Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 118 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×#4872 | C2 | semidirect |
| 3. C3×C5×#366 | C2 | semidirect |
| 4. C5×Dic3×C16 | C2 | semidirect |
| 5. C5×#4491 | C2 | semidirect |
| 14. C5×D48 | C4 | semidirect |
| 15. #69317 | C5 | direct (N × H) |
| 18. C5×#366 | D3 | semidirect |
| 29. C5×D24 | C2×C4 | semidirect |
| 30. C3×C5×C16 | C2×C4 | semidirect |
| 33. #4872 | C2×C5 | semidirect |
| 34. C3×#366 | C2×C5 | semidirect |
| 35. Dic3×C16 | C2×C5 | semidirect |
| 36. #4491 | C2×C5 | semidirect |
| 64. D48 | C4×C5 | semidirect |
| 75. C5×C16 | C4×D3 | semidirect |
| 78. #366 | C5×D3 | semidirect |
| 89. C5×Dic3 | D16 | semidirect |
| 98. D24 | C2×C4×C5 | semidirect |
| 99. C3×C16 | C2×C4×C5 | semidirect |
| 154. C16 | C4×C5×D3 | semidirect |
| 155. C3×C5 | C4×D16 | semidirect |
| 164. Dic3 | C5×D16 | semidirect |
| 184. C5 | #69317 | direct (N × H) |
| 194. C3 | C4×C5×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D48 | 2 |
| C5×#4872 | 2 |
| C3×C5×#366 | 2 |
| C5×Dic3×C16 | 2 |
| C5×#4491 | 2 |
| C4×C5×D16 | 3 |
| #69317 | 5 |