Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
540 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 16. #64931 | C4 | semidirect |
| 18. C5×#333 | C4 | semidirect |
| 19. #64766 | C4 | semidirect |
| 20. #64701 | C4 | semidirect |
| 102. #333 | AGL(1,𝔽5) | direct (N × H) |
| 166. AGL(1,𝔽5) | #333 | direct (N × H) |
| 246. C5 | C4×#333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| AGL(1,𝔽5)×C4⋊Q8 | 2 |
| D5⋊#333 | 2 |
| AGL(1,𝔽5)×C4⋊C8 | 2 |
| D5×#333 | 2 |
| #10598586 | 2 |
| C4×#333 | 5 |