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. C5×D3×Q32 | C2 | semidirect |
| 3. #11746342 | C2 | semidirect |
| 4. C3×#64742 | C2 | semidirect |
| 5. #11745827 | C2 | semidirect |
| 6. #11745826 | C2 | semidirect |
| 7. #11745816 | C2 | semidirect |
| 24. #64742 | D3 | semidirect |
| 40. D3×Q32 | D5 | semidirect |
| 170. C3×C5 | #2264 | semidirect |
| 195. C5 | #69384 | semidirect |
| 203. C3 | #10602286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Q32 | 2 |
| #11746838 | 2 |
| #11746342 | 2 |
| C3×#64742 | 2 |
| #11745827 | 2 |
| #11745826 | 2 |
| #11745816 | 2 |
| #10602286 | 3 |
| #69384 | 5 |