Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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×#2240 | C2 | semidirect |
| 2. #10602177 | C2 | semidirect |
| 3. #10602152 | C2 | semidirect |
| 5. #10602067 | C2 | semidirect |
| 6. #10599851 | C2 | semidirect |
| 7. C16×#168 | C2 | semidirect |
| 49. #2240 | D5 | semidirect |
| 77. #672 | SD16 | semidirect |
| 113. #168 | D16 | semidirect |
| 200. C5 | #12503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2240 | 2 |
| #10602177 | 2 |
| #10602152 | 2 |
| #10602083 | 2 |
| #10602067 | 2 |
| #10599851 | 2 |
| C16×#168 | 2 |
| #12503 | 5 |