Context. Due to the ever increasing number of observations during the past decades, Type Ia supernovae are nowadays regarded as a heterogeneous class of optical transients consisting of several subtypes. One of the largest of these subclasses is the class of Type Iax supernovae. They have been suggested to originate from pure deflagrations in carbon-oxygen Chandrasekhar mass white dwarfs because the outcome of this explosion scenario is in general agreement with their subluminous nature. Aims. Although a few deflagration studies have already been carried out, the full diversity of the class has not been captured yet. This, in particular, holds for the faint end of the subclass. We therefore present a parameter study of single-spot ignited deflagrations in Chandrasekhar mass white dwarfs varying the location of the ignition spark, the central density, the metallicity, and the composition of the white dwarf. We also explore a rigidly rotating progenitor to investigate whether the effect of rotation can spawn additional trends. Methods. We carried out three-dimensional hydrodynamic simulations employing the LEAFS code. Subsequently, detailed nucleosynthesis results were obtained with the nuclear network code YANN. In order to compare our results to observations, we calculated synthetic spectra and light curves with the ARTIS code. Results. The new set of models extends the range in brightness covered by previous studies to the lower end. Our single-spot ignited explosions produce ⁵⁶Ni masses from 5.8 × 10⁻³ to 9.2 × 10⁻² M_⊙. In spite of the wide exploration of the parameter space, the main characteristics of the models are primarily driven by the mass of ⁵⁶Ni and form a one-dimensional sequence. Secondary parameters seem to have too little impact to explain the observed trend in the faint part of the Type Iax supernova class. We report kick velocities of the gravitationally bound explosion remnants from 6.9 to 369.8 km s⁻¹. The magnitude as well as the direction of the natal kick is found to depend on the strength of the deflagration. Conclusions. This work corroborates the results of previous studies of deflagrations in Chandrasekhar mass white dwarfs. The wide exploration of the parameter space in initial conditions and viewing angle effects in the radiative transfer lead to a significant spread in the synthetic observables. The trends in observational properties toward the faint end of the class are, however, not reproduced. This motivates a quantification of the systematic uncertainties in the modeling procedure and the influence of the ⁵⁶Ni-rich bound remnant to get to the bottom of these discrepancies. Moreover, while the pure deflagration scenario remains a favorable explanation for bright and intermediate luminosity Type Iax supernovae, our results suggest that other mechanisms also contribute to this class of events.