Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
256 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 23. C5×#368 | C4 | semidirect |
| 24. #64726 | C4 | semidirect |
| 25. #64713 | C4 | semidirect |
| 26. #64713 | C4 | semidirect |
| 111. #368 | AGL(1,𝔽5) | semidirect |
| 236. C5 | #13175 | 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 |
| #10604101 | 2 |
| #10604091 | 2 |
| #10604087 | 2 |
| #10600153 | 2 |
| #10598628 | 2 |
| #10598627 | 2 |
| #13175 | 5 |