Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
200 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 55 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. #10602297 | C2 | semidirect |
| 2. C2×#64741 | C2 | semidirect |
| 3. C2×#64667 | C2 | semidirect |
| 5. C5×#1416 | C2 | semidirect |
| 6. #10598087 | C2 | semidirect |
| 7. #10598066 | C2 | semidirect |
| 40. #3926 | D4 | semidirect |
| 46. #1416 | D5 | semidirect |
| 172. C5 | #13699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602297 | 2 |
| C2×#64741 | 2 |
| C2×#64667 | 2 |
| #10600120 | 2 |
| C5×#1416 | 2 |
| #10598087 | 2 |
| #10598066 | 2 |
| #13699 | 5 |