Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
332 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 105 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. #10600587 | C2 | semidirect |
| 5. C2×C4×#672 | C2 | semidirect |
| 6. #10598220 | C2 | semidirect |
| 7. #10598219 | C2 | semidirect |
| 19. #64784 | C4 | semidirect |
| 20. #64782 | C4 | semidirect |
| 256. C5 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1974 | 2 |
| C2×#64787 | 2 |
| #10602870 | 2 |
| #10600587 | 2 |
| C2×C4×#672 | 2 |
| #10598220 | 2 |
| #10598219 | 2 |
| #13151 | 5 |