Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5542 | C2 | semidirect |
| 3. #11747078 | C2 | semidirect |
| 4. #11746912 | C2 | semidirect |
| 5. C3×D4⋊#168 | C2 | semidirect |
| 6. #11745857 | C2 | semidirect |
| 7. #11745843 | C2 | semidirect |
| 33. D4⋊#168 | D3 | semidirect |
| 58. #5542 | D5 | semidirect |
| 308. C3×C5 | #1628 | semidirect |
| 360. C5 | #68201 | semidirect |
| 377. C3 | #10602724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5542 | 2 |
| #11751116 | 2 |
| #11747078 | 2 |
| #11746912 | 2 |
| C3×D4⋊#168 | 2 |
| #11745857 | 2 |
| #11745843 | 2 |
| #10602724 | 3 |
| #68201 | 5 |