Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
212 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4912 | C2 | semidirect |
| 2. C3×C5×D32 | C2 | semidirect |
| 3. C5×#4520 | C2 | semidirect |
| 4. C5×Dic48 | C2 | semidirect |
| 5. C5×D3×C32 | C2 | semidirect |
| 14. #69376 | C5 | direct (N × H) |
| 18. C5×D32 | D3 | semidirect |
| 27. #4912 | C2×C5 | semidirect |
| 28. C3×D32 | C2×C5 | semidirect |
| 29. #4520 | C2×C5 | semidirect |
| 30. Dic48 | C2×C5 | semidirect |
| 31. D3×C32 | C2×C5 | semidirect |
| 64. D32 | C5×D3 | semidirect |
| 114. C3×C5 | #2262 | semidirect |
| 133. C5 | #69376 | direct (N × H) |
| 139. C3 | C5×#2262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4912 | 2 |
| C3×C5×D32 | 2 |
| C5×#4520 | 2 |
| C5×Dic48 | 2 |
| C5×D3×C32 | 2 |
| C5×#2262 | 3 |
| #69376 | 5 |