Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×C5×#361 | C2 | semidirect |
| 3. #10602826 | C2 | semidirect |
| 4. #10602231 | C2 | semidirect |
| 5. #10601512 | C2 | semidirect |
| 6. #10601478 | C2 | semidirect |
| 7. #10598309 | C2 | semidirect |
| 62. C2×#672 | D4 | semidirect |
| 65. C2×#361 | D5 | semidirect |
| 307. C5 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615567 | 2 |
| C2×C5×#361 | 2 |
| #10602826 | 2 |
| #10602231 | 2 |
| #10601512 | 2 |
| #10601478 | 2 |
| #10598309 | 2 |
| #13396 | 5 |