Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
474 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 135 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×#3407 | C2 | semidirect |
| 3. #10602800 | C2 | semidirect |
| 4. #10602231 | C2 | semidirect |
| 5. #10598301 | C2 | semidirect |
| 45. C5×M32 | D4 | semidirect |
| 56. #3407 | D5 | semidirect |
| 169. M32 | C22⋊D5 | semidirect |
| 265. C5 | #12982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3407 | 2 |
| #10615517 | 2 |
| #10602800 | 2 |
| #10602231 | 2 |
| #10598301 | 2 |
| #12982 | 5 |