Subgroups — C₈₃×D₁₆₉ #43242572

Order 28054.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₈₃	—	13	1	no	maximal
3	C₁₃×C₈₃	D₁₃	1	1	yes	characteristic
4	D₁₆₉	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₆₉	C₂×C₈₃	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₈₃	—	169	1	no	Hall
7	C₈₃	D₁₆₉	1	1	yes	characteristic, direct product factor, Sylow
8	D₁₃	—	13	1	no	—
9	C₁₃	D₁₃×C₈₃	1	1	yes	characteristic
10	C₂	—	169	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₃	D₁₆₉
commutator, cosocle, hypocenter	C₁₆₉	C₂×C₈₃
Frattini	C₁₃	D₁₃×C₈₃
Fitting	C₈₃×C₁₆₉	C₂
socle	C₁₃×C₈₃	D₁₃
LCS	G ▷ C₁₆₉
UCS	C₁ ◁ C₈₃

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.