Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
158 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | C5⋊S4 |
| commutator, hypocenter | C5×A4 | C2×C8 |
| Frattini | C4 | C2×C5⋊S4 |
| Fitting | C22×C5×C8 | D3 |
| socle | C23×C5 | C4×D3 |
| prime radical | C2×C5⋊S4 | C4 |
| cosocle | C4×C5×A4 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×C8×A4 | C2 | semidirect |
| 3. A4⋊#168 | C2 | semidirect |
| 10. C22×C5×C8 | D3 | semidirect |
| 18. C5⋊S4 | C8 | direct (N × H) |
| 23. C8×A4 | D5 | semidirect |
| 40. C5×A4 | C2×C8 | semidirect |
| 59. C5×C8 | S4 | semidirect |
| 63. C22×C8 | D15 | semidirect |
| 78. C22×C5 | D3×C8 | semidirect |
| 102. A4 | C8×D5 | semidirect |
| 123. C8 | C5⋊S4 | direct (N × H) |
| 126. C5 | C8×S4 | semidirect |
| 132. C22 | C8×D15 | 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 |
| A4⋊#168 | 2 |
| C8×C22⋊D5 | 3 |
| C8×D15 | 4 |
| C8×S4 | 5 |