Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
652 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4×C5×#99 | C2 | semidirect |
| 3. #10602395 | C2 | semidirect |
| 4. #10597980 | C2 | semidirect |
| 9. C2×#4020 | C4 | semidirect |
| 14. #65249 | C4 | semidirect |
| 16. C4×C4⋊Dic5 | C4 | semidirect |
| 53. C4×#99 | D5 | semidirect |
| 332. C5 | #11776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614109 | 2 |
| C4×C5×#99 | 2 |
| #10602395 | 2 |
| #10597980 | 2 |
| #11776 | 5 |