Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
622 conjugacy classes of subgroups.
The subgroup lattice has 126 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×D8 |
| commutator | C8 | C23×C4×C5 |
| Frattini, cosocle | C2×C8 | C24×C5 |
| socle | C2×C5 | C22×#107 |
| prime radical | C2×C5×#41 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C5 ◁ C2×C5×#41 ◁ C2×C5×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#2161 | C2 | semidirect |
| 4. C2×C5×#368 | C2 | semidirect |
| 14. #33414 | C5 | direct (N × H) |
| 30. #2161 | C2×C5 | semidirect |
| 31. C2×#368 | C2×C5 | semidirect |
| 115. C5 | #33414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#504 | 2 |
| C5×#2916 | 2 |
| C5×#2161 | 2 |
| C2×C5×#368 | 2 |
| #33414 | 5 |