Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
300 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D3×D5 |
| commutator, socle, prime radical, cosocle | C23×C3×C5 | C23 |
| Fitting | C22×C3×C4×C5 | C22 |
| hypercenter | C22×C4 | D3×D5 |
| hypocenter | C3×C5 | #398 |
| LCS | G ▷ C23×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 177. C3×C5 | #398 | semidirect |
| 228. C5 | #4657 | semidirect |
| 243. C3 | #65269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6712 | 2 |
| C2×C5×Dic3⋊C4 | 2 |
| C2×#6669 | 2 |
| C2×#6668 | 2 |
| C3×#3963 | 2 |
| #90994 | 2 |
| #65269 | 3 |
| #4657 | 5 |