Subgroups — C₁₇×C₁₁⋊#1044 #34035240

Order 18700.

64 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	2	no	maximal
4	D₅×C₁₁×C₁₇	—	5	2	no	—
5	D₅×C₁₁×C₁₇	—	10	2	no	—
6	C₁₇×#1044	—	11	1	no	maximal, Hall
7	C₁₁⋊#1044	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₁₇	—	2	2	no	—
9	C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	1	2	yes	complemented
10	C₁₇×C₅⋊D₅	D₁₁	1	1	yes	characteristic
11	C₁₇×Dic₁₁	—	25	1	no	Hall
12	C₁₁×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic
13	C₅²×C₁₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁×C₁₇	—	25	1	no	—
15	C₁₇×AGL(1,𝔽₅)	—	55	2	no	—
16	C₅²×C₁₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₁₁⋊AGL(1,𝔽₅)	—	5	2	no	—
18	C₁₁×C₁₇	#1044	1	1	yes	characteristic, complemented, Hall
19	D₅×C₁₇	—	5	2	no	—
20	D₅×C₁₇	—	10	2	no	—
21	D₅×C₁₁	—	5	2	no	—
22	D₅×C₁₁	—	10	2	no	—
23	#1044	—	11	1	no	Hall
24	C₅×C₁₇	—	2	2	no	—
25	C₅×C₁₇	C₁₁⋊AGL(1,𝔽₅)	1	2	yes	complemented
26	C₄×C₁₇	—	275	1	no	Hall
27	C₅×C₁₁	—	2	2	no	—
28	C₅×C₁₁	C₁₇×AGL(1,𝔽₅)	1	2	yes	complemented
29	C₅⋊D₅	C₁₇×D₁₁	1	1	yes	characteristic
30	Dic₁₁	—	25	1	no	Hall
31	C₂×C₁₇	—	25	1	no	—
32	C₅²	C₁₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₁₁	—	25	1	no	—
34	AGL(1,𝔽₅)	—	55	2	no	—
35	C₁₇	C₁₁⋊#1044	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₁	C₁₇×#1044	1	1	yes	characteristic, complemented, Sylow
37	D₅	—	5	2	no	—
38	D₅	—	10	2	no	—
39	C₅	—	2	2	no	—
40	C₅	C₁₇×C₁₁⋊AGL(1,𝔽₅)	1	2	yes	complemented
41	C₄	—	275	1	no	Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	C₁₁⋊#1044
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
7. C₁₁⋊#1044	C₁₇	direct (N × H)
9. C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	semidirect
13. C₅²×C₁₇	Dic₁₁	semidirect
16. C₅²×C₁₁	C₄×C₁₇	semidirect
18. C₁₁×C₁₇	#1044	semidirect
25. C₅×C₁₇	C₁₁⋊AGL(1,𝔽₅)	semidirect
28. C₅×C₁₁	C₁₇×AGL(1,𝔽₅)	semidirect
32. C₅²	C₁₇×Dic₁₁	semidirect
35. C₁₇	C₁₁⋊#1044	direct (N × H)
36. C₁₁	C₁₇×#1044	semidirect
40. 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×#1044	11
C₁₁⋊#1044	17

Subgroups — C17×C11⋊#1044 #34035240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₁₁⋊#1044 #34035240