Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2286 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 2286 conjugacy classes of subgroups — too many to draw. Only its 555 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D5 |
| commutator | C23×C5 | C23×C4 |
| Fitting | C23×C42×C5 | C2 |
| socle, cosocle | C24×C5 | C24 |
| prime radical | C25×C5 | C23 |
| hypercenter | C23×C42 | D5 |
| hypocenter | C5 | #14684 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C23×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10602327 | C2 | semidirect |
| 8. C22×C42×C5 | C4 | semidirect |
| 63. C22×C42 | Dic5 | semidirect |
| 170. C5 | #14684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C5 | 2 |
| C2×#65500 | 2 |
| #10602920 | 2 |
| #10602327 | 2 |
| #14684 | 5 |