Let Pq(n) be the set of all Subspaces in the vector space F n q. There is a Subspace distance dS(U, V ) between any two Subspaces U and V. A Subspace code is also a subset of Pq(n). It is known that dS(U, V ) ≥ dH(ν(πU), ν(πV )), where π ∈ Sn, ν(U) denotes the pivot vector of E(U) and E(U) is the reduced row echelon form of the generator matrix of U. In this paper, we show that if E(U) and E(V ) have at most one non-zero entry in each rows and each columns then the equality holds. Moreover, we introduce the sets GU, V = {π ∈ Sn | dS(U, V ) = dH(ν(πU), ν(πV ))} for any U, V ∈ Pq(n) and examine them in the spaces P2(4), P2(5), P2(6) and P3(4). It is shown that the groups 1, Z2, Z2 × Z2, S3, S4 and 1, Z2, Z2 × Z2, S3, D8, S3 × Z2, S4, S5 appears between these sets in P2(4) and P2(5), respectively. Moreover, the groups 1, Z2, Z2 ×Z2, S3, D8, Z2 ×Z2 ×Z2, S3 ×Z2, D8 ×Z2, S4, S3 × S3, S4 × Z2, (S3 × S3): 2, S5, S6 and 1, Z2, Z2 × Z2, S3, D8, S4 appears between these sets in P2(6) and P3(4), respectively.