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 |
|---|---|---|
| 3. #10599838 | C2 | semidirect |
| 4. C5×#1373 | C2 | semidirect |
| 5. #10598064 | C2 | semidirect |
| 35. #1373 | 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 |
|---|---|
| #10600101 | 2 |
| #10599849 | 2 |
| #10599838 | 2 |
| C5×#1373 | 2 |
| #10598064 | 2 |
| #12463 | 5 |