Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10598291 | C2 | semidirect |
| 5. #10597993 | C2 | semidirect |
| 32. #2253 | D5 | semidirect |
| 130. C5 | #12463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2253 | 2 |
| #10602151 | 2 |
| #10599849 | 2 |
| #10598291 | 2 |
| #10597993 | 2 |
| #12463 | 5 |