1 | no | — |
| 171 | C2×C4×C5 | C2×#67 | 1 | 1 | yes | characteristic |
| 172 | C2×C4×C5 | C2×#67 | 1 | 2 | yes | — |
| 173 | C22⋊D5 | — | 8 | 2 | no | — |
| 174 | C2×Dic5 | — | 2 | 2 | no | — |
| 175 | D20 | — | 4 | 2 | no | — |
| 176 | D20 | — | 8 | 1 | no | — |
| 177 | D20 | — | 12 | 2 | no | — |
| 178 | D20 | — | 12 | 2 | no | — |
| 179 | D20 | — | 12 | 1 | no | — |
| 180 | D20 | — | 12 | 1 | no | — |
| 181 | Dic10 | — | 4 | 2 | no | — |
| 182 | C5×C8 | — | 6 | 4 | no | — |
| 183 | #168 | — | 6 | 2 | no | — |
| 184 | C2×SD16 | — | 30 | 2 | no | — |
| 185 | C2×SD16 | — | 30 | 1 | no | — |
| 186 | C2×D8 | — | 30 | 2 | no | — |
| 187 | C2×D8 | — | 30 | 1 | no | — |
| 188 | #127 | — | 15 | 1 | no | — |
| 189 | #124 | — | 5 | 2 | no | — |
| 190 | #124 | — | 10 | 2 | no | — |
| 191 | #124 | — | 10 | 1 | no | — |
| 192 | #124 | D3×D5 | 1 | 1 | yes | characteristic |
| 193 | #120 | — | 10 | 2 | no | — |
| 194 | #120 | — | 10 | 1 | no | — |
| 195 | #97 | — | 3 | 2 | no | — |
| 196 | #97 | — | 15 | 1 | no | — |
| 197 | C2×C3×C5 | — | 8 | 1 | no | — |
| 198 | C2×C3×C5 | #453 | 1 | 1 | yes | characteristic |
| 199 | C2×C3×C5 | #453 | 1 | 2 | yes | — |
| 200 | D15 | — | 16 | 1 | no | — |
| 201 | C3×D5 | — | 8 | 2 | no | — |
| 202 | C23×C3 | — | 2 | 1 | no | — |
| 203 | C23×C3 | — | 10 | 2 | no | — |
| 204 | C23×C3 | — | 40 | 1 | no | — |
| 205 | C23×C3 | — | 40 | 2 | no | — |
| 206 | C22×D3 | — | 20 | 1 | no | — |
| 207 | C3×Q8 | — | 4 | 1 | no | — |
| 208 | C3×Q8 | — | 20 | 2 | no | — |
| 209 | C3×D4 | — | 4 | 1 | no | — |
| 210 | C3×D4 | — | 20 | 2 | no | — |
| 211 | C3×D4 | — | 40 | 1 | no | — |
| 212 | C3×D4 | — | 40 | 2 | no | — |
| 213 | C2×C3×C4 | — | 2 | 1 | no | — |
| 214 | C2×C3×C4 | — | 10 | 2 | no | — |
| 215 | C2×C3×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 216 | C2×C3×C4 | D4×D5 | 1 | 2 | yes | — |
| 217 | D12 | — | 20 | 1 | no | — |
| 218 | D12 | — | 20 | 2 | no | — |
| 219 | D12 | — | 20 | 1 | no | — |
| 220 | D12 | — | 20 | 2 | no | — |
| 221 | C3⋊C8 | — | 2 | 4 | no | — |
| 222 | C3⋊C8 | — | 10 | 2 | no | — |
| 223 | C22×C5 | — | 4 | 2 | no | — |
| 224 | C22×C5 | — | 4 | 1 | no | — |
| 225 | C22×C5 | #953 | 1 | 1 | yes | characteristic |
| 226 | C2×D5 | — | 4 | 2 | no | — |
| 227 | C2×D5 | — | 4 | 2 | no | — |
| 228 | C2×D5 | — | 4 | 2 | no | — |
| 229 | C2×D5 | — | 8 | 4 | no | — |
| 230 | C2×D5 | — | 24 | 1 | no | — |
| 231 | C2×D5 | — | 24 | 2 | no | — |
| 232 | C4×C5 | — | 2 | 1 | no | — |
| 233 | C4×C5 | — | 2 | 2 | no | — |
| 234 | C4×C5 | — | 4 | 1 | no | — |
| 235 | Dic5 | — | 4 | 2 | no | — |
| 236 | C24 | — | 10 | 1 | no | — |
| 237 | C2×Q8 | — | 5 | 2 | no | — |
| 238 | C2×Q8 | #1202 | 1 | 1 | yes | characteristic |
| 239 | C2×D4 | — | 5 | 2 | no | — |
| 240 | C2×D4 | — | 10 | 1 | no | — |
| 241 | C2×D4 | — | 10 | 2 | no | — |
| 242 | C2×D4 | — | 30 | 1 | no | — |
| 243 | C2×D4 | — | 30 | 2 | no | — |
| 244 | C2×D4 | #1202 | 1 | 1 | yes | characteristic |
| 245 | SD16 | — | 60 | 4 | no | — |
| 246 | SD16 | — | 60 | 2 | no | — |
| 247 | D8 | — | 60 | 4 | no | — |
| 248 | D8 | — | 60 | 2 | no | — |
| 249 | C2×C8 | — | 6 | 2 | no | — |
| 250 | C2×C8 | — | 30 | 1 | no | — |
| 251 | C22⋊C4 | — | 2 | 2 | no | — |
| 252 | C22⋊C4 | — | 10 | 2 | no | — |
| 253 | C22⋊C4 | — | 10 | 1 | no | — |
| 254 | C22⋊C4 | — | 10 | 2 | no | — |
| 255 | C22⋊C4 | — | 10 | 2 | no | — |
