Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
354 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#64733 | C2 | semidirect |
| 4. #10600633 | C2 | semidirect |
| 6. C5×#1377 | C2 | semidirect |
| 7. #10598307 | C2 | semidirect |
| 20. #64736 | C4 | semidirect |
| 60. #1377 | D5 | semidirect |
| 252. C5 | #13138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64736 | 2 |
| C2×#64733 | 2 |
| #10600633 | 2 |
| #10600618 | 2 |
| C5×#1377 | 2 |
| #10598307 | 2 |
| #13138 | 5 |