Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#64714 | C2 | semidirect |
| 5. #10600607 | C2 | semidirect |
| 6. #10598223 | C2 | semidirect |
| 7. #10598154 | C2 | semidirect |
| 19. #64784 | C4 | semidirect |
| 20. #64782 | C4 | semidirect |
| 274. C5 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1975 | 2 |
| #10602871 | 2 |
| C2×#64786 | 2 |
| C2×#64714 | 2 |
| #10600607 | 2 |
| #10598223 | 2 |
| #10598154 | 2 |
| #13143 | 5 |