Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
520 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C5×#3067 | C2 | semidirect |
| 2. #10615625 | C2 | semidirect |
| 3. #10615536 | C2 | semidirect |
| 4. C2×#64787 | C2 | semidirect |
| 5. #10602797 | C2 | semidirect |
| 6. C2×#64717 | C2 | semidirect |
| 7. #10598222 | C2 | semidirect |
| 91. #3067 | D5 | semidirect |
| 420. C5 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3067 | 2 |
| #10615625 | 2 |
| #10615536 | 2 |
| C2×#64787 | 2 |
| #10602797 | 2 |
| C2×#64717 | 2 |
| #10598222 | 2 |
| #13312 | 5 |