Subgroups — #14584033⋊C₅ #28358281

Order 13940.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇⋊(D₄₁⋊C₅)	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₄₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	#14584033	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	D₆₉₇	C₂×C₅	1	1	yes	characteristic
5	#4223⋊C₅	—	17	1	no	maximal, Hall
6	C₁₇×C₄₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
7	D₄₁⋊C₅	—	17	1	no	—
8	C₅×#595	—	41	1	no	maximal, Hall
9	C₄₁⋊C₅	#595	1	1	yes	characteristic, complemented, Hall
10	C₅×D₁₇	—	41	1	no	—
11	#4223	—	17	1	no	Hall
12	C₅×C₁₇	—	41	1	no	Hall
13	D₄₁	—	17	1	no	—
14	#595	—	205	1	no	Hall
15	C₄₁	C₅×#595	1	1	yes	characteristic, complemented, Sylow
16	D₁₇	—	205	1	no	—
17	C₄×C₅	—	697	1	no	Hall
18	C₁₇	#4223⋊C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	697	1	no	—
20	C₅	—	41	1	no	Sylow
21	C₄	—	3485	1	no	Sylow
22	C₂	—	3485	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₇×C₄₁	C₄×C₅
prime radical	C₁₇⋊(D₄₁⋊C₅)	C₂
cosocle	D₆₉₇	C₂×C₅
LCS	G ▷ C₁₇×C₄₁
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.