Subgroups — Dic₃₉₃₉ #30628734

Order 15756.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃₁₃	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₁₀₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₀₁	D₃	1	1	yes	characteristic
5	C₁₃×C₁₀₁	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₃₀₃	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₀₁	D₁₃	1	1	yes	characteristic
8	Dic₁₀₁	—	39	1	no	Hall
9	C₃×C₁₀₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₀₁	D₃₉	1	1	yes	characteristic
11	Dic₃₉	—	101	1	no	maximal, Hall
12	C₁₀₁	Dic₃₉	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₃	D₁₀₁	1	1	yes	characteristic
14	Dic₁₃	—	303	1	no	Hall
15	C₃×C₁₃	Dic₁₀₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	D₃₀₃	1	1	yes	characteristic
17	C₁₃	Dic₃₀₃	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	1313	1	no	Hall
19	C₂×C₃	D₁₃₁₃	1	1	yes	characteristic
20	C₄	—	3939	1	no	Sylow
21	C₃	Dic₁₃₁₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃₉₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₉₃₉
commutator, hypocenter	C₃×C₁₃×C₁₀₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₃×C₁₀₁	C₂
LCS	G ▷ C₃×C₁₃×C₁₀₁
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.