Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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, prime radical | C2×C3×C5×#41 | C2 |
| hypercenter | C2×#41 | D15 |
| hypocenter | C3×C5 | #536 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic30 | C2 | semidirect |
| 3. #91833 | C2 | semidirect |
| 4. #91825 | C2 | semidirect |
| 5. #91824 | C2 | semidirect |
| 6. #91815 | C2 | semidirect |
| 7. #91813 | C2 | semidirect |
| 161. C3×C5 | #536 | semidirect |
| 195. C5 | #5825 | semidirect |
| 206. C3 | #66159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#41 | 2 |
| C22×Dic30 | 2 |
| #91833 | 2 |
| #91825 | 2 |
| #91824 | 2 |
| #91815 | 2 |
| #91813 | 2 |
| #66159 | 3 |
| #5825 | 5 |