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You mustn't insist on going out alone this late at night.
Literal
Night this-much late alone [with-で] go-out-[nominalizer-なんて] insist-[prohibition-てはいけません].
A complex prohibition sentence. ~なんて (dismissive/exclamatory) here turns the proposed action into a dismissed category. 言い張る ('insist, maintain stubbornly') is a compound verb: 言う+張る ('stretch, stick to'). The whole structure: [verb] + なんて + 言い張る + てはいけません — 'must not insist on (such a thing as) X.'