Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 86 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×#124 | C2 | semidirect |
| 2. C2×C5×#216 | C2 | semidirect |
| 3. C2×C5×#215 | C2 | semidirect |
| 4. C2×C5×#214 | C2 | semidirect |
| 6. C5×#875 | C2 | semidirect |
| 7. C4×C5×C3⋊C8 | C2 | semidirect |
| 22. #5059 | C5 | direct (N × H) |
| 28. C5×#124 | D3 | semidirect |
| 46. C3×#124 | C2×C5 | semidirect |
| 47. C2×#216 | C2×C5 | semidirect |
| 48. C2×#215 | C2×C5 | semidirect |
| 49. C2×#214 | C2×C5 | semidirect |
| 51. #875 | C2×C5 | semidirect |
| 52. C4×C3⋊C8 | C2×C5 | semidirect |
| 111. #124 | C5×D3 | semidirect |
| 156. C3×C5 | #495 | semidirect |
| 191. C5 | #5059 | direct (N × H) |
| 202. C3 | C5×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#124 | 2 |
| C2×C5×#216 | 2 |
| C2×C5×#215 | 2 |
| C2×C5×#214 | 2 |
| C2×C5×#213 | 2 |
| C5×#875 | 2 |
| C4×C5×C3⋊C8 | 2 |
| C5×#495 | 3 |
| #5059 | 5 |