Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
458 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 3. D5⋊#362 | C2 | semidirect |
| 4. C2×#64908 | C2 | semidirect |
| 6. #10598629 | C2 | semidirect |
| 7. #10598625 | C2 | semidirect |
| 21. C5×#473 | C4 | semidirect |
| 23. #65481 | C4 | semidirect |
| 24. #65432 | C4 | semidirect |
| 25. #65185 | C4 | semidirect |
| 174. #473 | AGL(1,𝔽5) | semidirect |
| 415. C5 | #13072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#504 | 2 |
| D5×#473 | 2 |
| D5⋊#362 | 2 |
| C2×#64908 | 2 |
| #10604782 | 2 |
| #10598629 | 2 |
| #10598625 | 2 |
| #13072 | 5 |