Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 94 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×#4873 | C2 | semidirect |
| 5. C3×#64710 | C2 | semidirect |
| 6. #11745899 | C2 | semidirect |
| 7. Dic3×#672 | C2 | semidirect |
| 20. #90945 | C4 | semidirect |
| 27. #64710 | D3 | semidirect |
| 41. C5×Dic12 | C2×C4 | semidirect |
| 45. C3×#672 | C2×C4 | semidirect |
| 47. #4873 | D5 | semidirect |
| 109. #672 | C4×D3 | semidirect |
| 127. C5×Dic3 | SD32 | semidirect |
| 140. Dic12 | C4×D5 | semidirect |
| 219. C3×C5 | C4×SD32 | semidirect |
| 230. Dic3 | #3960 | semidirect |
| 254. C5 | #69337 | semidirect |
| 266. C3 | C4×#3960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4873 | 2 |
| #11747793 | 2 |
| C2×#90945 | 2 |
| #11746312 | 2 |
| C3×#64710 | 2 |
| #11745899 | 2 |
| Dic3×#672 | 2 |
| C4×#3960 | 3 |
| #69337 | 5 |