Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
514 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10617206 | C2 | semidirect |
| 3. #10604663 | C2 | semidirect |
| 4. #10604647 | C2 | semidirect |
| 5. C4×#4010 | C2 | semidirect |
| 6. #10598592 | C2 | semidirect |
| 7. #10598583 | C2 | semidirect |
| 21. C5×#477 | C4 | semidirect |
| 22. #65373 | C4 | semidirect |
| 23. #65316 | C4 | semidirect |
| 26. #65132 | C4 | semidirect |
| 150. #477 | AGL(1,𝔽5) | semidirect |
| 180. C5×Q8 | #104 | semidirect |
| 360. Q8 | #4010 | semidirect |
| 402. C5 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617206 | 2 |
| #10612824 | 2 |
| #10604663 | 2 |
| #10604647 | 2 |
| C4×#4010 | 2 |
| #10598592 | 2 |
| #10598583 | 2 |
| #8970 | 5 |