Subgroups — C₃×C₁₁⋊(C₁₁⋊#1043) #49137736

Order 36300.

672 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊(C₁₁⋊#1043)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	—	5	6	no	maximal
5	C₁₁²×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₁₁²	—	5	6	no	—
7	C₃×C₁₁⋊#1043	—	11	12	no	maximal
8	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	—	5	6	no	—
10	C₃×C₅×C₁₁²	AGL(1,𝔽₅)	1	6	yes	complemented
11	C₃×C₁₁×C₅⋊D₅	D₁₁	1	12	yes	—
12	C₃×C₁₁⋊Dic₁₁	—	25	1	no	Hall
13	D₅×C₁₁²	—	5	6	no	—
14	C₁₁⋊#1043	—	11	12	no	—
15	C₃×C₅²×C₁₁	Dic₁₁	1	12	yes	complemented
16	C₂×C₃×C₁₁²	—	25	1	no	—
17	C₃×C₁₁⋊AGL(1,𝔽₅)	—	55	72	no	—
18	C₅×C₁₁²	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
19	C₁₁×C₅⋊D₅	C₃×D₁₁	1	12	yes	—
20	C₁₁⋊Dic₁₁	—	25	1	no	Hall
21	C₃×C₁₁²	#1043	1	1	yes	characteristic, complemented, Hall
22	C₃×D₅×C₁₁	—	5	72	no	—
23	C₃×#1043	—	121	1	no	Hall
24	C₅²×C₁₁	C₃×Dic₁₁	1	12	yes	complemented
25	C₂×C₁₁²	—	25	1	no	—
26	C₁₁⋊AGL(1,𝔽₅)	—	55	72	no	—
27	C₃×C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	1	72	yes	complemented
28	C₃×C₅⋊D₅	C₁₁⋊D₁₁	1	1	yes	characteristic
29	C₃×Dic₁₁	—	275	12	no	—
30	C₁₁²	C₃×#1043	1	1	yes	characteristic, complemented, Sylow
31	D₅×C₁₁	—	5	72	no	—
32	#1043	—	121	1	no	Hall
33	C₃×C₅²	C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₁₁	—	25	12	no	—
35	C₃×AGL(1,𝔽₅)	—	605	6	no	—
36	C₅×C₁₁	C₃×C₁₁⋊AGL(1,𝔽₅)	1	72	yes	complemented
37	C₅⋊D₅	C₃×C₁₁⋊D₁₁	1	1	yes	characteristic
38	Dic₁₁	—	275	12	no	—
39	C₃×C₁₁	C₁₁⋊#1043	1	12	yes	complemented
40	C₃×D₅	—	5	6	no	—
41	C₅²	C₃×C₁₁⋊Dic₁₁	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₁	—	25	12	no	—
43	AGL(1,𝔽₅)	—	605	6	no	—
44	C₃×C₅	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	1	6	yes	complemented
45	C₃×C₄	—	3025	1	no	Hall
46	C₁₁	C₃×C₁₁⋊#1043	1	12	yes	complemented
47	D₅	—	5	6	no	—
48	C₂×C₃	—	25	1	no	—
49	C₅	C₃×C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	1	6	yes	complemented
50	C₄	—	3025	1	no	Sylow
51	C₃	C₁₁⋊(C₁₁⋊#1043)	1	1	yes	characteristic, direct product factor, Sylow
52	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₁₁⋊(C₁₁⋊#1043)
commutator, hypocenter	C₅²×C₁₁²	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₄
prime radical	C₃×C₁₁²×C₅⋊D₅	C₂
cosocle	C₁₁²×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₁₁²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₁₁⋊(C₁₁⋊#1043)	C₃	direct (N × H)
3. C₃×C₅²×C₁₁²	C₄	semidirect
8. C₅²×C₁₁²	C₃×C₄	semidirect
10. C₃×C₅×C₁₁²	AGL(1,𝔽₅)	semidirect
15. C₃×C₅²×C₁₁	Dic₁₁	semidirect
18. C₅×C₁₁²	C₃×AGL(1,𝔽₅)	semidirect
21. C₃×C₁₁²	#1043	semidirect
24. C₅²×C₁₁	C₃×Dic₁₁	semidirect
27. C₃×C₅×C₁₁	C₁₁⋊AGL(1,𝔽₅)	semidirect
30. C₁₁²	C₃×#1043	semidirect
33. C₃×C₅²	C₁₁⋊Dic₁₁	semidirect
36. C₅×C₁₁	C₃×C₁₁⋊AGL(1,𝔽₅)	semidirect
39. C₃×C₁₁	C₁₁⋊#1043	semidirect
41. C₅²	C₃×C₁₁⋊Dic₁₁	semidirect
44. C₃×C₅	C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	semidirect
46. C₁₁	C₃×C₁₁⋊#1043	semidirect
49. C₅	C₃×C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	semidirect
51. C₃	C₁₁⋊(C₁₁⋊#1043)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₁²×C₅⋊D₅	2
C₁₁⋊(C₁₁⋊#1043)	3
C₃×C₁₁⋊(C₁₁⋊AGL(1,𝔽₅))	5
C₃×C₁₁⋊#1043	11

Subgroups — C3×C11⋊(C11⋊#1043) #49137736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁⋊(C₁₁⋊#1043) #49137736