Finite Group DatabasebetaFinite Group DatabasebetaOrder 1620.
448 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊#1113 |
| commutator, cosocle, hypocenter | C34 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C22 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C3⋊(C3⋊D3) | C2 | semidirect |
| 2. C32×C5×C3⋊D3 | C2 | semidirect |
| 5. C34×C5 | C22 | semidirect |
| 6. C3⋊#1113 | C5 | direct (N × H) |
| 7. C5×C3⋊(C3⋊D3) | D3 | semidirect |
| 11. C3×C5×C3⋊D3 | D3 | semidirect |
| 17. C3×C3⋊(C3⋊D3) | C2×C5 | semidirect |
| 18. C32×C3⋊D3 | C2×C5 | semidirect |
| 22. C33×C5 | C2×D3 | semidirect |
| 23. C33×C5 | C2×D3 | semidirect |
| 30. C5×C3⋊D3 | C3⋊D3 | semidirect |
| 36. C34 | C22×C5 | semidirect |
| 39. C3⋊(C3⋊D3) | C5×D3 | semidirect |
| 43. C3×C3⋊D3 | C5×D3 | semidirect |
| 52. C32×C5 | D32 | semidirect |
| 53. C32×C5 | D32 | semidirect |
| 54. C32×C5 | C2×C3⋊D3 | semidirect |
| 68. C33 | C2×C5×D3 | semidirect |
| 69. C33 | C2×C5×D3 | semidirect |
| 75. C3⋊D3 | C5×C3⋊D3 | semidirect |
| 84. C3×C5 | D3×C3⋊D3 | semidirect |
| 85. C3×C5 | #1113 | semidirect |
| 96. C32 | C5×D32 | semidirect |
| 97. C32 | C5×D32 | semidirect |
| 98. C32 | C2×C5×C3⋊D3 | semidirect |
| 106. C5 | C3⋊#1113 | direct (N × H) |
| 111. C3 | C5×D3×C3⋊D3 | semidirect |
| 112. C3 | C5×#1113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C3⋊(C3⋊D3) | 2 |
| C32×C5×C3⋊D3 | 2 |
| C5×#1113 | 3 |
| C5×D3×C3⋊D3 | 3 |
| C3⋊#1113 | 5 |