Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
160 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 7. C2×C5×Dic6 | C4 | semidirect |
| 9. C5×C4⋊Dic3 | C4 | semidirect |
| 12. #4452 | C5 | direct (N × H) |
| 50. C2×Dic6 | C4×C5 | semidirect |
| 52. C4⋊Dic3 | C4×C5 | semidirect |
| 102. C3×C5 | #328 | semidirect |
| 134. C5 | #4452 | direct (N × H) |
| 145. C3 | C5×#328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#924 | 2 |
| C3×C5×#95 | 2 |
| C5×#830 | 2 |
| C5×#328 | 3 |
| #4452 | 5 |