Under former leader Hosni Mubarak, election season for Egypt's Muslim Brotherhood often meant arrests, beatings and pitched battles with riot police at polling stations.

In the new Egypt, the once-banned Islamist group faces very different challenges as it gears up for the start on Monday of the first free polls since Mubarak was deposed in February.

Hoping to gain a sizeable slice of seats in parliament, the group has cautiously avoided friction with the ruling military council, refusing to support this week's protests in Tahrir Square demanding the army immediately hand power to civilians.

This has strengthened perceptions that its main concern is to ensure that nothing disrupts its election chances, fuelling anger among protesters. A top Brotherhood leader was forced out of Tahrir on Monday when he tried to visit the square.

Their eye is on the elections and nothing else. They just want political gains, said one protester, shouting at another demonstrator who said he belonged to the Brotherhood's newly formed political wing, the Freedom and Justice Party (FJP).

The Brotherhood helped organise an initial anti-army protest in Tahrir on November 18, but stayed out of subsequent demonstrations in which 41 people were killed and 2,000 wounded.

In post-Mubarak Egypt, the group faces competition from newly formed liberal parties and rival Islamists who could suck away some support, but senior Brotherhood officials remain confident they will emerge as the biggest bloc in parliament.

We want to win, but not alone. We want the whole country to win in this democratic game, said Essam el-Erian, the FJP's deputy head, who spent years in and out of jail under Mubarak. He walked out of prison in February when police lost control.

The Brotherhood is a grassroots movement that for decades has operated a charity and welfare network that helped Egyptians neglected by the state. But that does not guarantee a triumph at the polls, analysts and disenchanted former members say.

INTERNAL DIVISIONS

The electoral alliance it forged ahead of the polls has splintered. One Islamist party quit, accusing the Brotherhood of seeking to hog too many seats on the coalition's candidate list.

The Brotherhood also has internal divisions, disillusioned former members say. Now that a share in power is a real prospect, it has yet to decide how its political role fits in with its traditional proselytising and social outreach work.

Brotherhood members themselves, even at leaderships levels, do not know what the relationship is ... between religion and state, says Mohamed El-Gebba, 27, a medical agent who spent 10 years in the movement, but left after the anti-Mubarak revolt.

Predicting how well the Brotherhood will do in the election is difficult. After years of rigged polls that ensured crushing wins for Mubarak's National Democratic Party, voters now face a bewildering array of mostly unfamiliar new parties.

The Brotherhood's best electoral showing was in 2005, when its candidates, running as thinly veiled independents to skirt a ban, won a fifth of seats, making it the biggest opposition bloc in parliament. It boycotted the widely rigged 2010 vote.

In the typically low turnouts of the Mubarak era, the Brotherhood was expert at getting out the vote. This time, analysts say turnout could be three times higher, perhaps 60 percent of Egypt's 50 million eligible voters, diluting the impact of the Brotherhood's disciplined voting machine.

But the organisation will have the advantage of name recognition to distinguish it from myriad other parties.

They are a strong party with experience in politics and fear God ... I am personally not very religious and do not pray regularly, but I trust people with good faith. Plus I don't have another option, said 32-year-old Ahmed Hassan.

Analysts suggest Islamists could win 40 percent of seats, with a big portion of those going to the Brotherhood.

RIVAL ISLAMISTS

The Brotherhood faces rival Islamist parties in a conspicuously pious country where most women wear Islamic headscarves and men pray publicly in offices or on pavements.

Even some devout Egyptians oppose what they see as the Brotherhood's bid to impose its vision of Islam on the nation.

I pray, I fast, I have faith, my whole family does. We don't need Islamists to teach us how to be Muslims. They are scaring us. We just want a government that improves our lives, said Nabaweya Elsayed, a housemaid who wears the veil.

Egyptians may be religious, but when they watch television, Arabic music clips and films featuring skimpily-dressed stars provide stiff competition to Islamic televangelist shows.

Brotherhood officials deny plans to impose Islamic law. They tend to avoid spelling out their plans for a civil state with an Islamic reference, reticence that fuels concerns of some.

Secular Egyptians worry Islamists may impose the veil and ban alcohol and mixed bathing, driving away Western tourists.

Asked about such restrictions, the FJP's secretary-general Saad el-Katatni told Reuters: I cannot draft a law that says an unveiled woman will be forbidden from this or that ... (but) I must make her feel that her punishment is in the afterlife.

He hinted the party might seek to ban alcohol for Egyptians and allow it only for tourists on private hotel beaches.

For non-Muslims, they have their particular ways, but for Egyptian society, even regardless of religion, it has its customs and traditions, Katatni explained.

Any such curbs could damage Egypt's vital tourist industry, which provides one in eight jobs.

POLITICAL GOALS

Many Brotherhood leaders and supporters have big business interests and the FJP says it espouses a free-market economy.

But recent statements by party leaders suggest a turn away from earlier pledges to model their platform on the tolerant model of Turkey's ruling party, which has Islamist roots.

We can benefit from the Turkish experience in economic growth, but Egypt is not Turkey, neither in its composition nor its people, tradition or culture, Katatni said.

The Muslim Brotherhood is widely recognised as Egypt's best-organised political organisation, but it can no longer count on picking up all the protest votes, as it did in the Mubarak era.

In October, a Brotherhood-backed list had mixed results in board elections for the medical syndicate, one of many professional associations in which the Islamist group has long had a strong if not dominant presence.

It won a 75 percent majority in an election for the syndicate's national board, but lost by wide margins in ballots for many provincial boards, including Cairo and Alexandria.

Few doubt the Brotherhood will be a strong contender in the fluid political landscape opened up by the uprising against Mubarak, but now that the unifying goal of his removal has been achieved, it faces challenges to its cohesion and discipline.

Gebba said he quit out of frustration at what he saw as the leaderhip's attempts to control young Brotherhood members during the uprising and deter them from interacting with other youth groups who put national pride above religion or ideology.

National interests had to come first ... Why should I ask permission to join a demonstration? he asked.

Gebba, who once worked for the Brotherhood to recruit support from new university entrants on campus tours, estimates that 6,000 youth members have left the group since February.

Katatni denies the Brotherhood is stifling its youthful supporters. He said it practises democracy on all levels, but complained: Some of the youth want to impose their opinions on the institution, which...operates according to its regulations.

The Brotherhood will be looking to success at the polls to silence its critics, but it may have to moderate its approach once it is in parliament, grappling with the realities of power.

They are a pragmatic force in essence and will alter their stance even if there is a rift between their slogans and actual behaviour, said political analyst Nabil Abdel Fattah.

There is no future for them in Egypt unless they adopt a more moderate, centrist, dynamic rhetoric.

(Additional reporting by Yasmine Saleh and Tom Perry; Editing by Edmund Blair)