Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 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. C4×C5×Dic6 | C2 | semidirect |
| 4. #91087 | C2 | semidirect |
| 5. #90989 | C2 | semidirect |
| 6. #90972 | C2 | semidirect |
| 20. #6655 | C4 | semidirect |
| 36. C5×Dic6 | C2×C4 | semidirect |
| 42. C3⋊#168 | C2×C4 | semidirect |
| 45. C4×Dic6 | D5 | semidirect |
| 122. Dic6 | C4×D5 | semidirect |
| 148. C3×C5 | #440 | semidirect |
| 182. C5 | #5018 | semidirect |
| 194. C3 | #65315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×Dic6 | 2 |
| C3×C4×D20 | 2 |
| C2×#6655 | 2 |
| #91087 | 2 |
| #90989 | 2 |
| #90972 | 2 |
| #90964 | 2 |
| #65315 | 3 |
| #5018 | 5 |