The study has classified the subgroups of Multiple Sclerosis (MS) using Support Vector Machines (SVM). C-Support Vector Classifier (C-SVC) algorithm, one of the SVM classifiers of multi class, has been utilized for the classification of MS subgroups. For this purpose, 120 MS patients (76 RRMS, 38 SPMS, 6 PPMS patients) have been included in the study. Through Magnetic Resonance Imaging (MRI), the number of lesion diameter and Expanded Disability Status Scale (EDSS) data are applied through C-SVC. Lesion data has been obtained from three separate regions of the brain which are brain stem, periventricular corpus callosum and upper cervical region. By applying the data onto Radial Basis Function kernel (RBF), Polynomial kernel, Sigmoid kernel and Linear kernel, four of the kernel types of C-SVC algorithm, the accuracy rates of MS subgroups classification and the computation time during the training procedure are computed and compared. By adding EDSS score into the dataset, the classification achievement rate has increased in all the kernel types based on the analyses conducted. Having applied C-SVC on MS subgroups, classification achievement of MS subgroups, namely that of RRMS, SPMS and PPMS has been measured.