Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
268 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 75 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×#2241 | C2 | semidirect |
| 3. #10602155 | C2 | semidirect |
| 4. #10602103 | C2 | semidirect |
| 7. #10597989 | C2 | semidirect |
| 46. #2241 | D5 | semidirect |
| 189. C5 | #12512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2241 | 2 |
| #10602174 | 2 |
| #10602155 | 2 |
| #10602103 | 2 |
| #10602090 | 2 |
| #10599851 | 2 |
| #10597989 | 2 |
| #12512 | 5 |