Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
168 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52 | C2×C4 |
| prime radical | C3×D15⋊D5 | C2 |
| cosocle | C32×C5⋊D5 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊(C3⋊#1044) | C2 | semidirect |
| 3. C3×C3⋊#1043 | C2 | semidirect |
| 6. C3×C5×D15 | C4 | semidirect |
| 14. C3⋊#1043 | D3 | semidirect |
| 16. C32×C52 | C2×C4 | semidirect |
| 22. C5×D15 | Dic3 | semidirect |
| 32. C3×D15 | AGL(1,𝔽5) | semidirect |
| 37. C3×C52 | C4×D3 | semidirect |
| 38. C3×C52 | C2×Dic3 | semidirect |
| 52. C32×C5 | C2×AGL(1,𝔽5) | semidirect |
| 58. D15 | ΓL(1,𝔽16) | semidirect |
| 67. C52 | D3×Dic3 | semidirect |
| 80. C3×C5 | D3×AGL(1,𝔽5) | semidirect |
| 81. C3×C5 | C2×ΓL(1,𝔽16) | semidirect |
| 93. C32 | D5⋊AGL(1,𝔽5) | semidirect |
| 101. C5 | D3×ΓL(1,𝔽16) | semidirect |
| 106. C3 | D5⋊ΓL(1,𝔽16) | semidirect |
| 107. C3 | #10597182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D15⋊D5 | 2 |
| C3⋊(C3⋊#1044) | 2 |
| C3×C3⋊#1043 | 2 |
| #10597182 | 3 |
| D5⋊ΓL(1,𝔽16) | 3 |
| D3×ΓL(1,𝔽16) | 5 |