Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
148 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 28 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 | C3×C5×C132 | C3×C4 |
| prime radical | C3×C5⋊#11759817 | C2 |
| cosocle | C3×C13×D65 | C2×C3 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#16810005 | C3 | semidirect |
| 4. C3×C5×#92788 | C4 | semidirect |
| 12. C5×#92788 | Dic3 | semidirect |
| 13. C3×C5×C132 | C3×C4 | semidirect |
| 19. C3×#92788 | AGL(1,𝔽5) | semidirect |
| 25. C5×C132 | C3×Dic3 | semidirect |
| 34. C3×C132 | C3×AGL(1,𝔽5) | semidirect |
| 36. #92788 | ΓL(1,𝔽16) | semidirect |
| 51. C3×C5×C13 | Dic13⋊C3 | semidirect |
| 52. C3×C5×C13 | AGL(1,𝔽13) | semidirect |
| 60. C132 | C3×ΓL(1,𝔽16) | semidirect |
| 78. C5×C13 | C3⋊(Dic13⋊C3) | semidirect |
| 79. C5×C13 | C3⋊AGL(1,𝔽13) | semidirect |
| 86. C3×C13 | #63122⋊C3 | semidirect |
| 87. C3×C13 | #63120⋊C3 | semidirect |
| 104. C3×C5 | #14523148 | semidirect |
| 106. C13 | C3⋊(#63122⋊C3) | semidirect |
| 107. C13 | C3⋊(#63120⋊C3) | semidirect |
| 115. C5 | C3⋊#14523148 | semidirect |
| 119. C3 | #23778459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5⋊#11759817 | 2 |
| C3⋊#16810005 | 3 |
| #23778459 | 3 |
| C3⋊#14523148 | 5 |
| C3⋊(#63120⋊C3) | 13 |
| C3⋊(#63122⋊C3) | 13 |