Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
206 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 123 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. #10598067 | C2 | direct (N × H) |
| 12. C2×#3926 | C4 | semidirect |
| 26. #3926 | C2×C4 | semidirect |
| 101. C2×C5 | #1424 | semidirect |
| 117. C5 | C2×#1424 | semidirect |
| 127. C2 | #10598067 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#366 | 2 |
| C2×#64724 | 2 |
| C22×#3926 | 2 |
| #10598067 | 2 |
| C2×#1424 | 5 |