Subgroups — (C₇₁⋊C₅)⋊Dic₁₇ #37563284

Order 24140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₇₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₂₀₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₇×C₇₁	C₂×C₅	1	1	yes	characteristic
5	Dic₇₁⋊C₅	—	17	1	no	maximal, Hall
6	C₁₇×C₇₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₇₁⋊C₅	D₁₇	1	1	yes	characteristic
8	C₇₁⋊C₅	Dic₁₇	1	1	yes	characteristic, complemented, Hall
9	C₅×Dic₁₇	—	71	1	no	maximal, Hall
10	Dic₇₁	—	17	1	no	Hall
11	C₂×C₅×C₁₇	—	71	1	no	—
12	C₂×C₇₁	C₅×D₁₇	1	1	yes	characteristic
13	C₅×C₁₇	—	71	1	no	Hall
14	C₇₁	C₅×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
15	Dic₁₇	—	355	1	no	Hall
16	C₂×C₁₇	D₇₁⋊C₅	1	1	yes	characteristic
17	C₄×C₅	—	1207	1	no	Hall
18	C₁₇	Dic₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	71	1	no	—
20	C₅	—	71	1	no	Sylow
21	C₄	—	6035	1	no	Sylow
22	C₂	C₁₇⋊(D₇₁⋊C₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₇⋊(D₇₁⋊C₅)
commutator, hypocenter	C₁₇×C₇₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₁₇×C₇₁	C₂×C₅
prime radical	C₂×C₁₇×C₇₁⋊C₅	C₂
LCS	G ▷ C₁₇×C₇₁
UCS	C₁ ◁ C₂

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.