Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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×#64787 | C2 | semidirect |
| 3. #10602871 | C2 | semidirect |
| 4. #10602809 | C2 | semidirect |
| 5. C2×#64781 | C2 | semidirect |
| 6. C2×#64710 | C2 | semidirect |
| 7. #10598214 | C2 | semidirect |
| 68. C2×#672 | D4 | semidirect |
| 340. C5 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3061 | 2 |
| C2×#64787 | 2 |
| #10602871 | 2 |
| #10602809 | 2 |
| C2×#64781 | 2 |
| C2×#64710 | 2 |
| #10598214 | 2 |
| #13385 | 5 |