diff --git a/docker/frontend/src/ui/ChipColumn.tsx b/docker/frontend/src/ui/ChipColumn.tsx
index 1a30d71..02350ec 100644
--- a/docker/frontend/src/ui/ChipColumn.tsx
+++ b/docker/frontend/src/ui/ChipColumn.tsx
@@ -117,7 +117,10 @@ export function ChipRow({
               chip.onClick();
             }}
           >
-            {list && glyph ? <span className="chip-glyph" aria-hidden="true">{glyph}</span> : null}
+            {/* A row that cannot be picked is not a name in the list, it is the
+                head the names stand under: no mark, the way a group heading
+                reads. */}
+            {list && glyph && !chip.disabled ? <span className="chip-glyph" aria-hidden="true">{glyph}</span> : null}
             {chip.color ? <span className="chip-dot" data-color={chip.color} style={{ background: chip.color }} /> : null}
             {/* The name is a box, not the bare text node it used to be: a flex
                 container turns a loose text node into an anonymous item of its