Subgroups — #37557752

Order 23769.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×C₁₃₉	C₃	1	1	yes	maximal, characteristic
2	C₁₉×C₁₃₉	C₉	1	1	yes	characteristic, complemented, Hall
3	C₁₃₉⋊C₉	—	19	1	no	maximal, Hall
4	C₃×C₁₃₉	—	19	1	no	—
5	#4296	—	139	1	no	maximal, Hall
6	C₁₃₉	#4296	1	1	yes	characteristic, complemented, Sylow
7	C₁₉⋊C₃	C₁₃₉⋊C₃	1	1	yes	characteristic
8	C₁₉	C₁₃₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
9	C₉	—	2641	1	no	Sylow
10	C₃	—	19	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₉×C₁₃₉	C₉
prime radical, cosocle	C₁₉⋊C₃×C₁₃₉	C₃
LCS	G ▷ C₁₉×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.