Subgroups — #66772

Order 340.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#595	—	5	1	no	maximal, Hall
4	D₁₇	D₅	1	1	yes	characteristic
5	Dic₅	—	17	1	no	maximal, Hall
6	C₁₇	Dic₅	1	1	yes	characteristic, complemented, Sylow
7	C₂×C₅	—	17	1	no	—
8	C₅	#595	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	85	1	no	Sylow
10	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇	C₄
prime radical, cosocle	C₅×D₁₇	C₂
LCS	G ▷ C₅×C₁₇
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.