Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
540 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 540 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×C5×C4⋊Q8 | C2 |
| prime radical | C2×#6821 | C2 |
| hypercenter | C4⋊Q8 | D15 |
| hypocenter | C3×C5 | #536 |
| 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 |
|---|---|---|
| 2. C2×Q8×D15 | C2 | semidirect |
| 3. C3×C5×C4⋊Q8 | C2 | semidirect |
| 4. #91836 | C2 | semidirect |
| 5. #91833 | C2 | semidirect |
| 6. #91785 | C2 | semidirect |
| 7. #91783 | C2 | semidirect |
| 8. #91764 | C2 | semidirect |
| 9. #91761 | C2 | semidirect |
| 33. C5×C4⋊Q8 | D3 | semidirect |
| 60. C3×C4⋊Q8 | D5 | semidirect |
| 139. C4⋊Q8 | D15 | semidirect |
| 198. C3×C5 | #536 | semidirect |
| 237. C5 | #5724 | semidirect |
| 250. C3 | #66058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6821 | 2 |
| C2×Q8×D15 | 2 |
| C3×C5×C4⋊Q8 | 2 |
| #91836 | 2 |
| #91833 | 2 |
| #91785 | 2 |
| #91783 | 2 |
| #91764 | 2 |
| #91761 | 2 |
| #66058 | 3 |
| #5724 | 5 |