Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
144 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 144 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. C2×C3×C5×C32 | C2 | semidirect |
| 3. C5×#4499 | C2 | semidirect |
| 12. #67595 | C5 | direct (N × H) |
| 15. C2×C5×C32 | D3 | semidirect |
| 25. C2×C3×C32 | C2×C5 | semidirect |
| 26. #4499 | C2×C5 | semidirect |
| 60. C2×C32 | C5×D3 | semidirect |
| 113. C3×C5 | #1401 | semidirect |
| 133. C5 | #67595 | direct (N × H) |
| 139. C3 | C5×#1401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4901 | 2 |
| C2×C3×C5×C32 | 2 |
| C5×#4499 | 2 |
| C5×#1401 | 3 |
| #67595 | 5 |