0000 = f0   gives a maximal monoid. It is a retraction with im = 0.
0003 = f3   gives a maximal monoid. It is a retraction with im = 03.
0020 = f8   gives a maximal monoid. It is a retraction with im = 02.
0022 = f10  gives a maximal monoid. It is a retraction with im = 02.
0023 = f11  gives a maximal monoid. It is a retraction with im = 023.
0033 = f15  gives a maximal monoid. It is a retraction with im = 03.
0100 = f16  gives a maximal monoid. It is a retraction with im = 01.
0101 = f17  gives a maximal monoid. It is a retraction with im = 01.
0103 = f19  gives a maximal monoid. It is a retraction with im = 013.
0110 = f20  gives a maximal monoid. It is a retraction with im = 01.
0111 = f21  gives a maximal monoid. It is a retraction with im = 01.
0113 = f23  gives a maximal monoid. It is a retraction with im = 013.
0120 = f24  gives a maximal monoid. It is a retraction with im = 012.
0121 = f25  gives a maximal monoid. It is a retraction with im = 012.
0122 = f26  gives a maximal monoid. It is a retraction with im = 012.
0132 = f30  gives a maximal monoid. It is a permutation of order 2. (23)
0133 = f31  gives a maximal monoid. It is a retraction with im = 013.
0213 = f39  gives a maximal monoid. It is a permutation of order 2. (12)
0220 = f40  gives a maximal monoid. It is a retraction with im = 02.
0222 = f42  gives a maximal monoid. It is a retraction with im = 02.
0223 = f43  gives a maximal monoid. It is a retraction with im = 023.
0303 = f51  gives a maximal monoid. It is a retraction with im = 03.
0321 = f57  gives a maximal monoid. It is a permutation of order 2. (13)
0323 = f59  gives a maximal monoid. It is a retraction with im = 023.
0333 = f63  gives a maximal monoid. It is a retraction with im = 03.
1023 = f75  gives a maximal monoid. It is a permutation of order 2. (01)
1032 = f78  gives a maximal monoid. It is a permutation of order 2. (01)(23)
1111 = f85  gives a maximal monoid. It is a retraction with im = 1.
1113 = f87  gives a maximal monoid. It is a retraction with im = 13.
1121 = f89  gives a maximal monoid. It is a retraction with im = 12.
1122 = f90  gives a maximal monoid. It is a retraction with im = 12.
1123 = f91  gives a maximal monoid. It is a retraction with im = 123.
1133 = f95  gives a maximal monoid. It is a retraction with im = 13.
2103 = f147 gives a maximal monoid. It is a permutation of order 2. (02)
2121 = f153 gives a maximal monoid. It is a retraction with im = 12.
2122 = f154 gives a maximal monoid. It is a retraction with im = 12.
2123 = f155 gives a maximal monoid. It is a retraction with im = 123.
2222 = f170 gives a maximal monoid. It is a retraction with im = 2.
2223 = f171 gives a maximal monoid. It is a retraction with im = 23.
2301 = f177 gives a maximal monoid. It is a permutation of order 2. (02)(13)
2323 = f187 gives a maximal monoid. It is a retraction with im = 23.
3113 = f215 gives a maximal monoid. It is a retraction with im = 13.
3120 = f216 gives a maximal monoid. It is a permutation of order 2. (03)
3123 = f219 gives a maximal monoid. It is a retraction with im = 123.
3133 = f223 gives a maximal monoid. It is a retraction with im = 13.
3210 = f228 gives a maximal monoid. It is a permutation of order 2. (03)(12)
3223 = f235 gives a maximal monoid. It is a retraction with im = 23.
3323 = f251 gives a maximal monoid. It is a retraction with im = 23.
3333 = f255 gives a maximal monoid. It is a retraction with im = 3.
