Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
348 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #10601618 | C2 | semidirect |
| 4. #10601606 | C2 | semidirect |
| 6. #10601310 | C2 | semidirect |
| 7. C5×#1307 | C2 | semidirect |
| 70. #1307 | D5 | semidirect |
| 284. C5 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610796 | 2 |
| #10601618 | 2 |
| #10601612 | 2 |
| #10601606 | 2 |
| #10601599 | 2 |
| #10601310 | 2 |
| C5×#1307 | 2 |
| #10527 | 5 |