Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #10601585 | C2 | semidirect |
| 5. #10601534 | C2 | semidirect |
| 6. #10600286 | C2 | semidirect |
| 7. C4×#3939 | C2 | semidirect |
| 13. #65382 | C4 | semidirect |
| 14. #65368 | C4 | semidirect |
| 15. #65365 | C4 | semidirect |
| 16. #65359 | C4 | semidirect |
| 194. #168 | #104 | semidirect |
| 354. C5 | #9722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615021 | 2 |
| C5×#1502 | 2 |
| #10602611 | 2 |
| #10601585 | 2 |
| #10601534 | 2 |
| #10600286 | 2 |
| C4×#3939 | 2 |
| #9722 | 5 |