Subgroups — C₁₃₉⋊#1181 #30633182

Order 16124.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₁₃₉	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₃₉	—	29	1	no	maximal, Hall
4	C₂×C₁₃₉	—	29	1	no	—
5	C₁₃₉	#1181	1	1	yes	characteristic, complemented, Sylow
6	#1181	—	139	1	no	maximal, Hall
7	D₂₉	D₁₃₉	1	1	yes	characteristic
8	C₂₉	Dic₁₃₉	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	4031	1	no	Sylow
10	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₉×C₁₃₉	C₄
prime radical, cosocle	D₂₉×C₁₃₉	C₂
LCS	G ▷ C₂₉×C₁₃₉
UCS	C₁

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.