diff --git a/example/bench.cpp b/example/bench.cpp
index 4be5049..25d75f3 100644
--- a/example/bench.cpp
+++ b/example/bench.cpp
@@ -17,7 +17,7 @@ int main() {
         tc::group::E(7),
         tc::group::B(6),
         tc::group::B(7),
-        tc::group::B(8),
+        tc::group::B(8)
     };
 
     for (const auto &group : groups) {
diff --git a/example/path.cpp b/example/path.cpp
index f18f6a2..9f4cd1e 100644
--- a/example/path.cpp
+++ b/example/path.cpp
@@ -9,7 +9,7 @@ int main() {
 
     for (size_t target = 1; target < vars.size(); target++) {
         auto &action = vars.path[target];
-        std::cout << action.coset << " * " << action.gen << " = " << target << std::endl;
+        std::cout << action.from_idx << " * " << action.gen << " = " << target << std::endl;
     }
 
     return 0;
diff --git a/include/tc/core.hpp b/include/tc/core.hpp
index ef196c5..9666ea2 100644
--- a/include/tc/core.hpp
+++ b/include/tc/core.hpp
@@ -6,15 +6,14 @@
 
 namespace tc {
     struct Action {
-        int coset = -1;
+        int from_idx = -1;
         int gen = -1;
-        int target = -1;
 
         Action() = default;
 
         Action(const Action &) = default;
 
-        Action(int coset, int gen, int target);
+        Action(int from_idx, int gen);
     };
 
     struct Cosets {
@@ -52,6 +51,8 @@ namespace tc {
         [[nodiscard]] Rel shift(int off) const;
     };
 
+    struct SubGroup;
+
     struct Group {
         const int ngens;
         std::vector<std::vector<int>> _mults;
@@ -67,11 +68,20 @@ namespace tc {
 
         [[nodiscard]] std::vector<Rel> rels() const;
 
+        [[nodiscard]] SubGroup subgroup(const std::vector<int> &gens) const;
+
         [[nodiscard]] Group product(const Group &other) const;
 
         [[nodiscard]] Group power(int p) const;
 
-        [[nodiscard]] Cosets solve(const std::vector<int>& sub_gens = {}) const;
+        [[nodiscard]] Cosets solve(const std::vector<int> &sub_gens = {}) const;
+    };
+
+    struct SubGroup : public Group {
+        const std::vector<int> gen_map;
+        const Group &parent;
+
+        SubGroup(const Group &parent, const std::vector<int> &gen_map);
     };
 
     Group operator*(const Group &g, const Group &h);
diff --git a/src/core.cpp b/src/core.cpp
index dcffb3b..c59f55c 100644
--- a/src/core.cpp
+++ b/src/core.cpp
@@ -4,8 +4,8 @@
 #include <sstream>
 
 namespace tc {
-    Action::Action(int coset, int gen, int target)
-        : coset(coset), gen(gen), target(target) {
+    Action::Action(int from_idx, int gen)
+        : from_idx(from_idx), gen(gen) {
     }
 
     Cosets::Cosets(int ngens)
@@ -21,8 +21,8 @@ namespace tc {
         data[coset * ngens + gen] = target;
         data[target * ngens + gen] = coset;
 
-        if (path[target].coset == -1) {
-            path[target] = Action(coset, gen, target);
+        if (path[target].from_idx == -1) {
+            path[target] = Action(coset, gen);
         }
     }
 
@@ -32,8 +32,8 @@ namespace tc {
         data[idx] = target;
         data[target * ngens + gen] = coset;
 
-        if (path[target].coset == -1) {
-            path[target] = Action(coset, gen, target);
+        if (path[target].from_idx == -1) {
+            path[target] = Action(coset, gen);
         }
     }
 
@@ -89,6 +89,10 @@ namespace tc {
         return res;
     }
 
+    SubGroup Group::subgroup(const std::vector<int> &gens) const {
+        return SubGroup(*this, gens);
+    }
+
     Group Group::product(const Group &other) const {
         std::stringstream ss;
         ss << name << "*" << other.name;
@@ -115,4 +119,15 @@ namespace tc {
 
         return g;
     }
-}
\ No newline at end of file
+
+    SubGroup::SubGroup(const Group &parent, const std::vector<int> &gen_map)
+        : Group(gen_map.size()), parent(parent), gen_map(gen_map) {
+
+        for (size_t i = 0; i < gen_map.size(); ++i) {
+            for (size_t j = 0; j < gen_map.size(); ++j) {
+                int mult = parent.get(gen_map[i], gen_map[j]);
+                set(Rel(i, j, mult));
+            }
+        }
+    }
+}