Extensions 1→N→G→Q→1 with N=C₁₂ and Q=C₂×F₅

Direct product G=N×Q with N=C₁₂ and Q=C₂×F₅

		d	ρ	Label	ID
F₅×C₂×C₁₂		120		F5xC2xC12	480,1050

Semidirect products G=N:Q with N=C₁₂ and Q=C₂×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁(C₂×F₅) = S₃×C₄⋊F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	60	8	C12:1(C2xF5)	480,996
C₁₂⋊₂(C₂×F₅) = D₆₀⋊₃C₄	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	60	8+	C12:2(C2xF5)	480,997
C₁₂⋊₃(C₂×F₅) = D₄×C₃⋊F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	60	8	C12:3(C2xF5)	480,1067
C₁₂⋊₄(C₂×F₅) = F₅×D₁₂	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	60	8+	C12:4(C2xF5)	480,995
C₁₂⋊₅(C₂×F₅) = C₄×S₃×F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	60	8	C12:5(C2xF5)	480,994
C₁₂⋊₆(C₂×F₅) = C₃×D₄×F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	60	8	C12:6(C2xF5)	480,1054
C₁₂⋊₇(C₂×F₅) = C₂×C₆₀⋊C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120		C12:7(C2xF5)	480,1064
C₁₂⋊₈(C₂×F₅) = C₂×C₄×C₃⋊F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120		C12:8(C2xF5)	480,1063
C₁₂⋊₉(C₂×F₅) = C₆×C₄⋊F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120		C12:9(C2xF5)	480,1051

