Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 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. #11751285 | C2 | semidirect |
| 4. C3×#64785 | C2 | semidirect |
| 5. #11745938 | C2 | semidirect |
| 7. #11745878 | C2 | semidirect |
| 16. C5×#829 | C4 | semidirect |
| 17. C5×#828 | C4 | semidirect |
| 27. #64785 | D3 | semidirect |
| 90. #829 | Dic5 | semidirect |
| 91. #828 | Dic5 | semidirect |
| 217. C3×C5 | #2180 | semidirect |
| 246. C5 | #69264 | semidirect |
| 255. C3 | #10602314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751285 | 2 |
| C5×#5179 | 2 |
| #11748073 | 2 |
| C3×#64785 | 2 |
| #11745938 | 2 |
| #11745912 | 2 |
| #11745878 | 2 |
| #10602314 | 3 |
| #69264 | 5 |