Subgroups — C₃⋊(C₁₀₃⋊#261) #30632585

Order 16068.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₁₀₃⋊#261	—	3	1	no	maximal, Hall
3	C₃×C₁₃×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₁₀₃	D₃	1	1	yes	characteristic
5	C₁₃×C₁₀₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	Dic₃₀₉	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₀₃	—	13	1	no	—
8	Dic₁₀₃	—	39	1	no	Hall
9	C₃×C₁₀₃	#261	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₀₃	—	13	1	no	—
11	C₃⋊#261	—	103	1	no	maximal, Hall
12	C₁₀₃	C₃⋊#261	1	1	yes	characteristic, complemented, Sylow
13	C₃×D₁₃	D₁₀₃	1	1	yes	characteristic
14	#261	—	309	1	no	Hall
15	C₃×C₁₃	Dic₁₀₃	1	1	yes	characteristic, complemented, Hall
16	D₁₃	D₃₀₉	1	1	yes	characteristic
17	C₁₃	Dic₃₀₉	1	1	yes	characteristic, complemented, Sylow
18	Dic₃	—	1339	1	no	Hall
19	C₂×C₃	—	13	1	no	—
20	C₄	—	4017	1	no	Sylow
21	C₃	C₁₀₃⋊#261	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₃×C₁₀₃	C₄
prime radical, cosocle	C₃×D₁₃×C₁₀₃	C₂
LCS	G ▷ C₃×C₁₃×C₁₀₃
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.