Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 86 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×C5×#689 | C2 | semidirect |
| 4. C5×#4015 | C2 | semidirect |
| 5. C5×#3935 | C2 | semidirect |
| 16. #65349 | C5 | direct (N × H) |
| 33. C2×#689 | C2×C5 | semidirect |
| 35. #4015 | C2×C5 | semidirect |
| 37. #3935 | C2×C5 | semidirect |
| 102. C52 | #497 | semidirect |
| 152. C5 | #65349 | direct (N × H) |
| 153. C5 | C5×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#687 | 2 |
| C5×#4015 | 2 |
| C5×#3935 | 2 |
| C5×#497 | 5 |
| #65349 | 5 |