Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
716 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 113 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×#64690 | C2 | semidirect |
| 3. #10600725 | C2 | semidirect |
| 4. #10600208 | C2 | semidirect |
| 5. C5×#1280 | C2 | semidirect |
| 53. #3963 | D4 | semidirect |
| 59. #1280 | D5 | semidirect |
| 403. C5 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10605112 | 2 |
| C2×#64690 | 2 |
| #10600725 | 2 |
| #10600208 | 2 |
| C5×#1280 | 2 |
| #10403 | 5 |