Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 94 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. C5×#5155 | C2 | semidirect |
| 3. C2×C5×#800 | C2 | semidirect |
| 4. C5×#4872 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. C5×Dic3⋊C16 | C2 | semidirect |
| 7. C5×#4492 | C2 | semidirect |
| 22. #69203 | C5 | direct (N × H) |
| 29. C5×#357 | D3 | semidirect |
| 50. #5155 | C2×C5 | semidirect |
| 52. C2×#800 | C2×C5 | semidirect |
| 53. #4872 | C2×C5 | semidirect |
| 54. C3×#357 | C2×C5 | semidirect |
| 55. Dic3⋊C16 | C2×C5 | semidirect |
| 56. #4492 | C2×C5 | semidirect |
| 127. #357 | C5×D3 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #69203 | direct (N × H) |
| 301. C3 | C5×#2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5155 | 2 |
| C2×C5×#826 | 2 |
| C2×C5×#800 | 2 |
| C5×#4872 | 2 |
| C3×C5×#357 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#4492 | 2 |
| C5×#2210 | 3 |
| #69203 | 5 |