Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5684 | C2 | semidirect |
| 2. C3×#65347 | C2 | semidirect |
| 3. #11747041 | C2 | semidirect |
| 4. #11746897 | C2 | semidirect |
| 5. #11746361 | C2 | semidirect |
| 6. #11745850 | C2 | semidirect |
| 7. #11745847 | C2 | semidirect |
| 32. #65347 | D3 | semidirect |
| 67. #5684 | D5 | semidirect |
| 350. C3×C5 | #1656 | semidirect |
| 406. C5 | #71327 | semidirect |
| 424. C3 | #10602745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5684 | 2 |
| C3×#65347 | 2 |
| #11747041 | 2 |
| #11746897 | 2 |
| #11746361 | 2 |
| #11745850 | 2 |
| #11745847 | 2 |
| #10602745 | 3 |
| #71327 | 5 |