Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
384 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 128 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. #91759 | C2 | semidirect |
| 2. C5×#869 | C2 | semidirect |
| 6. #91336 | C2 | semidirect |
| 7. Dic5×Dic6 | C2 | semidirect |
| 44. #869 | D5 | semidirect |
| 132. C3×C5 | #541 | semidirect |
| 157. C5 | #5518 | semidirect |
| 167. C3 | #66065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91759 | 2 |
| C5×#869 | 2 |
| C3×#4018 | 2 |
| #91361 | 2 |
| #91359 | 2 |
| #91336 | 2 |
| Dic5×Dic6 | 2 |
| #66065 | 3 |
| #5518 | 5 |