Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11750789 | C2 | semidirect |
| 2. C5×#4694 | C2 | semidirect |
| 4. #11746885 | C2 | semidirect |
| 5. C3×#64678 | C2 | semidirect |
| 6. #11745862 | C2 | semidirect |
| 7. #11745853 | C2 | semidirect |
| 31. #64678 | D3 | semidirect |
| 52. #4694 | D5 | semidirect |
| 263. C3×C5 | #1697 | semidirect |
| 310. C5 | #68584 | semidirect |
| 325. C3 | #10601995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750789 | 2 |
| C5×#4694 | 2 |
| #11747045 | 2 |
| #11746885 | 2 |
| C3×#64678 | 2 |
| #11745862 | 2 |
| #11745853 | 2 |
| #10601995 | 3 |
| #68584 | 5 |