Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
156 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊C3×#1042 |
| commutator, hypocenter | C52×C19 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C3×C4 |
| prime radical | C3×C5×D5×C19⋊C3 | C2 |
| cosocle | C5×D5×C19 | C2×C32 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C19×#1042 | C3 | semidirect |
| 3. C19⋊C3×#1042 | C3 | direct (N × H) |
| 4. C3×C52×C19⋊C3 | C4 | semidirect |
| 9. C19×#1042 | C32 | semidirect |
| 12. C3×C52×C19 | C3×C4 | semidirect |
| 13. C52×C19⋊C3 | C3×C4 | semidirect |
| 21. C3×C5×C19⋊C3 | Dic5 | semidirect |
| 22. C3×C5×C19⋊C3 | AGL(1,𝔽5) | semidirect |
| 28. C52×C19 | C32×C4 | semidirect |
| 34. C3×#1042 | C19⋊C3 | direct (N × H) |
| 36. C3×C5×C19 | C3×Dic5 | semidirect |
| 37. C3×C5×C19 | C3×AGL(1,𝔽5) | semidirect |
| 39. C5×C19⋊C3 | C3×Dic5 | semidirect |
| 40. C5×C19⋊C3 | C3×AGL(1,𝔽5) | semidirect |
| 48. C3×C19⋊C3 | #1042 | direct (N × H) |
| 53. #1042 | C3×C19⋊C3 | direct (N × H) |
| 55. C5×C19 | C32×Dic5 | semidirect |
| 56. C5×C19 | C32×AGL(1,𝔽5) | semidirect |
| 61. C3×C52 | C4×C19⋊C3 | semidirect |
| 66. C3×C19 | C3×#1042 | semidirect |
| 67. C19⋊C3 | C3×#1042 | direct (N × H) |
| 78. C52 | C3×C4×C19⋊C3 | semidirect |
| 81. C19 | C32×#1042 | semidirect |
| 87. C3×C5 | Dic5×C19⋊C3 | semidirect |
| 88. C3×C5 | AGL(1,𝔽5)×C19⋊C3 | semidirect |
| 97. C5 | C3×Dic5×C19⋊C3 | semidirect |
| 98. C5 | C3×AGL(1,𝔽5)×C19⋊C3 | semidirect |
| 101. C3 | C19⋊C3×#1042 | direct (N × H) |
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 |
| C3×C19×#1042 | 3 |
| C19⋊C3×#1042 | 3 |
| C3×AGL(1,𝔽5)×C19⋊C3 | 5 |
| C3×Dic5×C19⋊C3 | 5 |
| C32×#1042 | 19 |