| T | Name(s) | |G| | Parity | |CS10(G)| | Subfields | Other Representations | Resolvents |
|---|---|---|---|---|---|---|---|
| 1 | C(10)=5[x]2 | 10 = 2 · 5 | -1 | 10 | 2T1, 5T1 | 2: 2T1 5: 5T1 | |
| 2 | D(10)=5:2 | 10 = 2 · 5 | -1 | 10 | 2T1, 5T2 | 5T2 | 2: 2T1 |
| 3 | D_10(10)=[D(5)]2 | 20 = 22 · 5 | -1 | 2 | 2T1, 5T2 | 10T3, 20T4 | 2: 2T1, 2T1, 2T1 4: 4T2 10: 5T2 |
| 4 | 1/2[F(5)]2 | 20 = 22 · 5 | -1 | 2 | 2T1, 5T3 | 5T3, 20T5 | 2: 2T1 4: 4T1 |
| 5 | F(5)[x]2 | 40 = 23 · 5 | -1 | 2 | 2T1, 5T3 | 10T5, 20T9, 20T13 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 8: 8T2 20: 5T3 |
| 6 | [5^2]2 | 50 = 2 · 52 | -1 | 5 | 2T1 | 10T6 | 2: 2T1 5: 5T1 10: 5T2, 10T1 |
| 7 | A_5(10) | 60 = 22 · 3 · 5 | 1 | 1 | 5T4, 6T12, 12T33, 15T5, 20T15 | ||
| 8 | [2^4]5 | 80 = 24 · 5 | 1 | 2 | 5T1 | 10T8, 10T8, 16T178, 20T17, 20T17, 20T17, 20T17, 20T17, 20T17, 20T23 | 5: 5T1 |
| 9 | [1/2.D(5)^2]2 | 100 = 22 · 52 | -1 | 1 | 2T1 | 10T9, 20T28, 20T28 | 2: 2T1, 2T1, 2T1 4: 4T2 10: 5T2, 5T2 20: 10T3, 10T3 |
| 10 | 1/2[D(5)^2]2 | 100 = 22 · 52 | -1 | 1 | 2T1 | 10T10, 20T27, 20T27 | 2: 2T1 4: 4T1 20: 5T3, 5T3 |
| 11 | A(5)[x]2 | 120 = 23 · 3 · 5 | -1 | 2 | 2T1, 5T4 | 12T75, 12T76, 20T31, 20T36 | 2: 2T1 60: 5T4 |
| 12 | 1/2[S(5)]2=S_5(10a) | 120 = 23 · 3 · 5 | -1 | 2 | 2T1, 5T5 | 5T5, 6T14, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35 | 2: 2T1 |
| 13 | S_5(10d) | 120 = 23 · 3 · 5 | -1 | 1 | 5T5, 6T14, 10T12, 12T74, 15T10, 20T30, 20T32, 20T35 | 2: 2T1 | |
| 14 | [2^5]5 | 160 = 25 · 5 | -1 | 2 | 5T1 | 10T14, 10T14, 20T40, 20T40, 20T40, 20T40, 20T40, 20T40, 20T40, 20T40, 20T40, 20T40, 20T40, 20T40, 20T41, 20T41, 20T41, 20T41, 20T41, 20T41, 20T44, 20T44, 20T44, 20T46, 20T46, 20T46 | 2: 2T1 5: 5T1 10: 10T1 80: 10T8 |
| 15 | [2^4]D(5) | 160 = 25 · 5 | 1 | 2 | 5T2 | 10T15, 10T15, 10T16, 10T16, 10T16, 16T415, 20T38, 20T38, 20T38, 20T38, 20T38, 20T38, 20T39, 20T43, 20T43, 20T43, 20T45, 20T45, 20T45 | 2: 2T1 10: 5T2 |
| 16 | 1/2[2^5]D(5) | 160 = 25 · 5 | -1 | 2 | 5T2 | 10T15, 10T15, 10T15, 10T16, 10T16, 16T415, 20T38, 20T38, 20T38, 20T38, 20T38, 20T38, 20T39, 20T43, 20T43, 20T43, 20T45, 20T45, 20T45 | 2: 2T1 10: 5T2 |
