Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 103 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×#1772 | C2 | semidirect |
| 4. #10601442 | C2 | semidirect |
| 6. #10598223 | C2 | semidirect |
| 7. #10598149 | C2 | semidirect |
| 19. #64715 | C4 | semidirect |
| 62. #1772 | D5 | semidirect |
| 274. C5 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1772 | 2 |
| C2×#64715 | 2 |
| #10601445 | 2 |
| #10601442 | 2 |
| #10600569 | 2 |
| #10598223 | 2 |
| #10598149 | 2 |
| #13136 | 5 |