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Elements of the group are displayed as permutations of degree 20.
| Group | Label | Order | Size | Centralizer | Powers | Representative | |
|---|---|---|---|---|---|---|---|
| 2P | 3P | ||||||
| $A_4^2.S_4\wr C_2.C_4$ | 1A | $1$ | $1$ | $A_4^2.S_4\wr C_2.C_4$ | 1A | 1A | $()$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2A | $2$ | $1$ | $A_4^2.S_4\wr C_2.C_4$ | 1A | 2A | $(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2B | $2$ | $12$ | $C_2^6.C_3^3.C_2^4.C_2$ | 1A | 2B | $(6,7)(8,14)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2C | $2$ | $12$ | $C_2^6.C_3^3.C_2^4.C_2$ | 1A | 2C | $(6,7)(8,14)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2D | $2$ | $18$ | $A_4^2.C_2^3.C_2^4.C_2$ | 1A | 2D | $(2,12)(6,8)(7,14)(10,16)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2E | $2$ | $18$ | $A_4^2.C_2^3.C_2^4.C_2$ | 1A | 2E | $(3,4)(6,7)(8,14)(11,13)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2F | $2$ | $18$ | $A_4^2.C_2^3.C_2^4.C_2$ | 1A | 2F | $(3,4)(6,7)(8,14)(11,13)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2G | $2$ | $18$ | $A_4^2.C_2^3.C_2^4.C_2$ | 1A | 2G | $(2,10)(6,7)(8,14)(12,16)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2H | $2$ | $18$ | $C_2\times A_4^2.D_4^2.C_2$ | 1A | 2H | $(2,10)(3,4)(11,13)(12,16)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2I | $2$ | $18$ | $C_2\times A_4^2.D_4^2.C_2$ | 1A | 2I | $(2,10)(3,4)(11,13)(12,16)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2J | $2$ | $72$ | $A_4^2.C_2^5.C_2$ | 1A | 2J | $(7,8)(12,16)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2K | $2$ | $72$ | $A_4^2.C_2^5.C_2$ | 1A | 2K | $(1,5)(4,11)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2L | $2$ | $81$ | $C_2^5.C_2^6.C_2^2$ | 1A | 2L | $(1,5)(2,12)(3,11)(4,13)(6,14)(7,8)(9,15)(10,16)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2M | $2$ | $81$ | $C_2^5.C_2^6.C_2^2$ | 1A | 2M | $(1,15)(2,16)(3,11)(4,13)(5,9)(6,14)(7,8)(10,12)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2N | $2$ | $108$ | $A_4.C_2^6.C_2^3$ | 1A | 2N | $(1,9)(3,13)(4,11)(5,15)(6,8)(7,14)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2O | $2$ | $108$ | $A_4.C_2^6.C_2^3$ | 1A | 2O | $(1,15)(2,10)(3,11)(4,13)(5,9)(12,16)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2P | $2$ | $288$ | not computed | 1A | 2P | $(1,6)(2,11)(3,12)(4,16)(5,14)(7,15)(8,9)(10,13)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2Q | $2$ | $288$ | not computed | 1A | 2Q | $(1,6)(2,4)(3,10)(5,14)(7,15)(8,9)(11,16)(12,13)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2R | $2$ | $432$ | not computed | 1A | 2R | $(1,9)(2,12)(10,16)(11,13)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2S | $2$ | $432$ | not computed | 1A | 2S | $(1,15)(4,13)(6,7)(8,14)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2T | $2$ | $648$ | not computed | 1A | 2T | $(2,10)(6,7)(8,14)(9,15)(11,13)(12,16)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2U | $2$ | $648$ | not computed | 1A | 2U | $(2,10)(6,7)(8,14)(9,15)(11,13)(12,16)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2V | $2$ | $1296$ | not computed | 1A | 2V | $(4,13)(5,15)(6,7)(10,12)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 2W | $2$ | $1296$ | not computed | 1A | 2W | $(1,9)(2,12)(3,4)(7,14)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3A | $3$ | $32$ | $C_2\times A_4^2.A_4.C_6$ | 3A | 1A | $(10,16,12)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3B | $3$ | $128$ | $A_4^2.C_6^2$ | 3B | 1A | $(7,14,8)(10,16,12)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3C | $3$ | $128$ | $C_6\times A_4^2:S_3$ | 3C | 1A | $(5,15,9)(7,14,8)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3D | $3$ | $128$ | $(C_3\times A_4^2):C_{12}$ | 3D | 1A | $(5,15,9)(10,16,12)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3E | $3$ | $1024$ | not computed | 3E | 1A | $(1,5,9)(2,10,16)(4,11,13)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3F | $3$ | $1024$ | not computed | 3F | 1A | $(1,15,5)(7,8,14)(10,12,16)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3G | $3$ | $2048$ | not computed | 3G | 1A | $(1,15,9)(2,10,12)(3,11,4)(7,14,8)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 3H | $3$ | $2048$ | not computed | 3H | 1A | $(1,5,15)(2,12,10)(3,13,11)(6,14,7)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4A | $4$ | $72$ | $A_4^2.C_4.C_2^4$ | 2D | 4A | $(2,16,12,10)(6,8,14,7)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4B | $4$ | $72$ | $A_4^2.C_4.C_2^4$ | 2D | 4B | $(2,12,16,10)(6,8,14,7)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4C | $4$ | $144$ | not computed | 2B | 4C | $(2,10,16,12)(8,14)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4D | $4$ | $144$ | not computed | 2B | 4D | $(1,5,9,15)(4,11)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4E1 | $4$ | $288$ | not computed | 2A | 4E-1 | $(1,2)(3,8)(4,14)(5,16)(6,13)(7,11)(9,12)(10,15)(17,20,19,18)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4E-1 | $4$ | $288$ | not computed | 2A | 4E1 | $(1,2)(3,8)(4,14)(5,16)(6,13)(7,11)(9,12)(10,15)(17,18,19,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4F | $4$ | $432$ | not computed | 2B | 4F | $(1,5)(2,12)(6,7,14,8)(9,15)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4G | $4$ | $432$ | not computed | 2B | 4G | $(1,5)(2,16,12,10)(6,14)(9,15)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4H | $4$ | $432$ | not computed | 2B | 4H | $(3,11)(4,13)(6,8,14,7)(12,16)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4I | $4$ | $432$ | not computed | 2B | 4I | $(2,16,10,12)(3,4)(6,7)(11,13)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4J | $4$ | $432$ | not computed | 2D | 4J | $(1,5,9,15)(3,13,11,4)(6,7)(8,14)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4K | $4$ | $432$ | not computed | 2D | 4K | $(1,15,5,9)(2,16)(3,13,11,4)(10,12)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4L | $4$ | $648$ | not computed | 2D | 4L | $(1,5)(2,10,12,16)(3,4)(6,7,8,14)(9,15)(11,13)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4M | $4$ | $648$ | not computed | 2D | 4M | $(1,5)(2,10,12,16)(3,4)(6,7,8,14)(9,15)(11,13)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4N | $4$ | $1296$ | not computed | 2L | 4N | $(1,15,5,9)(2,16,12,10)(3,4,11,13)(6,7,14,8)(17,19)(18,20)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4O | $4$ | $1296$ | not computed | 2L | 4O | $(1,5,9,15)(2,10,12,16)(3,11,13,4)(6,8,7,14)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4P | $4$ | $1296$ | not computed | 2B | 4P | $(1,9,5,15)(2,10)(3,13)(6,14)(7,8)(12,16)$ |
| $A_4^2.S_4\wr C_2.C_4$ | 4Q | $4$ | $1296$ | not computed | 2B | 4Q | $(1,9,15,5)(2,10)(6,7)(8,14)(11,13)(12,16)(17,19)(18,20)$ |