Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
192 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C132 | C32×C4 |
| prime radical | C5⋊((C13⋊C3)⋊(D13⋊C3)) | C2 |
| cosocle | C5⋊(C13⋊D13) | C2×C32 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23778463 | C3 | semidirect |
| 3. #23778455 | C3 | semidirect |
| 4. #23778453 | C3 | semidirect |
| 5. C5×C13⋊C32 | C4 | semidirect |
| 10. #16810002 | C32 | semidirect |
| 12. C5×#92789 | C3×C4 | semidirect |
| 13. C5×#92788 | C3×C4 | semidirect |
| 14. C5×C13×C13⋊C3 | C3×C4 | semidirect |
| 20. C13⋊C32 | AGL(1,𝔽5) | semidirect |
| 25. C5×C132 | C32×C4 | semidirect |
| 33. #92789 | C3×AGL(1,𝔽5) | semidirect |
| 34. #92788 | C3×AGL(1,𝔽5) | semidirect |
| 35. C13×C13⋊C3 | C3×AGL(1,𝔽5) | semidirect |
| 50. C5×C13⋊C3 | AGL(1,𝔽13) | semidirect |
| 52. C132 | C32×AGL(1,𝔽5) | semidirect |
| 68. C5×C13 | C3×AGL(1,𝔽13) | semidirect |
| 79. C13⋊C3 | #63122⋊C3 | semidirect |
| 92. C13 | C3×#63122⋊C3 | semidirect |
| 101. C5 | #14523144⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊((C13⋊C3)⋊(D13⋊C3)) | 2 |
| #23778463 | 3 |
| #23778455 | 3 |
| #23778453 | 3 |
| #14523144⋊C3 | 5 |
| C3×#63122⋊C3 | 13 |