SPN construction is the most widely used overall construction of block ciphers at present, which is adopted by block ciphers such as AES and ARIA. The security analysis of SPN ciphers is a research hotspot in cryptanalysis. The application of the subspace trail cryptanalysis to the typical two-dimensional SPN ciphers and typical three-dimensional SPN ciphers can yield the corresponding subspace trails and general properties based on the subspace trails separately. These properties are independent of the secret key and the detailed definitions of the S-box and MixColumns matrix. They can be specifically described as follows: For a typical two-dimensional SPN cipher whose state can be formalized into a two-dimensional array of n×m, the number of different ciphertext pairs belonging to the same coset of the mixed subspace in the ciphertexts obtained by five rounds of encryption of all plaintexts belonging to the same coset of the quasi-diagonal subspace must be a multiple of 2^n–1. For a typical three-dimensional SPN cipher whose state can be formalized into a three-dimensional array of l×n×m, the number of different ciphertext pairs belonging to the same coset of the mixed subspace in the ciphertexts obtained by seven rounds of encryption of all plaintexts belonging to the same coset of the quasi-diagonal subspace must be a multiple of 2^nl–1. In addition, this study not only proves these properties but also makes experimental verification on the internal permutations of PHOTON and small-scale variants of Rijndael, 3D, and Saturnin algorithms. The experimental results are completely consistent with these properties.