| 17 | [5^2:4]2 | 200 = 23 · 52 | -1 | 1 | 2T1 | 10T17, 20T54, 20T54 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 8: 8T2 20: 5T3, 5T3 40: 10T5, 10T5 |
| 18 | [5^2:4]2_2 | 200 = 23 · 52 | 1 | 1 | 2T1 | 10T18, 10T18, 20T56, 20T56, 20T56 | 2: 2T1 4: 4T1 8: 8T1 |
| 19 | [5^2:4_2]2 | 200 = 23 · 52 | -1 | 1 | 2T1 | 10T21, 10T21, 20T48, 20T48, 20T50, 20T50, 20T55, 20T57, 20T57 | 2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3 |
| 20 | [5^2:4_2]2_2 | 200 = 23 · 52 | -1 | 1 | 2T1 | 10T20, 10T20, 20T47, 20T47, 20T47 | 2: 2T1, 2T1, 2T1 4: 4T2 8: 8T5 |
| 21 | [D(5)^2]2 | 200 = 23 · 52 | -1 | 1 | 2T1 | 10T19, 10T21, 20T48, 20T48, 20T50, 20T50, 20T55, 20T57, 20T57 | 2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3 |
| 22 | S(5)[x]2 | 240 = 24 · 3 · 5 | -1 | 2 | 2T1, 5T5 | 10T22, 12T123, 12T123, 20T62, 20T62, 20T65, 20T65, 20T70 | 2: 2T1, 2T1, 2T1 4: 4T2 120: 5T5 |
| 23 | [2^5]D(5) | 320 = 26 · 5 | -1 | 2 | 5T2 | 10T23, 10T23, 10T23, 10T23, 10T23, 20T71, 20T71, 20T71, 20T71, 20T71, 20T71, 20T73, 20T73, 20T73, 20T73, 20T73, 20T73, 20T76, 20T76, 20T76, 20T76, 20T76, 20T76, 20T81, 20T81, 20T81, 20T85, 20T85, 20T85, 20T85, 20T85, 20T85, 20T87, 20T87, 20T87, 20T87, 20T87, 20T87 | 2: 2T1, 2T1, 2T1 4: 4T2 10: 5T2 20: 10T3 160: 10T15 |
| 24 | [2^4]F(5) | 320 = 26 · 5 | 1 | 2 | 5T3 | 10T25, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88 | 2: 2T1 4: 4T1 20: 5T3 |
| 25 | 1/2[2^5]F(5) | 320 = 26 · 5 | -1 | 2 | 5T3 | 10T24, 16T711, 20T77, 20T78, 20T79, 20T80, 20T83, 20T88 | 2: 2T1 4: 4T1 20: 5T3 |
| 26 | L(10)=PSL(2,9) | 360 = 23 · 32 · 5 | 1 | 1 | 6T15, 6T15, 15T20, 15T20, 20T89 | ||
| 27 | [1/2.F(5)^2]2 | 400 = 24 · 52 | -1 | 1 | 2T1 | 10T27, 10T27, 20T90, 20T90, 20T90, 20T96, 20T96, 20T96, 20T97, 20T97, 20T97 | 2: 2T1, 2T1, 2T1, 2T1, 2T1, 2T1, 2T1 4: 4T2, 4T2, 4T2, 4T2, 4T2, 4T2, 4T2 8: 8T3 16: 8T11 |
| 28 | 1/2[F(5)^2]2 | 400 = 24 · 52 | 1 | 1 | 2T1 | 20T104, 20T107, 20T109, 20T115 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 8: 8T2 16: 8T7 |
