Subgroups — C₃×#13133579 #19103211

Order 5103.

692 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133579	C₃	1	27	yes	maximal, direct product factor
2	C₃×(C₇⋊C₉)⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₃×(C₃×ΓL(1,𝔽₈))⋊C₉	C₃	1	4	yes	maximal
4	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#6897	—	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	C₇×C₉²	C₃²	1	9	yes	complemented
10	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	36	yes	—
11	(C₇⋊C₉)⋊C₉	C₃²	1	72	yes	complemented
12	#6897	—	7	27	no	—
13	C₃×C₉⋊C₉	—	7	8	no	—
14	C₃×C₃²⋊C₉	—	7	4	no	—
15	C₃×C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	C₃³×C₇	C₃³	1	1	yes	characteristic
17	C₃²×ΓL(1,𝔽₈)	—	3	12	no	—
18	C₃²×ΓL(1,𝔽₈)	C₃³	1	3	yes	—
19	C₃×C₇×C₉	—	3	12	no	—
20	C₃×C₇×C₉	C₃³	1	12	yes	—
21	C₃×C₇⋊C₉	—	3	24	no	—
22	C₃×C₇⋊C₉	C₃³	1	24	yes	—
23	C₃⁴	—	7	1	no	—
24	C₃²×C₉	—	7	8	no	—
25	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	4	yes	—
26	C₉⋊C₉	—	7	72	no	—
27	C₃²⋊C₉	—	7	36	no	—
28	C₉²	C₃×ΓL(1,𝔽₈)	1	9	yes	complemented
29	C₃²×C₇	#737	1	12	yes	—
30	C₃²×C₇	C₃⁴	1	1	yes	characteristic
31	C₃×ΓL(1,𝔽₈)	—	3	12	no	—
32	C₃×ΓL(1,𝔽₈)	—	9	9	no	—
33	C₇×C₉	—	3	12	no	—
34	C₇⋊C₉	—	3	24	no	—
35	C₃³	—	7	3	no	—
36	C₃³	—	21	12	no	—
37	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
38	C₃×C₉	—	3	12	no	—
39	C₃×C₉	—	7	24	no	—
40	C₃×C₉	—	21	24	no	—
41	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	12	yes	—
42	C₃×C₇	#6897	1	9	yes	complemented
43	C₃×C₇	C₃×#737	1	4	yes	—
44	ΓL(1,𝔽₈)	—	9	3	no	—
45	C₃²	—	21	12	no	—
46	C₃²	—	63	9	no	—
47	C₃²	#10588061	1	12	yes	—
48	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
49	C₉	—	3	12	no	—
50	C₉	—	21	24	no	—
51	C₇	C₃×#6897	1	1	yes	characteristic, complemented, Sylow
52	C₃	—	63	3	no	—
53	C₃	#13133579	1	9	yes	direct product factor
54	C₃	C₃×#10588061	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×#6897
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
1. #13133579	C₃	direct (N × H)
2. C₃×(C₇⋊C₉)⋊C₉	C₃	semidirect
4. C₃×C₇×C₉²	C₃	semidirect
9. C₇×C₉²	C₃²	semidirect
11. (C₇⋊C₉)⋊C₉	C₃²	semidirect
15. C₃×C₉²	ΓL(1,𝔽₈)	semidirect
28. C₉²	C₃×ΓL(1,𝔽₈)	semidirect
42. C₃×C₇	#6897	semidirect
51. C₇	C₃×#6897	semidirect
53. C₃	#13133579	direct (N × H)

Subgroups — C3×#13133579 #19103211

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#13133579 #19103211