Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
294 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 21. C5×C4⋊C16 | C4 | semidirect |
| 22. #64721 | C4 | semidirect |
| 23. #64721 | C4 | semidirect |
| 24. C4⋊#672 | C4 | semidirect |
| 113. C4⋊C16 | AGL(1,𝔽5) | semidirect |
| 254. C5 | #13184 | 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 |
| C2×#64847 | 2 |
| C4×#3995 | 2 |
| #10603849 | 2 |
| #10600077 | 2 |
| #10598663 | 2 |
| #13184 | 5 |