diff --git a/distributed/scheduler.py b/distributed/scheduler.py
index 5a60eac5f92..f2126a80e41 100644
--- a/distributed/scheduler.py
+++ b/distributed/scheduler.py
@@ -1585,6 +1585,8 @@ class SchedulerState:
     _resources: object
     _saturated: set
     _tasks: dict
+    _task_groups: dict
+    _task_prefixes: dict
     _task_metadata: dict
     _total_nthreads: Py_ssize_t
     _total_occupancy: double
@@ -1635,6 +1637,8 @@ def __init__(
             self._tasks = tasks
         else:
             self._tasks = dict()
+        self._task_groups = dict()
+        self._task_prefixes = dict()
         self._task_metadata = dict()
         self._total_nthreads = 0
         self._total_occupancy = 0
@@ -1691,6 +1695,14 @@ def saturated(self):
     def tasks(self):
         return self._tasks
 
+    @property
+    def task_groups(self):
+        return self._task_groups
+
+    @property
+    def task_prefixes(self):
+        return self._task_prefixes
+
     @property
     def task_metadata(self):
         return self._task_metadata
@@ -1738,6 +1750,8 @@ def __pdict__(self):
             "unknown_durations": self._unknown_durations,
             "validate": self._validate,
             "tasks": self._tasks,
+            "task_groups": self._task_groups,
+            "task_prefixes": self._task_prefixes,
             "total_nthreads": self._total_nthreads,
             "total_occupancy": self._total_occupancy,
             "extensions": self._extensions,
@@ -2926,8 +2940,6 @@ def __init__(
 
         # Task state
         tasks = dict()
-        self.task_groups = dict()
-        self.task_prefixes = dict()
         for old_attr, new_attr, wrap in [
             ("priority", "priority", None),
             ("dependencies", "dependencies", _legacy_task_key_set),
@@ -3919,17 +3931,15 @@ def new_task(self, key, spec, state):
         tg: TaskGroup
         ts._state = state
         prefix_key = key_split(key)
-        try:
-            tp = self.task_prefixes[prefix_key]
-        except KeyError:
-            self.task_prefixes[prefix_key] = tp = TaskPrefix(prefix_key)
+        tp = parent._task_prefixes.get(prefix_key)
+        if tp is None:
+            parent._task_prefixes[prefix_key] = tp = TaskPrefix(prefix_key)
         ts._prefix = tp
 
         group_key = ts._group_key
-        try:
-            tg = self.task_groups[group_key]
-        except KeyError:
-            self.task_groups[group_key] = tg = TaskGroup(group_key)
+        tg = parent._task_groups.get(group_key)
+        if tg is None:
+            parent._task_groups[group_key] = tg = TaskGroup(group_key)
             tg._prefix = tp
             tp._groups.append(tg)
         tg.add(ts)
@@ -5891,12 +5901,12 @@ def transition(self, key, finish, *args, **kwargs):
                 if ts._state == "forgotten":
                     del parent._tasks[ts._key]
 
-            if ts._state == "forgotten" and ts._group._name in self.task_groups:
+            tg: TaskGroup = ts._group
+            if ts._state == "forgotten" and tg._name in parent._task_groups:
                 # Remove TaskGroup if all tasks are in the forgotten state
-                tg: TaskGroup = ts._group
                 if not any([tg._states.get(s) for s in ALL_TASK_STATES]):
                     ts._prefix._groups.remove(tg)
-                    del self.task_groups[tg._name]
+                    del parent._task_groups[tg._name]
 
             return recommendations
         except Exception as e: