Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
786 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C5 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C5 |
| Frattini, cosocle | C23×C4 | C23×C5 |
| prime radical | C25×C5 | C2×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C5 ◁ C24×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1280 | C2 | semidirect |
| 11. #8702 | C5 | direct (N × H) |
| 29. #1280 | C2×C5 | semidirect |
| 175. C5 | #8702 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#381 | 2 |
| C5×#1779 | 2 |
| C5×#1280 | 2 |
| #8702 | 5 |