Subgroups — C₃×#13133570 #19103192

Order 5103.

836 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133570	C₃	1	27	yes	maximal, direct product factor
2	C₃×(C₇⋊C₉)⋊C₉	C₃	1	9	yes	maximal, complemented
3	C₃×C₃²⋊(C₇⋊C₉)	C₃	1	3	yes	maximal
4	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic
5	C₃×#6895	—	7	1	no	maximal, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃²×C₇×C₉	—	3	9	no	—
8	C₃²×C₇×C₉	C₃²	1	9	yes	—
9	C₃²×C₇×C₉	C₃²	1	3	yes	—
10	C₃²×C₇⋊C₉	C₃²	1	9	yes	—
11	C₃²⋊(C₇⋊C₉)	C₃²	1	27	yes	—
12	(C₇⋊C₉)⋊C₉	C₃²	1	81	yes	complemented
13	C₃³×C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
14	#6895	—	7	27	no	—
15	C₃×C₉⋊C₉	—	7	9	no	—
16	C₃×C₃²⋊C₉	—	7	3	no	—
17	C₃³×C₇	—	3	9	no	—
18	C₃³×C₇	3₋¹⁺²	1	9	yes	—
19	C₃³×C₇	C₃³	1	3	yes	—
20	C₃³×C₇	C₃³	1	1	yes	characteristic
21	C₃×C₇×C₉	—	3	27	no	—
22	C₃×C₇×C₉	—	3	9	no	—
23	C₃×C₇×C₉	C₃³	1	9	yes	—
24	C₃×C₇⋊C₉	—	3	27	no	—
25	C₃×C₇⋊C₉	C₃³	1	27	yes	—
26	C₃⁴	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
27	C₃²×C₉	—	3	9	no	—
28	C₃²×C₉	—	7	9	no	—
29	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	9	yes	—
30	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
31	C₉⋊C₉	—	7	81	no	—
32	C₃²⋊C₉	—	7	27	no	—
33	C₃²×C₇	—	3	9	no	—
34	C₃²×C₇	—	3	27	no	—
35	C₃²×C₇	C₃×3₋¹⁺²	1	9	yes	—
36	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
37	C₃²×C₇	#737	1	9	yes	—
38	C₃²×C₇	C₃⁴	1	1	yes	characteristic
39	C₇×C₉	—	3	9	no	—
40	C₇⋊C₉	—	3	27	no	—
41	C₃³	—	3	9	no	—
42	C₃³	#4430	1	9	yes	—
43	C₃³	C₃²×ΓL(1,𝔽₈)	1	3	yes	—
44	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
45	C₃×C₉	—	3	27	no	—
46	C₃×C₉	—	3	9	no	—
47	C₃×C₉	—	7	27	no	—
48	C₃×C₉	—	21	27	no	—
49	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	9	yes	—
50	C₃×C₇	—	3	9	no	—
51	C₃×C₇	#6895	1	9	yes	complemented
52	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
53	C₃×C₇	C₃×#737	1	3	yes	—
54	C₃²	—	3	27	no	—
55	C₃²	—	3	9	no	—
56	C₃²	#10588061	1	9	yes	—
57	C₃²	C₃×#4430	1	9	yes	—
58	C₃²	C₃×#4430	1	3	yes	—
59	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
60	C₉	—	3	9	no	—
61	C₉	—	21	27	no	—
62	C₇	C₃×#6895	1	1	yes	characteristic, complemented, Sylow
63	C₃	—	3	9	no	—
64	C₃	#13133570	1	9	yes	direct product factor
65	C₃	C₃²×#4430	1	1	yes	characteristic
66	C₃	C₃×#10588061	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²×ΓL(1,𝔽₈)
commutator	C₃²×C₇	C₃⁴
Frattini	C₃²	C₃³×ΓL(1,𝔽₈)
Fitting	C₃³×C₇×C₉	C₃
socle	C₃³×C₇	C₃³
hypercenter	C₃³×C₉	ΓL(1,𝔽₈)
hypocenter	C₇	C₃×#6895
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃³ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
1. #13133570	C₃	direct (N × H)
2. C₃×(C₇⋊C₉)⋊C₉	C₃	semidirect
12. (C₇⋊C₉)⋊C₉	C₃²	semidirect
51. C₃×C₇	#6895	semidirect
62. C₇	C₃×#6895	semidirect
64. C₃	#13133570	direct (N × H)

Subgroups — C3×#13133570 #19103192

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#13133570 #19103192