Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
562 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 562 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×#65323 | C2 | semidirect |
| 3. C2×#65025 | C2 | semidirect |
| 4. C5×#1471 | C2 | semidirect |
| 5. #10600766 | C2 | semidirect |
| 6. #10600763 | C2 | semidirect |
| 7. #10598171 | C2 | semidirect |
| 81. #1471 | D5 | semidirect |
| 370. C5 | #9992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614358 | 2 |
| C2×#65323 | 2 |
| C2×#65025 | 2 |
| C5×#1471 | 2 |
| #10600766 | 2 |
| #10600763 | 2 |
| #10598171 | 2 |
| #9992 | 5 |