Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#4036 | C2 | semidirect |
| 3. C52×#106 | C2 | semidirect |
| 5. C5×#3946 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 20. #65160 | C5 | direct (N × H) |
| 36. #4036 | C2×C5 | semidirect |
| 39. C5×#106 | D5 | semidirect |
| 40. C5×#106 | C2×C5 | semidirect |
| 45. #3946 | C2×C5 | semidirect |
| 47. #3939 | C2×C5 | semidirect |
| 120. #106 | C5×D5 | semidirect |
| 124. C52 | #478 | semidirect |
| 187. C5 | #65160 | direct (N × H) |
| 188. C5 | C5×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4039 | 2 |
| C5×#4036 | 2 |
| C52×#106 | 2 |
| C5×#3953 | 2 |
| C5×#3946 | 2 |
| C5×#3941 | 2 |
| C5×#3939 | 2 |
| C5×#478 | 5 |
| #65160 | 5 |