Stereoisograms for three-membered heterocycles: V. Factor-group method for type-itemized enumeration of oxiranes under an \textit{RS}-stereoisomeric group. 

The preceding Part IV of this series has described the half-size-subgroup method for type-itemized enumeration of stereoisograms by adopting epoxide (oxirane) derivatives as probes. As a continuation of this series, the present Part V has proposed the factor-group method for type-itemized enumeration of stereoisograms. The two methods are compared by applying to epoxide (oxirane) derivatives as common probes. The merit of the factor-group method is emphasized by adopting the same mark table during the treatments of Category 1 to Category 3 for categorizing type-I to type-V stereoisograms. Thus, the coset decomposition of the \textit{RS}-stereoisomeric group ${\bf C}_{2v\widetilde{\sigma}\widehat{I}}$ by the subgroup ${\bf C}_{2}$ is calculated so as to give the corresponding factor group. After the mark table of the factor group is obtained, type-itemized enumerations of epoxide derivatives are conducted, where five types of stereoisograms are classified into the three categories. Isomer-classification schemes and isomer-classification diagrams are introduced in order to illustrate epoxide derivatives of respective compositions.