Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
468 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 132 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 | C22×D3×D5 |
| commutator, socle, cosocle | C22×C3×C5 | C24 |
| Fitting | C3×C42×C5 | C22 |
| prime radical | #91466 | C2 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #529 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C42×D15 | C2 | semidirect |
| 2. C5×#875 | C2 | semidirect |
| 3. C3×#4016 | C2 | semidirect |
| 5. #91435 | C2 | semidirect |
| 6. #91406 | C2 | semidirect |
| 7. #91400 | C2 | semidirect |
| 8. #91383 | C2 | semidirect |
| 9. #91367 | C2 | semidirect |
| 10. #91355 | C2 | semidirect |
| 11. #91344 | C2 | semidirect |
| 47. #4016 | D3 | semidirect |
| 75. #875 | D5 | semidirect |
| 231. C3×C5 | #529 | semidirect |
| 276. C5 | #5691 | semidirect |
| 293. C3 | #66014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×D15 | 2 |
| C5×#875 | 2 |
| C3×#4016 | 2 |
| #91466 | 2 |
| #91435 | 2 |
| #91406 | 2 |
| #91400 | 2 |
| #91383 | 2 |
| #91367 | 2 |
| #91355 | 2 |
| #91344 | 2 |
| #66014 | 3 |
| #5691 | 5 |