Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
450 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10601573 | C2 | semidirect |
| 5. #10601533 | C2 | semidirect |
| 6. #10601309 | C2 | semidirect |
| 7. #10601300 | C2 | semidirect |
| 275. C5 | #9769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65359 | 2 |
| C5×#1545 | 2 |
| #10602552 | 2 |
| #10601573 | 2 |
| #10601533 | 2 |
| #10601309 | 2 |
| #10601300 | 2 |
| #9769 | 5 |