Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. C5×#1574 | C2 | semidirect |
| 5. #10601288 | C2 | semidirect |
| 6. #10598227 | C2 | semidirect |
| 7. #10598227 | C2 | semidirect |
| 23. #64705 | C4 | semidirect |
| 24. #64705 | C4 | semidirect |
| 25. #64701 | C4 | semidirect |
| 26. #64701 | C4 | semidirect |
| 69. #1574 | D5 | semidirect |
| 301. C5 | #8935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611020 | 2 |
| C5×#1574 | 2 |
| #10601566 | 2 |
| #10601305 | 2 |
| #10601288 | 2 |
| #10598227 | 2 |
| #8935 | 5 |