She suggested that he apply / He denied having seen it (C1 Grammar)

When you report a recommendation with suggest, insist, recommend, demand, the that-clause keeps the base verb for every subject — the same form for he/she/it: "She suggested that he apply", not "applies". This is the formal, official choice — reach for it in reports, minutes and academic writing. You will also meet "suggested that he should apply": that is the standard formal pattern in British English, not a casual version of this one, so both belong in a report. Watch out: with suggest and insist the base verb marks a demand. "He insisted that she be told" asks for something to happen; "He insisted that she was told" reports what he claimed. For the negative, put not before the base verb — "insisted that he not be told" (never "doesn't be").

After suggest / insist / recommend: the base verb

After deny / admit: having + past participle

Deny and admit take an -ing form or a that-clause — what they do not take is a plain to-infinitive (never "denied to have seen"). The that-clause is the commonest choice of all: "He denied that he had seen the report". Among the -ing forms, plain seeing is the everyday default in formal writing too, and having + past participle adds one thing: it marks the act as finished before the reporting. Admit also allows to in front of the -ing form: "She admitted to having made an error".

After inform / remind: a person, then that

Inform and remind are formal reporting verbs that must name a person before the that-clause: inform / remind + someone + that .... Use inform to report telling news and remind to report prompting a memory — both suit official or careful contexts where "tell" would feel plain. The person object is what sets them apart: say and suggest never take a person this way ("say to someone", not "say someone"), so with inform and remind you name the person directly, with no "to".