Finite Group DatabasebetaFinite Group Databasebeta← C5×C19⋊C3×ΓL(1,𝔽16) #30685761
Order 17100.
124 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 124 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. C5×C19×ΓL(1,𝔽16) | C3 | semidirect |
| 4. C3×C52×C19⋊C3 | C4 | semidirect |
| 5. C19⋊C3×ΓL(1,𝔽16) | C5 | direct (N × H) |
| 13. C3×C52×C19 | C3×C4 | semidirect |
| 15. C52×C19⋊C3 | Dic3 | semidirect |
| 16. C19×ΓL(1,𝔽16) | C3×C5 | semidirect |
| 23. C3×C5×C19⋊C3 | C4×C5 | semidirect |
| 24. C3×C5×C19⋊C3 | AGL(1,𝔽5) | semidirect |
| 32. C52×C19 | C3×Dic3 | semidirect |
| 37. C5×ΓL(1,𝔽16) | C19⋊C3 | direct (N × H) |
| 40. C3×C5×C19 | C3×C4×C5 | semidirect |
| 41. C3×C5×C19 | C3×AGL(1,𝔽5) | semidirect |
| 46. C5×C19⋊C3 | C5×Dic3 | semidirect |
| 47. C5×C19⋊C3 | ΓL(1,𝔽16) | direct (N × H) |
| 55. C3×C19⋊C3 | C5×AGL(1,𝔽5) | semidirect |
| 64. C5×C19 | C3×C5×Dic3 | semidirect |
| 65. C5×C19 | C3×ΓL(1,𝔽16) | semidirect |
| 71. C3×C52 | C4×C19⋊C3 | semidirect |
| 72. ΓL(1,𝔽16) | C5×C19⋊C3 | direct (N × H) |
| 76. C3×C19 | C3×C5×AGL(1,𝔽5) | semidirect |
| 78. C19⋊C3 | C5×ΓL(1,𝔽16) | direct (N × H) |
| 91. C52 | Dic3×C19⋊C3 | semidirect |
| 94. C19 | C3×C5×ΓL(1,𝔽16) | semidirect |
| 103. C3×C5 | C4×C5×C19⋊C3 | semidirect |
| 104. C3×C5 | AGL(1,𝔽5)×C19⋊C3 | semidirect |
| 114. C5 | C5×Dic3×C19⋊C3 | semidirect |
| 115. C5 | C19⋊C3×ΓL(1,𝔽16) | direct (N × H) |
| 119. C3 | C5×AGL(1,𝔽5)×C19⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×D5×C19⋊C3 | 2 |
| C5×C19×ΓL(1,𝔽16) | 3 |
| C5×AGL(1,𝔽5)×C19⋊C3 | 3 |
| C19⋊C3×ΓL(1,𝔽16) | 5 |
| C5×Dic3×C19⋊C3 | 5 |
| C3×C5×ΓL(1,𝔽16) | 19 |