Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C5×#2141 | C2 | semidirect |
| 3. C2×#64785 | C2 | semidirect |
| 5. #10602220 | C2 | semidirect |
| 7. #10598216 | C2 | semidirect |
| 66. #2141 | D5 | semidirect |
| 299. C5 | #13397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615618 | 2 |
| C5×#2141 | 2 |
| C2×#64785 | 2 |
| #10602230 | 2 |
| #10602220 | 2 |
| #10601458 | 2 |
| #10598216 | 2 |
| #13397 | 5 |