Subgroups — C₅²×D₂₁₁⋊C₃ #44539559

Order 31650.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₂₁₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₂₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×D₂₁₁⋊C₃	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₂₁₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₂₁₁⋊C₃	C₂×C₅	1	6	yes	complemented
6	C₅×D₂₁₁	C₃×C₅	1	6	yes	complemented
7	D₂₁₁⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₂₁₁	C₂×C₃×C₅	1	6	yes	complemented
9	C₂₁₁⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
10	D₂₁₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
11	C₂₁₁	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₃×C₅²	—	211	1	no	maximal, Hall
13	C₃×C₅²	—	211	1	no	Hall
14	C₂×C₅²	—	211	1	no	Hall
15	C₂×C₃×C₅	—	211	6	no	—
16	C₅²	D₂₁₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	—	211	6	no	—
18	C₂×C₅	—	211	6	no	—
19	C₂×C₃	—	211	1	no	Hall
20	C₅	C₅×D₂₁₁⋊C₃	1	6	yes	direct product factor
21	C₃	—	211	1	no	Sylow
22	C₂	—	211	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₂₁₁⋊C₃
commutator, cosocle, hypocenter	C₂₁₁	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₂₁₁	C₂×C₃
LCS	G ▷ C₂₁₁
UCS	C₁ ◁ C₅²

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.