Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 460 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66018 | C2 | semidirect |
| 2. C5×#5058 | C2 | semidirect |
| 3. #11747042 | C2 | semidirect |
| 4. #11746905 | C2 | semidirect |
| 5. #11746361 | C2 | semidirect |
| 6. #11745849 | C2 | semidirect |
| 7. #11745846 | C2 | semidirect |
| 29. #66018 | D3 | semidirect |
| 70. #5058 | D5 | semidirect |
| 350. C3×C5 | #1656 | semidirect |
| 406. C5 | #71952 | semidirect |
| 424. C3 | #10602120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66018 | 2 |
| C5×#5058 | 2 |
| #11747042 | 2 |
| #11746905 | 2 |
| #11746361 | 2 |
| #11745849 | 2 |
| #11745846 | 2 |
| #10602120 | 3 |
| #71952 | 5 |