Finite Group Databasebeta

← C₄×C₁₉×C₁₃₉ #24902255

Subgroups — C₄×C₁₉×C₁₃₉ #24902255

Order 10564.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₁₃₉	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₃₉	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₁₃₉	C₂×C₁₉	1	1	yes	characteristic
5	C₁₃₉	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₄×C₁₉	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₉	C₂×C₁₃₉	1	1	yes	characteristic
8	C₁₉	C₄×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₄	C₁₉×C₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	C₂×C₁₉×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₉×C₁₃₉
socle, prime radical	C₂×C₁₉×C₁₃₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×C₁₃₉	C₄	direct (N × H)
3. C₄×C₁₃₉	C₁₉	direct (N × H)
5. C₁₃₉	C₄×C₁₉	direct (N × H)
6. C₄×C₁₉	C₁₃₉	direct (N × H)
8. C₁₉	C₄×C₁₃₉	direct (N × H)
9. C₄	C₁₉×C₁₃₉	direct (N × H)