Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 98 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. #10603849 | C2 | semidirect |
| 4. D5⋊#364 | C2 | semidirect |
| 5. #10598629 | C2 | semidirect |
| 12. C5×#443 | C4 | semidirect |
| 13. #65485 | C4 | semidirect |
| 15. #65184 | C4 | semidirect |
| 19. #64989 | C4 | semidirect |
| 134. #443 | AGL(1,𝔽5) | semidirect |
| 338. C5 | #12820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#443 | 2 |
| #10604856 | 2 |
| #10603849 | 2 |
| D5⋊#364 | 2 |
| #10598629 | 2 |
| #12820 | 5 |