C = rotation axis S = improper axis i = inversion center σ = plane of symmetry
Step #1
Examine for special groups.
 linear, no σ perpendicular to molecular axis  C_{∞v}
 linear, σ perpendicular to molecular axis  D_{∞h}
 tetrahedral  T_{d}
 octahedral  O_{h}
 dodecahedral or icosahedral  I_{h}
continue
Step #2
Examine for a C_{n} axis
C_{n} Present  C_{n} Absent 
Find C_{n} of highest n or unique n (This axis is taken to be vertical by convention.) 
σ present  C_{s} i present  C_{i} no symmetry elements other than E  C_{1} 
continue
Step #3
Examine for S_{2n} colinear with C_{n}
S_{2n} Present  S_{2n} Absent 
No other symmetry elements present except i  S_{2n} Other symmetry elements present (Go to Step 4) 
(Go to Step 4) 
continue
Step #4
Examine for n horizontal C_{2} axes
(where n is the order of highest order axis)
n C_{2} Axes Present  n C_{2} Axes Absent 
Horizontal plane (σ_{h}) present  D_{nh} 
Horizontal plane (σ_{h}) present  C_{nh} 
n Vertical planes (dihedral planes, σ_{d}, bisecting angles between C_{2} axes):
 Present  D_{nd}
 Absent  D_{n}

n Vertical planes (σ_{v}):
 Present  C_{nv}
 Absent  C_{n}
