Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C5×#2248 | C2 | semidirect |
| 2. #10602105 | C2 | semidirect |
| 3. #10602090 | C2 | semidirect |
| 5. #10602068 | C2 | semidirect |
| 6. #10599854 | C2 | semidirect |
| 7. C16×#168 | C2 | semidirect |
| 45. #2248 | D5 | semidirect |
| 182. C5 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2248 | 2 |
| #10602105 | 2 |
| #10602090 | 2 |
| #10602083 | 2 |
| #10602068 | 2 |
| #10599854 | 2 |
| C16×#168 | 2 |
| #12518 | 5 |