Subgroups — C₁₁×#13133347 #34035238

Order 18700.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₅⋊D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#66776	—	5	1	no	maximal
4	C₁₁×#66775	—	5	1	no	maximal
5	C₁₁×D₈₅	—	5	1	no	—
6	C₁₁×D₈₅	—	5	1	no	—
7	C₁₁×D₈₅	—	10	2	no	—
8	#13133347	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₁×#1044	—	17	1	no	maximal, Hall
10	C₅×C₁₁×C₁₇	—	2	2	no	—
11	C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
13	C₅⋊D₈₅	C₂×C₁₁	1	1	yes	characteristic
14	C₁₁×#595	—	25	1	no	Hall
15	C₁₁×C₅⋊D₅	—	17	1	no	—
16	C₅²×C₁₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₁₁×D₁₇	—	25	1	no	—
18	#66776	—	5	1	no	—
19	#66775	—	5	1	no	—
20	C₅²×C₁₁	#595	1	1	yes	characteristic, complemented, Hall
21	C₁₁×AGL(1,𝔽₅)	—	85	1	no	—
22	C₁₁×AGL(1,𝔽₅)	—	85	1	no	—
23	C₁₁×C₁₇	#1044	1	1	yes	characteristic, complemented, Hall
24	D₈₅	—	5	1	no	—
25	D₈₅	—	5	1	no	—
26	D₈₅	—	10	2	no	—
27	D₅×C₁₁	—	85	1	no	—
28	D₅×C₁₁	—	85	1	no	—
29	D₅×C₁₁	—	170	2	no	—
30	#1044	—	17	1	no	Hall
31	C₅×C₁₇	—	2	2	no	—
32	C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
33	C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
34	#595	—	25	1	no	Hall
35	C₅×C₁₁	—	2	2	no	—
36	C₅×C₁₁	#66775	1	1	yes	characteristic, complemented
37	C₅×C₁₁	#66776	1	1	yes	characteristic, complemented
38	C₅⋊D₅	—	17	1	no	—
39	C₄×C₁₁	—	425	1	no	Hall
40	D₁₇	—	25	1	no	—
41	C₅²	C₁₁×#595	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₁	—	425	1	no	—
43	AGL(1,𝔽₅)	—	85	1	no	—
44	AGL(1,𝔽₅)	—	85	1	no	—
45	C₁₇	C₁₁×#1044	1	1	yes	characteristic, complemented, Sylow
46	C₁₁	#13133347	1	1	yes	characteristic, direct product factor, Sylow
47	D₅	—	85	1	no	—
48	D₅	—	85	1	no	—
49	D₅	—	170	2	no	—
50	C₅	—	2	2	no	—
51	C₅	C₁₁×#66775	1	1	yes	characteristic, complemented
52	C₅	C₁₁×#66776	1	1	yes	characteristic, complemented
53	C₄	—	425	1	no	Sylow
54	C₂	—	425	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#13133347
commutator, hypocenter	C₅²×C₁₇	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₄
prime radical	C₁₁×C₅⋊D₈₅	C₂
cosocle	C₅⋊D₈₅	C₂×C₁₁
LCS	G ▷ C₅²×C₁₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₇	C₄	semidirect
8. #13133347	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	semidirect
12. C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	semidirect
16. C₅²×C₁₇	C₄×C₁₁	semidirect
20. C₅²×C₁₁	#595	semidirect
23. C₁₁×C₁₇	#1044	semidirect
32. C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	semidirect
33. C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	semidirect
36. C₅×C₁₁	#66775	semidirect
37. C₅×C₁₁	#66776	semidirect
41. C₅²	C₁₁×#595	semidirect
45. C₁₇	C₁₁×#1044	semidirect
46. C₁₁	#13133347	direct (N × H)
51. C₅	C₁₁×#66775	semidirect
52. C₅	C₁₁×#66776	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₅⋊D₈₅	2
C₁₁×#66776	5
C₁₁×#66775	5
#13133347	11
C₁₁×#1044	17

Subgroups — C11×#13133347 #34035238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13133347 #34035238