Subgroups — C₁₇×C₁₁⋊#1043 #34035233

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	C₁₇×C₁₁⋊AGL(1,𝔽₅)	—	5	6	no	maximal
4	D₅×C₁₁×C₁₇	—	5	6	no	—
5	C₁₇×#1043	—	11	1	no	maximal, Hall
6	C₁₁⋊#1043	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	1	6	yes	complemented
8	C₁₇×C₅⋊D₅	D₁₁	1	1	yes	characteristic
9	C₁₇×Dic₁₁	—	25	1	no	Hall
10	C₁₁×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic
11	C₅²×C₁₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₇	—	25	1	no	—
13	C₁₇×AGL(1,𝔽₅)	—	55	6	no	—
14	C₅²×C₁₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₁⋊AGL(1,𝔽₅)	—	5	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	—	11	1	no	Hall
20	C₅×C₁₇	C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
21	C₄×C₁₇	—	275	1	no	Hall
22	C₅×C₁₁	C₁₇×AGL(1,𝔽₅)	1	6	yes	complemented
23	C₅⋊D₅	C₁₇×D₁₁	1	1	yes	characteristic
24	Dic₁₁	—	25	1	no	Hall
25	C₂×C₁₇	—	25	1	no	—
26	C₅²	C₁₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁	—	25	1	no	—
28	AGL(1,𝔽₅)	—	55	6	no	—
29	C₁₇	C₁₁⋊#1043	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₁	C₁₇×#1043	1	1	yes	characteristic, complemented, Sylow
31	D₅	—	5	6	no	—
32	C₅	C₁₇×C₁₁⋊AGL(1,𝔽₅)	1	6	yes	complemented
33	C₄	—	275	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₁₁⋊#1043
commutator, hypocenter	C₅²×C₁₁	C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₄
prime radical	C₁₁×C₁₇×C₅⋊D₅	C₂
cosocle	C₁₁×C₅⋊D₅	C₂×C₁₇
LCS	G ▷ C₅²×C₁₁
UCS	C₁ ◁ C₁₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₇	C₄	semidirect
6. C₁₁⋊#1043	C₁₇	direct (N × H)
7. C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	semidirect
11. C₅²×C₁₇	Dic₁₁	semidirect
14. C₅²×C₁₁	C₄×C₁₇	semidirect
16. C₁₁×C₁₇	#1043	semidirect
20. C₅×C₁₇	C₁₁⋊AGL(1,𝔽₅)	semidirect
22. C₅×C₁₁	C₁₇×AGL(1,𝔽₅)	semidirect
26. C₅²	C₁₇×Dic₁₁	semidirect
29. C₁₇	C₁₁⋊#1043	direct (N × H)
30. C₁₁	C₁₇×#1043	semidirect
32. C₅	C₁₇×C₁₁⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×C₁₇×C₅⋊D₅	2
C₁₇×C₁₁⋊AGL(1,𝔽₅)	5
C₁₇×#1043	11
C₁₁⋊#1043	17

Subgroups — C17×C11⋊#1043 #34035233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₁₁⋊#1043 #34035233