Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D15 |
| commutator, socle | C2×C3×C5 | C22×C8 |
| Fitting | C3×C5×M32 | C2 |
| prime radical | #6817 | C4 |
| cosocle | C3×C5×C8 | C23 |
| hypercenter | M32 | D15 |
| hypocenter | C3×C5 | #504 |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C8 ◁ M32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×M32 | C2 | semidirect |
| 3. C2×C3⋊#672 | C2 | semidirect |
| 4. #91082 | C2 | semidirect |
| 5. C16×D15 | C2 | semidirect |
| 17. C5×M32 | D3 | semidirect |
| 30. C3×M32 | D5 | semidirect |
| 66. M32 | D15 | semidirect |
| 93. C3×C5 | #504 | semidirect |
| 113. C5 | #4907 | semidirect |
| 119. C3 | #65196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91790 | 2 |
| C3×C5×M32 | 2 |
| C2×C3⋊#672 | 2 |
| #91082 | 2 |
| C16×D15 | 2 |
| #65196 | 3 |
| #4907 | 5 |