Subgroups — C₃⋊(C₃⋊(D₇₁⋊C₅)) #20264136

Order 6390.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(D₇₁⋊C₅)	—	3	4	no	maximal
3	C₃⋊D₂₁₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃×C₇₁⋊C₅	D₃	1	4	yes	complemented
5	D₇₁⋊C₅	—	9	1	no	Hall
6	C₃²×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	D₂₁₃	—	3	4	no	—
8	C₇₁⋊C₅	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇₁	C₅×D₃	1	4	yes	complemented
10	D₇₁	—	9	1	no	Hall
11	C₅×C₃⋊D₃	—	71	1	no	maximal, Hall
12	C₇₁	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₅	—	71	1	no	Hall
14	C₅×D₃	—	213	4	no	—
15	C₃⋊D₃	—	71	1	no	Hall
16	C₃×C₅	—	71	4	no	—
17	C₂×C₅	—	639	1	no	Hall
18	C₃²	D₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	213	4	no	—
20	C₅	—	71	1	no	Sylow
21	C₃	C₃⋊(D₇₁⋊C₅)	1	4	yes	complemented
22	C₂	—	639	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇₁	C₂×C₅
LCS	G ▷ C₃²×C₇₁
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.