Subgroups — C₃×#13133587 #19103221

Order 5103.

788 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#4428	C₃	1	1	yes	maximal, characteristic
2	#13133587	C₃	1	27	yes	maximal, direct product factor
3	C₃×#10588036	C₃	1	2	yes	maximal, complemented
4	C₃×(C₇⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
5	C₃×(C₃×ΓL(1,𝔽₈))⋊C₉	C₃	1	3	yes	maximal
6	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×#6899	—	7	1	no	maximal, Sylow
8	C₃³×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
9	C₃²×C₇×C₉	C₃²	1	3	yes	—
10	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
11	C₃²×C₇⋊C₉	C₃²	1	2	yes	—
12	C₃²×C₇⋊C₉	C₃²	1	6	yes	—
13	C₃×#4428	—	3	9	no	—
14	C₃×#4428	C₃²	1	9	yes	—
15	C₇×C₉²	C₃²	1	9	yes	complemented
16	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	27	yes	—
17	#10588036	C₃²	1	18	yes	complemented
18	(C₇⋊C₉)⋊C₉	C₃²	1	54	yes	complemented
19	C₃²×3₋¹⁺²	—	7	1	no	—
20	#6899	—	7	27	no	—
21	C₃×C₉⋊C₉	—	7	6	no	—
22	C₃×C₉⋊C₉	—	7	2	no	—
23	C₃×C₃²⋊C₉	—	7	3	no	—
24	C₃×C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
25	C₃³×C₇	C₃³	1	1	yes	characteristic
26	C₃²×ΓL(1,𝔽₈)	—	3	3	no	—
27	C₃²×ΓL(1,𝔽₈)	—	3	9	no	—
28	C₃²×ΓL(1,𝔽₈)	C₃³	1	3	yes	—
29	C₃×C₇×C₉	—	3	9	no	—
30	C₃×C₇×C₉	3₋¹⁺²	1	9	yes	—
31	C₃×C₇×C₉	C₃³	1	9	yes	—
32	C₃×C₇×C₉	C₃³	1	3	yes	—
33	C₃×C₇⋊C₉	—	3	6	no	—
34	C₃×C₇⋊C₉	—	3	18	no	—
35	C₃×C₇⋊C₉	C₃³	1	6	yes	—
36	C₃×C₇⋊C₉	C₃³	1	18	yes	—
37	#4428	—	3	27	no	—
38	C₃⁴	—	7	1	no	—
39	C₃×3₋¹⁺²	—	7	9	no	—
40	C₃×3₋¹⁺²	—	21	9	no	—
41	C₃²×C₉	—	7	2	no	—
42	C₃²×C₉	—	7	6	no	—
43	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
44	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
45	C₉⋊C₉	—	7	54	no	—
46	C₉⋊C₉	—	7	18	no	—
47	C₃²⋊C₉	—	7	27	no	—
48	C₉²	C₃×ΓL(1,𝔽₈)	1	9	yes	complemented
49	C₃²×C₇	C₃×3₋¹⁺²	1	3	yes	—
50	C₃²×C₇	#737	1	9	yes	—
51	C₃²×C₇	C₃⁴	1	1	yes	characteristic
52	C₃×ΓL(1,𝔽₈)	—	3	3	no	—
53	C₃×ΓL(1,𝔽₈)	—	3	9	no	—
54	C₃×ΓL(1,𝔽₈)	—	9	9	no	—
55	C₇×C₉	—	3	9	no	—
56	C₇×C₉	C₃×3₋¹⁺²	1	9	yes	—
57	C₇⋊C₉	—	3	6	no	—
58	C₇⋊C₉	—	3	18	no	—
59	C₃³	—	7	3	no	—
60	C₃³	—	21	3	no	—
61	C₃³	—	21	9	no	—
62	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
63	3₋¹⁺²	—	21	27	no	—
64	C₃×C₉	—	3	9	no	—
65	C₃×C₉	—	7	18	no	—
66	C₃×C₉	—	7	6	no	—
67	C₃×C₉	—	21	6	no	—
68	C₃×C₉	—	21	18	no	—
69	C₃×C₉	#4428	1	9	yes	—
70	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	9	yes	—
71	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	3	yes	—
72	C₃×C₇	#6899	1	9	yes	complemented
73	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
74	C₃×C₇	C₃×#737	1	3	yes	—
75	ΓL(1,𝔽₈)	—	9	3	no	—
76	C₃²	—	21	3	no	—
77	C₃²	—	21	9	no	—
78	C₃²	—	63	9	no	—
79	C₃²	C₃×#4428	1	3	yes	—
80	C₃²	#10588061	1	9	yes	—
81	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
82	C₉	—	3	9	no	—
83	C₉	—	21	6	no	—
84	C₉	—	21	18	no	—
85	C₉	C₃×#4428	1	9	yes	—
86	C₇	C₃×#6899	1	1	yes	characteristic, complemented, Sylow
87	C₃	—	63	3	no	—
88	C₃	#13133587	1	9	yes	direct product factor
89	C₃	C₃²×#4428	1	1	yes	characteristic
90	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	C₃×C₇×C₉²	C₃
socle	C₃³×C₇	C₃³
hypercenter	C₃×C₉²	ΓL(1,𝔽₈)
hypocenter	C₇	C₃×#6899
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. #13133587	C₃	direct (N × H)
3. C₃×#10588036	C₃	semidirect
4. C₃×(C₇⋊C₉)⋊C₉	C₃	semidirect
6. C₃×C₇×C₉²	C₃	semidirect
15. C₇×C₉²	C₃²	semidirect
17. #10588036	C₃²	semidirect
18. (C₇⋊C₉)⋊C₉	C₃²	semidirect
24. C₃×C₉²	ΓL(1,𝔽₈)	semidirect
48. C₉²	C₃×ΓL(1,𝔽₈)	semidirect
72. C₃×C₇	#6899	semidirect
86. C₇	C₃×#6899	semidirect
88. C₃	#13133587	direct (N × H)

Subgroups — C3×#13133587 #19103221

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#13133587 #19103221