Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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×#2253 | C2 | semidirect |
| 4. #10598070 | C2 | semidirect |
| 5. #10598001 | C2 | semidirect |
| 30. #2253 | D5 | semidirect |
| 122. C5 | #13709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2253 | 2 |
| #10599860 | 2 |
| #10598071 | 2 |
| #10598070 | 2 |
| #10598001 | 2 |
| #13709 | 5 |