Finite Group DatabasebetaFinite Group DatabasebetaOrder 1080.
272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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 | C33×C5 | C2×C4 |
| prime radical | D5×C3⋊(C3⋊D3) | C2 |
| cosocle | C33×D5 | C22 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C3⋊ΓL(1,𝔽16) | C2 | semidirect |
| 3. C32×ΓL(1,𝔽16) | C2 | semidirect |
| 6. C3⋊(C3⋊D15) | C4 | semidirect |
| 7. C5×C3⋊(C3⋊D3) | C4 | semidirect |
| 13. C3⋊ΓL(1,𝔽16) | D3 | semidirect |
| 15. C3×ΓL(1,𝔽16) | D3 | semidirect |
| 17. C33×C5 | C2×C4 | semidirect |
| 38. ΓL(1,𝔽16) | C3⋊D3 | semidirect |
| 43. C3⋊(C3⋊D3) | AGL(1,𝔽5) | semidirect |
| 45. C32×C5 | C4×D3 | semidirect |
| 46. C32×C5 | C4×D3 | semidirect |
| 64. C33 | C2×AGL(1,𝔽5) | semidirect |
| 80. C3×C5 | #624 | semidirect |
| 81. C3×C5 | C4×C3⋊D3 | semidirect |
| 93. C32 | D3×AGL(1,𝔽5) | semidirect |
| 94. C32 | D3×AGL(1,𝔽5) | semidirect |
| 105. C5 | #6289 | semidirect |
| 110. C3 | C3⋊D3×AGL(1,𝔽5) | semidirect |
| 111. C3 | ΓL(1,𝔽16)⋊D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×C3⋊(C3⋊D3) | 2 |
| C3×C3⋊ΓL(1,𝔽16) | 2 |
| C32×ΓL(1,𝔽16) | 2 |
| ΓL(1,𝔽16)⋊D3 | 3 |
| C3⋊D3×AGL(1,𝔽5) | 3 |
| #6289 | 5 |