Finite Group DatabasebetaFinite Group DatabasebetaOrder 30420.
116 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 40 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. C5×C3⋊#10621730 | C3 | semidirect |
| 4. C3×C5×C13×C13⋊C3 | C4 | semidirect |
| 5. C3⋊#14523157 | C5 | direct (N × H) |
| 12. C5×C13×C13⋊C3 | Dic3 | semidirect |
| 13. C3×C5×C132 | C3×C4 | semidirect |
| 16. C3⋊#10621730 | C3×C5 | semidirect |
| 19. C3×C13×C13⋊C3 | C4×C5 | semidirect |
| 25. C5×C132 | C3×Dic3 | semidirect |
| 32. C3×C5×C13⋊C3 | #261 | semidirect |
| 33. C3×C132 | C3×C4×C5 | semidirect |
| 35. C13×C13⋊C3 | C5×Dic3 | semidirect |
| 52. C3×C5×C13 | Dic13⋊C3 | semidirect |
| 53. C3×C5×C13 | C3×#261 | semidirect |
| 55. C5×C13⋊C3 | C3⋊#261 | semidirect |
| 57. C132 | C3×C5×Dic3 | semidirect |
| 65. C3×C13⋊C3 | C5×#261 | semidirect |
| 74. C5×C13 | C3⋊(Dic13⋊C3) | semidirect |
| 75. C5×C13 | C3×C3⋊#261 | semidirect |
| 84. C3×C13 | C5×Dic13⋊C3 | semidirect |
| 85. C3×C13 | C3×C5×#261 | semidirect |
| 87. C13⋊C3 | C5×C3⋊#261 | semidirect |
| 98. C3×C5 | #14523157 | semidirect |
| 100. C13 | C5×C3⋊(Dic13⋊C3) | semidirect |
| 101. C13 | C3×C5×C3⋊#261 | semidirect |
| 109. C5 | C3⋊#14523157 | direct (N × H) |
| 113. C3 | C5×#14523157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D13×C13⋊C3 | 2 |
| C5×C3⋊#10621730 | 3 |
| C5×#14523157 | 3 |
| C3⋊#14523157 | 5 |
| C3×C5×C3⋊#261 | 13 |
| C5×C3⋊(Dic13⋊C3) | 13 |