Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2190 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C5 | C22⋊C4 |
| commutator | C22 | C22×C42×C5 |
| Frattini, cosocle | C22×C4 | C24×C5 |
| socle | C23×C5 | C2×C22⋊C4 |
| prime radical | C25×C5 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C5 ◁ C24×C4×C5 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C5×#1742 | C2 | direct (N × H) |
| 4. C2×C5×#343 | C2 | semidirect |
| 9. C22×C5×M16 | C4 | semidirect |
| 21. C5×#343 | C22 | semidirect |
| 22. C2×#1742 | C5 | direct (N × H) |
| 42. C2×C5×M16 | C2×C4 | semidirect |
| 64. #1742 | C2×C5 | direct (N × H) |
| 65. C2×#343 | C2×C5 | semidirect |
| 121. C22×M16 | C4×C5 | semidirect |
| 133. #343 | C22×C5 | semidirect |
| 198. C2×M16 | C2×C4×C5 | semidirect |
| 295. C2×C5 | #1742 | direct (N × H) |
| 343. C5 | C2×#1742 | direct (N × H) |
| 370. C2 | C5×#1742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×M16 | 2 |
| C22×C5×#117 | 2 |
| C5×#1742 | 2 |
| C2×C5×#343 | 2 |
| C2×#1742 | 5 |