Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
160 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #23778492 |
| commutator, hypocenter | C5×C132 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C3×C4 |
| prime radical | C3×C5×#11759816 | C2 |
| cosocle | C5×C13⋊D13 | C2×C32 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#16810011 | C3 | semidirect |
| 3. #23778492 | C3 | direct (N × H) |
| 4. C3×C5×#92789 | C4 | semidirect |
| 8. #16810011 | C32 | semidirect |
| 10. C5×#92789 | C3×C4 | semidirect |
| 11. C3×C5×C132 | C3×C4 | semidirect |
| 17. C3×#92789 | Dic5 | semidirect |
| 22. C5×C132 | C32×C4 | semidirect |
| 30. C3×C132 | C3×Dic5 | semidirect |
| 31. #92789 | C3×Dic5 | semidirect |
| 45. C3×C5×C13 | AGL(1,𝔽13) | semidirect |
| 46. C3×C5×C13 | AGL(1,𝔽13) | semidirect |
| 50. C132 | C32×Dic5 | semidirect |
| 67. C5×C13 | C3×AGL(1,𝔽13) | semidirect |
| 68. C5×C13 | C3×AGL(1,𝔽13) | semidirect |
| 75. C3×C13 | #63118⋊C3 | semidirect |
| 76. C3×C13 | #63118⋊C3 | semidirect |
| 88. C3×C5 | #14523147 | semidirect |
| 90. C13 | C3×#63118⋊C3 | semidirect |
| 91. C13 | C3×#63118⋊C3 | semidirect |
| 98. C5 | C3×#14523147 | semidirect |
| 101. C3 | #23778492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#11759816 | 2 |
| C3×#16810011 | 3 |
| #23778492 | 3 |
| C3×#14523147 | 5 |
| C3×#63118⋊C3 | 13 |