Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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×Q32 | C2 | semidirect |
| 3. C3×C5×Q64 | C2 | semidirect |
| 4. C5×#4522 | C2 | semidirect |
| 5. C5×#4521 | C2 | semidirect |
| 6. C5×#4449 | C2 | semidirect |
| 7. C5×#4447 | C2 | semidirect |
| 20. #69384 | C5 | direct (N × H) |
| 24. C5×Q64 | D3 | semidirect |
| 40. D3×Q32 | C2×C5 | semidirect |
| 41. C3×Q64 | C2×C5 | semidirect |
| 42. #4522 | C2×C5 | semidirect |
| 43. #4521 | C2×C5 | semidirect |
| 44. #4449 | C2×C5 | semidirect |
| 45. #4447 | C2×C5 | semidirect |
| 94. Q64 | C5×D3 | semidirect |
| 170. C3×C5 | #2264 | semidirect |
| 195. C5 | #69384 | direct (N × H) |
| 203. C3 | C5×#2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4919 | 2 |
| C5×D3×Q32 | 2 |
| C3×C5×Q64 | 2 |
| C5×#4522 | 2 |
| C5×#4521 | 2 |
| C5×#4449 | 2 |
| C5×#4447 | 2 |
| C5×#2264 | 3 |
| #69384 | 5 |