Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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. #11752715 | C2 | semidirect |
| 2. #11751173 | C2 | semidirect |
| 3. C5×#5076 | C2 | semidirect |
| 4. C3×#65361 | C2 | semidirect |
| 5. #11745862 | C2 | semidirect |
| 6. #11745838 | C2 | semidirect |
| 7. #11745835 | C2 | semidirect |
| 30. #65361 | D3 | semidirect |
| 61. #5076 | D5 | semidirect |
| 323. C3×C5 | #1624 | semidirect |
| 381. C5 | #71017 | semidirect |
| 400. C3 | #10602058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752715 | 2 |
| #11751173 | 2 |
| C5×#5076 | 2 |
| C3×#65361 | 2 |
| #11745862 | 2 |
| #11745838 | 2 |
| #11745835 | 2 |
| #10602058 | 3 |
| #71017 | 5 |