Subgroups — C₃×#13133554 #19103167

Order 5103.

1232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#4430	C₃	1	2	yes	maximal, complemented
2	C₃³×C₇⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#13133554	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₃²⋊(C₇⋊C₉)	C₃	1	9	yes	maximal, complemented
5	C₃²×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×#6893	—	7	1	no	maximal, Sylow
7	C₃⁴×C₇	C₃²	1	3	yes	—
8	C₃⁴×C₇	C₃²	1	1	yes	characteristic
9	C₃×C₇×H(3,𝔽₃)	—	3	9	no	—
10	C₃×C₇×H(3,𝔽₃)	C₃²	1	9	yes	—
11	C₃×#4430	—	3	18	no	—
12	C₃×#4430	C₃²	1	18	yes	complemented
13	C₃²×C₇⋊C₉	—	3	9	no	—
14	C₃²×C₇⋊C₉	C₃²	1	3	yes	—
15	C₃²×C₇⋊C₉	C₃²	1	6	yes	—
16	C₃²×C₇⋊C₉	C₃²	1	9	yes	complemented
17	C₃²⋊(C₇⋊C₉)	C₃²	1	81	yes	complemented
18	C₃²×3₋¹⁺²	—	7	2	no	—
19	C₃²×H(3,𝔽₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic
20	C₃³×C₉	—	7	1	no	—
21	#6893	—	7	27	no	—
22	C₃×C₃²⋊C₉	—	7	9	no	—
23	C₃³×C₇	—	3	9	no	—
24	C₃³×C₇	—	3	9	no	—
25	C₃³×C₇	—	3	27	no	—
26	C₃³×C₇	H(3,𝔽₃)	1	9	yes	—
27	C₃³×C₇	C₃³	1	9	yes	—
28	C₃³×C₇	C₃³	1	3	yes	—
29	C₃³×C₇	C₃³	1	1	yes	characteristic
30	C₇×H(3,𝔽₃)	—	3	27	no	—
31	#4430	—	3	54	no	—
32	C₃×C₇⋊C₉	—	3	9	no	—
33	C₃×C₇⋊C₉	—	3	27	no	—
34	C₃×C₇⋊C₉	—	3	18	no	—
35	C₃×C₇⋊C₉	C₃³	1	9	yes	—
36	C₃×C₇⋊C₉	C₃³	1	18	yes	—
37	C₃⁴	C₃×ΓL(1,𝔽₈)	1	3	yes	—
38	C₃⁴	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
39	C₃×3₋¹⁺²	—	7	18	no	—
40	C₃×3₋¹⁺²	—	21	18	no	—
41	C₃×H(3,𝔽₃)	—	3	9	no	—
42	C₃×H(3,𝔽₃)	C₃×ΓL(1,𝔽₈)	1	9	yes	—
43	C₃²×C₉	—	7	9	no	—
44	C₃²×C₉	—	7	3	no	—
45	C₃²×C₉	—	7	6	no	—
46	C₃²×C₉	—	21	9	no	—
47	C₃²⋊C₉	—	7	81	no	—
48	C₃²×C₇	—	3	9	no	—
49	C₃²×C₇	—	3	27	no	—
50	C₃²×C₇	—	3	9	no	—
51	C₃²×C₇	—	3	27	no	—
52	C₃²×C₇	—	9	27	no	—
53	C₃²×C₇	C₃×H(3,𝔽₃)	1	9	yes	—
54	C₃²×C₇	C₃×H(3,𝔽₃)	1	3	yes	—
55	C₃²×C₇	#737	1	9	yes	—
56	C₃²×C₇	C₃⁴	1	1	yes	characteristic
57	C₇⋊C₉	—	3	9	no	—
58	C₇⋊C₉	—	3	18	no	—
59	C₃³	—	3	9	no	—
60	C₃³	—	3	27	no	—
61	C₃³	—	3	9	no	—
62	C₃³	C₇⋊H(3,𝔽₃)	1	9	yes	—
63	C₃³	C₃²×ΓL(1,𝔽₈)	1	9	yes	—
64	C₃³	C₃²×ΓL(1,𝔽₈)	1	3	yes	—
65	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
66	3₋¹⁺²	—	21	54	no	—
67	H(3,𝔽₃)	—	3	27	no	—
68	C₃×C₉	—	7	9	no	—
69	C₃×C₉	—	7	18	no	—
70	C₃×C₉	—	21	27	no	—
71	C₃×C₉	—	21	9	no	—
72	C₃×C₉	—	21	18	no	—
73	C₃×C₇	—	3	9	no	—
74	C₃×C₇	—	9	9	no	—
75	C₃×C₇	#6893	1	9	yes	complemented
76	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
77	C₃×C₇	C₃×#737	1	3	yes	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	27	no	—
80	C₃²	—	3	9	no	—
81	C₃²	—	3	27	no	—
82	C₃²	—	9	27	no	—
83	C₃²	#10588062	1	9	yes	—
84	C₃²	C₃×C₇⋊H(3,𝔽₃)	1	9	yes	—
85	C₃²	C₃×C₇⋊H(3,𝔽₃)	1	3	yes	—
86	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
87	C₉	—	21	9	no	—
88	C₉	—	21	18	no	—
89	C₇	C₃×#6893	1	1	yes	characteristic, complemented, Sylow
90	C₃	—	3	9	no	—
91	C₃	—	9	9	no	—
92	C₃	#13133554	1	9	yes	direct product factor
93	C₃	C₃²×C₇⋊H(3,𝔽₃)	1	1	yes	characteristic
94	C₃	C₃×#10588062	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²×ΓL(1,𝔽₈)
commutator	C₃²×C₇	C₃⁴
Frattini	C₃²	C₃³×ΓL(1,𝔽₈)
Fitting	C₃²×C₇×H(3,𝔽₃)	C₃
socle	C₃³×C₇	C₃³
hypercenter	C₃²×H(3,𝔽₃)	ΓL(1,𝔽₈)
hypocenter	C₇	C₃×#6893
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃²×#4430	C₃	semidirect
2. C₃³×C₇⋊C₉	C₃	semidirect
3. #13133554	C₃	direct (N × H)
4. C₃×C₃²⋊(C₇⋊C₉)	C₃	semidirect
12. C₃×#4430	C₃²	semidirect
16. C₃²×C₇⋊C₉	C₃²	semidirect
17. C₃²⋊(C₇⋊C₉)	C₃²	semidirect
75. C₃×C₇	#6893	semidirect
89. C₇	C₃×#6893	semidirect
92. C₃	#13133554	direct (N × H)

Subgroups — C3×#13133554 #19103167

Conjugacy classes of subgroups

Complements

Subgroups — C₃×#13133554 #19103167