Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
456 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C2×D60 | C22 |
| hypercenter | C42 | D3×D5 |
| hypocenter | C3×C5 | #554 |
| 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 |
|---|---|---|
| 2. C5×#869 | C2 | semidirect |
| 3. C3×C4×Dic10 | C2 | semidirect |
| 4. #91437 | C2 | semidirect |
| 5. #91424 | C2 | semidirect |
| 7. #91390 | C2 | semidirect |
| 8. #91388 | C2 | semidirect |
| 34. C4×Dic10 | D3 | semidirect |
| 40. D60 | Q8 | semidirect |
| 55. #869 | D5 | semidirect |
| 165. C3×C5 | #554 | semidirect |
| 198. C5 | #5579 | semidirect |
| 210. C3 | #66064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D60 | 2 |
| C5×#869 | 2 |
| C3×C4×Dic10 | 2 |
| #91437 | 2 |
| #91424 | 2 |
| #91418 | 2 |
| #91390 | 2 |
| #91388 | 2 |
| #66064 | 3 |
| #5579 | 5 |