Subgroups — C₁₇×D₅₂₉ #31824593

Order 17986.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₇×D₂₃	—	23	1	no	maximal
4	C₅₂₉	C₂×C₁₇	1	1	yes	characteristic, complemented, Sylow
5	C₁₇×C₂₃	D₂₃	1	1	yes	characteristic
6	D₂₃	—	23	1	no	—
7	C₂×C₁₇	—	529	1	no	Hall
8	C₂₃	C₁₇×D₂₃	1	1	yes	characteristic
9	C₁₇	D₅₂₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	—	529	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₅₂₉
commutator, cosocle, hypocenter	C₅₂₉	C₂×C₁₇
Frattini	C₂₃	C₁₇×D₂₃
Fitting	C₁₇×C₅₂₉	C₂
socle	C₁₇×C₂₃	D₂₃
LCS	G ▷ C₅₂₉
UCS	C₁ ◁ C₁₇

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.