  Although fast radio bursts (FRBs) have been an active field in astronomy and
cosmology, their origin is still unknown to date. One of the interesting topics
is the classification of FRBs, which is closely related to the origin of FRBs.
Different physical mechanisms are required by different classes of FRBs. In the
literature, they usually could be classified into non-repeating and repeating
FRBs. Well motivated by the observations, here we are interested in the
possible subclassification of FRBs. By using the first CHIME/FRB catalog, we
propose to subclassify non-repeating (type I) FRBs into type Ia and Ib FRBs.
The distribution of type Ia FRBs is delayed with respect to the cosmic star
formation history (SFH), and hence they are probably associated with old
stellar populations, while the distribution of type Ib FRBs tracks SFH, and
hence they are probably associated with young stellar populations. Accordingly,
the physical criteria for this subclassification of type I FRBs have been
clearly determined. We find that there are some tight empirical correlations
for type Ia FRBs but not for type Ib FRBs, and vice versa. These make them
different in physical properties. Similarly, we suggest that repeating (type
II) FRBs could also be subclassified into type IIa and IIb FRBs. A universal
subclassification scheme is given at the end. This subclassification of FRBs
might help us to reveal quite different physical mechanisms behind them, and
improve their applications in astronomy and cosmology.
