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Here are all the F2L cases you need to learn for the 3x3.
Please submit any algorithms that are not included.

Sub Groups:

399

F2l-1

441

1.)

U R U' R'

442

2.)

R' F R F'

400

F2l-2

443

1.)

F R' F' R

444

2.)

(y) U' L' U L

498

3.)

r U R' U' M

401

F2l-3

445

1.)

R U R'

402

F2l-4

446

1.)

(y) L' U' L

447

2.)

F' U' F

403

F2l-5

448

1.)

(R U' R') (U R U' R')

404

F2l-6

449

1.)

(y) (L' U L) (U' L' U L)

450

2.)

(R U R' U') r U R' U' M

405

F2l-7

451

1.)

R' U' R' U' R' U R U R

452

2.)

B' R2 U' R' U R2 B

406

F2l-8

453

1.)

U R U' R' d' (L' U L)

407

F2l-9

454

1.)

U' R U R' U2 (R U' R')

408

F2l-10

455

1.)

d R' U' R U2 (R' U R)

458

2.)

U' r U' R' U R U r'

409

F2l-11

456

1.)

U' R U2' R' U2 (R U' R')

410

F2l-12

457

1.)

d R' U2 R U2' (R' U R)

411

F2l-13

459

1.)

(R U R') U2 (R U' R') U (R U' R')

460

2.)

(R U R') U2 R U' R2' (F R F')

412

F2l-14

461

1.)

(R U' R') U2 y' R' U' R

413

F2l-15

462

1.)

d (R' U' R) U' (R' U' R)

414

F2l-16

463

1.)

U' R U R' U (R U R')

415

F2l-17

464

1.)

U' R U2' R' d (R' U' R)

416

F2l-18

465

1.)

R' U2 R2 U R2' U R

466

2.)

(U R U' R') U' (R U R') U' (R U R')

467

3.)

(R U' R' U) (R U' R') U2 (R U' R')

417

F2l-19

468

1.)

d (R' U R) U' (R' U' R)

418

F2l-20

469

1.)

U' (R U' R') U (R U R')

419

F2l-21

470

1.)

(R U2 R') U' (R U R')

420

F2l-22

471

1.)

(y') (R' U2' R) U (R' U' R)

421

F2l-23

472

1.)

U (R U2' R') U (R U' R')

422

F2l-24

473

1.)

(y') U' (R' U2 R) U' (R' U R)

423

F2l-25

474

1.)

U2 (R U R') U (R U' R')

424

F2l-26

475

1.)

(r U' r') U2 (r U r')

425

F2l-27

476

1.)

U2 R2 U2' R' U' R U' R2'

426

F2l-28

477

1.)

(F U R U' R' F') (R U' R')

427

F2l-29

478

1.)

(y') (R' U' R) U (R' U' R)

428

F2l-30

479

1.)

(R U R') U' (R U R')

429

F2l-31

480

1.)

U' (R U' R') U2 (R U' R')

430

F2l-32

481

1.)

U (R U R') U2 (R U R')

431

F2l-33

482

1.)

U' (R U R') d (R' U' R)

432

F2l-34

483

1.)

d (R' U' R) d' (R U R')

484

2.)

(R U R') U (R U' R') y' U' (R' U R)

433

F2l-35

485

1.)

U' (R' F R F') (R U' R')

486

2.)

(R U' R') d (R' U R)

434

F2l-36

487

1.)

(R U R' U') (R U R' U') (R U R')

435

F2l-37

488

1.)

(R U' R') U' (R U R') U2 (R U' R')

436

F2l-38

489

1.)

(R U R') U2 (R U' R') U (R U R')

437

F2l-39

490

1.)

(R U' R') d (R' U' R) U' (R' U' R)

438

F2l-40

491

1.)

(R U' R') (r U' r') U2 (r U r')

439

F2l-41

492

1.)

R2' U2' (F R2 F') U2' R' U R'