Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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. #10598042 | C2 | direct (N × H) |
| 206. C2×C5 | #1413 | semidirect |
| 235. C5 | C2×#1413 | semidirect |
| 251. C2 | #10598042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65371 | 2 |
| C2×C5×#356 | 2 |
| C2×#64768 | 2 |
| #10598042 | 2 |
| C2×#1413 | 5 |