Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
316 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 316 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. #10602222 | C2 | semidirect |
| 6. #10600694 | C2 | semidirect |
| 7. #10598311 | C2 | semidirect |
| 55. #2153 | D5 | semidirect |
| 242. C5 | #13472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2153 | 2 |
| C2×#64736 | 2 |
| #10602222 | 2 |
| #10600696 | 2 |
| #10600694 | 2 |
| #10598311 | 2 |
| #13472 | 5 |