Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
472 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 2. #10604834 | C2 | semidirect |
| 3. #10604830 | C2 | semidirect |
| 4. #10604788 | C2 | semidirect |
| 5. #10604784 | C2 | semidirect |
| 6. #10603851 | C2 | semidirect |
| 7. D5⋊#364 | C2 | semidirect |
| 17. C5×#495 | C4 | semidirect |
| 18. #65470 | C4 | semidirect |
| 20. #65440 | C4 | semidirect |
| 22. #64985 | C4 | semidirect |
| 69. #3996 | D4 | semidirect |
| 72. #3993 | D4 | semidirect |
| 163. #495 | AGL(1,𝔽5) | semidirect |
| 399. C5 | #13259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10613551 | 2 |
| #10604834 | 2 |
| #10604830 | 2 |
| #10604788 | 2 |
| #10604784 | 2 |
| #10603851 | 2 |
| D5⋊#364 | 2 |
| #13259 | 5 |