Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. C2×C4×C5×C16 | C2 | semidirect |
| 5. #10600587 | C2 | semidirect |
| 6. #10598299 | C2 | semidirect |
| 7. #10598298 | C2 | semidirect |
| 21. #64729 | C4 | semidirect |
| 22. #64723 | C4 | semidirect |
| 57. C2×C4×C16 | D5 | semidirect |
| 256. C5 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C16 | 2 |
| C2×#64730 | 2 |
| #10602205 | 2 |
| #10600588 | 2 |
| #10600587 | 2 |
| #10598299 | 2 |
| #10598298 | 2 |
| #13151 | 5 |