Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
662 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 280 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×#64852 | C2 | direct (N × H) |
| 12. #64852 | C22 | direct (N × H) |
| 97. C22×C5 | #368 | semidirect |
| 128. C2×C5 | C2×#368 | semidirect |
| 150. C5 | C22×#368 | semidirect |
| 155. C22 | #64852 | direct (N × H) |
| 163. C2 | C2×#64852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3996 | 2 |
| C22×D5×C16 | 2 |
| C2×#64852 | 2 |
| C22×#368 | 5 |