Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 123 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×#1451 | C2 | semidirect |
| 3. #10601573 | C2 | semidirect |
| 5. #10600672 | C2 | semidirect |
| 7. #10600524 | C2 | semidirect |
| 63. #1451 | D5 | semidirect |
| 267. C5 | #9812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64983 | 2 |
| C5×#1451 | 2 |
| #10601573 | 2 |
| #10601567 | 2 |
| #10600672 | 2 |
| #10600669 | 2 |
| #10600524 | 2 |
| #9812 | 5 |