Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 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. C2×#64847 | C2 | semidirect |
| 4. #10604087 | C2 | semidirect |
| 6. #10598661 | C2 | semidirect |
| 7. #10598628 | C2 | semidirect |
| 25. C5×#359 | C4 | semidirect |
| 26. #64787 | C4 | semidirect |
| 27. #64730 | C4 | semidirect |
| 28. #64717 | C4 | semidirect |
| 147. #359 | AGL(1,𝔽5) | semidirect |
| 329. C5 | #12948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617444 | 2 |
| D5⋊#360 | 2 |
| C2×#64847 | 2 |
| #10604087 | 2 |
| #10600034 | 2 |
| #10598661 | 2 |
| #10598628 | 2 |
| #12948 | 5 |