Subgroups — C₁₁⋊#13133345 #34035236

Order 18700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#66774	—	5	6	no	maximal
4	D₅×C₁₁×C₁₇	—	5	6	no	—
5	#13133345	—	11	1	no	maximal, Hall
6	C₁₁⋊#1043	—	17	1	no	maximal, Hall
7	C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	1	6	yes	complemented
8	C₁₇×C₅⋊D₅	D₁₁	1	1	yes	characteristic
9	Dic₁₈₇	—	25	1	no	Hall
10	C₁₁×C₅⋊D₅	D₁₇	1	1	yes	characteristic
11	C₅²×C₁₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₇	—	25	1	no	—
13	#66774	—	55	6	no	—
14	C₅²×C₁₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₁⋊AGL(1,𝔽₅)	—	85	6	no	—
16	C₁₁×C₁₇	#1043	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₇	—	5	6	no	—
18	D₅×C₁₁	—	5	6	no	—
19	#1043	—	187	1	no	Hall
20	C₅×C₁₇	C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
21	Dic₁₇	—	275	1	no	Hall
22	C₅×C₁₁	#66774	1	6	yes	complemented
23	C₅⋊D₅	D₁₈₇	1	1	yes	characteristic
24	Dic₁₁	—	425	1	no	Hall
25	C₂×C₁₇	—	25	1	no	—
26	C₅²	Dic₁₈₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	25	1	no	—
28	AGL(1,𝔽₅)	—	935	6	no	—
29	C₁₇	C₁₁⋊#1043	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	#13133345	1	1	yes	characteristic, complemented, Sylow
31	D₅	—	5	6	no	—
32	C₅	C₁₁⋊#66774	1	6	yes	complemented
33	C₄	—	4675	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₁×C₁₇	C₄
prime radical, cosocle	C₁₁×C₁₇×C₅⋊D₅	C₂
LCS	G ▷ C₅²×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.