Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1254 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 331 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. C2×#64768 | C2 | direct (N × H) |
| 14. #64768 | C22 | direct (N × H) |
| 149. C22×C5 | #356 | semidirect |
| 198. C2×C5 | C2×#356 | semidirect |
| 228. C5 | C22×#356 | semidirect |
| 231. C22 | #64768 | direct (N × H) |
| 243. C2 | C2×#64768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C4⋊Q8 | 2 |
| C22×#3968 | 2 |
| C2×#64768 | 2 |
| C22×#356 | 5 |