Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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. #10602257 | C2 | semidirect |
| 2. #10602251 | C2 | semidirect |
| 3. #10600166 | C2 | semidirect |
| 4. #10600150 | C2 | semidirect |
| 5. C5×#1419 | C2 | semidirect |
| 6. #10598090 | C2 | semidirect |
| 7. #10598074 | C2 | semidirect |
| 38. Dic40 | D4 | semidirect |
| 42. D80 | D4 | semidirect |
| 51. #1419 | D5 | semidirect |
| 183. C5 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602257 | 2 |
| #10602251 | 2 |
| #10600166 | 2 |
| #10600150 | 2 |
| C5×#1419 | 2 |
| #10598090 | 2 |
| #10598074 | 2 |
| #13692 | 5 |