Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D5 |
| commutator, socle, cosocle | C23×C5 | C25 |
| Fitting | C5×#2845 | C2 |
| prime radical | C23×D5 | C24 |
| hypercenter | #2845 | D5 |
| hypocenter | C5 | C2×#2845 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#2845 | C2 | semidirect |
| 3. #10609675 | C2 | semidirect |
| 5. #10605950 | C2 | semidirect |
| 46. #2845 | D5 | direct (N × H) |
| 157. D5 | #2845 | direct (N × H) |
| 176. C5 | C2×#2845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2845 | 2 |
| D5×#398 | 2 |
| #10609675 | 2 |
| D5×#382 | 2 |
| #10605950 | 2 |
| C2×#2845 | 5 |