# Extensions 1→N→G→Q→1 with N=D4 and Q=C2×Dic5

Direct product G=N×Q with N=D4 and Q=C2×Dic5
dρLabelID
C2×D4×Dic5160C2xD4xDic5320,1467

Semidirect products G=N:Q with N=D4 and Q=C2×Dic5
extensionφ:Q→Out NdρLabelID
D41(C2×Dic5) = D8×Dic5φ: C2×Dic5/Dic5C2 ⊆ Out D4160D4:1(C2xDic5)320,776
D42(C2×Dic5) = D8⋊Dic5φ: C2×Dic5/Dic5C2 ⊆ Out D4160D4:2(C2xDic5)320,779
D43(C2×Dic5) = C2×D4⋊Dic5φ: C2×Dic5/C2×C10C2 ⊆ Out D4160D4:3(C2xDic5)320,841
D44(C2×Dic5) = C4○D4⋊Dic5φ: C2×Dic5/C2×C10C2 ⊆ Out D4160D4:4(C2xDic5)320,859
D45(C2×Dic5) = C2×D42Dic5φ: C2×Dic5/C2×C10C2 ⊆ Out D480D4:5(C2xDic5)320,862
D46(C2×Dic5) = C24.38D10φ: trivial image80D4:6(C2xDic5)320,1470
D47(C2×Dic5) = C4○D4×Dic5φ: trivial image160D4:7(C2xDic5)320,1498
D48(C2×Dic5) = C10.1062- 1+4φ: trivial image160D4:8(C2xDic5)320,1499

Non-split extensions G=N.Q with N=D4 and Q=C2×Dic5
extensionφ:Q→Out NdρLabelID
D4.1(C2×Dic5) = SD16×Dic5φ: C2×Dic5/Dic5C2 ⊆ Out D4160D4.1(C2xDic5)320,788
D4.2(C2×Dic5) = SD16⋊Dic5φ: C2×Dic5/Dic5C2 ⊆ Out D4160D4.2(C2xDic5)320,791
D4.3(C2×Dic5) = D85Dic5φ: C2×Dic5/Dic5C2 ⊆ Out D4804D4.3(C2xDic5)320,823
D4.4(C2×Dic5) = D84Dic5φ: C2×Dic5/Dic5C2 ⊆ Out D4804D4.4(C2xDic5)320,824
D4.5(C2×Dic5) = (D4×C10)⋊18C4φ: C2×Dic5/C2×C10C2 ⊆ Out D480D4.5(C2xDic5)320,842
D4.6(C2×Dic5) = C20.(C2×D4)φ: C2×Dic5/C2×C10C2 ⊆ Out D4160D4.6(C2xDic5)320,860
D4.7(C2×Dic5) = (D4×C10)⋊21C4φ: C2×Dic5/C2×C10C2 ⊆ Out D4804D4.7(C2xDic5)320,863
D4.8(C2×Dic5) = C2×D4.Dic5φ: trivial image160D4.8(C2xDic5)320,1490
D4.9(C2×Dic5) = C20.76C24φ: trivial image804D4.9(C2xDic5)320,1491

׿
×
𝔽