Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 2. Dic240 | C2 | semidirect |
| 4. C3×Dic80 | C2 | semidirect |
| 5. #11745828 | C2 | semidirect |
| 19. Dic80 | D3 | direct (N × H) |
| 93. C5×D3 | Q64 | semidirect |
| 113. C3×C5 | C2×Q64 | semidirect |
| 129. D3 | Dic80 | direct (N × H) |
| 130. C5 | D3×Q64 | semidirect |
| 136. C3 | C2×Dic80 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×Dic40 | 2 |
| Dic240 | 2 |
| C5×D3×C32 | 2 |
| C3×Dic80 | 2 |
| #11745828 | 2 |
| C2×Dic80 | 3 |
| D3×Q64 | 5 |