Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
556 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 556 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. #11752677 | C2 | semidirect |
| 2. #11751174 | C2 | semidirect |
| 3. C5×#5075 | C2 | semidirect |
| 4. C3×#65361 | C2 | semidirect |
| 5. #11745854 | C2 | semidirect |
| 6. #11745842 | C2 | semidirect |
| 7. #11745834 | C2 | semidirect |
| 30. #65361 | D3 | semidirect |
| 63. #5075 | D5 | semidirect |
| 105. C5×Dic6 | D8 | semidirect |
| 294. Dic6 | #686 | semidirect |
| 343. C3×C5 | #1621 | semidirect |
| 405. C5 | #71013 | semidirect |
| 424. C3 | #10601825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752677 | 2 |
| #11751174 | 2 |
| C5×#5075 | 2 |
| C3×#65361 | 2 |
| #11745854 | 2 |
| #11745842 | 2 |
| #11745834 | 2 |
| #10601825 | 3 |
| #71013 | 5 |