Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×C5×#442 | C2 | semidirect |
| 3. C5×#4717 | C2 | semidirect |
| 4. C5×#4563 | C2 | semidirect |
| 5. C5×#4488 | C2 | semidirect |
| 6. C5×#4487 | C2 | semidirect |
| 7. C5×#4466 | C2 | semidirect |
| 16. C5×#827 | C4 | semidirect |
| 17. C5×#826 | C4 | semidirect |
| 22. #70918 | C5 | direct (N × H) |
| 25. C5×#442 | D3 | semidirect |
| 41. C5×Dic12 | C2×C4 | semidirect |
| 42. C5×D24 | C2×C4 | semidirect |
| 47. C5×C3⋊C16 | C2×C4 | semidirect |
| 48. C3×#442 | C2×C5 | semidirect |
| 50. #4717 | C2×C5 | semidirect |
| 51. #4563 | C2×C5 | semidirect |
| 52. #4488 | C2×C5 | semidirect |
| 53. #4487 | C2×C5 | semidirect |
| 54. #4466 | C2×C5 | semidirect |
| 91. #827 | C4×C5 | semidirect |
| 92. #826 | C4×C5 | semidirect |
| 117. #442 | C5×D3 | semidirect |
| 143. Dic12 | C2×C4×C5 | semidirect |
| 144. D24 | C2×C4×C5 | semidirect |
| 149. C3⋊C16 | C2×C4×C5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #70918 | 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 |
|---|---|
| C3×C5×#442 | 2 |
| C5×#5147 | 2 |
| C5×#4717 | 2 |
| C5×#4563 | 2 |
| C5×#4488 | 2 |
| C5×#4487 | 2 |
| C5×#4466 | 2 |
| C5×AGL(1,ℤ/16) | 3 |
| #70918 | 5 |