Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
254 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 3. #10598653 | C2 | direct (N × H) |
| 7. C2×#3928 | C4 | semidirect |
| 22. #3928 | C2×C4 | semidirect |
| 88. C2×C5 | #1397 | semidirect |
| 102. C5 | C2×#1397 | semidirect |
| 110. C2 | #10598653 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3928 | 2 |
| C2×C16×Dic5 | 2 |
| #10598653 | 2 |
| C2×#1397 | 5 |