Subgroups — C₁₁×#13049931 #28384751

Order 14300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₅⋊D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#63121	—	5	1	no	maximal
4	C₁₁×#63122	—	5	1	no	maximal
5	C₁₁×D₆₅	—	5	1	no	—
6	C₁₁×D₆₅	—	5	1	no	—
7	C₁₁×D₆₅	—	10	2	no	—
8	#13049931	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₁₁×#1044	—	13	1	no	maximal, Hall
10	C₅×C₁₁×C₁₃	—	2	2	no	—
11	C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
12	C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
13	C₅⋊D₆₅	C₂×C₁₁	1	1	yes	characteristic
14	C₁₁×#261	—	25	1	no	Hall
15	C₁₁×C₅⋊D₅	—	13	1	no	—
16	C₅²×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₁₁×D₁₃	—	25	1	no	—
18	C₅²×C₁₁	#261	1	1	yes	characteristic, complemented, Hall
19	#63122	—	5	1	no	—
20	#63121	—	5	1	no	—
21	C₁₁×AGL(1,𝔽₅)	—	65	1	no	—
22	C₁₁×AGL(1,𝔽₅)	—	65	1	no	—
23	C₁₁×C₁₃	#1044	1	1	yes	characteristic, complemented, Hall
24	D₆₅	—	5	1	no	—
25	D₆₅	—	5	1	no	—
26	D₆₅	—	10	2	no	—
27	D₅×C₁₁	—	65	1	no	—
28	D₅×C₁₁	—	65	1	no	—
29	D₅×C₁₁	—	130	2	no	—
30	#1044	—	13	1	no	Hall
31	C₅×C₁₃	—	2	2	no	—
32	C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
33	C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
34	C₅×C₁₁	—	2	2	no	—
35	C₅×C₁₁	#63121	1	1	yes	characteristic, complemented
36	C₅×C₁₁	#63122	1	1	yes	characteristic, complemented
37	#261	—	25	1	no	Hall
38	C₅⋊D₅	—	13	1	no	—
39	C₄×C₁₁	—	325	1	no	Hall
40	D₁₃	—	25	1	no	—
41	C₅²	C₁₁×#261	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₁	—	325	1	no	—
43	AGL(1,𝔽₅)	—	65	1	no	—
44	AGL(1,𝔽₅)	—	65	1	no	—
45	C₁₃	C₁₁×#1044	1	1	yes	characteristic, complemented, Sylow
46	C₁₁	#13049931	1	1	yes	characteristic, direct product factor, Sylow
47	D₅	—	65	1	no	—
48	D₅	—	65	1	no	—
49	D₅	—	130	2	no	—
50	C₅	—	2	2	no	—
51	C₅	C₁₁×#63122	1	1	yes	characteristic, complemented
52	C₅	C₁₁×#63121	1	1	yes	characteristic, complemented
53	C₄	—	325	1	no	Sylow
54	C₂	—	325	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#13049931
commutator, hypocenter	C₅²×C₁₃	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₃	C₄
prime radical	C₁₁×C₅⋊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
8. #13049931	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	semidirect
12. C₅×C₁₁×C₁₃	AGL(1,𝔽₅)	semidirect
16. C₅²×C₁₃	C₄×C₁₁	semidirect
18. C₅²×C₁₁	#261	semidirect
23. C₁₁×C₁₃	#1044	semidirect
32. C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	semidirect
33. C₅×C₁₃	C₁₁×AGL(1,𝔽₅)	semidirect
35. C₅×C₁₁	#63121	semidirect
36. C₅×C₁₁	#63122	semidirect
41. C₅²	C₁₁×#261	semidirect
45. C₁₃	C₁₁×#1044	semidirect
46. C₁₁	#13049931	direct (N × H)
51. C₅	C₁₁×#63122	semidirect
52. C₅	C₁₁×#63121	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₅⋊D₆₅	2
C₁₁×#63121	5
C₁₁×#63122	5
#13049931	11
C₁₁×#1044	13

Subgroups — C11×#13049931 #28384751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13049931 #28384751