Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
226 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 70 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×Dic20 | C2 | semidirect |
| 3. C5×#3961 | C2 | semidirect |
| 4. C5×#3959 | C2 | semidirect |
| 5. C5×#3944 | C2 | semidirect |
| 16. #65484 | C5 | direct (N × H) |
| 31. C2×Dic20 | C2×C5 | semidirect |
| 35. #3961 | C2×C5 | semidirect |
| 36. #3959 | C2×C5 | semidirect |
| 37. #3944 | C2×C5 | semidirect |
| 103. C52 | #510 | semidirect |
| 150. C5 | #65484 | direct (N × H) |
| 151. C5 | C5×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#135 | 2 |
| C2×C5×Dic20 | 2 |
| C5×#3961 | 2 |
| C5×#3959 | 2 |
| C5×#3944 | 2 |
| C5×#510 | 5 |
| #65484 | 5 |