Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
644 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 106 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. #10604030 | C2 | semidirect |
| 5. #10598589 | C2 | semidirect |
| 17. C5×#331 | C4 | semidirect |
| 18. #64764 | C4 | semidirect |
| 19. #64705 | C4 | semidirect |
| 44. C5×C4⋊C8 | C2×C4 | semidirect |
| 46. C4⋊#168 | C2×C4 | semidirect |
| 106. #331 | AGL(1,𝔽5) | semidirect |
| 167. C4⋊C8 | C2×AGL(1,𝔽5) | semidirect |
| 278. C5 | #8920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617369 | 2 |
| #10604616 | 2 |
| #10604030 | 2 |
| D5×#331 | 2 |
| #10598589 | 2 |
| #8920 | 5 |