Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
256 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 38 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 |
|---|---|---|
| 2. C3⋊#16810004 | C3 | direct (N × H) |
| 4. C32×C5×C132 | C4 | semidirect |
| 12. C3×C5×C132 | Dic3 | semidirect |
| 13. C3×C5×C132 | C3×C4 | semidirect |
| 19. C32×C132 | AGL(1,𝔽5) | semidirect |
| 26. C5×C132 | C3×Dic3 | semidirect |
| 33. C32×C5×C13 | #261 | semidirect |
| 34. C32×C5×C13 | #261 | semidirect |
| 36. C3×C132 | C3×AGL(1,𝔽5) | semidirect |
| 37. C3×C132 | ΓL(1,𝔽16) | semidirect |
| 60. C3×C5×C13 | C3×#261 | semidirect |
| 61. C3×C5×C13 | C3×#261 | semidirect |
| 62. C3×C5×C13 | C3⋊#261 | semidirect |
| 63. C3×C5×C13 | C3⋊#261 | semidirect |
| 65. C132 | C3×ΓL(1,𝔽16) | semidirect |
| 74. C32×C13 | #63121 | semidirect |
| 75. C32×C13 | #63122 | semidirect |
| 87. C5×C13 | C3×C3⋊#261 | semidirect |
| 88. C5×C13 | C3×C3⋊#261 | semidirect |
| 93. C32×C5 | #10621729 | semidirect |
| 99. C3×C13 | C3×#63122 | semidirect |
| 100. C3×C13 | C3×#63121 | semidirect |
| 101. C3×C13 | C3⋊#63121 | semidirect |
| 102. C3×C13 | C3⋊#63122 | semidirect |
| 113. C3×C5 | C3×#10621729 | semidirect |
| 114. C3×C5 | C3⋊#10621729 | semidirect |
| 116. C13 | C3×C3⋊#63122 | semidirect |
| 117. C13 | C3×C3⋊#63121 | semidirect |
| 121. C32 | #16810004 | semidirect |
| 125. C5 | C3×C3⋊#10621729 | semidirect |
| 128. C3 | C3×#16810004 | semidirect |
| 129. C3 | C3⋊#16810004 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5⋊(C13⋊D13) | 2 |
| C3⋊#16810004 | 3 |
| C3×#16810004 | 3 |
| C3×C3⋊#10621729 | 5 |
| C3×C3⋊#63121 | 13 |
| C3×C3⋊#63122 | 13 |