Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
422 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 115 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×#2162 | C2 | semidirect |
| 3. #10600538 | C2 | semidirect |
| 4. #10597994 | C2 | semidirect |
| 16. C4×C5×C16 | C22 | semidirect |
| 18. C4⋊#672 | C22 | semidirect |
| 48. #2162 | D5 | semidirect |
| 96. C4×C16 | C2×D5 | semidirect |
| 231. C5 | #11631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D20 | 2 |
| C5×#2162 | 2 |
| #10600538 | 2 |
| #10597994 | 2 |
| #11631 | 5 |