Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1830 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1830 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C2×C5×#376 | C2 |
| socle, prime radical | C24×C5 | C24 |
| hypercenter | C2×#376 | D5 |
| hypocenter | C5 | C2×#2645 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10605139 | C2 | direct (N × H) |
| 151. C2×C5 | #2645 | semidirect |
| 175. C5 | C2×#2645 | semidirect |
| 187. C2 | #10605139 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#376 | 2 |
| C2×#65218 | 2 |
| C2×#65217 | 2 |
| #10605139 | 2 |
| C2×C5⋊#401 | 2 |
| C2×#64947 | 2 |
| C2×#2645 | 5 |