| 29 | [2^5]F(5) | 640 = 27 · 5 | -1 | 2 | 5T3 | 10T29, 20T129, 20T131, 20T131, 20T132, 20T133, 20T134, 20T135, 20T137, 20T137, 20T140 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 8: 8T2 20: 5T3 40: 10T5 320: 10T24 |
| 30 | L(10):2=PGL(2,9) | 720 = 24 · 32 · 5 | -1 | 1 | 12T182, 20T146 | 2: 2T1 | |
| 31 | M(10)=L(10)'2 | 720 = 24 · 32 · 5 | 1 | 1 | 12T181, 20T148, 20T150, 20T150 | 2: 2T1 | |
| 32 | S_6(10)=L(10):2 | 720 = 24 · 32 · 5 | -1 | 1 | 6T16, 6T16, 12T183, 12T183, 15T28, 15T28, 20T145, 20T149, 20T149 | 2: 2T1 | |
| 33 | [F(5)^2]2 | 800 = 25 · 52 | -1 | 1 | 2T1 | 20T155, 20T161, 20T167, 20T169 | 2: 2T1, 2T1, 2T1 4: 4T1, 4T1, 4T2 8: 4T3, 4T3, 8T2 16: 8T10 32: 8T17 |
| 34 | [2^4]A(5) | 960 = 26 · 3 · 5 | 1 | 2 | 5T4 | 16T1081, 20T172, 20T177 | 60: 5T4 |
| 35 | L(10).2^2=P|L(2,9) | 1440 = 25 · 32 · 5 | -1 | 1 | 12T220, 20T201, 20T204, 20T208 | 2: 2T1, 2T1, 2T1 4: 4T2 | |
| 36 | [2^5]A(5) | 1920 = 27 · 3 · 5 | -1 | 2 | 5T4 | 20T224, 20T225, 20T230 | 2: 2T1 60: 5T4 120: 10T11 960: 10T34 |
| 37 | [2^4]S(5) | 1920 = 27 · 3 · 5 | 1 | 2 | 5T5 | 10T38, 16T1328, 20T218, 20T219, 20T222, 20T223, 20T226 | 2: 2T1 120: 5T5 |
| 38 | 1/2[2^5]S(5) | 1920 = 27 · 3 · 5 | -1 | 2 | 5T5 | 10T37, 16T1328, 20T218, 20T219, 20T222, 20T223, 20T226 | 2: 2T1 120: 5T5 |
| 39 | [2^5]S(5) | 3840 = 28 · 3 · 5 | -1 | 2 | 5T5 | 10T39, 20T275, 20T279, 20T279, 20T285, 20T285, 20T288, 20T288, 20T289, 20T289 | 2: 2T1, 2T1, 2T1 4: 4T2 120: 5T5 240: 10T22 1920: 10T37 |
| 40 | [A(5)^2]2 | 7200 = 25 · 32 · 52 | -1 | 1 | 2T1 | 12T269, 20T363 | 2: 2T1 |
| 41 | [1/2.S(5)^2]2=[A(5):2]2 | 14400 = 26 · 32 · 52 | -1 | 1 | 2T1 | 12T279, 20T456, 20T459 | 2: 2T1, 2T1, 2T1 4: 4T2 |
| 42 | 1/2[S(5)^2]2 | 14400 = 26 · 32 · 52 | 1 | 1 | 2T1 | 12T278, 20T457, 20T461 | 2: 2T1 4: 4T1 |
| 43 | [S(5)^2]2 | 28800 = 27 · 32 · 52 | -1 | 1 | 2T1 | 12T288, 20T539, 20T540, 20T542, 20T544 | 2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3 |
| 44 | A10 | 1814400 = 27 · 34 · 52 · 7 | 1 | 1 | |||
| 45 | S10 | 3628800 = 28 · 34 · 52 · 7 | -1 | 1 | 20T1007 | 2: 2T1 |