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We examine the properties of the host galaxies of 22 623 narrow-line active galactic nuclei (AGN) with 0.02 < z < 0.3 selected from a complete sample of 122 808 galaxies from the Sloan Digital Sky Survey. We focus on the luminosity of the [O iii]λ5007 emission line as a tracer of the strength of activity in the nucleus. We study how AGN host properties compare with those of normal galaxies and how they depend on L[O iii]. We find that AGN of all luminosities reside almost exclusively in massive galaxies and have distributions of sizes, stellar surface mass densities and concentrations that are similar to those of ordinary early-type galaxies in our sample. The host galaxies of low-luminosity AGN have stellar populations similar to normal early types. The hosts of high-luminosity AGN have much younger mean stellar ages. The young stars are not preferentially located near the nucleus of the galaxy, but are spread …