Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
482 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 92 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. D5⋊#362 | C2 | semidirect |
| 3. #10604832 | C2 | semidirect |
| 6. #10603851 | C2 | semidirect |
| 7. D5⋊#364 | C2 | semidirect |
| 17. C5×#495 | C4 | semidirect |
| 18. #65480 | C4 | semidirect |
| 20. #65444 | C4 | semidirect |
| 22. #64985 | C4 | semidirect |
| 166. #495 | AGL(1,𝔽5) | semidirect |
| 401. C5 | #13260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#495 | 2 |
| D5⋊#362 | 2 |
| #10604832 | 2 |
| D5⋊#361 | 2 |
| #10604786 | 2 |
| #10603851 | 2 |
| D5⋊#364 | 2 |
| #13260 | 5 |