General contractor insurance

What kind of insurance works best for a GC doing jobs using subcontractors who sometimes may not carry insurance especially with handymen like installing a cabinet or replacing a light fixture. What if the handyman hits a screw in the electric cable and causes a fire. Would my GC insurance ( general liability) cover that damage or does he need to have his own since I subbed work to him. When would my GL insurance come in play since I am never working but only managing the jobs?