Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2117 | C2 | semidirect |
| 3. #10602806 | C2 | semidirect |
| 4. #10602243 | C2 | semidirect |
| 5. #10602235 | C2 | semidirect |
| 6. C2×#64733 | C2 | semidirect |
| 7. #10598310 | C2 | semidirect |
| 56. C5×M32 | D4 | semidirect |
| 72. #2117 | D5 | semidirect |
| 210. M32 | C22⋊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 |
|---|---|
| #10615531 | 2 |
| C5×#2117 | 2 |
| #10602806 | 2 |
| #10602243 | 2 |
| #10602235 | 2 |
| C2×#64733 | 2 |
| #10598310 | 2 |
| #13400 | 5 |