Subgroups — C₃⋊(C₃⋊(D₇₁⋊C₂₅)) #44544014

Order 31950.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(D₇₁⋊C₂₅)	—	3	4	no	maximal
3	C₅×C₃⋊D₂₁₃	C₅	1	1	yes	maximal, characteristic
4	C₃×C₇₁⋊C₂₅	D₃	1	4	yes	complemented
5	D₇₁⋊C₂₅	—	9	1	no	Hall
6	C₃²×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic
7	C₅×D₂₁₃	—	3	4	no	—
8	C₇₁⋊C₂₅	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊D₂₁₃	C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×C₇₁	C₅×D₃	1	4	yes	—
11	C₅×D₇₁	—	9	1	no	—
12	C₃²×C₇₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
13	C₃⋊D₃×C₂₅	—	71	1	no	maximal, Hall
14	D₂₁₃	—	3	4	no	—
15	C₅×C₇₁	C₅×C₃⋊D₃	1	1	yes	characteristic
16	C₃²×C₂₅	—	71	1	no	Hall
17	C₃×C₇₁	D₃×C₂₅	1	4	yes	complemented
18	D₃×C₂₅	—	213	4	no	—
19	D₇₁	—	9	1	no	Hall
20	C₅×C₃⋊D₃	—	71	1	no	—
21	C₃×C₂₅	—	71	4	no	—
22	C₇₁	C₃⋊D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₂₅	—	639	1	no	Hall
24	C₃²×C₅	D₇₁⋊C₅	1	1	yes	characteristic
25	C₅×D₃	—	213	4	no	—
26	C₂₅	—	71	1	no	Sylow
27	C₃⋊D₃	—	71	1	no	Hall
28	C₃×C₅	C₃⋊(D₇₁⋊C₅)	1	4	yes	—
29	C₂×C₅	—	639	1	no	—
30	C₃²	D₇₁⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	213	4	no	—
32	C₅	C₃⋊(C₃⋊(D₇₁⋊C₅))	1	1	yes	characteristic
33	C₃	C₃⋊(D₇₁⋊C₂₅)	1	4	yes	complemented
34	C₂	—	639	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₃⋊(C₃⋊(D₇₁⋊C₅))
commutator, hypocenter	C₃²×C₇₁	C₂×C₂₅
Fitting, socle, cosocle	C₃²×C₅×C₇₁	C₂×C₅
prime radical	C₅×C₃⋊D₂₁₃	C₅
LCS	G ▷ C₃²×C₇₁
UCS	C₁ ◁ C₅

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.