Subgroups — D₁₂₀₅₃ #37562991

Order 24106.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₇₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇₀₉	—	17	1	no	maximal, Hall
3	C₇₀₉	D₁₇	1	1	yes	characteristic, complemented, Sylow
4	D₁₇	—	709	1	no	maximal, Hall
5	C₁₇	D₇₀₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	12053	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₇₀₉	C₂
LCS	G ▷ C₁₇×C₇₀₉
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.