Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
384 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 69 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×#1669 | C2 | semidirect |
| 3. #10602109 | C2 | semidirect |
| 4. #10602106 | C2 | semidirect |
| 5. D4⋊#672 | C2 | semidirect |
| 6. #10597964 | C2 | semidirect |
| 7. #10597963 | C2 | semidirect |
| 60. #1669 | D5 | semidirect |
| 269. C5 | #12321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611177 | 2 |
| C5×#1669 | 2 |
| #10602109 | 2 |
| #10602106 | 2 |
| D4⋊#672 | 2 |
| #10597964 | 2 |
| #10597963 | 2 |
| #12321 | 5 |