Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D15 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C4×C5×D4 | C2 |
| hypercenter | C4×D4 | D15 |
| hypocenter | C3×C5 | #555 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4×C5×D4 | C2 | semidirect |
| 2. #91827 | C2 | semidirect |
| 3. #91819 | C2 | semidirect |
| 4. #91815 | C2 | semidirect |
| 5. #91781 | C2 | semidirect |
| 6. #91774 | C2 | semidirect |
| 7. C4×D60 | C2 | semidirect |
| 8. #91758 | C2 | semidirect |
| 27. C4×C5×D4 | D3 | semidirect |
| 49. C3×C4×D4 | D5 | semidirect |
| 122. C4×D4 | D15 | semidirect |
| 173. C3×C5 | #555 | semidirect |
| 211. C5 | #5563 | semidirect |
| 225. C3 | #65897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×D4 | 2 |
| #91827 | 2 |
| #91819 | 2 |
| #91815 | 2 |
| #91781 | 2 |
| #91774 | 2 |
| C4×D60 | 2 |
| #91758 | 2 |
| #65897 | 3 |
| #5563 | 5 |