Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 2. #11751189 | C2 | semidirect |
| 3. C5×#5090 | C2 | semidirect |
| 4. C3×#65376 | C2 | semidirect |
| 5. #11745854 | C2 | semidirect |
| 6. #11745842 | C2 | semidirect |
| 7. #11745834 | C2 | semidirect |
| 30. #65376 | D3 | semidirect |
| 61. #5090 | D5 | semidirect |
| 321. C3×C5 | #1641 | semidirect |
| 376. C5 | #71112 | semidirect |
| 393. C3 | #10601854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752677 | 2 |
| #11751189 | 2 |
| C5×#5090 | 2 |
| C3×#65376 | 2 |
| #11745854 | 2 |
| #11745842 | 2 |
| #11745834 | 2 |
| #10601854 | 3 |
| #71112 | 5 |