Subgroups — #30629613

Order 15892.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉×C₁₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₁₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₃₇	—	29	1	no	maximal, Hall
4	C₂×C₁₃₇	—	29	1	no	—
5	C₁₃₇	#1181	1	1	yes	characteristic, complemented, Sylow
6	#1181	—	137	1	no	maximal, Hall
7	D₂₉	D₁₃₇	1	1	yes	characteristic
8	C₂₉	Dic₁₃₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	3973	1	no	Sylow
10	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₉×C₁₃₇	C₄
prime radical, cosocle	D₂₉×C₁₃₇	C₂
LCS	G ▷ C₂₉×C₁₃₇
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.