Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
716 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 109 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. C5×#1787 | C2 | semidirect |
| 4. #10602925 | C2 | semidirect |
| 6. #10598167 | C2 | semidirect |
| 7. #10598116 | C2 | semidirect |
| 14. #65520 | C4 | semidirect |
| 16. #65518 | C4 | semidirect |
| 80. #1787 | D5 | semidirect |
| 441. C5 | #9471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615799 | 2 |
| #10610333 | 2 |
| C5×#1787 | 2 |
| #10602925 | 2 |
| #10600323 | 2 |
| #10598167 | 2 |
| #10598116 | 2 |
| #9471 | 5 |