We present detailed image analysis of rest-frame optical images of 235 low-redshift ($z leq$ 0.35) type 1 active galactic nuclei (AGNs) observed with the Hubble Space Telescope. The high-resolution images enable us to perform rigorous two-dimensional image modeling to decouple the luminous central point source from the host galaxy, which, when warranted, is further decomposed into its principal structural components (bulge, bar, and disk). In many cases, care must be taken to account for structural complexities such as spiral arms, tidal features, and overlapping or interacting companion galaxies. We employ Fourier modes to characterize the degree of asymmetry of the light distribution of the stars, as a quantitative measure of morphological distortion due to interactions or mergers. We examine the dependence of the physical parameters of the host galaxies on the properties of the AGNs, namely radio-loudness and the width of the broad emission lines. In accordance with previous studies, narrow-line (H$beta$ FWHM $leq 2000$ km~s$^{-1}$) type 1 AGNs, in contrast to their broad-line (H$beta$ FWHM $> 2000$ km~s$^{-1}$) counterparts, are preferentially hosted in later type, lower luminosity galaxies, which have a higher incidence of pseudo-bulges, are more frequently barred, and are less morphologically disturbed. This suggests narrow-line type 1 AGNs experienced a more quiescent evolutionary history driven primarily by internal secular evolution instead of external dynamical perturbations. The fraction of AGN hosts showing merger signatures is larger for more luminous sources. Radio-loud AGNs generally preferentially live in earlier type (bulge-dominated), more massive hosts, although a minority of them appears to contain a significant disk component. We do not find convincing evidence for enhanced merger signatures in the radio-loud population.
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