Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
542 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 97 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×#501 | C2 | semidirect |
| 4. #10602579 | C2 | semidirect |
| 5. C2×#64763 | C2 | semidirect |
| 7. #10598150 | C2 | semidirect |
| 77. C2×#501 | D5 | semidirect |
| 355. C5 | #10086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#501 | 2 |
| C2×#65378 | 2 |
| #10614802 | 2 |
| #10602579 | 2 |
| C2×#64763 | 2 |
| C2×#64684 | 2 |
| #10598150 | 2 |
| #10086 | 5 |