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. #11750801 | C2 | semidirect |
| 2. C5×#4700 | C2 | semidirect |
| 4. C3×#64681 | C2 | semidirect |
| 5. #11745945 | C2 | semidirect |
| 6. #11745908 | C2 | semidirect |
| 7. #11745906 | C2 | semidirect |
| 20. #90948 | C4 | semidirect |
| 21. #90945 | C4 | semidirect |
| 22. #90944 | C4 | semidirect |
| 23. #90939 | C4 | semidirect |
| 31. #64681 | D3 | semidirect |
| 54. #4700 | D5 | semidirect |
| 240. C3×C5 | #2179 | semidirect |
| 273. C5 | #69085 | semidirect |
| 282. C3 | #10601715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750801 | 2 |
| C5×#4700 | 2 |
| #11747546 | 2 |
| C3×#64681 | 2 |
| #11745945 | 2 |
| #11745908 | 2 |
| #11745906 | 2 |
| #10601715 | 3 |
| #69085 | 5 |