Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1230 conjugacy classes of subgroups; only the 456 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 456 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. #10603784 | C2 | direct (N × H) |
| 133. C2×C5 | #1843 | semidirect |
| 155. C5 | C2×#1843 | semidirect |
| 167. C2 | #10603784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4004 | 2 |
| C22×C4⋊#170 | 2 |
| C2×#64937 | 2 |
| #10603784 | 2 |
| C2×#1843 | 5 |