Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
296 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 13. #64886 | C4 | semidirect |
| 15. C4×#674 | C4 | semidirect |
| 18. C5×#364 | C4 | semidirect |
| 19. #64731 | C4 | semidirect |
| 20. #64683 | C4 | semidirect |
| 88. #364 | AGL(1,𝔽5) | semidirect |
| 201. C5 | #12667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604115 | 2 |
| #10603851 | 2 |
| C4×#3990 | 2 |
| D5×#364 | 2 |
| #10598672 | 2 |
| #12667 | 5 |