Non-split extensions G=N.Q with N=C₁₂ and Q=C₂×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁(C₂×F₅) = D₆₀⋊C₄	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8+	C12.1(C2xF5)	480,227
C₁₂.₂(C₂×F₅) = Dic₆⋊F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8-	C12.2(C2xF5)	480,229
C₁₂.₃(C₂×F₅) = D₁₂⋊₄F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8-	C12.3(C2xF5)	480,231
C₁₂.₄(C₂×F₅) = D₆₀⋊₂C₄	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8+	C12.4(C2xF5)	480,233
C₁₂.₅(C₂×F₅) = Dic₅.Dic₆	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.5(C2xF5)	480,235
C₁₂.₆(C₂×F₅) = Dic₅.₄Dic₆	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.6(C2xF5)	480,236
C₁₂.₇(C₂×F₅) = D₁₀.Dic₆	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	240	8	C12.7(C2xF5)	480,237
C₁₂.₈(C₂×F₅) = D₁₀.₂Dic₆	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	240	8	C12.8(C2xF5)	480,238
C₁₂.₉(C₂×F₅) = D₂₀⋊Dic₃	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.9(C2xF5)	480,312
C₁₂.₁₀(C₂×F₅) = Dic₁₀⋊Dic₃	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.10(C2xF5)	480,313
C₁₂.₁₁(C₂×F₅) = Dic₁₀⋊₂Dic₃	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.11(C2xF5)	480,314
C₁₂.₁₂(C₂×F₅) = D₂₀⋊₂Dic₃	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.12(C2xF5)	480,315
C₁₂.₁₃(C₂×F₅) = C₄⋊F₅⋊₃S₃	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.13(C2xF5)	480,983
C₁₂.₁₄(C₂×F₅) = Dic₆⋊₅F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8-	C12.14(C2xF5)	480,984
C₁₂.₁₅(C₂×F₅) = S₃×C₄.F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.15(C2xF5)	480,988
C₁₂.₁₆(C₂×F₅) = D₁₂.F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	240	8-	C12.16(C2xF5)	480,989
C₁₂.₁₇(C₂×F₅) = D₁₅⋊M₄(2)	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.17(C2xF5)	480,991
C₁₂.₁₈(C₂×F₅) = Dic₆.F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	240	8+	C12.18(C2xF5)	480,992
C₁₂.₁₉(C₂×F₅) = Dic₁₀.Dic₃	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	240	8	C12.19(C2xF5)	480,1066
C₁₂.₂₀(C₂×F₅) = D₂₀.Dic₃	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	240	8	C12.20(C2xF5)	480,1068
C₁₂.₂₁(C₂×F₅) = Q₈×C₃⋊F₅	φ: C₂×F₅/D₅ → C₂² ⊆ Aut C₁₂	120	8	C12.21(C2xF5)	480,1069
C₁₂.₂₂(C₂×F₅) = D₁₂⋊F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8+	C12.22(C2xF5)	480,228
C₁₂.₂₃(C₂×F₅) = Dic₃₀⋊C₄	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8-	C12.23(C2xF5)	480,230
C₁₂.₂₄(C₂×F₅) = D₁₂⋊₂F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8-	C12.24(C2xF5)	480,232
C₁₂.₂₅(C₂×F₅) = D₆₀⋊₅C₄	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8+	C12.25(C2xF5)	480,234
C₁₂.₂₆(C₂×F₅) = F₅×Dic₆	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8-	C12.26(C2xF5)	480,982
C₁₂.₂₇(C₂×F₅) = D₁₂.₂F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8-	C12.27(C2xF5)	480,987
C₁₂.₂₈(C₂×F₅) = D₆₀.C₄	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8+	C12.28(C2xF5)	480,990
C₁₂.₂₉(C₂×F₅) = F₅×C₃⋊C₈	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.29(C2xF5)	480,223
C₁₂.₃₀(C₂×F₅) = C₃₀.C₄²	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.30(C2xF5)	480,224
C₁₂.₃₁(C₂×F₅) = C₃₀.₃C₄²	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.31(C2xF5)	480,225
C₁₂.₃₂(C₂×F₅) = C₃₀.₄C₄²	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.32(C2xF5)	480,226
C₁₂.₃₃(C₂×F₅) = S₃×C₅⋊C₁₆	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8	C12.33(C2xF5)	480,239
C₁₂.₃₄(C₂×F₅) = D₁₅⋊C₁₆	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8	C12.34(C2xF5)	480,240
C₁₂.₃₅(C₂×F₅) = C₁₅⋊M₅(2)	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8	C12.35(C2xF5)	480,241
C₁₂.₃₆(C₂×F₅) = D₃₀.C₈	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8	C12.36(C2xF5)	480,242
