Subgroups — C₃×#16861520⋊C₃ #49147002

Order 36900.

96 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	C₃	1	3	yes	maximal, direct product factor
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	C₂×C₃	1	3	yes	—
7	#16861520	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₄₁×C₅²⋊C₃	C₃×C₄	1	3	yes	complemented
9	C₃×C₅²×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃×#11717963	—	15	2	no	—
11	C₄₁×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic
12	C₃²×Dic₄₁	—	25	1	no	maximal, Hall
13	C₃×D₅×C₄₁	—	15	2	no	—
14	C₅²×C₄₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
15	C₃×#1043⋊C₃	—	41	1	no	maximal, Hall
16	#11717963	—	15	2	no	—
17	C₂×C₃²×C₄₁	—	25	1	no	—
18	C₃×C₅×C₄₁	—	3	2	no	—
19	C₃×Dic₄₁	—	25	3	no	—
20	C₃×Dic₄₁	—	25	1	no	—
21	C₃×(C₅⋊D₅)⋊C₃	D₄₁	1	1	yes	characteristic
22	D₅×C₄₁	—	15	2	no	—
23	C₃²×C₄₁	—	25	1	no	Hall
24	C₃×#1043	—	41	1	no	—
25	#1043⋊C₃	—	41	3	no	—
26	C₂×C₃×C₄₁	—	25	3	no	—
27	C₂×C₃×C₄₁	—	25	1	no	—
28	C₃×C₅²⋊C₃	Dic₄₁	1	1	yes	characteristic, complemented, Hall
29	C₅×C₄₁	—	3	2	no	—
30	Dic₄₁	—	25	1	no	Hall
31	C₃×C₅⋊D₅	C₃×D₄₁	1	1	yes	characteristic
32	(C₅⋊D₅)⋊C₃	C₃×D₄₁	1	3	yes	—
33	C₃×C₄₁	—	25	3	no	—
34	C₃×C₄₁	#1043⋊C₃	1	1	yes	characteristic, complemented
35	#1043	—	41	1	no	Hall
36	C₂×C₄₁	—	25	1	no	—
37	C₃×C₅²	C₃×Dic₄₁	1	1	yes	characteristic, complemented
38	C₅²⋊C₃	C₃×Dic₄₁	1	3	yes	complemented
39	C₃×AGL(1,𝔽₅)	—	615	2	no	—
40	C₅⋊D₅	C₃²×D₄₁	1	1	yes	characteristic
41	C₄₁	C₃×#1043⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₃²×C₄	—	1025	1	no	Hall
43	C₃×D₅	—	15	2	no	—
44	C₅²	C₃²×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
45	AGL(1,𝔽₅)	—	615	2	no	—
46	C₂×C₃²	—	25	1	no	—
47	C₃×C₅	—	3	2	no	—
48	C₃×C₄	—	1025	1	no	—
49	C₃×C₄	—	1025	3	no	—
50	D₅	—	15	2	no	—
51	C₃²	—	25	1	no	Sylow
52	C₂×C₃	—	25	3	no	—
53	C₂×C₃	—	25	1	no	—
54	C₅	—	3	2	no	—
55	C₄	—	1025	1	no	Sylow
56	C₃	—	25	3	no	—
57	C₃	#16861520⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#16861520⋊C₃
commutator, hypocenter	C₅²×C₄₁	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₄₁	C₃×C₄
prime radical	C₃×C₄₁×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₄₁×C₅⋊D₅	C₂×C₃²
LCS	G ▷ C₅²×C₄₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#16861520	C₃	semidirect
3. #16861520⋊C₃	C₃	direct (N × H)
4. C₃×C₄₁×C₅²⋊C₃	C₄	semidirect
7. #16861520	C₃²	semidirect
8. C₄₁×C₅²⋊C₃	C₃×C₄	semidirect
9. C₃×C₅²×C₄₁	C₃×C₄	semidirect
14. C₅²×C₄₁	C₃²×C₄	semidirect
28. C₃×C₅²⋊C₃	Dic₄₁	semidirect
34. C₃×C₄₁	#1043⋊C₃	semidirect
37. C₃×C₅²	C₃×Dic₄₁	semidirect
38. C₅²⋊C₃	C₃×Dic₄₁	semidirect
41. C₄₁	C₃×#1043⋊C₃	semidirect
44. C₅²	C₃²×Dic₄₁	semidirect
57. C₃	#16861520⋊C₃	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×C₄₁×(C₅⋊D₅)⋊C₃	2
C₃×#16861520	3
#16861520⋊C₃	3
C₃²×Dic₄₁	25
C₃×#1043⋊C₃	41

Subgroups — C3×#16861520⋊C3 #49147002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#16861520⋊C₃ #49147002