Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
540 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2140 | C2 | semidirect |
| 3. C2×#64783 | C2 | semidirect |
| 4. C2×#64736 | C2 | semidirect |
| 5. #10601455 | C2 | semidirect |
| 6. #10601445 | C2 | semidirect |
| 7. #10598301 | C2 | semidirect |
| 54. C5×#107 | D4 | semidirect |
| 68. #2140 | D5 | semidirect |
| 200. #107 | C22⋊D5 | semidirect |
| 308. C5 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65440 | 2 |
| C5×#2140 | 2 |
| C2×#64783 | 2 |
| C2×#64736 | 2 |
| #10601455 | 2 |
| #10601445 | 2 |
| #10598301 | 2 |
| #13413 | 5 |