Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 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. C5×#2148 | C2 | semidirect |
| 3. #10602869 | C2 | semidirect |
| 4. #10602230 | C2 | semidirect |
| 5. #10601512 | C2 | semidirect |
| 6. C2×#64714 | C2 | semidirect |
| 7. #10598310 | C2 | semidirect |
| 66. #3944 | D4 | semidirect |
| 70. #2148 | D5 | semidirect |
| 333. C5 | #13400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615647 | 2 |
| C5×#2148 | 2 |
| #10602869 | 2 |
| #10602230 | 2 |
| #10601512 | 2 |
| C2×#64714 | 2 |
| #10598310 | 2 |
| #13400 | 5 |