Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 124 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#64846 | C2 | semidirect |
| 5. #10598660 | C2 | semidirect |
| 16. C22⋊#674 | C4 | semidirect |
| 17. #64887 | C4 | semidirect |
| 19. C5×C22⋊C16 | C4 | semidirect |
| 20. C22⋊#672 | C4 | semidirect |
| 21. #64727 | C4 | semidirect |
| 44. C2×#674 | C2×C4 | semidirect |
| 51. C2×C5×C16 | C2×C4 | semidirect |
| 52. C2×#672 | C2×C4 | semidirect |
| 118. C22⋊C16 | AGL(1,𝔽5) | semidirect |
| 185. C2×C16 | C2×AGL(1,𝔽5) | semidirect |
| 192. C22×C5 | #347 | semidirect |
| 200. C2×D5 | #347 | semidirect |
| 300. C5 | #12605 | semidirect |
| 312. C22 | #64846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3992 | 2 |
| #10604706 | 2 |
| C2×#64846 | 2 |
| #10599899 | 2 |
| #10598660 | 2 |
| #12605 | 5 |