We've heard a lot about Islam in America during the 2016 presidential election. There've been debates on terrorism, discrimination, radicalization, and, thanks in part to one Donald Trump, Islamophobia.

But with all this talk about Muslims in America, there's something that gets less attention: What do actual American Muslims think?

Now we have a lot more information on this question: a new survey on American Muslim attitudes. It shows a complex picture of American Muslim views, which challenges some of the most commonly held stereotypes — and fears — about Islam in America.

That survey comes from the Institute for Social Policy and Understanding, an independent, nonpartisan think tank that focuses on American Muslims, which this January surveyed Muslims, Jews, Protestants, and Catholics to examine their attitudes on various issues, including politics, religion, violence, and identity. It just released its final report this week.

Here are the five things I found most interesting when I looked through the data:

1) Muslims strongly prefer Democrats (but a few actually like Trump)

Democratic presidential candidates Hillary Clinton and Bernie Sanders are way more popular with Muslims than are any Republican candidates. Clinton received 40 percent support from Muslims and Sanders 27 percent.

Interestingly, Muslims are slightly more likely to favor Bernie Sanders, who is Jewish, than Jews are: 27 percent of Muslims support him compared with 24 percent of Jews. But it's pretty close.

Muslim support for Democrats is perhaps not surprising, considering that many of the GOP candidates have expressed less-than-positive views of Islam and Muslims.

Yet somehow Donald Trump received the most support among the GOP candidates. Four percent of Muslims say they support Trump, compared with 2 percent for Sen. Ted Cruz and 1 percent for Sen. Marco Rubio. (Data for Gov. John Kasich was not publicly released; we asked for it but have not received it as of publication.)

These findings largely back up the findings of the Council on American-Islamic Relations' recent Super Tuesday poll. That poll, which surveyed 1,850 registered Muslim voters in six states holding primary elections that day, found that almost half (46 percent) supported Hillary Clinton, followed by Bernie Sanders (25 percent).

On the Republican side, 11 percent supported Donald Trump. Marco Rubio was the next-highest GOP candidate, with 4 percent support among Muslim voters polled.

The fact that Trump has any support at all among Muslims is pretty shocking, but the reason could be that he's rich and successful and thus may seem like a better bet for improving the US economy (which Muslims care about just like most other Americans). (You can read my previous article on this here for more on why this might be happening.)

2) Muslims who attend mosque are much more active in local communities and politics

The survey found no correlation between frequent mosque attendance and support for violence against civilians. (Yes, they asked.) So that's one stereotype down.

However, frequent mosque attendance is correlated with higher levels of civic engagement. Muslims who say they regularly attend a mosque are more likely to work with their neighbors to solve community problems, be registered to vote, and to plan to vote.

This speaks to an important misconception: that terrorist radicalization happens at the mosque. In fact, the opposite is true; it's where religious and community leaders condemn and seek to correct extremist views.

But more than that, as the survey data shows, mosque attendance corresponds with engagement in American civic life, not withdrawal from it.

And Muslims who say their faith is important to their identity are more likely to say that being American is also important to their identity, the survey found.

In other words, despite a too-common misconception of Muslim religiosity as at odds with an American identity, the two seem to go together; it correlates with civic engagement outside of the mosque as well. Though mosques are sometimes portrayed as scary and alien — think of the protests against mosque construction in some areas in recent years — they are in fact harbingers of integration and engagement.

3) Protestants are more likely than Muslims to think their religion should be the main source of law in America

One of the most common accusations about Muslims from Islamophobes is that they want to institute Sharia, or Islamic law, here in America.

But the overwhelming majority of American Muslims do not think Islam should be the main source of US law, and more than half (55 percent) said their religion should not be a source of American law at all.

Meanwhile, it turns out that more Protestants (12 percent) actually believe their own religion should be the main source of American law than do Muslims (10 percent):

Compared with Catholics or Jews, that minority of Muslims who answered "the main source," while still quite small, is larger. Ten percent isn't nothing.

But the point is that these results look very different from the warnings you sometimes hear that Muslim Americans are engaged in a vast conspiracy to install Sharia law. You don't hear many warnings that Protestants are inherently unfit for office because their religion makes them seek to subvert the Constitution with strict readings of the Bible, or because a Republican presidential candidate says God's law trumps Supreme Court decisions.

4) Islamophobia is being experienced widely

Almost two in three Muslims — 60 percent — reported facing some level of discrimination in the past year because of their religion, with 18 percent reporting regular discrimination and 26 percent reporting occasional discrimination.

Muslims by far report experiencing more discrimination because of their religion than any of the other religious groups polled. The vast majority of Protestants (84 percent) and Catholics (83 percent) reported never having experienced such discrimination.

So Islamophobia isn't just something that happens at Trump rallies or on the airwaves. It's something that happens in real life to large numbers of Americans, and for some of them it has become a regular part of life.

It's a serious problem, and it deserves to be taken seriously. (And it's worth keeping this experience in mind the next time you hear a cable news host complain about the "war on Christmas.")

5) Yet Muslims are the religious group most satisfied with the way things are going in the country

Despite reportedly experiencing more discrimination than any of the other faith groups, a majority of Muslims (68 percent) say they are satisfied with the way the country is going, compared with only 38 percent of Jews and 18 percent of both Catholics and Protestants.

That's pretty striking — Muslims seem to show an unusually high degree of optimism in the United States and the direction it's heading, despite the rise in Islamophobia. That buy-in, again, really cuts against the portrayal of Muslims as somehow apart, when in fact Muslim Americans seem enthusiastic about the US.

The survey also found a staggering 78 percent approval rating, among Muslims, for President Obama — way above his national approval rating of about 50 percent. (The survey was taken just before the White House announced that Obama would speak at a Maryland Islamic center.)

Islamophobia in America goes much deeper than Donald Trump