Finite Group DatabasebetaFinite Group DatabasebetaOrder 27900.
160 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 33 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 | C3×C52×C31 | C3×C4 |
| prime radical | C3×C5⋊D5×C31⋊C3 | C2 |
| cosocle | C3×C31×C5⋊D5 | C2×C3 |
| LCS | G ▷ C3×C52×C31 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×C3⋊#1044 | C3 | semidirect |
| 4. C3×C52×C31⋊C3 | C4 | semidirect |
| 13. C52×C31⋊C3 | Dic3 | semidirect |
| 14. C3×C52×C31 | C3×C4 | semidirect |
| 19. C3×C5×C31⋊C3 | AGL(1,𝔽5) | semidirect |
| 28. C52×C31 | C3×Dic3 | semidirect |
| 32. C3×C5×C31 | C3×AGL(1,𝔽5) | semidirect |
| 36. C5×C31⋊C3 | ΓL(1,𝔽16) | semidirect |
| 42. C3⋊#1044 | C31⋊C3 | direct (N × H) |
| 44. C3×C31⋊C3 | #1044 | semidirect |
| 51. C5×C31 | C3×ΓL(1,𝔽16) | semidirect |
| 57. C3×C31 | C3×#1044 | semidirect |
| 59. C31⋊C3 | C3⋊#1044 | direct (N × H) |
| 64. C3×C52 | C4×C31⋊C3 | semidirect |
| 72. C31 | C3×C3⋊#1044 | semidirect |
| 79. C52 | Dic3×C31⋊C3 | semidirect |
| 87. C3×C5 | AGL(1,𝔽5)×C31⋊C3 | semidirect |
| 97. C5 | ΓL(1,𝔽16)×C31⋊C3 | semidirect |
| 101. C3 | C31⋊C3×#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5⋊D5×C31⋊C3 | 2 |
| C31×C3⋊#1044 | 3 |
| C31⋊C3×#1044 | 3 |
| ΓL(1,𝔽16)×C31⋊C3 | 5 |
| C3×C3⋊#1044 | 31 |