Subgroups — C₃⋊D₅₅₅₉ #45688693

Order 33354.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₅₅₉	—	3	4	no	maximal
3	C₃×C₁₇×C₁₀₉	D₃	1	4	yes	complemented
4	D₁₈₅₃	—	9	1	no	Hall
5	C₃⋊D₃₂₇	—	17	1	no	maximal, Hall
6	C₁₇×C₁₀₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₁₀₉	D₁₇	1	1	yes	characteristic, complemented, Hall
8	D₃₂₇	—	51	4	no	—
9	C₃×C₁₀₉	D₅₁	1	4	yes	complemented
10	C₃⋊D₅₁	—	109	1	no	maximal, Hall
11	D₁₀₉	—	153	1	no	Hall
12	C₃²×C₁₇	D₁₀₉	1	1	yes	characteristic, complemented, Hall
13	C₁₀₉	C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
14	D₅₁	—	327	4	no	—
15	C₃×C₁₇	D₃₂₇	1	4	yes	complemented
16	D₁₇	—	981	1	no	Hall
17	C₃⋊D₃	—	1853	1	no	Hall
18	C₁₇	C₃⋊D₃₂₇	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₈₅₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	5559	4	no	—
21	C₃	D₅₅₅₉	1	4	yes	complemented
22	C₂	—	16677	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₇×C₁₀₉	C₂
LCS	G ▷ C₃²×C₁₇×C₁₀₉
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.