Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
124 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 52 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 | C3×C52 | C3×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C19 | C4 |
| prime radical | C32×C5×D5×C19 | C2 |
| cosocle | C3×C5×D5 | C2×C3×C19 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C3×C19 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C19×C3⋊#1042 | C3 | direct (N × H) |
| 4. C32×C52×C19 | C4 | semidirect |
| 14. C3×C52×C19 | Dic3 | semidirect |
| 15. C3×C52×C19 | C3×C4 | semidirect |
| 21. C3×C3⋊#1042 | C19 | direct (N × H) |
| 23. C32×C5×C19 | Dic5 | semidirect |
| 24. C32×C5×C19 | AGL(1,𝔽5) | semidirect |
| 32. C52×C19 | C3×Dic3 | semidirect |
| 37. C3⋊#1042 | C3×C19 | direct (N × H) |
| 44. C3×C5×C19 | C3×Dic5 | semidirect |
| 45. C3×C5×C19 | Dic15 | semidirect |
| 46. C3×C5×C19 | C3×AGL(1,𝔽5) | semidirect |
| 47. C3×C5×C19 | ΓL(1,𝔽16) | semidirect |
| 50. C32×C52 | C4×C19 | semidirect |
| 55. C32×C19 | #1042 | semidirect |
| 64. C5×C19 | C3×Dic15 | semidirect |
| 65. C5×C19 | C3×ΓL(1,𝔽16) | semidirect |
| 70. C3×C52 | Dic3×C19 | semidirect |
| 71. C3×C52 | C3×C4×C19 | semidirect |
| 77. C3×C19 | C3×#1042 | semidirect |
| 78. C3×C19 | C3⋊#1042 | direct (N × H) |
| 81. C32×C5 | C19×Dic5 | semidirect |
| 82. C32×C5 | C19×AGL(1,𝔽5) | semidirect |
| 91. C52 | C3×Dic3×C19 | semidirect |
| 94. C19 | C3×C3⋊#1042 | direct (N × H) |
| 101. C3×C5 | C3×C19×Dic5 | semidirect |
| 102. C3×C5 | C19×Dic15 | semidirect |
| 103. C3×C5 | C3×C19×AGL(1,𝔽5) | semidirect |
| 104. C3×C5 | C19×ΓL(1,𝔽16) | semidirect |
| 109. C32 | C19×#1042 | semidirect |
| 114. C5 | C3×C19×Dic15 | semidirect |
| 115. C5 | C3×C19×ΓL(1,𝔽16) | semidirect |
| 118. C3 | C3×C19×#1042 | semidirect |
| 119. 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 |
|---|---|
| C32×C5×D5×C19 | 2 |
| C19×C3⋊#1042 | 3 |
| C3×C19×#1042 | 3 |
| C3×C19×ΓL(1,𝔽16) | 5 |
| C3×C19×Dic15 | 5 |
| C3×C3⋊#1042 | 19 |