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15 minutes.
First 4 minutes, starts with 1 person, increases group by 1 until size 5. (+4)
Then, need to make groups of 2, so 5 choose 2 is 10, but down by 2 since the groups of 2 and 3 from part 1 don't account. (+8)
Add 1 person. At that point, the small group of 4 can do 2 arrangements (all 4, 2+2, if you left the right combinations from their 5 choose 2). (+2)
Finally, add 1 person to the big group, then finally tell Jane. You can't have the final untold group of 2, since all those combinations have already been done. (+1)

Edited: down to 15 min.

AB | CDEFGHIJ
ABC | DEFGHIJ
ABCD | EFGHIJ
ABCDE | FGHIJ
AC | BDE | HJ | FGI
AD | BCE | FH | GIJ
AE | BCD | FI | GHJ
BC | ADE | FJ | GHI
BD | ACE | GH | FIJ
BE | ACD | GI | FHJ
CD | ABE | GJ | FHI
CE | ADE | HI | FGJ
ABCDEF | GHIJ
ABCDEFG | HIJ
ABCDEFGH | IJ
ABCDEFGHIJ

15 minutes.
First 4 minutes, starts with 1 person, increases group by 1 until size 5. (+4)
Then, need to make groups of 2, so 5 choose 2 is 10, but down by 2 since the groups of 2 and 3 from part 1 don't account. (+8)
Add 1 person. At that point, the small group of 4 can do 2 arrangements (all 4, 2+2, if you left the right combinations from their 5 choose 2). (+2)
Finally, add 1 person to the big group, then finally tell Jane. You can't have the final untold group of 2, since all those combinations have already been done. (+1)

Edited: down to 15 min.

AB | CDEFGHIJ
ABC | DEFGHIJ
ABCD | EFGHIJ
ABCDE | FGHIJ
AC | BDE | HJ | FGI
AD | BCE | FH | GIJ
AE | BCD | FI | GHJ
BC | ADE | FJ | GHI
BD | ACE | GH | FIJ
BE | ACD | GI | FHJ
CD | ABE | GJ | FHI
CE | ABD | HI | FGJ
ABCDEF | GHIJ
ABCDEFG | HIJ
ABCDEFGH | IJ
ABCDEFGHIJ

15 minutes.
First 4 minutes, starts with 1 person, increases group by 1 until size 5. (+4)
Then, need to make groups of 2, so 5 choose 2 is 10, but down by 2 since the groups of 2 and 3 from part 1 don't account. (+8)
Add 1 person. At that point, the small group of 4 can do 2 arrangements (all 4, 2+2, if you left the right combinations from their 5 choose 2). (+2)
Finally, add 1 person to the big group, then finally tell Jane. You can't have the final untold group of 2, since all those combinations have already been done. (+1)

Edited: down to 15 min.

AB | CDEFGHIJ
ABC | DEFGHIJ
ABCD | EFGHIJ
ABCDE | FGHIJ
AC | BDE | HJ | FGI
AD | BCE | FH | GIJ
AE | BCD | FI | GHJ
BC | ADE | FJ | GHI
BD | ACE | GH | FHI
BE | ACD | GI | FHJ
CD | ABE | GJ | FHI
CE | ADE | HI | FGJ
ABCDEF | GHIJ
ABCDEFG | HIJ
ABCDEFGH | IJ
ABCDEFGHIJ

15 minutes.
First 4 minutes, starts with 1 person, increases group by 1 until size 5. (+4)
Then, need to make groups of 2, so 5 choose 2 is 10, but down by 2 since the groups of 2 and 3 from part 1 don't account. (+8)
Add 1 person. At that point, the small group of 4 can do 2 arrangements (all 4, 2+2, if you left the right combinations from their 5 choose 2). (+2)
Finally, add 1 person to the big group, then finally tell Jane. You can't have the final untold group of 2, since all those combinations have already been done. (+1)

Edited: down to 15 min.

AB | CDEFGHIJ
ABC | DEFGHIJ
ABCD | EFGHIJ
ABCDE | FGHIJ
AC | BDE | HJ | FGI
AD | BCE | FH | GIJ
AE | BCD | FI | GHJ
BC | ADE | FJ | GHI
BD | ACE | GH | FIJ
BE | ACD | GI | FHJ
CD | ABE | GJ | FHI
CE | ADE | HI | FGJ
ABCDEF | GHIJ
ABCDEFG | HIJ
ABCDEFGH | IJ
ABCDEFGHIJ

15 minutes.
First 4 minutes, starts with 1 person, increases group by 1 until size 5. (+4)
Then, need to make groups of 2, so 5 choose 2 is 10, but down by 2 since the groups of 2 and 3 from part 1 don't account. (+8)
Add 1 person. At that point, the small group of 4 can do 2 arrangements (all 4, 2+2, if you left the right combinations from their 5 choose 2). (+2)
Finally, add 1 person to the big group, then finally tell Jane. You can't have the final untold group of 2, since all those combinations have already been done. (+1)

Edited: down to 15 min.

AB | CDEFGHIJ
ABC | DEFGHIJ
ABCD | EFGHIJ
ABCDE | FGHIJ
AC | BDE | FG | HIJ
AD | BCE | FH | GIJ
AE | BCD | FI | GHJ
BC | ADE | FJ | GHI
BD | ACE | HJ | FGI
BE | ACD | GI | FHJ
CD | ABE | GJ | FHI
CE | ADE | HI | FGJ
ABCDEF | GHIJ
ABCF | DE | GH | IJ
ABCDEFI | GHJ
ABCDEFGHIJ

15 minutes.
First 4 minutes, starts with 1 person, increases group by 1 until size 5. (+4)
Then, need to make groups of 2, so 5 choose 2 is 10, but down by 2 since the groups of 2 and 3 from part 1 don't account. (+8)
Add 1 person. At that point, the small group of 4 can do 2 arrangements (all 4, 2+2, if you left the right combinations from their 5 choose 2). (+2)
Finally, add 1 person to the big group, then finally tell Jane. You can't have the final untold group of 2, since all those combinations have already been done. (+1)

Edited: down to 15 min.

AB | CDEFGHIJ
ABC | DEFGHIJ
ABCD | EFGHIJ
ABCDE | FGHIJ
AC | BDE | HJ | FGI
AD | BCE | FH | GIJ
AE | BCD | FI | GHJ
BC | ADE | FJ | GHI
BD | ACE | GH | FHI
BE | ACD | GI | FHJ
CD | ABE | GJ | FHI
CE | ADE | HI | FGJ
ABCDEF | GHIJ
ABCDEFG | HIJ
ABCDEFGH | IJ
ABCDEFGHIJ