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Elements of the group are displayed as permutations of degree 20.
| Group | Label | Order | Size | Centralizer | Powers | Representative |
|---|---|---|---|---|---|---|
| 2P | ||||||
| $(C_4\times D_4^2).D_4$ | 1A | $1$ | $1$ | not computed | 1A | $()$ |
| $(C_4\times D_4^2).D_4$ | 2A | $2$ | $1$ | not computed | 1A | $(5,20)(10,15)$ |
| $(C_4\times D_4^2).D_4$ | 2B | $2$ | $1$ | not computed | 1A | $(1,19)(2,3)(4,7)(5,20)(6,8)(9,12)(10,15)(11,13)(14,17)(16,18)$ |
| $(C_4\times D_4^2).D_4$ | 2C | $2$ | $1$ | not computed | 1A | $(1,19)(2,3)(4,7)(6,8)(9,12)(11,13)(14,17)(16,18)$ |
| $(C_4\times D_4^2).D_4$ | 2D | $2$ | $2$ | not computed | 1A | $(1,14)(2,6)(3,8)(4,12)(7,9)(11,16)(13,18)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2E | $2$ | $2$ | not computed | 1A | $(1,14)(2,6)(3,8)(4,12)(5,20)(7,9)(10,15)(11,16)(13,18)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2F | $2$ | $2$ | not computed | 1A | $(1,14)(2,8)(3,6)(4,12)(7,9)(11,18)(13,16)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2G | $2$ | $2$ | not computed | 1A | $(1,14)(2,8)(3,6)(4,12)(5,20)(7,9)(10,15)(11,18)(13,16)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2H | $2$ | $2$ | not computed | 1A | $(2,3)(6,8)(11,13)(16,18)$ |
| $(C_4\times D_4^2).D_4$ | 2I | $2$ | $2$ | not computed | 1A | $(2,3)(5,20)(6,8)(10,15)(11,13)(16,18)$ |
| $(C_4\times D_4^2).D_4$ | 2J | $2$ | $4$ | not computed | 1A | $(4,7)(9,12)(11,13)(16,18)$ |
| $(C_4\times D_4^2).D_4$ | 2K | $2$ | $4$ | not computed | 1A | $(4,7)(5,20)(9,12)(10,15)(11,13)(16,18)$ |
| $(C_4\times D_4^2).D_4$ | 2L | $2$ | $4$ | not computed | 1A | $(4,9)(7,12)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2M | $2$ | $4$ | not computed | 1A | $(4,9)(5,20)(7,12)(10,15)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2N | $2$ | $4$ | not computed | 1A | $(4,12)(7,9)(11,18)(13,16)$ |
| $(C_4\times D_4^2).D_4$ | 2O | $2$ | $4$ | not computed | 1A | $(4,12)(5,20)(7,9)(10,15)(11,18)(13,16)$ |
| $(C_4\times D_4^2).D_4$ | 2P | $2$ | $4$ | not computed | 1A | $(2,6)(3,8)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2Q | $2$ | $4$ | not computed | 1A | $(2,6)(3,8)(5,20)(10,15)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2R | $2$ | $4$ | not computed | 1A | $(1,14)(2,3)(4,7)(6,8)(9,12)(11,18)(13,16)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2S | $2$ | $4$ | not computed | 1A | $(1,14)(2,3)(4,7)(5,20)(6,8)(9,12)(10,15)(11,18)(13,16)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2T | $2$ | $4$ | not computed | 1A | $(1,14)(2,3)(4,12)(6,8)(7,9)(11,13)(16,18)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2U | $2$ | $4$ | not computed | 1A | $(1,14)(2,3)(4,12)(5,20)(6,8)(7,9)(10,15)(11,13)(16,18)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2V | $2$ | $4$ | not computed | 1A | $(1,14)(2,6)(3,8)(4,9)(7,12)(11,18)(13,16)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2W | $2$ | $4$ | not computed | 1A | $(1,14)(2,6)(3,8)(4,9)(5,20)(7,12)(10,15)(11,18)(13,16)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2X | $2$ | $4$ | not computed | 1A | $(1,14)(2,8)(3,6)(4,7)(9,12)(11,13)(16,18)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2Y | $2$ | $4$ | not computed | 1A | $(1,14)(2,8)(3,6)(4,7)(5,20)(9,12)(10,15)(11,13)(16,18)(17,19)$ |
