Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
532 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 110 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. #10604976 | C2 | semidirect |
| 4. #10604967 | C2 | semidirect |
| 6. #10598774 | C2 | semidirect |
| 7. #10598773 | C2 | semidirect |
| 40. C2×#688 | C8 | semidirect |
| 82. C2×C5×Q8 | C2×C8 | semidirect |
| 123. C2×#168 | C2×C8 | semidirect |
| 252. C2×Q8 | D5⋊C8 | semidirect |
| 341. C5 | #9087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617089 | 2 |
| C2×#65106 | 2 |
| #10604976 | 2 |
| #10604967 | 2 |
| #10604270 | 2 |
| #10598774 | 2 |
| #10598773 | 2 |
| #9087 | 5 |