| 256 | C42 | — | 10 | 1 | no | — |
| 257 | C42 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 258 | C3×C5 | #1655 | 1 | 1 | yes | characteristic, complemented, Hall |
| 259 | C22×C3 | — | 4 | 1 | no | — |
| 260 | C22×C3 | — | 4 | 2 | no | — |
| 261 | C22×C3 | — | 20 | 2 | no | — |
| 262 | C22×C3 | — | 20 | 2 | no | — |
| 263 | C22×C3 | — | 20 | 2 | no | — |
| 264 | C22×C3 | — | 40 | 4 | no | — |
| 265 | C22×C3 | #4028 | 1 | 1 | yes | characteristic |
| 266 | C2×D3 | — | 40 | 1 | no | — |
| 267 | C2×D3 | — | 40 | 2 | no | — |
| 268 | C3×C4 | — | 2 | 1 | no | — |
| 269 | C3×C4 | — | 2 | 2 | no | — |
| 270 | C3×C4 | — | 4 | 1 | no | — |
| 271 | C3×C4 | — | 20 | 2 | no | — |
| 272 | C2×C5 | — | 8 | 1 | no | — |
| 273 | C2×C5 | #5241 | 1 | 1 | yes | characteristic |
| 274 | C2×C5 | #5241 | 1 | 2 | yes | — |
| 275 | D5 | — | 8 | 2 | no | — |
| 276 | D5 | — | 48 | 1 | no | — |
| 277 | C23 | — | 2 | 1 | no | — |
| 278 | C23 | — | 10 | 2 | no | — |
| 279 | C23 | — | 40 | 1 | no | — |
| 280 | C23 | — | 40 | 2 | no | — |
| 281 | C23 | — | 60 | 1 | no | — |
| 282 | Q8 | — | 4 | 1 | no | — |
| 283 | Q8 | — | 20 | 2 | no | — |
| 284 | D4 | — | 4 | 1 | no | — |
| 285 | D4 | — | 20 | 2 | no | — |
| 286 | D4 | — | 40 | 1 | no | — |
| 287 | D4 | — | 40 | 2 | no | — |
| 288 | D4 | — | 60 | 1 | no | — |
| 289 | D4 | — | 60 | 2 | no | — |
| 290 | D4 | — | 60 | 1 | no | — |
| 291 | D4 | — | 60 | 2 | no | — |
| 292 | C2×C4 | — | 2 | 1 | no | — |
| 293 | C2×C4 | — | 10 | 2 | no | — |
| 294 | C2×C4 | C2×#1202 | 1 | 1 | yes | characteristic |
| 295 | C2×C4 | D5×#67 | 1 | 2 | yes | — |
| 296 | C8 | — | 6 | 4 | no | — |
| 297 | C8 | — | 30 | 2 | no | — |
| 298 | C2×C3 | — | 8 | 1 | no | — |
| 299 | C2×C3 | — | 40 | 2 | no | — |
| 300 | C2×C3 | #65036 | 1 | 1 | yes | characteristic |
| 301 | C2×C3 | #65111 | 1 | 2 | yes | — |
| 302 | D3 | — | 80 | 1 | no | — |
| 303 | C5 | #71948 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 304 | C22 | — | 4 | 1 | no | — |
| 305 | C22 | — | 4 | 2 | no | — |
| 306 | C22 | — | 20 | 2 | no | — |
| 307 | C22 | — | 20 | 2 | no | — |
| 308 | C22 | — | 20 | 2 | no | — |
| 309 | C22 | — | 40 | 4 | no | — |
| 310 | C22 | — | 120 | 1 | no | — |
| 311 | C22 | — | 120 | 2 | no | — |
| 312 | C22 | #91564 | 1 | 1 | yes | characteristic |
| 313 | C4 | — | 2 | 1 | no | — |
| 314 | C4 | — | 2 | 2 | no | — |
| 315 | C4 | — | 4 | 1 | no | — |
| 316 | C4 | — | 20 | 2 | no | — |
| 317 | C3 | #10599143 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 318 | C2 | — | 8 | 1 | no | — |
| 319 | C2 | — | 40 | 2 | no | — |
| 320 | C2 | — | 240 | 1 | no | — |
| 321 | C2 | #11749138 | 1 | 1 | yes | characteristic |
| 322 | C2 | #11749418 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66017 | C2 | semidirect |
| 2. #11751159 | C2 | semidirect |
| 3. #11747036 | C2 | semidirect |
| 4. C5×#4540 | C2 | semidirect |
| 5. #11745846 | C2 | semidirect |
| 10. #91763 | C22 | semidirect |
| 18. #91087 | C22 | semidirect |
| 19. C5×#803 | C22 | semidirect |
| 21. #66017 | D3 | semidirect |
| 52. #4540 | D5 | semidirect |
| 100. #803 | C2×D5 | semidirect |
| 258. C3×C5 | #1655 | semidirect |
| 303. C5 | #71948 | semidirect |
| 317. C3 | #10599143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66017 | 2 |
| #11751159 | 2 |
| #11747036 | 2 |
| C5×#4540 | 2 |
| #11745846 | 2 |
| #10599143 | 3 |
| #71948 | 5 |