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Extensions 1→N→G→Q→1 with N=C10 and Q=C4×Q8

Direct product G=N×Q with N=C10 and Q=C4×Q8
dρLabelID
Q8×C2×C20320Q8xC2xC20320,1518

Semidirect products G=N:Q with N=C10 and Q=C4×Q8
extensionφ:Q→Aut NdρLabelID
C10⋊(C4×Q8) = C2×Q8×F5φ: C4×Q8/Q8 → C4 ⊆ Aut C1080C10:(C4xQ8)320,1599
C10⋊2(C4×Q8) = C2×C4×Dic10φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10:2(C4xQ8)320,1139
C10⋊3(C4×Q8) = C2×Dic5⋊3Q8φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10:3(C4xQ8)320,1168
C10⋊4(C4×Q8) = C2×Q8×Dic5φ: C4×Q8/C2×Q8 → C2 ⊆ Aut C10320C10:4(C4xQ8)320,1483

Non-split extensions G=N.Q with N=C10 and Q=C4×Q8
extensionφ:Q→Aut NdρLabelID
C10.1(C4×Q8) = Dic10⋊C8φ: C4×Q8/Q8 → C4 ⊆ Aut C10320C10.1(C4xQ8)320,1041
C10.2(C4×Q8) = Dic5.M4(2)φ: C4×Q8/Q8 → C4 ⊆ Aut C10320C10.2(C4xQ8)320,1045
C10.3(C4×Q8) = C20.M4(2)φ: C4×Q8/Q8 → C4 ⊆ Aut C10320C10.3(C4xQ8)320,1047
C10.4(C4×Q8) = C4⋊C4×F5φ: C4×Q8/Q8 → C4 ⊆ Aut C1080C10.4(C4xQ8)320,1048
C10.5(C4×Q8) = C4⋊C4⋊5F5φ: C4×Q8/Q8 → C4 ⊆ Aut C1080C10.5(C4xQ8)320,1049
C10.6(C4×Q8) = C20⋊(C4⋊C4)φ: C4×Q8/Q8 → C4 ⊆ Aut C1080C10.6(C4xQ8)320,1050
C10.7(C4×Q8) = Q8×C5⋊C8φ: C4×Q8/Q8 → C4 ⊆ Aut C10320C10.7(C4xQ8)320,1124
C10.8(C4×Q8) = C20.6M4(2)φ: C4×Q8/Q8 → C4 ⊆ Aut C10320C10.8(C4xQ8)320,1126
C10.9(C4×Q8) = (C2×F5)⋊Q8φ: C4×Q8/Q8 → C4 ⊆ Aut C1080C10.9(C4xQ8)320,1128
C10.10(C4×Q8) = (C2×C20)⋊Q8φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.10(C4xQ8)320,273
C10.11(C4×Q8) = C10.49(C4×D4)φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.11(C4xQ8)320,274
C10.12(C4×Q8) = C4⋊Dic5⋊15C4φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.12(C4xQ8)320,281
C10.13(C4×Q8) = C10.52(C4×D4)φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.13(C4xQ8)320,282
C10.14(C4×Q8) = C8×Dic10φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.14(C4xQ8)320,305
C10.15(C4×Q8) = C40⋊11Q8φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.15(C4xQ8)320,306
C10.16(C4×Q8) = C40⋊Q8φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.16(C4xQ8)320,328
C10.17(C4×Q8) = C20⋊7(C4⋊C4)φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.17(C4xQ8)320,555
C10.18(C4×Q8) = (C2×C20)⋊10Q8φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.18(C4xQ8)320,556
C10.19(C4×Q8) = C4×C10.D4φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.19(C4xQ8)320,558
C10.20(C4×Q8) = C10.92(C4×D4)φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.20(C4xQ8)320,560
C10.21(C4×Q8) = C4×C4⋊Dic5φ: C4×Q8/C42 → C2 ⊆ Aut C10320C10.21(C4xQ8)320,561
C10.22(C4×Q8) = Dic5⋊2C42φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.22(C4xQ8)320,276
C10.23(C4×Q8) = C10.51(C4×D4)φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.23(C4xQ8)320,279
C10.24(C4×Q8) = C2.(C4×D20)φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.24(C4xQ8)320,280
C10.25(C4×Q8) = Dic5.5M4(2)φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.25(C4xQ8)320,455
C10.26(C4×Q8) = Dic10⋊5C8φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.26(C4xQ8)320,457
C10.27(C4×Q8) = C42.198D10φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.27(C4xQ8)320,458
C10.28(C4×Q8) = C10.96(C4×D4)φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.28(C4xQ8)320,599
C10.29(C4×Q8) = C20⋊4(C4⋊C4)φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.29(C4xQ8)320,600
C10.30(C4×Q8) = (C2×Dic5)⋊6Q8φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.30(C4xQ8)320,601
C10.31(C4×Q8) = C4⋊C4×Dic5φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.31(C4xQ8)320,602
C10.32(C4×Q8) = C10.97(C4×D4)φ: C4×Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.32(C4xQ8)320,605
C10.33(C4×Q8) = C4⋊C4⋊5Dic5φ: C4×Q8/C2×Q8 → C2 ⊆ Aut C10320C10.33(C4xQ8)320,608
C10.34(C4×Q8) = C20⋊6(C4⋊C4)φ: C4×Q8/C2×Q8 → C2 ⊆ Aut C10320C10.34(C4xQ8)320,612
C10.35(C4×Q8) = Q8×C5⋊2C8φ: C4×Q8/C2×Q8 → C2 ⊆ Aut C10320C10.35(C4xQ8)320,650
C10.36(C4×Q8) = C42.210D10φ: C4×Q8/C2×Q8 → C2 ⊆ Aut C10320C10.36(C4xQ8)320,651
C10.37(C4×Q8) = (Q8×C10)⋊17C4φ: C4×Q8/C2×Q8 → C2 ⊆ Aut C10320C10.37(C4xQ8)320,857
C10.38(C4×Q8) = C4⋊C4×C20central extension (φ=1)320C10.38(C4xQ8)320,879
C10.39(C4×Q8) = C5×C23.63C23central extension (φ=1)320C10.39(C4xQ8)320,888
C10.40(C4×Q8) = C5×C23.65C23central extension (φ=1)320C10.40(C4xQ8)320,890
C10.41(C4×Q8) = C5×C23.67C23central extension (φ=1)320C10.41(C4xQ8)320,892
C10.42(C4×Q8) = Q8×C40central extension (φ=1)320C10.42(C4xQ8)320,946
C10.43(C4×Q8) = C5×C8⋊4Q8central extension (φ=1)320C10.43(C4xQ8)320,947

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