Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 1. C52×#135 | C2 | semidirect |
| 2. C5×#4050 | C2 | semidirect |
| 3. C5×#3961 | C2 | semidirect |
| 4. C5×#3960 | C2 | semidirect |
| 5. C5×#3959 | C2 | semidirect |
| 6. C5×#3958 | C2 | semidirect |
| 7. C2×C5×#672 | C2 | semidirect |
| 20. #65483 | C5 | direct (N × H) |
| 34. C5×#135 | D5 | semidirect |
| 35. C5×#135 | C2×C5 | semidirect |
| 36. #4050 | C2×C5 | semidirect |
| 42. #3961 | C2×C5 | semidirect |
| 43. #3960 | C2×C5 | semidirect |
| 44. #3959 | C2×C5 | semidirect |
| 45. #3958 | C2×C5 | semidirect |
| 46. C2×#672 | C2×C5 | semidirect |
| 116. #135 | C5×D5 | semidirect |
| 122. C52 | #508 | semidirect |
| 176. C5 | #65483 | direct (N × H) |
| 177. C5 | C5×#508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#135 | 2 |
| C5×#4050 | 2 |
| C5×#3961 | 2 |
| C5×#3960 | 2 |
| C5×#3959 | 2 |
| C5×#3958 | 2 |
| C2×C5×#672 | 2 |
| C5×#508 | 5 |
| #65483 | 5 |