Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1504 conjugacy classes of subgroups.
The subgroup lattice has 296 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×C3×C42×C5 | C4 | semidirect |
| 12. C2×C4×Dic15 | C4 | semidirect |
| 13. #91115 | C4 | direct (N × H) |
| 42. C2×C42×C5 | Dic3 | semidirect |
| 59. C2×C3×C4×C5 | C42 | semidirect |
| 68. C2×Dic15 | C42 | semidirect |
| 73. C2×C3×C42 | Dic5 | semidirect |
| 111. C3×C4×C5 | #95 | semidirect |
| 141. C2×C4×C5 | C4×Dic3 | semidirect |
| 158. C2×C42 | Dic15 | semidirect |
| 178. C2×C3×C4 | C4×Dic5 | semidirect |
| 201. C4×C5 | C3⋊#95 | semidirect |
| 220. C3×C5 | C4×#95 | semidirect |
| 234. C3×C4 | #3963 | semidirect |
| 259. C2×C4 | C4×Dic15 | semidirect |
| 271. C5 | C4×C3⋊#95 | semidirect |
| 286. C4 | #91115 | direct (N × H) |
| 287. C3 | C4×#3963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C42×C5 | 2 |
| C22×C4×Dic15 | 2 |
| C2×#91115 | 2 |
| C4×#3963 | 3 |
| C4×C3⋊#95 | 5 |