Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
158 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊(C5⋊S4) |
| commutator, cosocle | C4×C5×A4 | C22 |
| Frattini | C4 | C2×C5⋊S4 |
| Fitting | C22×C5×C8 | D3 |
| socle | C23×C5 | D12 |
| hypercenter | C8 | C5⋊S4 |
| hypocenter | C5×A4 | D8 |
| LCS | G ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊(C5⋊S4) | C2 | semidirect |
| 2. C5×C8×A4 | C2 | semidirect |
| 8. C22×C5×C8 | D3 | semidirect |
| 18. C8×A4 | D5 | semidirect |
| 30. C5×A4 | D8 | semidirect |
| 45. C5×C8 | S4 | semidirect |
| 47. C22×C8 | D15 | semidirect |
| 59. C22×C5 | D24 | semidirect |
| 77. A4 | D40 | semidirect |
| 93. C8 | C5⋊S4 | semidirect |
| 96. C5 | #5402 | semidirect |
| 102. C22 | D120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C5⋊S4) | 2 |
| C5×C8×A4 | 2 |
| #65404 | 3 |
| D120 | 4 |
| #5402 | 5 |