Subgroups — C₇₁⋊#66772 #37563306

Order 24140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇₁⋊#595	—	5	1	no	maximal, Hall
4	D₁₇×C₇₁	D₅	1	1	yes	characteristic
5	Dic₃₅₅	—	17	1	no	maximal, Hall
6	C₁₇×C₇₁	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×C₇₁	—	17	1	no	—
8	C₅×C₇₁	#595	1	1	yes	characteristic, complemented, Hall
9	#66772	—	71	1	no	maximal, Hall
10	Dic₇₁	—	85	1	no	Hall
11	C₅×D₁₇	D₇₁	1	1	yes	characteristic
12	C₂×C₇₁	—	17	1	no	—
13	C₅×C₁₇	Dic₇₁	1	1	yes	characteristic, complemented, Hall
14	C₇₁	#66772	1	1	yes	characteristic, complemented, Sylow
15	#595	—	355	1	no	Hall
16	D₁₇	D₃₅₅	1	1	yes	characteristic
17	Dic₅	—	1207	1	no	Hall
18	C₁₇	Dic₃₅₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	17	1	no	—
20	C₅	C₇₁⋊#595	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6035	1	no	Sylow
22	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇×C₇₁	C₄
prime radical, cosocle	C₅×D₁₇×C₇₁	C₂
LCS	G ▷ C₅×C₁₇×C₇₁
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.