Prince George's Councilman Parris N. Glendening opened his campaign to succeed County Executive Lawrence J. Hogan yesterday, proclaiming himself as the Democratic Party's "consensus candidate" and attacking what he called the "deliberate divisiveness" of Hogan's administration.

Surrounded by many of the men who made up the core of the county's Democratic organization for the past 12 years Glendening, 39, made official what he has spent the past two years planning: He wants the county government's top job.

Speaking to a crowd of more than 200 at the student union of the University of Maryland, where he teaches political science, he became the first major political figure to announce for the position. Though Glendening is the third Democrat to enter the race, he is the only candidate of either party who has formed a committee, actively raised money and sought support from citizen and political groups.

Glendening directed some of his remarks yesterday at Hogan, who is seeking the Republican nomination to oppose Sen. Paul S. Sarbanes. Hogan's 1983 county budget cut education spending because he said the county needed to spend more on public safety. "I reject the policies and rhetoric which pits one group against another," Glendening said yesterday. "I reject budget strategies and political speeches that are designed to create a confrontation between our teachers and our police officers."

At yesterday's announcement Glendening was introduced by Rep. Steny H. Hoyer (D-Md.). His supporters include former county executive Winfield M. Kelly Jr., state Sens. Arthur Dorman and Tommie Broadwater, a host of municipal officials and state delegates and much of the present council.

Lt. Gov. Samuel Bogley and council member Sue V. Mills, both highly popular officials with a similar base of conservative support, have been considered contenders for the Democratic nomination. Last week, however, Mills announced her intention to run for reelection to the council and Bogley, whose infant son died last month, has consistently declined to make his political plans clear.

Glendening, who has raised more than $100,000 for the race, said he believed that Bogley would not be an opponent. Two other men, John Lee Ball, of Hyattsville, and Arthur B. Haynes, an Anacostia High School teacher who lives in Capitol Heights, have filed papers with the Elections Board indicating their intention to run.

Glendening said his next task would be to improve his name recognition with county voters. Two council members close to his campaign noted that Glendening will have to broaden his support from his base in northern Prince George's. Only one elected official for the southern half of the county attended his rally yesterday, the council members noted.

The Glendening campaign swept across the county yesterday. The candidate went from a street festival in Laurel to a picnic in Brandywine. After the rally at the University of Maryland, complete with balloons and a pep band, Glendening stopped at a roller-skating fund-raiser, an Upper Marlboro festival and a church fund-raiser.

This week, Glendening said he begins a week-long series of radio commericals designed to improve his name recognition. He said his most recent poll, completed last week, showed that 60 percent of the county's registered Democrats who voted in two out of the last three primaries recognized his name..