Subgroups — C₃⋊(C₅⋊(D₂₁₁⋊C₅)) #44539549

Order 31650.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(D₂₁₁⋊C₅)	—	3	1	no	maximal, Hall
3	C₃⋊(D₂₁₁⋊C₅)	—	5	1	no	maximal
4	D₃₁₆₅	C₅	1	1	yes	maximal, characteristic, complemented
5	C₅×C₂₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₂₁₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₃×C₂₁₁⋊C₅	—	2	2	no	—
8	C₃×C₂₁₁⋊C₅	D₅	1	1	yes	characteristic, complemented
9	D₁₀₅₅	—	3	1	no	—
10	D₂₁₁⋊C₅	—	15	1	no	—
11	D₆₃₃	—	5	1	no	Hall
12	C₅×C₂₁₁	C₅×D₃	1	1	yes	characteristic, complemented
13	C₂₁₁⋊C₅	—	2	2	no	—
14	C₂₁₁⋊C₅	D₁₅	1	1	yes	characteristic, complemented
15	C₃×C₂₁₁	C₅×D₅	1	1	yes	characteristic, complemented, Hall
16	D₂₁₁	—	15	1	no	Hall
17	C₂₁₁	C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
18	C₅×D₁₅	—	211	1	no	maximal, Hall
19	C₃×C₅²	—	211	1	no	Hall
20	C₅×D₅	—	633	1	no	Hall
21	D₁₅	—	211	1	no	—
22	C₅×D₃	—	1055	1	no	—
23	C₅²	—	211	1	no	Sylow
24	C₃×C₅	—	422	2	no	—
25	C₃×C₅	—	211	1	no	—
26	C₃×C₅	D₂₁₁⋊C₅	1	1	yes	characteristic, complemented
27	C₂×C₅	—	3165	1	no	—
28	D₅	—	633	1	no	—
29	D₃	—	1055	1	no	Hall
30	C₅	—	422	2	no	—
31	C₅	—	211	1	no	—
32	C₅	C₃⋊(D₂₁₁⋊C₅)	1	1	yes	characteristic, complemented
33	C₃	C₅⋊(D₂₁₁⋊C₅)	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	3165	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₂₁₁	C₂×C₅
LCS	G ▷ C₃×C₅×C₂₁₁
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.