The influenza virus continually evolves because of the high mutation rate, resulting in dramatic changes in its pathogenicity and other biological properties. This study aimed to evaluate the evolution of certain essential properties, understand the connections between them, and find the molecular basis for the manifestation of these properties. To that end, 21 A(H1N1)pdm09 influenza viruses were tested for their pathogenicity and toxicity in a mouse model with a ts/non-ts phenotype manifestation and HA thermal stability. The results demonstrated that, for a strain to have high pathogenicity, it must express a toxic effect, have a non-ts phenotype, and have a thermally stable HA. The ancestor A/California/07/2009 (H1N1)pdm influenza virus expressed the non-ts phenotype, after which the cycling trend of the ts/non-ts phenotype was observed in new strains of A(H1N1)pdm09 influenza viruses, indicating that the ratio of the ts phenotype will increase in the coming years. Of the 21 tested viruses, A/South Africa/3626/2013 had the high pathogenicity in the mouse model. Sequence alignment analysis showed that this virus has three unique mutations in the polymerase complex, two of which are in the PB2 gene and one that is in the PB1 gene. Further study of these mutations might explain the distinguishing pathogenicity.