Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 100 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×#5727 | C2 | semidirect |
| 2. C3×#65377 | C2 | semidirect |
| 3. #11747068 | C2 | semidirect |
| 5. #11746368 | C2 | semidirect |
| 6. #11745843 | C2 | semidirect |
| 7. #11745837 | C2 | semidirect |
| 28. #65377 | D3 | semidirect |
| 60. #5727 | D5 | semidirect |
| 97. C5×D12 | SD16 | semidirect |
| 103. C5×Dic6 | D8 | semidirect |
| 270. D12 | #688 | semidirect |
| 276. Dic6 | #686 | semidirect |
| 322. C3×C5 | #1627 | semidirect |
| 376. C5 | #71205 | semidirect |
| 393. C3 | #10602707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5727 | 2 |
| C3×#65377 | 2 |
| #11747068 | 2 |
| #11747033 | 2 |
| #11746368 | 2 |
| #11745843 | 2 |
| #11745837 | 2 |
| #10602707 | 3 |
| #71205 | 5 |