Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
346 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 15. #64889 | C4 | semidirect |
| 16. #64861 | C4 | semidirect |
| 19. C5×#364 | C4 | semidirect |
| 20. #64731 | C4 | semidirect |
| 21. #64683 | C4 | semidirect |
| 98. #364 | AGL(1,𝔽5) | semidirect |
| 218. C5 | #12659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604114 | 2 |
| C4×#3992 | 2 |
| D5⋊#364 | 2 |
| D5×#364 | 2 |
| #10598671 | 2 |
| #12659 | 5 |