Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4700 | C2 | semidirect |
| 2. C3×#64989 | C2 | semidirect |
| 4. #11746282 | C2 | semidirect |
| 5. #11745946 | C2 | semidirect |
| 6. #11745905 | C2 | semidirect |
| 7. #11745903 | C2 | semidirect |
| 20. #90946 | C4 | semidirect |
| 21. #90941 | C4 | semidirect |
| 22. #90940 | C4 | semidirect |
| 23. #90937 | C4 | semidirect |
| 27. #64989 | D3 | semidirect |
| 54. #4700 | D5 | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #70922 | semidirect |
| 282. C3 | #10601715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4700 | 2 |
| C3×#64989 | 2 |
| #11747538 | 2 |
| #11746282 | 2 |
| #11745946 | 2 |
| #11745905 | 2 |
| #11745903 | 2 |
| #10601715 | 3 |
| #70922 | 5 |