Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10614670 | C2 | semidirect |
| 3. #10614046 | C2 | semidirect |
| 4. #10602512 | C2 | semidirect |
| 5. #10602392 | C2 | semidirect |
| 6. #10600359 | C2 | semidirect |
| 7. #10598124 | C2 | semidirect |
| 60. #4015 | D4 | semidirect |
| 61. #4015 | D4 | semidirect |
| 81. #3935 | D4 | semidirect |
| 82. C4×#168 | D4 | semidirect |
| 389. C5 | #10022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2631 | 2 |
| #10614670 | 2 |
| #10614046 | 2 |
| #10602512 | 2 |
| #10602392 | 2 |
| #10600359 | 2 |
| #10598124 | 2 |
| #10022 | 5 |