Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
864 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 864 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 |
|---|---|---|
| 4. C2×#64759 | C2 | semidirect |
| 5. #10598128 | C2 | semidirect |
| 7. C2×C5×#123 | C4 | semidirect |
| 9. C22×C5×C22⋊C4 | C4 | semidirect |
| 13. C5×#386 | C4 | semidirect |
| 17. C5×#379 | C4 | semidirect |
| 155. C2×#123 | Dic5 | semidirect |
| 157. C22×C22⋊C4 | Dic5 | semidirect |
| 165. #386 | Dic5 | semidirect |
| 170. #379 | Dic5 | semidirect |
| 330. C22×C5 | #352 | semidirect |
| 506. C5 | #13080 | semidirect |
| 540. C22 | #64759 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2405 | 2 |
| C22×#3965 | 2 |
| #10602923 | 2 |
| C2×#64759 | 2 |
| #10598128 | 2 |
| #13080 | 5 |