Subgroups — C₁₁×#13133348 #34035239

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	C₁₁×#66774	—	5	2	no	maximal
4	D₅×C₁₁×C₁₇	—	5	2	no	—
5	D₅×C₁₁×C₁₇	—	10	2	no	—
6	#13133348	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×#1044	—	17	1	no	maximal, Hall
8	C₅×C₁₁×C₁₇	—	2	2	no	—
9	C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	1	2	yes	complemented
10	C₁₇×C₅⋊D₅	C₂×C₁₁	1	1	yes	characteristic
11	C₁₁×Dic₁₇	—	25	1	no	Hall
12	C₁₁×C₅⋊D₅	D₁₇	1	1	yes	characteristic
13	C₅²×C₁₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₁×C₁₇	—	25	1	no	—
15	#66774	—	5	2	no	—
16	C₅²×C₁₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
17	C₁₁×AGL(1,𝔽₅)	—	85	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	—	17	1	no	Hall
24	C₅×C₁₇	—	2	2	no	—
25	C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	1	2	yes	complemented
26	Dic₁₇	—	25	1	no	Hall
27	C₅×C₁₁	—	2	2	no	—
28	C₅×C₁₁	#66774	1	2	yes	complemented
29	C₅⋊D₅	C₁₁×D₁₇	1	1	yes	characteristic
30	C₄×C₁₁	—	425	1	no	Hall
31	C₂×C₁₇	—	25	1	no	—
32	C₅²	C₁₁×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₁₁	—	25	1	no	—
34	AGL(1,𝔽₅)	—	85	2	no	—
35	C₁₇	C₁₁×#1044	1	1	yes	characteristic, complemented, Sylow
36	C₁₁	#13133348	1	1	yes	characteristic, direct product factor, Sylow
37	D₅	—	5	2	no	—
38	D₅	—	10	2	no	—
39	C₅	—	2	2	no	—
40	C₅	C₁₁×#66774	1	2	yes	complemented
41	C₄	—	425	1	no	Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#13133348
commutator, hypocenter	C₅²×C₁₇	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₇	C₄
prime radical	C₁₁×C₁₇×C₅⋊D₅	C₂
cosocle	C₁₇×C₅⋊D₅	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
6. #13133348	C₁₁	direct (N × H)
9. C₅×C₁₁×C₁₇	AGL(1,𝔽₅)	semidirect
13. C₅²×C₁₇	C₄×C₁₁	semidirect
16. C₅²×C₁₁	Dic₁₇	semidirect
18. C₁₁×C₁₇	#1044	semidirect
25. C₅×C₁₇	C₁₁×AGL(1,𝔽₅)	semidirect
28. C₅×C₁₁	#66774	semidirect
32. C₅²	C₁₁×Dic₁₇	semidirect
35. C₁₇	C₁₁×#1044	semidirect
36. C₁₁	#13133348	direct (N × H)
40. C₅	C₁₁×#66774	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
C₁₁×#66774	5
#13133348	11
C₁₁×#1044	17

Subgroups — C11×#13133348 #34035239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13133348 #34035239