Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
490 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #10615511 | C2 | semidirect |
| 3. C5×#1812 | C2 | semidirect |
| 4. #10601445 | C2 | semidirect |
| 5. #10598216 | C2 | semidirect |
| 12. #65424 | C4 | semidirect |
| 49. C2×#672 | D4 | semidirect |
| 53. #1812 | D5 | semidirect |
| 233. C5 | #13074 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615530 | 2 |
| #10615511 | 2 |
| C5×#1812 | 2 |
| #10601445 | 2 |
| #10598216 | 2 |
| #13074 | 5 |