Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
628 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 114 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. C3×C5×#492 | C2 | semidirect |
| 3. C5×#5084 | C2 | semidirect |
| 4. C5×#4544 | C2 | semidirect |
| 5. C5×#4459 | C2 | semidirect |
| 9. C3×C5×C4⋊Q8 | C22 | semidirect |
| 14. C3×C4×C5×C8 | C22 | semidirect |
| 17. C5×C4⋊(C3⋊C8) | C22 | semidirect |
| 18. #71266 | C5 | direct (N × H) |
| 20. C5×#492 | D3 | semidirect |
| 42. C3×#492 | C2×C5 | semidirect |
| 43. #5084 | C2×C5 | semidirect |
| 44. #4544 | C2×C5 | semidirect |
| 45. #4459 | C2×C5 | semidirect |
| 48. C5×C4⋊Q8 | C2×D3 | semidirect |
| 56. C4×C5×C8 | C2×D3 | semidirect |
| 72. C5×D12 | SD16 | semidirect |
| 79. C3×C4⋊Q8 | C22×C5 | semidirect |
| 84. C3×C4×C8 | C22×C5 | semidirect |
| 87. C4⋊(C3⋊C8) | C22×C5 | semidirect |
| 106. #492 | C5×D3 | semidirect |
| 160. C4⋊Q8 | C2×C5×D3 | semidirect |
| 168. C4×C8 | C2×C5×D3 | semidirect |
| 187. D12 | C5×SD16 | semidirect |
| 221. C3×C5 | #1629 | semidirect |
| 261. C5 | #71266 | direct (N × H) |
| 274. C3 | C5×#1629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5717 | 2 |
| C3×C5×#492 | 2 |
| C5×#5084 | 2 |
| C5×#4544 | 2 |
| C5×#4459 | 2 |
| C5×#1629 | 3 |
| #71266 | 5 |