Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
480 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 190 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D3 |
| commutator, cosocle | C22×C3 | C24×C5 |
| Frattini | C22 | C23×C5×D3 |
| Fitting | C3×C5×#117 | C2 |
| socle | C22×C3×C5 | C24 |
| hypercenter | C5×#117 | D3 |
| hypocenter | C3 | C5×#540 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×#117 | C2 | semidirect |
| 2. C5×#930 | C2 | semidirect |
| 3. C5×#894 | C2 | semidirect |
| 4. C5×#884 | C2 | semidirect |
| 5. C5×#874 | C2 | semidirect |
| 6. C4×C5×D12 | C2 | semidirect |
| 7. C5×#870 | C2 | semidirect |
| 22. #5535 | C5 | direct (N × H) |
| 29. C5×#117 | D3 | semidirect |
| 42. C3×#117 | C2×C5 | semidirect |
| 43. #930 | C2×C5 | semidirect |
| 44. #894 | C2×C5 | semidirect |
| 45. #884 | C2×C5 | semidirect |
| 46. #874 | C2×C5 | semidirect |
| 47. C4×D12 | C2×C5 | semidirect |
| 48. #870 | C2×C5 | semidirect |
| 105. #117 | C5×D3 | semidirect |
| 146. C3×C5 | #540 | semidirect |
| 178. C5 | #5535 | direct (N × H) |
| 190. C3 | C5×#540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#117 | 2 |
| C5×#930 | 2 |
| C5×#894 | 2 |
| C5×#884 | 2 |
| C5×#874 | 2 |
| C4×C5×D12 | 2 |
| C5×#870 | 2 |
| C5×#540 | 3 |
| #5535 | 5 |