Finite Group DatabasebetaFinite Group Databasebeta← C5×C3⋊(#10625193⋊C3) #45686293
Order 33300.
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 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. C5×C3⋊#10625193 | C3 | semidirect |
| 4. C3×C52×C37⋊C3 | C4 | semidirect |
| 5. C3⋊(#10625193⋊C3) | C5 | direct (N × H) |
| 14. C52×C37⋊C3 | Dic3 | semidirect |
| 15. C3×C52×C37 | C3×C4 | semidirect |
| 16. C3⋊#10625193 | C3×C5 | semidirect |
| 22. C3×C5×C37⋊C3 | C4×C5 | semidirect |
| 23. C3×C5×C37⋊C3 | AGL(1,𝔽5) | semidirect |
| 31. C52×C37 | C3×Dic3 | semidirect |
| 37. C3×C5×C37 | C3×C4×C5 | semidirect |
| 38. C3×C5×C37 | C3×AGL(1,𝔽5) | semidirect |
| 43. C5×C37⋊C3 | C5×Dic3 | semidirect |
| 44. C5×C37⋊C3 | ΓL(1,𝔽16) | semidirect |
| 50. C3×C37⋊C3 | C5×AGL(1,𝔽5) | semidirect |
| 58. C5×C37 | C3×C5×Dic3 | semidirect |
| 59. C5×C37 | C3×ΓL(1,𝔽16) | semidirect |
| 66. C3×C37 | C3×C5×AGL(1,𝔽5) | semidirect |
| 68. C37⋊C3 | C5×ΓL(1,𝔽16) | semidirect |
| 74. C3×C52 | Dic37⋊C3 | semidirect |
| 84. C37 | C3×C5×ΓL(1,𝔽16) | semidirect |
| 92. C52 | C3⋊(Dic37⋊C3) | semidirect |
| 103. C3×C5 | C5×Dic37⋊C3 | semidirect |
| 104. C3×C5 | #10625193⋊C3 | semidirect |
| 114. C5 | C5×C3⋊(Dic37⋊C3) | semidirect |
| 115. C5 | C3⋊(#10625193⋊C3) | direct (N × H) |
| 119. C3 | C5×#10625193⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D5×C37⋊C3 | 2 |
| C5×C3⋊#10625193 | 3 |
| C5×#10625193⋊C3 | 3 |
| C3⋊(#10625193⋊C3) | 5 |
| C5×C3⋊(Dic37⋊C3) | 5 |
| C3×C5×ΓL(1,𝔽16) | 37 |