Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2153 | C2 | semidirect |
| 4. #10602220 | C2 | semidirect |
| 6. #10600686 | C2 | semidirect |
| 7. #10598310 | C2 | semidirect |
| 57. #2153 | D5 | semidirect |
| 259. C5 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2153 | 2 |
| C2×#64738 | 2 |
| #10602241 | 2 |
| #10602220 | 2 |
| #10600690 | 2 |
| #10600686 | 2 |
| #10598310 | 2 |
| #13469 | 5 |