Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
566 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 566 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⋊#361 | C2 | semidirect |
| 3. #10604786 | C2 | semidirect |
| 4. #10603851 | C2 | semidirect |
| 5. D5⋊#364 | C2 | semidirect |
| 13. C5×#493 | C4 | semidirect |
| 15. #65440 | C4 | semidirect |
| 17. #64984 | C4 | semidirect |
| 52. #3995 | D4 | semidirect |
| 53. #3994 | D4 | semidirect |
| 124. #493 | AGL(1,𝔽5) | semidirect |
| 311. C5 | #13261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#493 | 2 |
| D5⋊#361 | 2 |
| #10604786 | 2 |
| #10603851 | 2 |
| D5⋊#364 | 2 |
| #13261 | 5 |