Subgroups — C₅₉⋊#89137 #38787705

Order 25724.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×D₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₅₉×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#89137	—	59	1	no	maximal, Hall
4	Dic₅₉	—	109	1	no	maximal, Hall
5	D₁₀₉	D₅₉	1	1	yes	characteristic
6	C₂×C₅₉	—	109	1	no	—
7	C₁₀₉	Dic₅₉	1	1	yes	characteristic, complemented, Sylow
8	C₅₉	#89137	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	6431	1	no	Sylow
10	C₂	—	109	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅₉×C₁₀₉	C₄
prime radical, cosocle	C₅₉×D₁₀₉	C₂
LCS	G ▷ C₅₉×C₁₀₉
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.