pw.x doesn't find all the symmetries you expected.

See above to learn how PWscf finds symmetry operations. Some of them might be missing because:

• the number of significant figures in the atomic positions is not large enough. In file PW/eqvect.f90, the variable accep is used to decide whether a rotation is a symmetry operation. Its current value (10^-5 ) is quite strict: a rotated atom must coincide with another atom to 5 significant digits. You may change the value of accep and recompile.
• they are not acceptable symmetry operations of the Bravais lattice. This is the case for C₆₀ , for instance: the I_h icosahedral group of C₆₀ contains 5-fold rotations that are incompatible with translation symmetry.
• the system is rotated with respect to symmetry axis. For instance: a C₆₀ molecule in the fcc lattice will have 24 symmetry operations (T_h group) only if the double bond is aligned along one of the crystal axis; if C₆₀ is rotated in some arbitrary way, pw.x may not find any symmetry, apart from inversion.
• they contain a fractional translation that is incompatible with the FFT grid (see previous paragraph). Note that if you change cutoff or unit cell volume, the automatically computed FFT grid changes, and this may explain changes in symmetry (and in the number of k-points as a consequence) for no apparent good reason (only if you have fractional translations in the system, though).
• a fractional translation, without rotation, is a symmetry operation of the system. This means that the cell is actually a supercell. In this case, all symmetry operations containing fractional translations are disabled. The reason is that in this rather exotic case there is no simple way to select those symmetry operations forming a true group, in the mathematical sense of the term.