Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
882 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 187 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×#564 | C2 | semidirect |
| 3. #10602753 | C2 | direct (N × H) |
| 4. C2×#64763 | C2 | semidirect |
| 6. C5×#564 | C22 | semidirect |
| 14. #64763 | C22 | semidirect |
| 33. C2×#564 | D5 | semidirect |
| 54. #564 | C2×D5 | semidirect |
| 114. C2×C5 | #1658 | semidirect |
| 128. C5 | C2×#1658 | semidirect |
| 137. C2 | #10602753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#564 | 2 |
| C2×#65356 | 2 |
| #10602753 | 2 |
| C2×#64763 | 2 |
| C2×#1658 | 5 |