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Extensions 1→N→G→Q→1 with N=C4 and Q=C5×C4○D4

Direct product G=N×Q with N=C4 and Q=C5×C4○D4
dρLabelID
C4○D4×C20160C4oD4xC20320,1519

Semidirect products G=N:Q with N=C4 and Q=C5×C4○D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C5×C4○D4) = C5×C22.26C24φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4:1(C5xC4oD4)320,1534
C4⋊2(C5×C4○D4) = C5×D4⋊6D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4:2(C5xC4oD4)320,1549
C4⋊3(C5×C4○D4) = C5×Q8⋊6D4φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4160C4:3(C5xC4oD4)320,1552

Non-split extensions G=N.Q with N=C4 and Q=C5×C4○D4
extensionφ:Q→Aut NdρLabelID
C4.1(C5×C4○D4) = D8×C20φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.1(C5xC4oD4)320,938
C4.2(C5×C4○D4) = SD16×C20φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.2(C5xC4oD4)320,939
C4.3(C5×C4○D4) = Q16×C20φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4320C4.3(C5xC4oD4)320,940
C4.4(C5×C4○D4) = C5×SD16⋊C4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.4(C5xC4oD4)320,941
C4.5(C5×C4○D4) = C5×Q16⋊C4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4320C4.5(C5xC4oD4)320,942
C4.6(C5×C4○D4) = C5×D8⋊C4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.6(C5xC4oD4)320,943
C4.7(C5×C4○D4) = C5×C8⋊8D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.7(C5xC4oD4)320,966
C4.8(C5×C4○D4) = C5×C8⋊7D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.8(C5xC4oD4)320,967
C4.9(C5×C4○D4) = C5×C8.18D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.9(C5xC4oD4)320,968
C4.10(C5×C4○D4) = C5×C8⋊D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.10(C5xC4oD4)320,969
C4.11(C5×C4○D4) = C5×C8⋊2D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.11(C5xC4oD4)320,970
C4.12(C5×C4○D4) = C5×C8.D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.12(C5xC4oD4)320,971
C4.13(C5×C4○D4) = C5×C4.4D8φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.13(C5xC4oD4)320,987
C4.14(C5×C4○D4) = C5×C4.SD16φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4320C4.14(C5xC4oD4)320,988
C4.15(C5×C4○D4) = C5×C42.78C22φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.15(C5xC4oD4)320,989
C4.16(C5×C4○D4) = C5×C42.28C22φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.16(C5xC4oD4)320,990
C4.17(C5×C4○D4) = C5×C42.29C22φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.17(C5xC4oD4)320,991
C4.18(C5×C4○D4) = C5×C42.30C22φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4320C4.18(C5xC4oD4)320,992
C4.19(C5×C4○D4) = C5×C23.37C23φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.19(C5xC4oD4)320,1535
C4.20(C5×C4○D4) = C5×C22.34C24φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.20(C5xC4oD4)320,1542
C4.21(C5×C4○D4) = C5×C22.35C24φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.21(C5xC4oD4)320,1543
C4.22(C5×C4○D4) = C5×C22.36C24φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C4160C4.22(C5xC4oD4)320,1544
C4.23(C5×C4○D4) = C5×D4⋊Q8φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.23(C5xC4oD4)320,975
C4.24(C5×C4○D4) = C5×Q8⋊Q8φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4320C4.24(C5xC4oD4)320,976
C4.25(C5×C4○D4) = C5×D4⋊2Q8φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.25(C5xC4oD4)320,977
C4.26(C5×C4○D4) = C5×C4.Q16φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4320C4.26(C5xC4oD4)320,978
C4.27(C5×C4○D4) = C5×D4.Q8φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.27(C5xC4oD4)320,979
C4.28(C5×C4○D4) = C5×Q8.Q8φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4320C4.28(C5xC4oD4)320,980
C4.29(C5×C4○D4) = C5×C22.D8φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.29(C5xC4oD4)320,981
C4.30(C5×C4○D4) = C5×C23.46D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.30(C5xC4oD4)320,982
C4.31(C5×C4○D4) = C5×C23.19D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.31(C5xC4oD4)320,983
C4.32(C5×C4○D4) = C5×C23.47D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.32(C5xC4oD4)320,984
C4.33(C5×C4○D4) = C5×C23.48D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.33(C5xC4oD4)320,985
C4.34(C5×C4○D4) = C5×C23.20D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.34(C5xC4oD4)320,986
C4.35(C5×C4○D4) = C5×C22.46C24φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.35(C5xC4oD4)320,1554
C4.36(C5×C4○D4) = C5×C22.47C24φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.36(C5xC4oD4)320,1555
C4.37(C5×C4○D4) = C5×D4⋊3Q8φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.37(C5xC4oD4)320,1556
C4.38(C5×C4○D4) = C5×C22.49C24φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.38(C5xC4oD4)320,1557
C4.39(C5×C4○D4) = C5×C22.50C24φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C4160C4.39(C5xC4oD4)320,1558
C4.40(C5×C4○D4) = C5×C4⋊D8φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4160C4.40(C5xC4oD4)320,960
C4.41(C5×C4○D4) = C5×C4⋊SD16φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4160C4.41(C5xC4oD4)320,961
C4.42(C5×C4○D4) = C5×D4.D4φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4160C4.42(C5xC4oD4)320,962
C4.43(C5×C4○D4) = C5×C4⋊2Q16φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4320C4.43(C5xC4oD4)320,963
C4.44(C5×C4○D4) = C5×D4.2D4φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4160C4.44(C5xC4oD4)320,964
C4.45(C5×C4○D4) = C5×Q8.D4φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4160C4.45(C5xC4oD4)320,965
C4.46(C5×C4○D4) = C5×Q8⋊3Q8φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4320C4.46(C5xC4oD4)320,1559
C4.47(C5×C4○D4) = C5×C22.53C24φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C4160C4.47(C5xC4oD4)320,1561
C4.48(C5×C4○D4) = C5×C42.12C4central extension (φ=1)160C4.48(C5xC4oD4)320,932
C4.49(C5×C4○D4) = C5×C42.6C4central extension (φ=1)160C4.49(C5xC4oD4)320,933
C4.50(C5×C4○D4) = C5×C42.7C22central extension (φ=1)160C4.50(C5xC4oD4)320,934
C4.51(C5×C4○D4) = D4×C40central extension (φ=1)160C4.51(C5xC4oD4)320,935
C4.52(C5×C4○D4) = C5×C8⋊9D4central extension (φ=1)160C4.52(C5xC4oD4)320,936
C4.53(C5×C4○D4) = C5×C8⋊6D4central extension (φ=1)160C4.53(C5xC4oD4)320,937
C4.54(C5×C4○D4) = Q8×C40central extension (φ=1)320C4.54(C5xC4oD4)320,946
C4.55(C5×C4○D4) = C5×C8⋊4Q8central extension (φ=1)320C4.55(C5xC4oD4)320,947
C4.56(C5×C4○D4) = C5×C23.36C23central extension (φ=1)160C4.56(C5xC4oD4)320,1531

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