Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 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. C5×#1007 | C2 | semidirect |
| 2. C3×C5×#124 | C2 | semidirect |
| 3. C5×#932 | C2 | semidirect |
| 4. C5×#836 | C2 | semidirect |
| 5. C5×#805 | C2 | semidirect |
| 18. #5062 | C5 | direct (N × H) |
| 21. C5×#124 | D3 | semidirect |
| 38. #1007 | C2×C5 | semidirect |
| 39. C3×#124 | C2×C5 | semidirect |
| 40. #932 | C2×C5 | semidirect |
| 41. #836 | C2×C5 | semidirect |
| 42. #805 | C2×C5 | semidirect |
| 90. #124 | C5×D3 | semidirect |
| 130. C3×C5 | #454 | semidirect |
| 161. C5 | #5062 | direct (N × H) |
| 170. C3 | C5×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1007 | 2 |
| C3×C5×#124 | 2 |
| C5×#932 | 2 |
| C5×#836 | 2 |
| C5×#805 | 2 |
| C5×#454 | 3 |
| #5062 | 5 |