diff --git a/skglm/tests/test_validation.py b/skglm/tests/test_validation.py
index 25c23c9a7..7e998bfb8 100644
--- a/skglm/tests/test_validation.py
+++ b/skglm/tests/test_validation.py
@@ -1,35 +1,89 @@
 import pytest
+import numpy as np
+from scipy import sparse
 
-from skglm.penalties import L1
-from skglm.datafits import Poisson, Huber
-from skglm.solvers import FISTA, ProxNewton
+from skglm.penalties import L1, WeightedL1GroupL2, WeightedGroupL2
+from skglm.datafits import Poisson, Huber, QuadraticGroup, LogisticGroup
+from skglm.solvers import FISTA, ProxNewton, GroupBCD, GramCD, GroupProxNewton
+
+from skglm.utils.data import grp_converter
 from skglm.utils.data import make_correlated_data
 from skglm.utils.jit_compilation import compiled_clone
 
 
 def test_datafit_penalty_solver_compatibility():
-    X, y, _ = make_correlated_data(n_samples=3, n_features=5)
+    grp_size, n_features = 3, 9
+    n_samples = 10
+    X, y, _ = make_correlated_data(n_samples, n_features)
+    X_sparse = sparse.csc_array(X)
+
+    n_groups = n_features // grp_size
+    weights_groups = np.ones(n_groups)
+    weights_features = np.ones(n_features)
+    grp_indices, grp_ptr = grp_converter(grp_size, n_features)
 
+    # basic compatibility checks
     with pytest.raises(
         AttributeError, match="Missing `raw_grad` and `raw_hessian`"
     ):
         ProxNewton()._validate(
             X, y, compiled_clone(Huber(1.)), compiled_clone(L1(1.))
         )
-
     with pytest.raises(
         AttributeError, match="Missing `get_global_lipschitz`"
     ):
         FISTA()._validate(
             X, y, compiled_clone(Poisson()), compiled_clone(L1(1.))
         )
-
     with pytest.raises(
         AttributeError, match="Missing `get_global_lipschitz`"
     ):
         FISTA()._validate(
             X, y, compiled_clone(Poisson()), compiled_clone(L1(1.))
         )
+    # check Gram Solver
+    with pytest.raises(
+        AttributeError, match="`GramCD` supports only `Quadratic` datafit"
+    ):
+        GramCD()._validate(
+            X, y, compiled_clone(Poisson()), compiled_clone(L1(1.))
+        )
+    # check working set strategy subdiff
+    with pytest.raises(
+        AttributeError, match="Penalty must implement `subdiff_distance`"
+    ):
+        GroupBCD()._validate(
+            X, y,
+            datafit=compiled_clone(QuadraticGroup(grp_ptr, grp_indices)),
+            penalty=compiled_clone(
+                WeightedL1GroupL2(
+                    1., weights_groups, weights_features, grp_ptr, grp_indices)
+            )
+        )
+    # checks for sparsity
+    with pytest.raises(
+        ValueError,
+        match="Sparse matrices are not yet supported in `GroupProxNewton` solver."
+    ):
+        GroupProxNewton()._validate(
+            X_sparse, y,
+            datafit=compiled_clone(QuadraticGroup(grp_ptr, grp_indices)),
+            penalty=compiled_clone(
+                WeightedL1GroupL2(
+                    1., weights_groups, weights_features, grp_ptr, grp_indices)
+            )
+        )
+    with pytest.raises(
+        AttributeError,
+        match="LogisticGroup is not compatible with solver GroupBCD with sparse data."
+    ):
+        GroupBCD()._validate(
+            X_sparse, y,
+            datafit=compiled_clone(LogisticGroup(grp_ptr, grp_indices)),
+            penalty=compiled_clone(
+                WeightedGroupL2(1., weights_groups, grp_ptr, grp_indices)
+            )
+        )
 
 
 if __name__ == "__main__":