Subgroups — C₁₁×#13049935 #28384757

Order 14300.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#63118	—	5	1	no	maximal
4	C₁₁×#63122	—	5	1	no	maximal
5	C₁₁×D₆₅	D₅	1	1	yes	characteristic
6	C₅×C₁₁×D₁₃	—	5	1	no	—
7	#13049935	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₁×#1042	—	13	1	no	maximal, Hall
9	C₅×C₁₁×C₁₃	—	4	1	no	—
10	C₅×C₁₁×C₁₃	Dic₅	1	1	yes	characteristic, complemented
11	C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	C₅×D₆₅	C₂×C₁₁	1	1	yes	characteristic
13	C₁₁×#261	—	25	1	no	Hall
14	C₅×D₅×C₁₁	—	13	1	no	—
15	C₅²×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₁₁×D₁₃	—	5	1	no	—
17	C₅²×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
18	#63122	—	5	1	no	—
19	#63118	—	5	1	no	—
20	C₁₁×AGL(1,𝔽₅)	—	65	1	no	—
21	C₁₁×Dic₅	—	65	1	no	—
22	C₁₁×C₁₃	#1042	1	1	yes	characteristic, complemented, Hall
23	D₆₅	D₅×C₁₁	1	1	yes	characteristic
24	C₅×D₁₃	—	5	1	no	—
25	C₂×C₅×C₁₁	—	65	1	no	—
26	D₅×C₁₁	—	13	1	no	—
27	#1042	—	13	1	no	Hall
28	C₅×C₁₃	—	4	1	no	—
29	C₅×C₁₃	C₁₁×Dic₅	1	1	yes	characteristic, complemented
30	C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
31	C₅×C₁₁	—	4	1	no	—
32	C₅×C₁₁	#63118	1	1	yes	characteristic, complemented
33	C₅×C₁₁	#63122	1	1	yes	characteristic, complemented
34	#261	—	25	1	no	Hall
35	C₅×D₅	—	13	1	no	—
36	C₄×C₁₁	—	325	1	no	Hall
37	D₁₃	—	5	1	no	—
38	C₅²	C₁₁×#261	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₁₁	—	65	1	no	—
40	AGL(1,𝔽₅)	—	65	1	no	—
41	Dic₅	—	65	1	no	—
42	C₁₃	C₁₁×#1042	1	1	yes	characteristic, complemented, Sylow
43	C₁₁	#13049935	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₅	—	65	1	no	—
45	D₅	—	13	1	no	—
46	C₅	—	4	1	no	—
47	C₅	C₁₁×#63122	1	1	yes	characteristic, complemented
48	C₅	C₁₁×#63118	1	1	yes	characteristic, complemented
49	C₄	—	325	1	no	Sylow
50	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#13049935
commutator, hypocenter	C₅²×C₁₃	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₃	C₄
prime radical	C₅×C₁₁×D₆₅	C₂
cosocle	C₅×D₆₅	C₂×C₁₁
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₃	C₄	semidirect
7. #13049935	C₁₁	direct (N × H)
10. C₅×C₁₁×C₁₃	Dic₅	semidirect
11. C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	semidirect
15. C₅²×C₁₃	C₄×C₁₁	semidirect
17. C₅²×C₁₁	#261	semidirect
22. C₁₁×C₁₃	#1042	semidirect
29. C₅×C₁₃	C₁₁×Dic₅	semidirect
30. C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	semidirect
32. C₅×C₁₁	#63118	semidirect
33. C₅×C₁₁	#63122	semidirect
38. C₅²	C₁₁×#261	semidirect
42. C₁₃	C₁₁×#1042	semidirect
43. C₁₁	#13049935	direct (N × H)
47. C₅	C₁₁×#63122	semidirect
48. C₅	C₁₁×#63118	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₁×D₆₅	2
C₁₁×#63118	5
C₁₁×#63122	5
#13049935	11
C₁₁×#1042	13

Subgroups — C11×#13049935 #28384757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13049935 #28384757