  Quantification of the velocity and magnetic field reversals in dynamo remains
an interesting challenge. In this paper, using group-theoretic analysis, we
classify the reversing and non-reversing Fourier modes during a dynamo reversal
in a Cartesian box. Based on odd-even parities of the wavenumber indices, we
categorise the velocity and magnetic Fourier modes into 8 classes each. Then,
using the properties of the nonlinear interactions in magnetohydrodynamics, we
show that these 16 elements form Klein 16-group $Z_2 \times Z_2 \times Z_2
\times Z_2$. We demonstrate that field reversals in a class of Taylor-Green
dynamo, as well as the reversals in earlier experiments and models, belong to
one of the classes predicted by our group-theoretic arguments.
