Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×C5×#427 | C2 | semidirect |
| 3. #10602756 | C2 | semidirect |
| 4. C2×#64708 | C2 | semidirect |
| 5. #10598212 | C2 | semidirect |
| 13. #65405 | C4 | semidirect |
| 14. #65404 | C4 | semidirect |
| 48. C5×#106 | D4 | semidirect |
| 57. C2×#427 | D5 | semidirect |
| 184. #106 | C22⋊D5 | semidirect |
| 289. C5 | #13002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#427 | 2 |
| #10615473 | 2 |
| #10602756 | 2 |
| C2×#64708 | 2 |
| #10598212 | 2 |
| #13002 | 5 |