We used high-resolution HST imaging and e-MERLIN 1.5-GHz observations of galaxy cores from the LeMMINGs survey to investigate the relation between optical structural properties and nuclear radio emission for a large sample of galaxies. We performed accurate, multi-component decompositions of new surface brightness profiles extracted from HST images for 163 LeMMINGs galaxies and fitted up to six galaxy components (e.g. bulges, discs, AGN, bars, rings, spiral arms, and nuclear star clusters) simultaneously with Sérsic and/or core-Sérsic models. By adding such decomposition data for ten LeMMINGs galaxies from our past work, the final sample of 173 nearby galaxies (102 Ss, 42 S0s, 23 Es, plus six Irr) with a typical bulge stellar mass of M∗,bulge ∼ 106 − 1012.5 M⊙ encompasses all optical spectral classes: low-ionisation nuclear emission-line region (LINER), Seyfert, Absorption Line Galaxy (ALG), and H II. We show that the bulge mass can be significantly overestimated in many galaxies when components such as bars, rings, and spirals are not included in the fits. We additionally implemented a Monte Carlo method to determine errors on the bulge, disc, and other fitted structural parameters. Moving (in the opposite direction) across the Hubble sequence, that is from the irregular to elliptical galaxies, we confirm that bulges become larger, more prominent, and round. Such bulge dominance is associated with a brighter radio core luminosity. We also find that the radio detection fraction increases with bulge mass. At M∗,bulge ≥ 1011 M⊙, the radio detection fraction is 77%, declining to 24% for M∗,bulge < 1010 M⊙. Furthermore, we observe that core-Sérsic bulges tend to be systematically round and to possess high radio core luminosities and boxy-distorted or pure elliptical isophotes. However, there is no evidence for the previously alleged strong tendency of galaxies' central structures (i.e. a sharp Sérsic, core-Sérsic dichotomy) with their radio loudness, isophote shape, and flattening.

Full Tables B.1-B.5 are only available at the CDS via anonymous ftp to cdsarc.cds.unistra.fr (ftp://130.79.128.5) or via https://cdsarc.cds.unistra.fr/viz-bin/cat/J/A+A/675/A105