Subgroups — C₅×#16861895 #35208693

Order 20740.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₁₀₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₆₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#16861895	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	D₁₀₃₇	C₂×C₅	1	1	yes	characteristic
5	C₅×#6923	—	17	1	no	maximal, Hall
6	C₁₇×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×D₆₁	—	17	1	no	—
8	C₅×#595	—	61	1	no	maximal, Hall
9	C₅×C₆₁	#595	1	1	yes	characteristic, complemented, Hall
10	#6923	—	17	1	no	Hall
11	C₅×D₁₇	—	61	1	no	—
12	D₆₁	—	17	1	no	—
13	C₅×C₁₇	#6923	1	1	yes	characteristic, complemented, Hall
14	#595	—	61	1	no	Hall
15	C₆₁	C₅×#595	1	1	yes	characteristic, complemented, Sylow
16	D₁₇	—	61	1	no	—
17	C₄×C₅	—	1037	1	no	Hall
18	C₁₇	C₅×#6923	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	1037	1	no	—
20	C₅	#16861895	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	—	1037	1	no	Sylow
22	C₂	—	1037	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.