Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 98 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. C5×C4⋊C16 | C4 | semidirect |
| 17. #64721 | C4 | semidirect |
| 18. C4⋊#672 | C4 | semidirect |
| 90. C4⋊C16 | AGL(1,𝔽5) | semidirect |
| 151. C4×C5 | #365 | semidirect |
| 218. C5 | #13185 | semidirect |
| 231. C4 | ΓL(1,𝔽81) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×ΓL(1,𝔽81) | 2 |
| #10603858 | 2 |
| C4×#3993 | 2 |
| #10600077 | 2 |
| #10598663 | 2 |
| #13185 | 5 |