Subgroups — Dic₅₇ #6579

Order 228.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₉	C₂	1	1	yes	maximal, characteristic
2	Dic₁₉	—	3	1	no	maximal, Hall
3	C₃×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉	D₃	1	1	yes	characteristic
5	C₁₉	Dic₃	1	1	yes	characteristic, complemented, Sylow
6	Dic₃	—	19	1	no	maximal, Hall
7	C₂×C₃	D₁₉	1	1	yes	characteristic
8	C₄	—	57	1	no	Sylow
9	C₃	Dic₁₉	1	1	yes	characteristic, complemented, Sylow
10	C₂	D₅₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅₇
commutator, hypocenter	C₃×C₁₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂

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.