Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
154 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 154 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.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×#11759813 |
| commutator, cosocle, hypocenter | C3×#92789 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C2×D3 |
| LCS | G ▷ C3×#92789 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C3⋊#11759813 | C2 | semidirect |
| 2. C5×D3×#92789 | C2 | semidirect |
| 3. C3×C5×#11759813 | C2 | semidirect |
| 6. C3×C5×#92789 | C22 | semidirect |
| 7. D3×#11759813 | C5 | direct (N × H) |
| 9. C5×D3×C132 | D3 | semidirect |
| 14. C5×#11759813 | D3 | direct (N × H) |
| 16. C3⋊#11759813 | C2×C5 | semidirect |
| 17. D3×#92789 | C2×C5 | semidirect |
| 18. C3×#11759813 | C2×C5 | semidirect |
| 20. C5×#92789 | C2×D3 | semidirect |
| 21. C3×C5×C132 | C2×D3 | semidirect |
| 27. C3×#92789 | C22×C5 | semidirect |
| 30. D3×C132 | C5×D3 | semidirect |
| 35. #11759813 | C5×D3 | direct (N × H) |
| 36. C5×C132 | D32 | semidirect |
| 41. C3×C132 | C2×C5×D3 | semidirect |
| 43. #92789 | C2×C5×D3 | semidirect |
| 66. C132 | C5×D32 | semidirect |
| 112. C5×D3 | #11759813 | direct (N × H) |
| 127. C3×C5 | C2×#11759813 | semidirect |
| 144. D3 | C5×#11759813 | direct (N × H) |
| 145. C5 | D3×#11759813 | direct (N × H) |
| 149. C3 | C2×C5×#11759813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C3⋊#11759813 | 2 |
| C5×D3×#92789 | 2 |
| C3×C5×#11759813 | 2 |
| C5×D3×C13×D13 | 3 |
| C2×C5×#11759813 | 3 |
| D3×#11759813 | 5 |
| C5×D32 | 169 |