C₁₂.₃₇(C₂×F₅) = (C₄×S₃)⋊F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.37(C2xF5)	480,985
C₁₂.₃₈(C₂×F₅) = S₃×D₅⋊C₈	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.38(C2xF5)	480,986
C₁₂.₃₉(C₂×F₅) = C₅⋊C₈⋊D₆	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.39(C2xF5)	480,993
C₁₂.₄₀(C₂×F₅) = C₃×D₂₀⋊C₄	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.40(C2xF5)	480,287
C₁₂.₄₁(C₂×F₅) = C₃×D₄⋊F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.41(C2xF5)	480,288
C₁₂.₄₂(C₂×F₅) = C₃×Q₈⋊F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.42(C2xF5)	480,289
C₁₂.₄₃(C₂×F₅) = C₃×Q₈⋊₂F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.43(C2xF5)	480,290
C₁₂.₄₄(C₂×F₅) = C₃×D₄.F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8	C12.44(C2xF5)	480,1053
C₁₂.₄₅(C₂×F₅) = C₃×Q₈.F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	240	8	C12.45(C2xF5)	480,1055
C₁₂.₄₆(C₂×F₅) = C₃×Q₈×F₅	φ: C₂×F₅/F₅ → C₂ ⊆ Aut C₁₂	120	8	C12.46(C2xF5)	480,1056
C₁₂.₄₇(C₂×F₅) = C₁₂₀⋊C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.47(C2xF5)	480,298
C₁₂.₄₈(C₂×F₅) = D₅.D₂₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.48(C2xF5)	480,299
C₁₂.₄₉(C₂×F₅) = C₄₀.Dic₃	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240	4	C12.49(C2xF5)	480,300
C₁₂.₅₀(C₂×F₅) = C₂₄.₁F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240	4	C12.50(C2xF5)	480,301
C₁₂.₅₁(C₂×F₅) = C₂×C₁₂.F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240		C12.51(C2xF5)	480,1061
C₁₂.₅₂(C₂×F₅) = C₆₀.₅₉(C₂×C₄)	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.52(C2xF5)	480,1062
C₁₂.₅₃(C₂×F₅) = (C₂×C₁₂)⋊₆F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.53(C2xF5)	480,1065
C₁₂.₅₄(C₂×F₅) = C₂₄.F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240	4	C12.54(C2xF5)	480,294
C₁₂.₅₅(C₂×F₅) = C₁₂₀.C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240	4	C12.55(C2xF5)	480,295
C₁₂.₅₆(C₂×F₅) = C₈×C₃⋊F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.56(C2xF5)	480,296
C₁₂.₅₇(C₂×F₅) = C₂₄⋊F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.57(C2xF5)	480,297
C₁₂.₅₈(C₂×F₅) = C₂×C₁₅⋊C₁₆	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	480		C12.58(C2xF5)	480,302
C₁₂.₅₉(C₂×F₅) = C₆₀.C₈	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240	4	C12.59(C2xF5)	480,303
C₁₂.₆₀(C₂×F₅) = C₂×C₆₀.C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240		C12.60(C2xF5)	480,1060
C₁₂.₆₁(C₂×F₅) = C₃×C₄₀⋊C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.61(C2xF5)	480,273
C₁₂.₆₂(C₂×F₅) = C₃×D₅.D₈	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	120	4	C12.62(C2xF5)	480,274
C₁₂.₆₃(C₂×F₅) = C₃×C₄₀.C₄	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240	4	C12.63(C2xF5)	480,275
C₁₂.₆₄(C₂×F₅) = C₃×D₁₀.Q₈	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240	4	C12.64(C2xF5)	480,276
C₁₂.₆₅(C₂×F₅) = C₆×C₄.F₅	φ: C₂×F₅/D₁₀ → C₂ ⊆ Aut C₁₂	240		C12.65(C2xF5)	480,1048
C₁₂.₆₆(C₂×F₅) = C₃×D₅⋊C₁₆	central extension (φ=1)	240	4	C12.66(C2xF5)	480,269
C₁₂.₆₇(C₂×F₅) = C₃×C₈.F₅	central extension (φ=1)	240	4	C12.67(C2xF5)	480,270
C₁₂.₆₈(C₂×F₅) = F₅×C₂₄	central extension (φ=1)	120	4	C12.68(C2xF5)	480,271
C₁₂.₆₉(C₂×F₅) = C₃×C₈⋊F₅	central extension (φ=1)	120	4	C12.69(C2xF5)	480,272
C₁₂.₇₀(C₂×F₅) = C₆×C₅⋊C₁₆	central extension (φ=1)	480		C12.70(C2xF5)	480,277
C₁₂.₇₁(C₂×F₅) = C₃×C₂₀.C₈	central extension (φ=1)	240	4	C12.71(C2xF5)	480,278
C₁₂.₇₂(C₂×F₅) = C₆×D₅⋊C₈	central extension (φ=1)	240		C12.72(C2xF5)	480,1047
C₁₂.₇₃(C₂×F₅) = C₃×D₅⋊M₄(2)	central extension (φ=1)	120	4	C12.73(C2xF5)	480,1049
C₁₂.₇₄(C₂×F₅) = C₃×D₁₀.C₂³	central extension (φ=1)	120	4	C12.74(C2xF5)	480,1052

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Extensions 1→N→G→Q→1 with N=C12 and Q=C2×F5

Extensions 1→N→G→Q→1 with N=C₁₂ and Q=C₂×F₅