Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1614 conjugacy classes of subgroups; only the 792 normal subgroups are shown.
This group has 1614 conjugacy classes of subgroups — too many to draw. Only its 792 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. #10603773 | C2 | direct (N × H) |
| 8. C2×#4002 | C4 | semidirect |
| 10. C2×C4×#170 | C4 | semidirect |
| 29. #4002 | C2×C4 | semidirect |
| 30. C4×#170 | C2×C4 | semidirect |
| 133. C2×C5 | #1726 | semidirect |
| 155. C5 | C2×#1726 | semidirect |
| 167. C2 | #10603773 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4002 | 2 |
| C22×C4×#170 | 2 |
| C2×#64937 | 2 |
| #10603773 | 2 |
| C2×#1726 | 5 |