Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1078 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 2. C2×#65413 | C2 | semidirect |
| 3. C2×C5×#338 | C2 | semidirect |
| 4. #10599515 | C2 | direct (N × H) |
| 12. #65413 | C22 | semidirect |
| 14. C5×#338 | C22 | semidirect |
| 43. C2×#338 | D5 | semidirect |
| 88. #338 | C2×D5 | semidirect |
| 190. C2×C5 | #2069 | semidirect |
| 219. C5 | C2×#2069 | semidirect |
| 237. C2 | #10599515 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3955 | 2 |
| C2×#65413 | 2 |
| C2×C5×#338 | 2 |
| #10599515 | 2 |
| C2×#2069 | 5 |