Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
2190 conjugacy classes of subgroups.
The subgroup lattice has 500 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 | #95 |
| 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 |
|---|---|---|
| 4. C2×C5×#344 | C2 | direct (N × H) |
| 13. C22×C5×M16 | C4 | semidirect |
| 14. C22×C5×M16 | C4 | semidirect |
| 15. C22×C5×M16 | C4 | semidirect |
| 19. C23×C5×C8 | C4 | semidirect |
| 27. C5×#344 | C22 | direct (N × H) |
| 28. C22×#344 | C5 | direct (N × H) |
| 58. C2×C5×M16 | C2×C4 | semidirect |
| 59. C2×C5×M16 | C2×C4 | semidirect |
| 60. C2×C5×M16 | C2×C4 | semidirect |
| 68. C22×C5×C8 | C2×C4 | semidirect |
| 83. C2×#344 | C2×C5 | direct (N × H) |
| 144. C5×M16 | C22×C4 | semidirect |
| 150. C2×C5×C8 | C22×C4 | semidirect |
| 165. C22×M16 | C4×C5 | semidirect |
| 166. C22×M16 | C4×C5 | semidirect |
| 167. C22×M16 | C4×C5 | semidirect |
| 171. C23×C8 | C4×C5 | semidirect |
| 179. #344 | C22×C5 | direct (N × H) |
| 270. C2×M16 | C2×C4×C5 | semidirect |
| 271. C2×M16 | C2×C4×C5 | semidirect |
| 272. C2×M16 | C2×C4×C5 | semidirect |
| 280. C22×C8 | C2×C4×C5 | semidirect |
| 303. C22×C5 | #344 | direct (N × H) |
| 380. M16 | C22×C4×C5 | semidirect |
| 386. C2×C8 | C22×C4×C5 | semidirect |
| 399. C2×C5 | C2×#344 | direct (N × H) |
| 462. C5 | C22×#344 | direct (N × H) |
| 474. C22 | C5×#344 | direct (N × H) |
| 497. C2 | C2×C5×#344 | 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 |
| C2×C5×#344 | 2 |
| C22×#344 | 5 |