Extensions 1→N→G→Q→1 with N=C10 and Q=C2×C42

Direct product G=N×Q with N=C10 and Q=C2×C42
dρLabelID
C22×C4×C20320C2^2xC4xC20320,1513

Semidirect products G=N:Q with N=C10 and Q=C2×C42
extensionφ:Q→Aut NdρLabelID
C10⋊(C2×C42) = C22×C4×F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10:(C2xC4^2)320,1590
C102(C2×C42) = D5×C2×C42φ: C2×C42/C42C2 ⊆ Aut C10160C10:2(C2xC4^2)320,1143
C103(C2×C42) = C22×C4×Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10:3(C2xC4^2)320,1454

Non-split extensions G=N.Q with N=C10 and Q=C2×C42
extensionφ:Q→Aut NdρLabelID
C10.1(C2×C42) = C4×D5⋊C8φ: C2×C42/C2×C4C4 ⊆ Aut C10160C10.1(C2xC4^2)320,1013
C10.2(C2×C42) = C42.5F5φ: C2×C42/C2×C4C4 ⊆ Aut C10160C10.2(C2xC4^2)320,1014
C10.3(C2×C42) = C4×C4.F5φ: C2×C42/C2×C4C4 ⊆ Aut C10160C10.3(C2xC4^2)320,1015
C10.4(C2×C42) = C42×F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.4(C2xC4^2)320,1023
C10.5(C2×C42) = C424F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.5(C2xC4^2)320,1024
C10.6(C2×C42) = C4×C4⋊F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.6(C2xC4^2)320,1025
C10.7(C2×C42) = Dic5.C42φ: C2×C42/C2×C4C4 ⊆ Aut C10160C10.7(C2xC4^2)320,1029
C10.8(C2×C42) = C22⋊C4×F5φ: C2×C42/C2×C4C4 ⊆ Aut C1040C10.8(C2xC4^2)320,1036
C10.9(C2×C42) = D10.C42φ: C2×C42/C2×C4C4 ⊆ Aut C10160C10.9(C2xC4^2)320,1039
C10.10(C2×C42) = C4⋊C4×F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.10(C2xC4^2)320,1048
C10.11(C2×C42) = C2×C8×F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.11(C2xC4^2)320,1054
C10.12(C2×C42) = C2×C8⋊F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.12(C2xC4^2)320,1055
C10.13(C2×C42) = C20.12C42φ: C2×C42/C2×C4C4 ⊆ Aut C10804C10.13(C2xC4^2)320,1056
C10.14(C2×C42) = M4(2)×F5φ: C2×C42/C2×C4C4 ⊆ Aut C10408C10.14(C2xC4^2)320,1064
C10.15(C2×C42) = M4(2)⋊5F5φ: C2×C42/C2×C4C4 ⊆ Aut C10808C10.15(C2xC4^2)320,1066
C10.16(C2×C42) = C2×C4×C5⋊C8φ: C2×C42/C2×C4C4 ⊆ Aut C10320C10.16(C2xC4^2)320,1084
C10.17(C2×C42) = C2×C10.C42φ: C2×C42/C2×C4C4 ⊆ Aut C10320C10.17(C2xC4^2)320,1087
C10.18(C2×C42) = C4×C22.F5φ: C2×C42/C2×C4C4 ⊆ Aut C10160C10.18(C2xC4^2)320,1088
C10.19(C2×C42) = C2×D10.3Q8φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.19(C2xC4^2)320,1100
C10.20(C2×C42) = C4×C22⋊F5φ: C2×C42/C2×C4C4 ⊆ Aut C1080C10.20(C2xC4^2)320,1101
C10.21(C2×C42) = Dic5.15C42φ: C2×C42/C42C2 ⊆ Aut C10320C10.21(C2xC4^2)320,275
C10.22(C2×C42) = Dic52C42φ: C2×C42/C42C2 ⊆ Aut C10320C10.22(C2xC4^2)320,276
C10.23(C2×C42) = D5×C2.C42φ: C2×C42/C42C2 ⊆ Aut C10160C10.23(C2xC4^2)320,290
C10.24(C2×C42) = D102C42φ: C2×C42/C42C2 ⊆ Aut C10160C10.24(C2xC4^2)320,293
C10.25(C2×C42) = D5×C4×C8φ: C2×C42/C42C2 ⊆ Aut C10160C10.25(C2xC4^2)320,311
