Subgroups — C₃⋊D₅₂₅₃ #44538580

Order 31518.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₂₅₃	—	3	4	no	maximal
3	C₃×C₁₇×C₁₀₃	D₃	1	4	yes	complemented
4	D₁₇₅₁	—	9	1	no	Hall
5	C₃⋊D₃₀₉	—	17	1	no	maximal, Hall
6	C₁₇×C₁₀₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₁₀₃	D₁₇	1	1	yes	characteristic, complemented, Hall
8	D₃₀₉	—	51	4	no	—
9	C₃×C₁₀₃	D₅₁	1	4	yes	complemented
10	C₃⋊D₅₁	—	103	1	no	maximal, Hall
11	D₁₀₃	—	153	1	no	Hall
12	C₃²×C₁₇	D₁₀₃	1	1	yes	characteristic, complemented, Hall
13	C₁₀₃	C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
14	D₅₁	—	309	4	no	—
15	C₃×C₁₇	D₃₀₉	1	4	yes	complemented
16	D₁₇	—	927	1	no	Hall
17	C₃⋊D₃	—	1751	1	no	Hall
18	C₁₇	C₃⋊D₃₀₉	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₇₅₁	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	5253	4	no	—
21	C₃	D₅₂₅₃	1	4	yes	complemented
22	C₂	—	15759	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₇×C₁₀₃	C₂
LCS	G ▷ C₃²×C₁₇×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.