Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
230 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 147 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. #10598081 | C2 | direct (N × H) |
| 62. C2×Dic5 | C32 | semidirect |
| 90. Dic5 | C2×C32 | semidirect |
| 106. C2×C5 | C4⋊C32 | semidirect |
| 123. C5 | C2×C4⋊C32 | semidirect |
| 133. C2 | #10598081 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C32 | 2 |
| C2×C16×Dic5 | 2 |
| C22×#3926 | 2 |
| #10598081 | 2 |
| C2×C4⋊C32 | 5 |