diff --git a/changelog.d/3969.bugfix b/changelog.d/3969.bugfix
new file mode 100644
index 000000000..ca2759e91
--- /dev/null
+++ b/changelog.d/3969.bugfix
@@ -0,0 +1 @@
+Fix HTTP error response codes for federated group requests.
diff --git a/synapse/handlers/groups_local.py b/synapse/handlers/groups_local.py
index 53e5e2648..173315af6 100644
--- a/synapse/handlers/groups_local.py
+++ b/synapse/handlers/groups_local.py
@@ -20,7 +20,7 @@ from six import iteritems
 
 from twisted.internet import defer
 
-from synapse.api.errors import SynapseError
+from synapse.api.errors import HttpResponseException, SynapseError
 from synapse.types import get_domain_from_id
 
 logger = logging.getLogger(__name__)
@@ -37,9 +37,23 @@ def _create_rerouter(func_name):
             )
         else:
             destination = get_domain_from_id(group_id)
-            return getattr(self.transport_client, func_name)(
+            d = getattr(self.transport_client, func_name)(
                 destination, group_id, *args, **kwargs
             )
+
+            # Capture errors returned by the remote homeserver and
+            # re-throw specific errors as SynapseErrors. This is so
+            # when the remote end responds with things like 403 Not
+            # In Group, we can communicate that to the client instead
+            # of a 500.
+            def h(failure):
+                failure.trap(HttpResponseException)
+                e = failure.value
+                if e.code == 403:
+                    raise e.to_synapse_error()
+                return failure
+            d.addErrback(h)
+            return d
     return f
 
 
diff --git a/synapse/http/matrixfederationclient.py b/synapse/http/matrixfederationclient.py
index fcc02fc77..24b6110c2 100644
--- a/synapse/http/matrixfederationclient.py
+++ b/synapse/http/matrixfederationclient.py
@@ -230,7 +230,7 @@ class MatrixFederationHttpClient(object):
         Returns:
             Deferred: resolves with the http response object on success.
 
-            Fails with ``HTTPRequestException``: if we get an HTTP response
+            Fails with ``HttpResponseException``: if we get an HTTP response
                 code >= 300.
 
             Fails with ``NotRetryingDestination`` if we are not yet ready
@@ -480,7 +480,7 @@ class MatrixFederationHttpClient(object):
             Deferred: Succeeds when we get a 2xx HTTP response. The result
             will be the decoded JSON body.
 
-            Fails with ``HTTPRequestException`` if we get an HTTP response
+            Fails with ``HttpResponseException`` if we get an HTTP response
             code >= 300.
 
             Fails with ``NotRetryingDestination`` if we are not yet ready
@@ -534,7 +534,7 @@ class MatrixFederationHttpClient(object):
             Deferred: Succeeds when we get a 2xx HTTP response. The result
             will be the decoded JSON body.
 
-            Fails with ``HTTPRequestException`` if we get an HTTP response
+            Fails with ``HttpResponseException`` if we get an HTTP response
             code >= 300.
 
             Fails with ``NotRetryingDestination`` if we are not yet ready
@@ -589,7 +589,7 @@ class MatrixFederationHttpClient(object):
             Deferred: Succeeds when we get a 2xx HTTP response. The result
             will be the decoded JSON body.
 
-            Fails with ``HTTPRequestException`` if we get an HTTP response
+            Fails with ``HttpResponseException`` if we get an HTTP response
             code >= 300.
 
             Fails with ``NotRetryingDestination`` if we are not yet ready
@@ -640,7 +640,7 @@ class MatrixFederationHttpClient(object):
             Deferred: Succeeds when we get a 2xx HTTP response. The result
             will be the decoded JSON body.
 
-            Fails with ``HTTPRequestException`` if we get an HTTP response
+            Fails with ``HttpResponseException`` if we get an HTTP response
             code >= 300.
 
             Fails with ``NotRetryingDestination`` if we are not yet ready
@@ -684,7 +684,7 @@ class MatrixFederationHttpClient(object):
             Deferred: resolves with an (int,dict) tuple of the file length and
             a dict of the response headers.
 
-            Fails with ``HTTPRequestException`` if we get an HTTP response code
+            Fails with ``HttpResponseException`` if we get an HTTP response code
             >= 300
 
             Fails with ``NotRetryingDestination`` if we are not yet ready