Subgroups — C₃⋊(#16861520⋊C₃) #49147026

Order 36900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#16861520	C₃	1	1	yes	maximal, characteristic, complemented
3	#16861520⋊C₃	—	3	1	no	maximal
4	C₃×C₄₁×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₄₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₄₁×(C₅⋊D₅)⋊C₃	—	2	1	no	—
7	C₄₁×(C₅⋊D₅)⋊C₃	D₃	1	1	yes	characteristic
8	#16861520	—	3	1	no	Hall
9	C₄₁×C₅²⋊C₃	—	2	1	no	—
10	C₄₁×C₅²⋊C₃	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃⋊#11717963	—	15	2	no	—
13	C₄₁×C₅⋊D₅	C₃×D₃	1	1	yes	characteristic
14	C₃×Dic₁₂₃	—	25	1	no	maximal, Hall
15	C₃×D₅×C₄₁	—	15	2	no	—
16	C₅²×C₄₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
17	C₃⋊(#1043⋊C₃)	—	41	1	no	maximal, Hall
18	#11717963	—	45	2	no	—
19	C₂×C₃²×C₄₁	—	25	1	no	—
20	C₃×C₅×C₄₁	—	3	2	no	—
21	Dic₁₂₃	—	25	1	no	—
22	C₃×Dic₄₁	—	75	1	no	—
23	C₃×(C₅⋊D₅)⋊C₃	D₄₁	1	1	yes	characteristic
24	D₅×C₄₁	—	15	2	no	—
25	C₃²×C₄₁	—	25	1	no	Hall
26	C₃⋊#1043	—	41	1	no	—
27	#1043⋊C₃	—	123	1	no	—
28	C₂×C₃×C₄₁	—	25	1	no	—
29	C₂×C₃×C₄₁	—	25	1	no	—
30	C₂×C₃×C₄₁	—	50	1	no	—
31	C₃×C₅²⋊C₃	Dic₄₁	1	1	yes	characteristic, complemented, Hall
32	C₅×C₄₁	—	3	2	no	—
33	Dic₄₁	—	75	1	no	Hall
34	C₃×C₅⋊D₅	C₃×D₄₁	1	1	yes	characteristic
35	(C₅⋊D₅)⋊C₃	—	2	1	no	—
36	(C₅⋊D₅)⋊C₃	D₁₂₃	1	1	yes	characteristic
37	C₃×C₄₁	—	25	1	no	—
38	C₃×C₄₁	—	50	1	no	—
39	C₃×C₄₁	#1043⋊C₃	1	1	yes	characteristic, complemented
40	#1043	—	123	1	no	Hall
41	C₂×C₄₁	—	25	1	no	—
42	C₃×C₅²	C₃×Dic₄₁	1	1	yes	characteristic, complemented
43	C₅²⋊C₃	—	2	1	no	—
44	C₅²⋊C₃	Dic₁₂₃	1	1	yes	characteristic, complemented
45	ΓL(1,𝔽₁₆)	—	615	2	no	—
46	C₅⋊D₅	C₃×D₁₂₃	1	1	yes	characteristic
47	C₄₁	C₃⋊(#1043⋊C₃)	1	1	yes	characteristic, complemented, Sylow
48	C₃×Dic₃	—	1025	1	no	Hall
49	C₃×D₅	—	15	2	no	—
50	C₅²	C₃×Dic₁₂₃	1	1	yes	characteristic, complemented, Sylow
51	AGL(1,𝔽₅)	—	1845	2	no	—
52	C₂×C₃²	—	25	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	3075	1	no	—
55	Dic₃	—	1025	1	no	—
56	D₅	—	15	2	no	—
57	C₃²	—	25	1	no	Sylow
58	C₂×C₃	—	25	1	no	—
59	C₂×C₃	—	25	1	no	—
60	C₂×C₃	—	50	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	3075	1	no	Sylow
63	C₃	—	25	1	no	—
64	C₃	—	50	1	no	—
65	C₃	#16861520⋊C₃	1	1	yes	characteristic, complemented
66	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₄₁	C₃×C₄
prime radical	C₃×C₄₁×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₃×C₄₁×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₃×C₅²×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃⋊#16861520	C₃	semidirect
4. C₃×C₄₁×C₅²⋊C₃	C₄	semidirect
10. C₄₁×C₅²⋊C₃	Dic₃	semidirect
11. C₃×C₅²×C₄₁	C₃×C₄	semidirect
16. C₅²×C₄₁	C₃×Dic₃	semidirect
31. C₃×C₅²⋊C₃	Dic₄₁	semidirect
39. C₃×C₄₁	#1043⋊C₃	semidirect
42. C₃×C₅²	C₃×Dic₄₁	semidirect
44. C₅²⋊C₃	Dic₁₂₃	semidirect
47. C₄₁	C₃⋊(#1043⋊C₃)	semidirect
50. C₅²	C₃×Dic₁₂₃	semidirect
65. C₃	#16861520⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₁×(C₅⋊D₅)⋊C₃	2
C₃⋊#16861520	3
#16861520⋊C₃	3
C₃×Dic₁₂₃	25
C₃⋊(#1043⋊C₃)	41

Subgroups — C3⋊(#16861520⋊C3) #49147026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#16861520⋊C₃) #49147026