Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×C5×SD32 | C2 | semidirect |
| 2. #10615605 | C2 | semidirect |
| 3. C2×#65468 | C2 | semidirect |
| 5. #10602826 | C2 | semidirect |
| 6. #10602271 | C2 | semidirect |
| 7. #10602268 | C2 | semidirect |
| 8. #10602205 | C2 | semidirect |
| 9. #10602194 | C2 | semidirect |
| 21. Q16×Dic5 | C22 | semidirect |
| 22. C2×#3961 | C22 | semidirect |
| 24. C2×#3960 | C22 | semidirect |
| 32. #64729 | C22 | semidirect |
| 33. #64723 | C22 | semidirect |
| 34. #64721 | C22 | semidirect |
| 41. C2×C5×Q16 | D4 | semidirect |
| 79. C22×SD32 | D5 | semidirect |
| 200. C2×Q16 | C22⋊D5 | semidirect |
| 332. C5 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×SD32 | 2 |
| #10615605 | 2 |
| C2×#65468 | 2 |
| #10615561 | 2 |
| #10602826 | 2 |
| #10602271 | 2 |
| #10602268 | 2 |
| #10602205 | 2 |
| #10602194 | 2 |
| #33587 | 5 |