Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #10601564 | C2 | semidirect |
| 5. #10601308 | C2 | semidirect |
| 6. C5×#1299 | C2 | semidirect |
| 7. #10598156 | C2 | semidirect |
| 23. #65004 | C4 | semidirect |
| 24. #65003 | C4 | semidirect |
| 25. #64992 | C4 | semidirect |
| 26. #64991 | C4 | semidirect |
| 95. #1299 | D5 | semidirect |
| 371. C5 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610785 | 2 |
| #10610270 | 2 |
| #10601581 | 2 |
| #10601564 | 2 |
| #10601308 | 2 |
| C5×#1299 | 2 |
| #10598156 | 2 |
| #8998 | 5 |