Subgroups — C₁₁×C₁₇×#1042 #34035243

Order 18700.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×C₁₇×AGL(1,𝔽₅)	—	5	1	no	maximal
4	C₁₁×C₁₇×Dic₅	—	5	1	no	maximal
5	C₂×C₅×C₁₁×C₁₇	—	5	1	no	—
6	D₅×C₁₁×C₁₇	D₅	1	1	yes	characteristic
7	C₁₇×#1042	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×#1042	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₁₁×C₁₇	—	4	1	no	—
10	C₅×C₁₁×C₁₇	Dic₅	1	1	yes	characteristic, complemented
11	C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	C₅×D₅×C₁₇	C₂×C₁₁	1	1	yes	characteristic
13	C₄×C₁₁×C₁₇	—	25	1	no	Hall
14	C₅×D₅×C₁₁	C₂×C₁₇	1	1	yes	characteristic
15	C₅²×C₁₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₁×C₁₇	—	5	1	no	—
17	C₁₇×AGL(1,𝔽₅)	—	5	1	no	—
18	C₁₇×Dic₅	—	5	1	no	—
19	C₅²×C₁₁	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
20	C₁₁×AGL(1,𝔽₅)	—	5	1	no	—
21	C₁₁×Dic₅	—	5	1	no	—
22	C₁₁×C₁₇	#1042	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₅×C₁₇	—	5	1	no	—
24	D₅×C₁₇	D₅×C₁₁	1	1	yes	characteristic
25	C₂×C₅×C₁₁	—	5	1	no	—
26	D₅×C₁₁	D₅×C₁₇	1	1	yes	characteristic
27	#1042	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
28	C₅×C₁₇	—	4	1	no	—
29	C₅×C₁₇	C₁₁×Dic₅	1	1	yes	characteristic, complemented
30	C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
31	C₄×C₁₇	—	25	1	no	Hall
32	C₅×C₁₁	—	4	1	no	—
33	C₅×C₁₁	C₁₇×Dic₅	1	1	yes	characteristic, complemented
34	C₅×C₁₁	C₁₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
35	C₅×D₅	C₂×C₁₁×C₁₇	1	1	yes	characteristic
36	C₄×C₁₁	—	25	1	no	Hall
37	C₂×C₁₇	—	5	1	no	—
38	C₅²	C₄×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₁₁	—	5	1	no	—
40	AGL(1,𝔽₅)	—	5	1	no	—
41	Dic₅	—	5	1	no	—
42	C₁₇	C₁₁×#1042	1	1	yes	characteristic, direct product factor, Sylow
43	C₁₁	C₁₇×#1042	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₅	—	5	1	no	—
45	D₅	D₅×C₁₁×C₁₇	1	1	yes	characteristic
46	C₅	—	4	1	no	—
47	C₅	C₁₁×C₁₇×Dic₅	1	1	yes	characteristic, complemented
48	C₅	C₁₁×C₁₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
49	C₄	—	25	1	no	Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₁₇	#1042
commutator, hypocenter	C₅²	C₄×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₄
prime radical	C₅×D₅×C₁₁×C₁₇	C₂
cosocle	C₅×D₅	C₂×C₁₁×C₁₇
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₇	C₄	semidirect
7. C₁₇×#1042	C₁₁	direct (N × H)
8. C₁₁×#1042	C₁₇	direct (N × H)
10. C₅×C₁₁×C₁₇	Dic₅	semidirect
11. C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	semidirect
15. C₅²×C₁₇	C₄×C₁₁	semidirect
19. C₅²×C₁₁	C₄×C₁₇	semidirect
22. C₁₁×C₁₇	#1042	direct (N × H)
27. #1042	C₁₁×C₁₇	direct (N × H)
29. C₅×C₁₇	C₁₁×Dic₅	semidirect
30. C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	semidirect
33. C₅×C₁₁	C₁₇×Dic₅	semidirect
34. C₅×C₁₁	C₁₇×AGL(1,𝔽₅)	semidirect
38. C₅²	C₄×C₁₁×C₁₇	semidirect
42. C₁₇	C₁₁×#1042	direct (N × H)
43. C₁₁	C₁₇×#1042	direct (N × H)
47. C₅	C₁₁×C₁₇×Dic₅	semidirect
48. C₅	C₁₁×C₁₇×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
C₅×D₅×C₁₁×C₁₇	2
C₁₁×C₁₇×AGL(1,𝔽₅)	5
C₁₁×C₁₇×Dic₅	5
C₁₇×#1042	11
C₁₁×#1042	17

Subgroups — C11×C17×#1042 #34035243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₇×#1042 #34035243