  Due to the increasing number of observations Type Ia supernovae are nowadays
regarded as a heterogeneous class of objects consisting of several subclasses.
One of the largest of these is the class of Type Iax supernovae (SNe Iax) which
have been suggested to originate from pure deflagrations in CO
Chandrasekhar-mass white dwarfs (WDs). Although a few deflagration studies have
been carried out, the full diversity of the class is not captured yet. We
therefore present a parameter study of single-spot ignited deflagrations with
varying ignition locations, central densities, metallicities and compositions.
We also explore a rigidly rotating progenitor and carry out 3D hydrodynamic
simulations, nuclear network calculations and radiative transfer. The new
models extend the range in brightness covered by previous studies to the lower
end. Our explosions produce $^{56}$Ni masses from $5.8 \times 10^{-3}$ to $9.2
\times 10^{-2}\,M_\odot$. In spite of the wide exploration of the parameter
space the main characteristics of the models are primarily driven by the mass
of $^{56}$Ni. Secondary parameters have too little impact to explain the
observed trend among faint SNe~Iax. We report kick velocities of the bound
explosion remnants from $6.9$ to $369.8\,$km$\,s^{-1}$. The wide exploration of
the parameter space and viewing-angle effects in the radiative transfer lead to
a significant spread in the synthetic observables. The trends towards 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 $^{56}$Ni-rich bound remnant. While the pure deflagration scenario remains
a favorable explanation for bright and intermediate luminosity SNe~Iax, the
possibility that SNe~Iax do not consist of a single explosion scenario needs to
be considered.
