Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
338 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 3. C2×ΓL(1,𝔽81) | C2 | semidirect |
| 4. #10604072 | C2 | semidirect |
| 6. #10598660 | C2 | semidirect |
| 7. #10598622 | C2 | semidirect |
| 21. C5×#358 | C4 | semidirect |
| 22. #64784 | C4 | semidirect |
| 23. #64729 | C4 | semidirect |
| 24. #64711 | C4 | semidirect |
| 121. #358 | AGL(1,𝔽5) | semidirect |
| 289. C5 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10604844 | 2 |
| C2×#64907 | 2 |
| C2×ΓL(1,𝔽81) | 2 |
| #10604072 | 2 |
| #10600014 | 2 |
| #10598660 | 2 |
| #10598622 | 2 |
| #13143 | 5 |