Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
572 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 110 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×D3×#99 | C2 | semidirect |
| 3. C3×C5×#354 | C2 | semidirect |
| 4. C5×#4541 | C2 | semidirect |
| 5. C5×#4474 | C2 | semidirect |
| 7. C2×C5×#239 | C4 | semidirect |
| 10. C5×#947 | C4 | semidirect |
| 15. C5×#874 | C4 | semidirect |
| 16. C5×#872 | C4 | semidirect |
| 20. #69157 | C5 | direct (N × H) |
| 24. C5×#354 | D3 | semidirect |
| 27. C2×C3×C5×Q8 | C2×C4 | semidirect |
| 36. C2×C5×D12 | C2×C4 | semidirect |
| 42. C3×C42×C5 | C2×C4 | semidirect |
| 48. C4×C5×Dic3 | C2×C4 | semidirect |
| 50. D3×#99 | C2×C5 | semidirect |
| 51. C3×#354 | C2×C5 | semidirect |
| 52. #4541 | C2×C5 | semidirect |
| 53. #4474 | C2×C5 | semidirect |
| 93. C2×#239 | C4×C5 | semidirect |
| 96. #947 | C4×C5 | semidirect |
| 101. #874 | C4×C5 | semidirect |
| 102. #872 | C4×C5 | semidirect |
| 108. C2×C5×Q8 | C4×D3 | semidirect |
| 128. C42×C5 | C4×D3 | semidirect |
| 132. #354 | C5×D3 | semidirect |
| 153. C2×C3×Q8 | C2×C4×C5 | semidirect |
| 162. C2×D12 | C2×C4×C5 | semidirect |
| 168. C3×C42 | C2×C4×C5 | semidirect |
| 174. C4×Dic3 | C2×C4×C5 | semidirect |
| 264. C2×Q8 | C4×C5×D3 | semidirect |
| 284. C42 | C4×C5×D3 | semidirect |
| 285. C3×C5 | #2127 | semidirect |
| 341. C5 | #69157 | direct (N × H) |
| 360. C3 | C5×#2127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5674 | 2 |
| C5×D3×#99 | 2 |
| C3×C5×#354 | 2 |
| C5×#4541 | 2 |
| C5×#4474 | 2 |
| C5×#2127 | 3 |
| #69157 | 5 |