Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
220 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 95 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. C5×#1370 | C2 | semidirect |
| 5. #10598045 | C2 | semidirect |
| 6. #10598045 | C2 | semidirect |
| 7. #10597931 | C2 | semidirect |
| 49. #1370 | D5 | semidirect |
| 198. C5 | #12014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10600068 | 2 |
| #10600067 | 2 |
| #10598840 | 2 |
| C5×#1370 | 2 |
| #10598045 | 2 |
| #10597931 | 2 |
| #12014 | 5 |