Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 7. C2×#3990 | C4 | semidirect |
| 8. C2×D5⋊C16 | C4 | semidirect |
| 12. #64895 | C4 | semidirect |
| 14. C5×H(3,ℤ/4) | C4 | semidirect |
| 15. #64777 | C4 | semidirect |
| 88. H(3,ℤ/4) | AGL(1,𝔽5) | semidirect |
| 216. C5 | #7228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604765 | 2 |
| #10604743 | 2 |
| #10599503 | 2 |
| #7228 | 5 |