Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
500 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 16. #64768 | C4 | direct (N × H) |
| 175. C4×C5 | #356 | semidirect |
| 249. C5 | C4×#356 | semidirect |
| 265. C4 | #64768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×C4⋊Q8 | 2 |
| C2×#64768 | 2 |
| C4×#3968 | 2 |
| #10598135 | 2 |
| C4×#356 | 5 |