Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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×#2248 | C2 | semidirect |
| 2. #10602106 | C2 | semidirect |
| 3. #10602090 | C2 | semidirect |
| 4. #10602083 | C2 | semidirect |
| 5. #10602069 | C2 | semidirect |
| 6. #10599853 | C2 | semidirect |
| 7. #10597989 | C2 | semidirect |
| 45. #2248 | D5 | semidirect |
| 72. C5×C16 | D8 | semidirect |
| 73. #672 | D8 | semidirect |
| 162. C16 | #686 | semidirect |
| 188. C5 | #12519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2248 | 2 |
| #10602106 | 2 |
| #10602090 | 2 |
| #10602083 | 2 |
| #10602069 | 2 |
| #10599853 | 2 |
| #10597989 | 2 |
| #12519 | 5 |