Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 192 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. C3×C5×#125 | C2 | semidirect |
| 3. C5×#810 | C2 | semidirect |
| 5. C4×C5×C3⋊C8 | C2 | semidirect |
| 14. #5068 | C5 | direct (N × H) |
| 15. C5×#125 | D3 | semidirect |
| 28. C3×#125 | C2×C5 | semidirect |
| 30. #810 | C2×C5 | semidirect |
| 32. C4×C3⋊C8 | C2×C5 | semidirect |
| 63. #125 | C5×D3 | semidirect |
| 93. C3×C5 | #488 | semidirect |
| 115. C5 | #5068 | direct (N × H) |
| 123. C3 | C5×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#125 | 2 |
| C5×#875 | 2 |
| C5×#810 | 2 |
| C5×#809 | 2 |
| C4×C5×C3⋊C8 | 2 |
| C5×#488 | 3 |
| #5068 | 5 |