Finite Group DatabasebetaFinite Group DatabasebetaOrder 1620.
348 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #1113 |
| commutator, cosocle, hypocenter | C33 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C3×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C5×C3⋊D3 | C2 | semidirect |
| 2. C5×#1113 | C3 | direct (N × H) |
| 4. C34×C5 | C22 | semidirect |
| 5. C3×#1113 | C5 | direct (N × H) |
| 7. C3×C5×C3⋊D3 | D3 | semidirect |
| 8. C3×C5×C3⋊D3 | C2×C3 | semidirect |
| 13. C32×C3⋊D3 | C2×C5 | semidirect |
| 19. C33×C5 | C2×D3 | semidirect |
| 20. C33×C5 | C22×C3 | semidirect |
| 21. #1113 | C3×C5 | direct (N × H) |
| 24. C5×C3⋊D3 | C3×D3 | semidirect |
| 31. C34 | C22×C5 | semidirect |
| 35. C3×C3⋊D3 | C5×D3 | semidirect |
| 36. C3×C3⋊D3 | C2×C3×C5 | semidirect |
| 50. C32×C5 | D32 | semidirect |
| 51. C32×C5 | C2×C3×D3 | semidirect |
| 64. C33 | C2×C5×D3 | semidirect |
| 65. C33 | C22×C3×C5 | semidirect |
| 68. C3⋊D3 | C3×C5×D3 | semidirect |
| 80. C3×C5 | C3×D32 | semidirect |
| 81. C3×C5 | #1113 | direct (N × H) |
| 96. C32 | C5×D32 | semidirect |
| 97. C32 | C2×C3×C5×D3 | semidirect |
| 103. C5 | C3×#1113 | direct (N × H) |
| 110. C3 | C3×C5×D32 | semidirect |
| 111. C3 | C5×#1113 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×C3⋊D3 | 2 |
| C5×#1113 | 3 |
| C3×C5×D32 | 3 |
| C3×#1113 | 5 |