diff --git a/CHANGES.md b/CHANGES.md
index 9a5387c..06b0f30 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -17,6 +17,7 @@
     restriction from every `Size` and `Order` argument
   - Fix `AllPrimitiveGroups` and friends to honour every `NrMovedPoints`
     argument, not just the first one
+  - Fix `ShallowCopy` and `List` for `PrimitiveGroupsIterator`
   - Fix the dimension in the names of PrimitiveGroup(1057,1) and (1057,2)
   - Fix 29 socle types recorded with a rank one too high
   - Fix the corrupted name of PrimitiveGroup(625,657)
diff --git a/lib/primitiv.gi b/lib/primitiv.gi
index fd96c44..03ec221 100644
--- a/lib/primitiv.gi
+++ b/lib/primitiv.gi
@@ -1206,6 +1206,23 @@ local g;
   return g;
 end);
 
+# needed by List, which iterates over a copy; the components are either
+# immutable or replaced, never changed in place, so copying them suffices
+InstallMethod(ShallowCopy,"primitive groups iterator",true,
+  [IsPrimGrpIterRep and IsIterator],0,
+function(it)
+local new;
+  new:=Objectify(NewType(IteratorsFamily,
+                         IsIterator and IsPrimGrpIterRep and IsMutable),rec());
+  new!.deg:=it!.deg;
+  new!.degi:=it!.degi;
+  new!.nr:=it!.nr;
+  new!.prop:=it!.prop;
+  new!.gut:=it!.gut;
+  new!.next:=it!.next;
+  return new;
+end);
+
 #############################################################################
 ##
 #F  AllPrimitiveGroups( <fun>, <res>, ... ) . . . . . . . selection function
diff --git a/tst/testinstall/bugfix.tst b/tst/testinstall/bugfix.tst
index 2aa5dda..939dbd3 100644
--- a/tst/testinstall/bugfix.tst
+++ b/tst/testinstall/bugfix.tst
@@ -250,5 +250,21 @@ true
 gap> PRIMGRP_EntryFromDescription(["NoSuchThing"], 6, 1);
 Error, unknown construction "NoSuchThing" for entry 1 of degree 6
 
+# List on an iterator works on a ShallowCopy of it, which must advance
+# independently of the original.
+# See <https://github.com/gap-packages/primgrp/issues/102>
+gap> it := PrimitiveGroupsIterator(NrMovedPoints, 5);;
+gap> NextIterator(it);
+C(5)
+gap> List(it);
+[ D(2*5), AGL(1, 5), A(5), S(5) ]
+gap> copy := ShallowCopy(it);;
+gap> [ NextIterator(copy), NextIterator(copy) ];
+[ D(2*5), AGL(1, 5) ]
+gap> NextIterator(it);
+D(2*5)
+gap> List(PrimitiveGroupsIterator(NrMovedPoints, 5, IsSolvable, false));
+[ A(5), S(5) ]
+
 #
 gap> STOP_TEST("bugfix.tst", 1);