The magnetic and superconducting properties of an Eu(Fe 0.81 Co 0.19 ) 2 As 2 single crystal are investigated by means of ac magnetic susceptibility, dc magnetization, specific heat, transverse resistivity and Hall effect measurements in magnetic fields up to 9 T, applied parallel and perpendicular to the c-axis. The compound exhibits the coexistence of magnetism and superconductivity (SC), characterized by structural distortion (SD) and/or spin-density-wave (SDW) ordering at T SD/SDW = 78 ± 4 K, cantedantiferromagnetic (C-AF) ordering at the Néel temperature T N = 16.5 ± 0.5 K and SC at the critical temperature T c = 5.3 ± 0.2 K at zero field. Upon applying fields both the C-AF and SC states evolve in an unconventional manner. Magnetic field distinctly affects the spin canting, resulting in separation of the C-AF into two new phases: the C-AF and ferromagnetic (F) ones. The unusual behavior of the SC state produces field-induced SC in the H ⊥c configuration as an outcome of the weakening orbital pair-breaking effect. From the experimental data we derive the field-temperature phase diagrams for Eu(Fe 0.81 Co 0.19 ) 2 As 2 . A comparison of experimental results is made with theory developed for type II superconductors and then some important thermodynamic parameters characteristic of the superconducting state of Eu(Fe 0.81 Co 0.19 ) 2 As 2 are deduced such as the specific heat jump at T c , C p (T c )/γ n T c , the electron-phonon coupling constant e-ph , the upper critical field H c2 , coherence length ξ , the Fermi wave-vector k F , effective mass m * , Hall mobility µ H , magnetic penetration depth and the Ginzburg-Landau parameter κ.