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×#64736 | C2 | semidirect |
| 3. #10602231 | C2 | semidirect |
| 4. #10601458 | C2 | semidirect |
| 5. #10601445 | C2 | semidirect |
| 6. #10601443 | C2 | semidirect |
| 7. C5×#1384 | C2 | semidirect |
| 60. C2×#672 | D4 | semidirect |
| 69. #1384 | 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 |
|---|---|
| #10610914 | 2 |
| C2×#64736 | 2 |
| #10602231 | 2 |
| #10601458 | 2 |
| #10601445 | 2 |
| #10601443 | 2 |
| C5×#1384 | 2 |
| #13396 | 5 |