Considering the similarity of the real-space configurations for the opposite spin sublattices in both antiferromagnets (AFMs) and altermagnets (AMs), the relationship between them should be profound. In this work, we demonstrate that AFMs and AMs can be connected with spin groups and their subgroups. Consequently, the breaking of the combined inversion or translation operation with time-reversal symmetry $(\mathcal{PT}$ or $\mathbf{t}\mathcal{T})$ in AFMs will induce transition from AFM to AM. We systematically list all collinear spin point groups and space groups that can realize the transition for the three types of AFMs: $\mathcal{PT}$, $\mathbf{t}\mathcal{T}$, and $\mathcal{PT}\text{−}\mathbf{t}\mathcal{T}$. Moreover, we propose that Floquet engineering using circularly polarized light and surface cutting engineering are effective approaches to break $\mathcal{PT}$ and $\mathbf{t}\mathcal{T}$ symmetries of AFM, respectively, achieving the transition. Interestingly, the features and magnitude of AM spin splitting can be tuned by adjusting various parameters of Floquet engineering. In our work, we not only establish a theoretical framework for the transition from AFM to AM but also provide practical approaches utilizing the achievements in AFMs for 100 years to obtain AMs, significantly expanding the scope of AM materials for both theoretical studies and future practical applications.

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• Electronic structure
• Magnetic order
• Magnetic phase transitions
• Magnetism
• Altermagnets
• Antiferromagnets
• Symmetries
• Bloch-Floquet theorem
• First-principles calculations
• Tight-binding model