Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
424 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 424 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×Q8 | C2 |
| prime radical | C2×D60 | C22 |
| hypercenter | C4×Q8 | D15 |
| hypocenter | C3×C5 | #556 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4×C5×Q8 | C2 | semidirect |
| 2. #91835 | C2 | semidirect |
| 3. #91787 | C2 | semidirect |
| 4. #91781 | C2 | semidirect |
| 7. #91758 | C2 | semidirect |
| 8. C4×Dic30 | C2 | semidirect |
| 27. C4×C5×Q8 | D3 | semidirect |
| 47. C3×C4×Q8 | D5 | semidirect |
| 116. C4×Q8 | D15 | semidirect |
| 162. C3×C5 | #556 | semidirect |
| 194. C5 | #5584 | semidirect |
| 206. C3 | #65918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| #91835 | 2 |
| #91787 | 2 |
| #91781 | 2 |
| #91764 | 2 |
| C4×D60 | 2 |
| #91758 | 2 |
| C4×Dic30 | 2 |
| #65918 | 3 |
| #5584 | 5 |