Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
476 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D3×D5 |
| commutator, socle, cosocle | C23×C3×C5 | C23 |
| Fitting | C24×C3×C5 | C22 |
| prime radical | C22×C5×#67 | C2 |
| hypercenter | C24 | D3×D5 |
| hypocenter | C3×C5 | #394 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#6719 | C2 | semidirect |
| 3. C2×C3×C22⋊Dic5 | C2 | semidirect |
| 4. C2×#6668 | C2 | semidirect |
| 5. C2×(C2×D3)⋊Dic5 | C2 | semidirect |
| 6. C2×(C2×D3)⋊Dic5 | C2 | semidirect |
| 7. #90994 | C2 | semidirect |
| 29. C2×C22⋊Dic5 | D3 | semidirect |
| 62. C2×C3×Dic5 | D4 | semidirect |
| 157. C2×Dic5 | #67 | semidirect |
| 246. C3×C5 | #394 | semidirect |
| 322. C5 | #4961 | semidirect |
| 349. C3 | #65511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#67 | 2 |
| C2×#6719 | 2 |
| C2×C3×C22⋊Dic5 | 2 |
| C2×#6668 | 2 |
| C2×(C2×D3)⋊Dic5 | 2 |
| #90994 | 2 |
| #65511 | 3 |
| #4961 | 5 |