Finite Group DatabasebetaFinite Group DatabasebetaOrder 27900.
160 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊(C31⋊#1044) | C3 | direct (N × H) |
| 4. C32×C52×C31 | C4 | semidirect |
| 13. C3×C52×C31 | Dic3 | semidirect |
| 14. C3×C52×C31 | C3×C4 | semidirect |
| 19. C32×C5×C31 | AGL(1,𝔽5) | semidirect |
| 28. C52×C31 | C3×Dic3 | semidirect |
| 35. C3×C5×C31 | C3×AGL(1,𝔽5) | semidirect |
| 36. C3×C5×C31 | ΓL(1,𝔽16) | semidirect |
| 44. C32×C31 | #1044 | semidirect |
| 45. C32×C52 | Dic31 | semidirect |
| 51. C5×C31 | C3×ΓL(1,𝔽16) | semidirect |
| 58. C3×C31 | C3×#1044 | semidirect |
| 59. C3×C31 | C3⋊#1044 | semidirect |
| 63. C3×C52 | C3×Dic31 | semidirect |
| 64. C3×C52 | Dic93 | semidirect |
| 70. C32×C5 | C31⋊AGL(1,𝔽5) | semidirect |
| 72. C31 | C3×C3⋊#1044 | semidirect |
| 79. C52 | C3×Dic93 | semidirect |
| 86. C3×C5 | C3×C31⋊AGL(1,𝔽5) | semidirect |
| 87. C3×C5 | C3⋊(C31⋊AGL(1,𝔽5)) | semidirect |
| 92. C32 | C31⋊#1044 | semidirect |
| 97. C5 | C3×C3⋊(C31⋊AGL(1,𝔽5)) | semidirect |
| 100. C3 | C3×C31⋊#1044 | semidirect |
| 101. C3 | C3⋊(C31⋊#1044) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C31×C5⋊D5 | 2 |
| C3⋊(C31⋊#1044) | 3 |
| C3×C31⋊#1044 | 3 |
| C3×C3⋊(C31⋊AGL(1,𝔽5)) | 5 |
| C3×C3⋊#1044 | 31 |