Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10601560 | C2 | semidirect |
| 4. #10601321 | C2 | semidirect |
| 6. #10601214 | C2 | semidirect |
| 7. C5×#1301 | C2 | semidirect |
| 68. #1301 | D5 | semidirect |
| 320. C5 | #10443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65137 | 2 |
| #10601567 | 2 |
| #10601560 | 2 |
| #10601321 | 2 |
| #10601295 | 2 |
| #10601214 | 2 |
| C5×#1301 | 2 |
| #10443 | 5 |