Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 102 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×#4894 | C2 | semidirect |
| 3. C5×#4869 | C2 | semidirect |
| 4. C3×C5×#365 | C2 | semidirect |
| 5. C5×#4512 | C2 | semidirect |
| 6. C5×#4495 | C2 | semidirect |
| 7. C5×#4488 | C2 | semidirect |
| 20. C5×#800 | C4 | semidirect |
| 21. C5×D48 | C4 | semidirect |
| 22. #69310 | C5 | direct (N × H) |
| 26. C5×#365 | D3 | semidirect |
| 39. C5×Dic12 | C2×C4 | semidirect |
| 42. C5×D24 | C2×C4 | semidirect |
| 46. C3×C5×C16 | C2×C4 | semidirect |
| 49. #4894 | C2×C5 | semidirect |
| 50. #4869 | C2×C5 | semidirect |
| 51. C3×#365 | C2×C5 | semidirect |
| 52. #4512 | C2×C5 | semidirect |
| 53. #4495 | C2×C5 | semidirect |
| 54. #4488 | C2×C5 | semidirect |
| 95. #800 | C4×C5 | semidirect |
| 96. D48 | C4×C5 | semidirect |
| 114. C5×C16 | C4×D3 | semidirect |
| 118. #365 | C5×D3 | semidirect |
| 141. Dic12 | C2×C4×C5 | semidirect |
| 144. D24 | C2×C4×C5 | semidirect |
| 148. C3×C16 | C2×C4×C5 | semidirect |
| 224. C16 | C4×C5×D3 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #69310 | direct (N × H) |
| 270. C3 | C5×AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4908 | 2 |
| C5×#4894 | 2 |
| C5×#4869 | 2 |
| C3×C5×#365 | 2 |
| C5×#4512 | 2 |
| C5×#4495 | 2 |
| C5×#4488 | 2 |
| C5×AGL(1,ℤ/16) | 3 |
| #69310 | 5 |