Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10604119 | C2 | semidirect |
| 4. #10604058 | C2 | semidirect |
| 6. #10598671 | C2 | semidirect |
| 7. #10598606 | C2 | semidirect |
| 27. C5×#360 | C4 | semidirect |
| 28. #64786 | C4 | semidirect |
| 29. #64738 | C4 | semidirect |
| 30. #64708 | C4 | semidirect |
| 161. #360 | AGL(1,𝔽5) | semidirect |
| 362. C5 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5⋊#444 | 2 |
| #10604858 | 2 |
| #10604119 | 2 |
| #10604058 | 2 |
| #10600044 | 2 |
| #10598671 | 2 |
| #10598606 | 2 |
| #12944 | 5 |