Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
378 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42×C5 | S4 |
| commutator, hypocenter | A4 | C4×C5×C8 |
| Frattini | C2×C4 | C2×C5×S4 |
| Fitting | C22×C42×C5 | D3 |
| socle | C24×C5 | C2×Dic3 |
| prime radical | C22×C5×A4 | C2×C4 |
| cosocle | C2×C4×A4 | C22×C5 |
| LCS | G ▷ A4 | |
| UCS | C1 ◁ C42×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C5×A4⋊C8 | C4 | direct (N × H) |
| 8. C4×A4⋊C8 | C5 | direct (N × H) |
| 15. C4×C5×A4 | C8 | semidirect |
| 41. A4⋊C8 | C4×C5 | direct (N × H) |
| 50. C22×C4×C5 | C3⋊C8 | semidirect |
| 68. C5×A4 | C4×C8 | semidirect |
| 72. C4×A4 | C5×C8 | semidirect |
| 121. C22×C5 | C4×C3⋊C8 | semidirect |
| 125. C4×C5 | A4⋊C8 | direct (N × H) |
| 134. C22×C4 | C5×C3⋊C8 | semidirect |
| 148. A4 | C4×C5×C8 | semidirect |
| 177. C5 | C4×A4⋊C8 | direct (N × H) |
| 185. C22 | C4×C5×C3⋊C8 | semidirect |
| 189. C4 | C5×A4⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5×A4 | 2 |
| C2×C5×A4⋊C8 | 2 |
| C4×C5×C22⋊C8 | 3 |
| C4×C5×C3⋊C8 | 4 |
| C4×A4⋊C8 | 5 |