Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4878 | C2 | semidirect |
| 4. C3×#64710 | C2 | semidirect |
| 5. #11745940 | C2 | semidirect |
| 6. Dic3⋊#672 | C2 | semidirect |
| 25. #64710 | D3 | semidirect |
| 43. #4878 | D5 | semidirect |
| 201. C3×C5 | #2228 | semidirect |
| 234. C5 | #69354 | semidirect |
| 246. C3 | #10602149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4878 | 2 |
| #11747793 | 2 |
| #11746312 | 2 |
| C3×#64710 | 2 |
| #11745940 | 2 |
| Dic3⋊#672 | 2 |
| #11745896 | 2 |
| #10602149 | 3 |
| #69354 | 5 |