diff --git a/moto/iam/responses.py b/moto/iam/responses.py
index <HASH>..<HASH> 100644
--- a/moto/iam/responses.py
+++ b/moto/iam/responses.py
@@ -1349,6 +1349,7 @@ LIST_GROUPS_FOR_USER_TEMPLATE = """<ListGroupsForUserResponse>
             <GroupName>{{ group.name }}</GroupName>
             <GroupId>{{ group.id }}</GroupId>
             <Arn>{{ group.arn }}</Arn>
+            <CreateDate>{{ group.created_iso_8601 }}</CreateDate>
         </member>
         {% endfor %}
     </Groups>
@@ -1651,6 +1652,7 @@ LIST_GROUPS_FOR_USER_TEMPLATE = """<ListGroupsForUserResponse>
             <GroupName>{{ group.name }}</GroupName>
             <GroupId>{{ group.id }}</GroupId>
             <Arn>{{ group.arn }}</Arn>
+            <CreateDate>{{ group.created_iso_8601 }}</CreateDate>
         </member>
         {% endfor %}
     </Groups>
Add CreateDate to iam list_groups_for_user.

Add the CreateDate field to the list_groups_for_user to match the
correct AWS response. Fixes #<I>