We demonstrated a 414.9 W large-mode-area Er/Yb co-doped fiber amplifier with a good time-domain stability, seeded by a 1568 nm random fiber laser (RFL) seed with a half-open cavity. We believe this to be the highest output power of the RFL in a 1.5 µm band to date. At the maximum output power, the optical efficiency was 36.9% and the 3 dB linewidth was 0.69 nm. The 1535 nm fiber lasers were used as the pumping source of the main amplifier to avoid the parasitic lasing of Yb ions. The spectral linewidth broadening was suppressed during the amplification process due to the stable temporal output of the RFL seed. The M2 factor increased from 2.28 at 145.7 W to 2.83 at 280.8 W. Our research provides a robust approach for achieving high-power and high-spectral-purity RFLs in the 1.5 µm band.