Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
430 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 12. C4×C5×Q16 | C4 | semidirect |
| 13. Q16×Dic5 | C4 | semidirect |
| 16. #65162 | C4 | semidirect |
| 19. C4×Dic20 | C4 | semidirect |
| 125. C4×Q16 | AGL(1,𝔽5) | semidirect |
| 315. C5 | #12814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×Q16 | 2 |
| C2×#64908 | 2 |
| #10603849 | 2 |
| D5⋊(C4⋊C16) | 2 |
| #10598619 | 2 |
| #12814 | 5 |