Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 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 |
|---|---|---|
| 20. #4857 | C5 | direct (N × H) |
| 130. C3×C5 | #479 | semidirect |
| 157. C5 | #4857 | direct (N × H) |
| 167. C3 | C5×#479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#890 | 2 |
| C5×#887 | 2 |
| C3×C5×#106 | 2 |
| C5×#816 | 2 |
| C5×Dic3⋊C8 | 2 |
| C5×#810 | 2 |
| C5×#807 | 2 |
| C5×#479 | 3 |
| #4857 | 5 |