Subgroups — C₃×#13133594 #19103243

Order 5103.

1076 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#4427	C₃	1	4	yes	maximal
2	#13133594	C₃	1	27	yes	maximal, direct product factor
3	C₃×#10588035	C₃	1	8	yes	maximal, complemented
4	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#6900	—	7	1	no	maximal, Sylow
6	C₃³×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
7	C₃²×C₇×C₉	C₃²	1	4	yes	—
8	C₃²×C₇⋊C₉	C₃²	1	8	yes	—
9	C₃×#4427	—	3	36	no	—
10	C₃×#4427	C₃²	1	36	yes	—
11	C₇×C₉²	C₃²	1	9	yes	complemented
12	#10588035	C₃²	1	72	yes	complemented
13	C₃²×3₋¹⁺²	—	7	4	no	—
14	#6900	—	7	27	no	—
15	C₃×C₉⋊C₉	—	7	8	no	—
16	C₃×C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
17	C₃³×C₇	C₃³	1	1	yes	characteristic
18	C₃²×ΓL(1,𝔽₈)	—	3	12	no	—
19	C₃²×ΓL(1,𝔽₈)	C₃³	1	3	yes	—
20	C₃×C₇×C₉	3₋¹⁺²	1	36	yes	complemented
21	C₃×C₇×C₉	C₃³	1	12	yes	—
22	C₃×C₇⋊C₉	—	3	24	no	—
23	C₃×C₇⋊C₉	C₃³	1	24	yes	—
24	#4427	—	3	108	no	—
25	C₃⁴	—	7	1	no	—
26	C₃×3₋¹⁺²	—	7	36	no	—
27	C₃×3₋¹⁺²	—	21	36	no	—
28	C₃²×C₉	—	7	8	no	—
29	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	4	yes	—
30	C₉⋊C₉	—	7	72	no	—
31	C₉²	C₃×ΓL(1,𝔽₈)	1	9	yes	complemented
32	C₃²×C₇	C₃×3₋¹⁺²	1	12	yes	—
33	C₃²×C₇	C₃⁴	1	1	yes	characteristic
34	C₃×ΓL(1,𝔽₈)	—	3	12	no	—
35	C₃×ΓL(1,𝔽₈)	—	9	9	no	—
36	C₇×C₉	C₃×3₋¹⁺²	1	36	yes	complemented
37	C₇⋊C₉	—	3	24	no	—
38	C₃³	—	7	3	no	—
39	C₃³	—	21	12	no	—
40	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
41	3₋¹⁺²	—	21	108	no	—
42	C₃×C₉	—	7	24	no	—
43	C₃×C₉	—	21	24	no	—
44	C₃×C₉	#4427	1	36	yes	complemented
45	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	12	yes	—
46	C₃×C₇	#6900	1	9	yes	complemented
47	C₃×C₇	C₃²×3₋¹⁺²	1	4	yes	—
48	ΓL(1,𝔽₈)	—	9	3	no	—
49	C₃²	—	21	12	no	—
50	C₃²	—	63	9	no	—
51	C₃²	C₃×#4427	1	12	yes	—
52	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
53	C₉	—	21	24	no	—
54	C₉	C₃×#4427	1	36	yes	complemented
55	C₇	C₃×#6900	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	63	3	no	—
57	C₃	#13133594	1	9	yes	direct product factor
58	C₃	C₃²×#4427	1	4	yes	—

	subgroup	G/H
center	C₃³	C₃²×ΓL(1,𝔽₈)
commutator	C₃²×C₇	C₃⁴
Frattini	C₃²	C₃³×ΓL(1,𝔽₈)
Fitting	C₃×C₇×C₉²	C₃
socle	C₃³×C₇	C₃³
hypercenter	C₃×C₉²	ΓL(1,𝔽₈)
hypocenter	C₇	C₃×#6900
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. #13133594	C₃	direct (N × H)
3. C₃×#10588035	C₃	semidirect
4. C₃×C₇×C₉²	C₃	semidirect
11. C₇×C₉²	C₃²	semidirect
12. #10588035	C₃²	semidirect
16. C₃×C₉²	ΓL(1,𝔽₈)	semidirect
20. C₃×C₇×C₉	3₋¹⁺²	semidirect
31. C₉²	C₃×ΓL(1,𝔽₈)	semidirect
36. C₇×C₉	C₃×3₋¹⁺²	semidirect
44. C₃×C₉	#4427	semidirect
46. C₃×C₇	#6900	semidirect
54. C₉	C₃×#4427	semidirect
55. C₇	C₃×#6900	semidirect
57. C₃	#13133594	direct (N × H)

Subgroups — C3×#13133594 #19103243

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#13133594 #19103243