Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. #10604723 | C2 | semidirect |
| 3. C2×#64887 | C2 | semidirect |
| 4. #10598805 | C2 | semidirect |
| 5. #10598611 | C2 | semidirect |
| 6. C2×D5×D8 | C4 | semidirect |
| 12. C5×#466 | C4 | semidirect |
| 14. #65404 | C4 | semidirect |
| 17. D5×#107 | C4 | semidirect |
| 20. #64893 | C22 | semidirect |
| 22. #64887 | C22 | semidirect |
| 120. #466 | AGL(1,𝔽5) | semidirect |
| 339. C5 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#466 | 2 |
| #10604723 | 2 |
| C2×#64887 | 2 |
| #10598805 | 2 |
| #10598611 | 2 |
| #11886 | 5 |