Subgroups — C₇₁×#66774 #37563302

Order 24140.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
3	Dic₁₇×C₇₁	—	5	1	no	maximal, Hall
4	C₂×C₁₇×C₇₁	—	5	1	no	—
5	AGL(1,𝔽₅)×C₇₁	—	17	1	no	maximal, Hall
6	C₁₇×C₇₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₇₁	D₁₇	1	1	yes	characteristic
8	C₅×C₇₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
9	#66774	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₇₁	—	85	1	no	Hall
11	D₅×C₁₇	C₂×C₇₁	1	1	yes	characteristic
12	C₂×C₇₁	—	5	1	no	—
13	C₅×C₁₇	C₄×C₇₁	1	1	yes	characteristic, complemented, Hall
14	C₇₁	#66774	1	1	yes	characteristic, direct product factor, Sylow
15	Dic₁₇	—	5	1	no	Hall
16	C₂×C₁₇	—	5	1	no	—
17	AGL(1,𝔽₅)	—	17	1	no	Hall
18	C₁₇	AGL(1,𝔽₅)×C₇₁	1	1	yes	characteristic, complemented, Sylow
19	D₅	D₁₇×C₇₁	1	1	yes	characteristic
20	C₅	Dic₁₇×C₇₁	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	85	1	no	Sylow
22	C₂	—	5	1	no	—

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.