Subgroups — #66774

Order 340.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₇	—	5	1	no	maximal, Hall
4	C₂×C₁₇	—	5	1	no	—
5	AGL(1,𝔽₅)	—	17	1	no	maximal, Hall
6	C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
7	D₅	D₁₇	1	1	yes	characteristic
8	C₅	Dic₁₇	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	85	1	no	Sylow
10	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇	C₄
prime radical, cosocle	D₅×C₁₇	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.