Subgroups — C₇₁⋊#90646 #44544037

Order 31950.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₁×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₀₆₅	—	3	1	no	maximal
3	C₃×C₅²×C₇₁	D₃	1	1	yes	characteristic
4	C₅×D₃₅₅	—	9	1	no	Hall
5	D₁₀₆₅	—	3	1	no	—
6	C₅×D₂₁₃	—	15	1	no	—
7	C₅²×C₇₁	D₉	1	1	yes	characteristic, complemented, Hall
8	D₆₃₉	—	25	1	no	maximal, Hall
9	C₃×C₅×C₇₁	—	3	1	no	—
10	C₃×C₅×C₇₁	—	3	1	no	—
11	D₃₅₅	—	9	1	no	—
12	C₅×D₇₁	—	45	1	no	—
13	C₉×C₇₁	—	25	1	no	Hall
14	#90646	—	71	1	no	maximal, Hall
15	D₂₁₃	—	15	1	no	—
16	C₅×C₇₁	—	3	1	no	—
17	C₅×C₇₁	—	3	1	no	—
18	C₅²⋊C₉	D₇₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇₁	#3874	1	1	yes	characteristic
20	C₅×D₁₅	—	213	1	no	—
21	D₇₁	—	45	1	no	Hall
22	C₃×C₅²	D₂₁₃	1	1	yes	characteristic
23	C₇₁	#90646	1	1	yes	characteristic, complemented, Sylow
24	C₅×D₅	—	639	1	no	Hall
25	D₁₅	—	213	1	no	—
26	C₅×D₃	—	1065	1	no	—
27	C₅²	D₆₃₉	1	1	yes	characteristic, complemented, Sylow
28	D₉	—	1775	1	no	Hall
29	C₃×C₅	—	3	1	no	—
30	C₃×C₅	—	3	1	no	—
31	C₂×C₅	—	3195	1	no	—
32	D₅	—	639	1	no	—
33	C₉	—	25	1	no	Sylow
34	D₃	—	1065	1	no	—
35	C₅	—	3	1	no	—
36	C₅	—	3	1	no	—
37	C₃	C₇₁⋊#3874	1	1	yes	characteristic
38	C₂	—	3195	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₇₁×C₅²⋊C₉	C₂
Frattini	C₃	C₇₁⋊#3874
Fitting, socle	C₃×C₅²×C₇₁	D₃
LCS	G ▷ C₇₁×C₅²⋊C₉
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.