Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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. #10601679 | C2 | semidirect |
| 3. #10599862 | C2 | semidirect |
| 4. #10599336 | C2 | semidirect |
| 5. C5×#1333 | C2 | semidirect |
| 6. #10598006 | C2 | semidirect |
| 7. #10597959 | C2 | semidirect |
| 66. #1333 | D5 | semidirect |
| 259. C5 | #12400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611349 | 2 |
| #10601679 | 2 |
| #10599862 | 2 |
| #10599336 | 2 |
| C5×#1333 | 2 |
| #10598006 | 2 |
| #10597959 | 2 |
| #12400 | 5 |