Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
204 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | AGL(1,𝔽5)×S4 |
| commutator, hypocenter | C5×A4 | C2×C16 |
| Fitting | C22×C4×C5 | C4×D3 |
| socle | C23×C5 | D3×C8 |
| prime radical | C2×C5×S4 | C8 |
| cosocle | A4×#168 | C22 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. A4×#674 | C2 | semidirect |
| 3. A4⋊#674 | C2 | semidirect |
| 11. C22×#674 | D3 | semidirect |
| 41. C5×S4 | C16 | semidirect |
| 65. #674 | S4 | direct (N × H) |
| 74. C5×A4 | C2×C16 | semidirect |
| 114. S4 | #674 | direct (N × H) |
| 123. C22×C5 | D3×C16 | semidirect |
| 148. A4 | C2×#674 | semidirect |
| 172. C5 | C16×S4 | semidirect |
| 178. C22 | D3×#674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| S4×#168 | 2 |
| A4×#674 | 2 |
| A4⋊#674 | 2 |
| D4×#674 | 3 |
| D3×#674 | 4 |
| C16×S4 | 5 |