Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
252 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 82 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×#4034 | C2 | semidirect |
| 3. C52×#106 | C2 | semidirect |
| 5. C5×#3946 | C2 | semidirect |
| 7. C5×#3940 | C2 | semidirect |
| 20. #65159 | C5 | direct (N × H) |
| 29. C5×D20 | Q8 | semidirect |
| 37. #4034 | C2×C5 | semidirect |
| 40. C5×#106 | D5 | semidirect |
| 41. C5×#106 | C2×C5 | semidirect |
| 46. #3946 | C2×C5 | semidirect |
| 48. #3940 | C2×C5 | semidirect |
| 112. D20 | C5×Q8 | semidirect |
| 123. #106 | C5×D5 | semidirect |
| 127. C52 | #476 | semidirect |
| 191. C5 | #65159 | direct (N × H) |
| 192. C5 | C5×#476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4039 | 2 |
| C5×#4034 | 2 |
| C52×#106 | 2 |
| C5×#3953 | 2 |
| C5×#3946 | 2 |
| C5×#3941 | 2 |
| C5×#3940 | 2 |
| C5×#476 | 5 |
| #65159 | 5 |