Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
386 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 72 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×C5×#131⋊C3 | C2 | semidirect |
| 3. C5×#520⋊C3 | C2 | semidirect |
| 4. C5×#2897 | C3 | semidirect |
| 6. C5×#994 | C4 | semidirect |
| 12. #2897⋊C3 | C5 | direct (N × H) |
| 28. C2×#131⋊C3 | C2×C5 | semidirect |
| 29. #520⋊C3 | C2×C5 | semidirect |
| 33. C5×H(5,𝔽2) | C3×C4 | semidirect |
| 52. #2897 | C3×C5 | semidirect |
| 61. #994 | C4×C5 | semidirect |
| 160. H(5,𝔽2) | C3×C4×C5 | semidirect |
| 292. C5 | #2897⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#994 | 2 |
| C2×C5×#131⋊C3 | 2 |
| C5×#520⋊C3 | 2 |
| C5×#2897 | 3 |
| C3×C5×#103 | 4 |
| #2897⋊C3 | 5 |