Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
932 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 142 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×#543 | C2 | semidirect |
| 3. C5×#4526 | C2 | semidirect |
| 10. #71897 | C5 | direct (N × H) |
| 11. C5×#543 | D3 | semidirect |
| 18. C23×C5×D3 | Q8 | semidirect |
| 26. C3×#543 | C2×C5 | semidirect |
| 28. #4526 | C2×C5 | semidirect |
| 68. #543 | C5×D3 | semidirect |
| 88. C23×D3 | C5×Q8 | semidirect |
| 163. C3×C5 | #2029 | semidirect |
| 203. C5 | #71897 | direct (N × H) |
| 217. C3 | C5×#2029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#543 | 2 |
| C5×#4955 | 2 |
| C5×#4526 | 2 |
| C5×#2029 | 3 |
| #71897 | 5 |