Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | C5⋊S4 |
| commutator, hypocenter | C5×A4 | C42 |
| Frattini | C22 | C2×C5⋊S4 |
| Fitting | C23×C4×C5 | D3 |
| socle | C24×C5 | C2×D3 |
| prime radical, cosocle | C22×C5×A4 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C4×C5×A4 | C4 | semidirect |
| 6. A4⋊Dic5 | C4 | direct (N × H) |
| 24. C22×C4×C5 | Dic3 | semidirect |
| 34. C5×A4 | C42 | semidirect |
| 38. C4×A4 | Dic5 | semidirect |
| 76. C22×C5 | C4×Dic3 | semidirect |
| 79. C4×C5 | SL(2,ℤ/4) | semidirect |
| 88. C22×C4 | Dic15 | semidirect |
| 96. A4 | C4×Dic5 | semidirect |
| 123. C5 | C4×SL(2,ℤ/4) | semidirect |
| 131. C22 | C4×Dic15 | semidirect |
| 136. C4 | A4⋊Dic5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×A4 | 2 |
| C2×A4⋊Dic5 | 2 |
| C4×C22⋊Dic5 | 3 |
| C4×Dic15 | 4 |
| C4×SL(2,ℤ/4) | 5 |