Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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×#366 | C4 | semidirect |
| 22. #64725 | C4 | semidirect |
| 23. #64710 | C4 | semidirect |
| 24. #64709 | C4 | semidirect |
| 92. C5×C16 | C4⋊C4 | semidirect |
| 93. #672 | C4⋊C4 | semidirect |
| 106. #366 | AGL(1,𝔽5) | semidirect |
| 211. C16 | C4⋊AGL(1,𝔽5) | semidirect |
| 242. C5 | #13174 | 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×#64845 | 2 |
| #10604082 | 2 |
| #10604076 | 2 |
| #10600119 | 2 |
| #10598622 | 2 |
| #10598621 | 2 |
| #13174 | 5 |