Producing A Summary Table Of Amounts Per Status Per User

I want to produce a summary table of amounts per status per user.

I have 2 tables:

Invoices:

Code:
user_id, amount, status
1, £10, S
2, £20, P
3, £30, P
3, £40, E

Users:

Code:
user_id, name
1, user A
2, user B
3, user C

And I want to produce a summary table like this:

Code:
S P E Total
user A £10 £10
user B £20 £20
user C £30 £40 £70

What I have is:

Code:
SELECT Users.name,
(SELECT SUM(amount) FROM Invoices AS t1 WHERE t1.user_id = Invoices.user_id AND (t1.status = 'S')),
(SELECT SUM(amount) FROM Invoices AS t1 WHERE t1.user_id = Invoices.user_id AND (t1.status = 'P')),
(SELECT SUM(amount) FROM Invoices AS t1 WHERE t1.user_id = Invoices.user_id AND (t1.status = 'E')),
(SELECT SUM(amount) FROM Invoices AS t1 WHERE t1.user_id = Invoices .user_id AND (t1.status IN ('S','P','E')))
FROM Invoices
LEFT JOIN Users ON Users.user_id = Invoices .user_id
GROUP BY Invoices.user_id, Users.name
ORDER BY Users.name

This does give me what I want, however the real situation has lots of status codes, many more fields in the Invoices table, hundreds of users and hundred of thousands of records in the Invoice table and I have run out of system memory.