Finite Group DatabasebetaFinite Group DatabasebetaOrder 1620.
108 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 26 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⋊#4176 | C2 | semidirect |
| 2. C5×#4176 | C2 | semidirect |
| 3. D5×#731 | C2 | semidirect |
| 6. C5×#731 | C22 | semidirect |
| 14. C3×C9×D5 | D3 | semidirect |
| 20. #4176 | D5 | direct (N × H) |
| 23. C3×C5×C9 | C2×D3 | semidirect |
| 36. #731 | C2×D5 | semidirect |
| 65. C3×C9 | D3×D5 | semidirect |
| 85. D5 | #4176 | direct (N × H) |
| 99. C5 | C2×#4176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊#4176 | 2 |
| C5×#4176 | 2 |
| D5×#731 | 2 |
| D5×#272 | 3 |
| D3×C9×D5 | 3 |
| C2×#4176 | 5 |