Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
510 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 1. C2×D5⋊M32 | C2 | semidirect |
| 3. C2×#64903 | C2 | semidirect |
| 4. #10604722 | C2 | semidirect |
| 5. #10598621 | C2 | semidirect |
| 15. C5×#466 | C4 | semidirect |
| 16. #65446 | C4 | semidirect |
| 17. #65405 | C4 | semidirect |
| 19. #65176 | C4 | semidirect |
| 58. #3990 | D4 | semidirect |
| 131. #466 | AGL(1,𝔽5) | semidirect |
| 232. C2×D5 | #360 | semidirect |
| 338. C5 | #13065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊M32 | 2 |
| #10612445 | 2 |
| C2×#64903 | 2 |
| #10604722 | 2 |
| #10598621 | 2 |
| #13065 | 5 |