C10.26(C2×C42) = C4×C8⋊D5φ: C2×C42/C42C2 ⊆ Aut C10160C10.26(C2xC4^2)320,314
C10.27(C2×C42) = D10.5C42φ: C2×C42/C42C2 ⊆ Aut C10160C10.27(C2xC4^2)320,316
C10.28(C2×C42) = D5×C8⋊C4φ: C2×C42/C42C2 ⊆ Aut C10160C10.28(C2xC4^2)320,331
C10.29(C2×C42) = D10.6C42φ: C2×C42/C42C2 ⊆ Aut C10160C10.29(C2xC4^2)320,334
C10.30(C2×C42) = D10.7C42φ: C2×C42/C42C2 ⊆ Aut C10160C10.30(C2xC4^2)320,335
C10.31(C2×C42) = C4×C10.D4φ: C2×C42/C42C2 ⊆ Aut C10320C10.31(C2xC4^2)320,558
C10.32(C2×C42) = C4×D10⋊C4φ: C2×C42/C42C2 ⊆ Aut C10160C10.32(C2xC4^2)320,565
C10.33(C2×C42) = C2×C4×C52C8φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.33(C2xC4^2)320,547
C10.34(C2×C42) = C2×C42.D5φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.34(C2xC4^2)320,548
C10.35(C2×C42) = C4×C4.Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10160C10.35(C2xC4^2)320,549
C10.36(C2×C42) = C42×Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.36(C2xC4^2)320,557
C10.37(C2×C42) = C424Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.37(C2xC4^2)320,559
C10.38(C2×C42) = C4×C4⋊Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.38(C2xC4^2)320,561
C10.39(C2×C42) = C22⋊C4×Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10160C10.39(C2xC4^2)320,568
C10.40(C2×C42) = C4⋊C4×Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.40(C2xC4^2)320,602
C10.41(C2×C42) = C20.35C42φ: C2×C42/C22×C4C2 ⊆ Aut C10160C10.41(C2xC4^2)320,624
C10.42(C2×C42) = C2×C8×Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.42(C2xC4^2)320,725
C10.43(C2×C42) = C2×C408C4φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.43(C2xC4^2)320,727
C10.44(C2×C42) = C20.42C42φ: C2×C42/C22×C4C2 ⊆ Aut C10160C10.44(C2xC4^2)320,728
C10.45(C2×C42) = M4(2)×Dic5φ: C2×C42/C22×C4C2 ⊆ Aut C10160C10.45(C2xC4^2)320,744
C10.46(C2×C42) = C20.37C42φ: C2×C42/C22×C4C2 ⊆ Aut C10160C10.46(C2xC4^2)320,749
C10.47(C2×C42) = C2×C10.10C42φ: C2×C42/C22×C4C2 ⊆ Aut C10320C10.47(C2xC4^2)320,835
C10.48(C2×C42) = C4×C23.D5φ: C2×C42/C22×C4C2 ⊆ Aut C10160C10.48(C2xC4^2)320,836
C10.49(C2×C42) = C10×C2.C42central extension (φ=1)320C10.49(C2xC4^2)320,876
C10.50(C2×C42) = C5×C424C4central extension (φ=1)320C10.50(C2xC4^2)320,877
C10.51(C2×C42) = C22⋊C4×C20central extension (φ=1)160C10.51(C2xC4^2)320,878
C10.52(C2×C42) = C4⋊C4×C20central extension (φ=1)320C10.52(C2xC4^2)320,879
C10.53(C2×C42) = C10×C8⋊C4central extension (φ=1)320C10.53(C2xC4^2)320,904
C10.54(C2×C42) = M4(2)×C20central extension (φ=1)160C10.54(C2xC4^2)320,905
C10.55(C2×C42) = C5×C82M4(2)central extension (φ=1)160C10.55(C2xC4^2)320,906

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