| $(C_4\times D_4^2).D_4$ | 2Z | $2$ | $4$ | not computed | 1A | $(2,6)(3,8)(4,7)(9,12)(11,18)(13,16)$ |
| $(C_4\times D_4^2).D_4$ | 2AA | $2$ | $4$ | not computed | 1A | $(2,8)(3,6)(4,7)(9,12)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2AB | $2$ | $4$ | not computed | 1A | $(1,4)(2,11)(3,13)(6,16)(7,19)(8,18)(9,17)(12,14)$ |
| $(C_4\times D_4^2).D_4$ | 2AC | $2$ | $4$ | not computed | 1A | $(1,4)(2,13)(3,11)(6,18)(7,19)(8,16)(9,17)(12,14)$ |
| $(C_4\times D_4^2).D_4$ | 2AD | $2$ | $4$ | not computed | 1A | $(2,6)(3,8)(4,7)(5,20)(9,12)(10,15)(11,18)(13,16)$ |
| $(C_4\times D_4^2).D_4$ | 2AE | $2$ | $4$ | not computed | 1A | $(2,8)(3,6)(4,7)(5,20)(9,12)(10,15)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2AF | $2$ | $4$ | not computed | 1A | $(1,4)(2,11)(3,13)(5,20)(6,16)(7,19)(8,18)(9,17)(10,15)(12,14)$ |
| $(C_4\times D_4^2).D_4$ | 2AG | $2$ | $4$ | not computed | 1A | $(1,4)(2,13)(3,11)(5,20)(6,18)(7,19)(8,16)(9,17)(10,15)(12,14)$ |
| $(C_4\times D_4^2).D_4$ | 2AH | $2$ | $8$ | not computed | 1A | $(2,3)(4,9)(6,8)(7,12)(11,18)(13,16)$ |
| $(C_4\times D_4^2).D_4$ | 2AI | $2$ | $8$ | not computed | 1A | $(2,3)(4,9)(5,20)(6,8)(7,12)(10,15)(11,18)(13,16)$ |
| $(C_4\times D_4^2).D_4$ | 2AJ | $2$ | $8$ | not computed | 1A | $(2,3)(4,12)(6,8)(7,9)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2AK | $2$ | $8$ | not computed | 1A | $(2,3)(4,12)(5,20)(6,8)(7,9)(10,15)(11,16)(13,18)$ |
| $(C_4\times D_4^2).D_4$ | 2AL | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,11)(6,17)(7,13)(8,14)(9,16)(12,18)$ |
| $(C_4\times D_4^2).D_4$ | 2AM | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,11)(5,20)(6,17)(7,13)(8,14)(9,16)(10,15)(12,18)$ |
| $(C_4\times D_4^2).D_4$ | 2AN | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,13)(6,17)(7,11)(8,14)(9,18)(12,16)$ |
| $(C_4\times D_4^2).D_4$ | 2AO | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,13)(5,20)(6,17)(7,11)(8,14)(9,18)(10,15)(12,16)$ |
| $(C_4\times D_4^2).D_4$ | 2AP | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,16)(6,17)(7,18)(8,14)(9,11)(12,13)$ |
| $(C_4\times D_4^2).D_4$ | 2AQ | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,16)(5,20)(6,17)(7,18)(8,14)(9,11)(10,15)(12,13)$ |
| $(C_4\times D_4^2).D_4$ | 2AR | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,18)(6,17)(7,16)(8,14)(9,13)(11,12)$ |
| $(C_4\times D_4^2).D_4$ | 2AS | $2$ | $8$ | not computed | 1A | $(1,2)(3,19)(4,18)(5,20)(6,17)(7,16)(8,14)(9,13)(10,15)(11,12)$ |
| $(C_4\times D_4^2).D_4$ | 2AT | $2$ | $8$ | not computed | 1A | $(1,4)(2,16)(3,18)(6,11)(7,19)(8,13)(9,17)(12,14)$ |
| $(C_4\times D_4^2).D_4$ | 2AU | $2$ | $8$ | not computed | 1A | $(1,4)(2,16)(3,18)(5,20)(6,11)(7,19)(8,13)(9,17)(10,15)(12,14)$ |
| $(C_4\times D_4^2).D_4$ | 2AV | $2$ | $16$ | not computed | 1A | $(2,11)(3,13)(6,18)(8,16)(9,12)(14,17)$ |
| $(C_4\times D_4^2).D_4$ | 2AW | $2$ | $16$ | not computed | 1A | $(2,11)(3,13)(5,20)(6,18)(8,16)(9,12)(10,15)(14,17)$ |