Subgroups — C₁₁⋊C₅×#595 #16836670

Order 3740.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#595	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×D₁₇	C₂×C₅	1	1	yes	characteristic
5	C₅×#595	—	11	1	no	maximal, Hall
6	C₄×C₁₁⋊C₅	—	17	1	no	maximal, Hall
7	C₁₁×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×D₁₇	—	11	1	no	—
9	C₂×C₁₁⋊C₅	—	17	1	no	—
10	C₅×C₁₇	—	11	1	no	Hall
11	#595	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁⋊C₅	#595	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₁₁	—	17	1	no	Hall
14	D₁₇	C₂×C₁₁⋊C₅	1	1	yes	characteristic
15	C₂×C₁₁	—	17	1	no	—
16	C₄×C₅	—	187	1	no	Hall
17	C₁₇	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
18	C₁₁	C₅×#595	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₅	—	187	1	no	—
20	C₅	—	11	1	no	Sylow
21	C₄	—	17	1	no	Sylow
22	C₂	—	17	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₁₇	C₄×C₅
prime radical	D₁₇×C₁₁⋊C₅	C₂
cosocle	C₁₁×D₁₇	C₂×C₅
LCS	G ▷ C₁₁×C₁₇
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.