Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
558 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 117. C2×C4×C5 | Q32 | semidirect |
| 240. C2×C4 | #3961 | semidirect |
| 250. C5 | #13330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#494 | 2 |
| C22×#3961 | 2 |
| C2×#64784 | 2 |
| #10600568 | 2 |
| #10598148 | 2 |
| #13330 | 5 |