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Extensions 1→N→G→Q→1 with N=C10 and Q=C22×Dic3

Direct product G=N×Q with N=C10 and Q=C22×Dic3
dρLabelID
Dic3×C22×C10480Dic3xC2^2xC10480,1163

Semidirect products G=N:Q with N=C10 and Q=C22×Dic3
extensionφ:Q→Aut NdρLabelID
C10⋊(C22×Dic3) = C23×C3⋊F5φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10120C10:(C2^2xDic3)480,1206
C10⋊2(C22×Dic3) = C22×D5×Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10:2(C2^2xDic3)480,1112
C10⋊3(C22×Dic3) = C23×Dic15φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10480C10:3(C2^2xDic3)480,1178

Non-split extensions G=N.Q with N=C10 and Q=C22×Dic3
extensionφ:Q→Aut NdρLabelID
C10.1(C22×Dic3) = C2×C60.C4φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10240C10.1(C2^2xDic3)480,1060
C10.2(C22×Dic3) = C2×C12.F5φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10240C10.2(C2^2xDic3)480,1061
C10.3(C22×Dic3) = C60.59(C2×C4)φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C101204C10.3(C2^2xDic3)480,1062
C10.4(C22×Dic3) = C2×C4×C3⋊F5φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10120C10.4(C2^2xDic3)480,1063
C10.5(C22×Dic3) = C2×C60⋊C4φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10120C10.5(C2^2xDic3)480,1064
C10.6(C22×Dic3) = (C2×C12)⋊6F5φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C101204C10.6(C2^2xDic3)480,1065
C10.7(C22×Dic3) = Dic10.Dic3φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C102408C10.7(C2^2xDic3)480,1066
C10.8(C22×Dic3) = D4×C3⋊F5φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10608C10.8(C2^2xDic3)480,1067
C10.9(C22×Dic3) = D20.Dic3φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C102408C10.9(C2^2xDic3)480,1068
C10.10(C22×Dic3) = Q8×C3⋊F5φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C101208C10.10(C2^2xDic3)480,1069
C10.11(C22×Dic3) = C22×C15⋊C8φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10480C10.11(C2^2xDic3)480,1070
C10.12(C22×Dic3) = C2×C15⋊8M4(2)φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10240C10.12(C2^2xDic3)480,1071
C10.13(C22×Dic3) = C2×D10.D6φ: C22×Dic3/C2×C6 → C4 ⊆ Aut C10120C10.13(C2^2xDic3)480,1072
C10.14(C22×Dic3) = C2×D5×C3⋊C8φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.14(C2^2xDic3)480,357
C10.15(C22×Dic3) = D5×C4.Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C101204C10.15(C2^2xDic3)480,358
C10.16(C22×Dic3) = D20.3Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C102404C10.16(C2^2xDic3)480,359
C10.17(C22×Dic3) = D20.2Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C102404C10.17(C2^2xDic3)480,360
C10.18(C22×Dic3) = C2×C20.32D6φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.18(C2^2xDic3)480,369
C10.19(C22×Dic3) = Dic3×Dic10φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10480C10.19(C2^2xDic3)480,406
C10.20(C22×Dic3) = Dic15⋊6Q8φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10480C10.20(C2^2xDic3)480,407
C10.21(C22×Dic3) = (D5×C12)⋊C4φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.21(C2^2xDic3)480,433
C10.22(C22×Dic3) = (C4×D5)⋊Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.22(C2^2xDic3)480,434
C10.23(C22×Dic3) = C4×D5×Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.23(C2^2xDic3)480,467
C10.24(C22×Dic3) = D5×C4⋊Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.24(C2^2xDic3)480,488
C10.25(C22×Dic3) = Dic3×D20φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.25(C2^2xDic3)480,501
C10.26(C22×Dic3) = D20⋊8Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.26(C2^2xDic3)480,510
C10.27(C22×Dic3) = C2×Dic3×Dic5φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10480C10.27(C2^2xDic3)480,603
C10.28(C22×Dic3) = (C6×Dic5)⋊7C4φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.28(C2^2xDic3)480,604
C10.29(C22×Dic3) = C2×D10⋊Dic3φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.29(C2^2xDic3)480,611
C10.30(C22×Dic3) = C2×C30.Q8φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10480C10.30(C2^2xDic3)480,617
C10.31(C22×Dic3) = D5×C6.D4φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10120C10.31(C2^2xDic3)480,623
C10.32(C22×Dic3) = Dic3×C5⋊D4φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.32(C2^2xDic3)480,629
C10.33(C22×Dic3) = Dic15⋊16D4φ: C22×Dic3/C2×Dic3 → C2 ⊆ Aut C10240C10.33(C2^2xDic3)480,635
C10.34(C22×Dic3) = C22×C15⋊3C8φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10480C10.34(C2^2xDic3)480,885
C10.35(C22×Dic3) = C2×C60.7C4φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10240C10.35(C2^2xDic3)480,886
C10.36(C22×Dic3) = C2×C4×Dic15φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10480C10.36(C2^2xDic3)480,887
C10.37(C22×Dic3) = C2×C60⋊5C4φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10480C10.37(C2^2xDic3)480,890
C10.38(C22×Dic3) = C23.26D30φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10240C10.38(C2^2xDic3)480,891
C10.39(C22×Dic3) = D4×Dic15φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10240C10.39(C2^2xDic3)480,899
C10.40(C22×Dic3) = Q8×Dic15φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10480C10.40(C2^2xDic3)480,910
C10.41(C22×Dic3) = D4.Dic15φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C102404C10.41(C2^2xDic3)480,913
C10.42(C22×Dic3) = C2×C30.38D4φ: C22×Dic3/C22×C6 → C2 ⊆ Aut C10240C10.42(C2^2xDic3)480,917
C10.43(C22×Dic3) = C2×C10×C3⋊C8central extension (φ=1)480C10.43(C2^2xDic3)480,799
C10.44(C22×Dic3) = C10×C4.Dic3central extension (φ=1)240C10.44(C2^2xDic3)480,800
C10.45(C22×Dic3) = Dic3×C2×C20central extension (φ=1)480C10.45(C2^2xDic3)480,801
C10.46(C22×Dic3) = C10×C4⋊Dic3central extension (φ=1)480C10.46(C2^2xDic3)480,804
C10.47(C22×Dic3) = C5×C23.26D6central extension (φ=1)240C10.47(C2^2xDic3)480,805
C10.48(C22×Dic3) = C5×D4×Dic3central extension (φ=1)240C10.48(C2^2xDic3)480,813
C10.49(C22×Dic3) = C5×Q8×Dic3central extension (φ=1)480C10.49(C2^2xDic3)480,824
C10.50(C22×Dic3) = C5×D4.Dic3central extension (φ=1)2404C10.50(C2^2xDic3)480,827
C10.51(C22×Dic3) = C10×C6.D4central extension (φ=1)240C10.51(C2^2xDic3)480,831

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