Finite Group DatabasebetaFinite Group DatabasebetaOrder 1620.
192 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 22 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 | C3⋊#4380 |
| commutator, hypocenter | C33×C5 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C34×C5 | C4 |
| prime radical | C32×C3⋊D15 | C2 |
| cosocle | C3×C3⋊D15 | C2×C3 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#4380 | C3 | direct (N × H) |
| 4. C34×C5 | C4 | semidirect |
| 18. C33×C5 | Dic3 | semidirect |
| 19. C33×C5 | C3×C4 | semidirect |
| 27. C34 | AGL(1,𝔽5) | semidirect |
| 45. C32×C5 | C3×Dic3 | semidirect |
| 46. C32×C5 | #157 | semidirect |
| 58. C33 | C3×AGL(1,𝔽5) | semidirect |
| 59. C33 | ΓL(1,𝔽16) | semidirect |
| 71. C3×C5 | C3×#157 | semidirect |
| 72. C3×C5 | C3⋊#157 | semidirect |
| 87. C32 | C3×ΓL(1,𝔽16) | semidirect |
| 88. C32 | #4380 | semidirect |
| 93. C5 | C3×C3⋊#157 | semidirect |
| 100. C3 | C3×#4380 | semidirect |
| 101. C3 | C3⋊#4380 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C3⋊D15 | 2 |
| C3⋊#4380 | 3 |
| C3×#4380 | 3 |
| C3×C3⋊#157 | 5 |
| C3×ΓL(1,𝔽16) | 9 |