Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×D5×Q32 | C2 | semidirect |
| 3. #11746343 | C2 | semidirect |
| 4. C5×#4521 | C2 | semidirect |
| 5. #11745828 | C2 | semidirect |
| 6. #11745822 | C2 | semidirect |
| 7. #11745815 | C2 | semidirect |
| 21. D5×Q32 | D3 | semidirect |
| 44. #4521 | D5 | semidirect |
| 170. C3×C5 | #2264 | semidirect |
| 195. C5 | #71493 | semidirect |
| 203. C3 | #10600174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×Q32 | 2 |
| #11746832 | 2 |
| #11746343 | 2 |
| C5×#4521 | 2 |
| #11745828 | 2 |
| #11745822 | 2 |
| #11745815 | 2 |
| #10600174 | 3 |
| #71493 | 5 |