Subgroups — C₃×C₁₃×#6912 #23745078

Order 9477.

980 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	3	yes	maximal
2	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6912	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₁₃×#733	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	18	no	—
7	C₃×C₁₃×3₋¹⁺²	—	3	6	no	—
8	C₃×C₁₃×3₋¹⁺²	—	3	6	no	—
9	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
10	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
11	C₃×C₁₃×3₋¹⁺²	C₃²	1	27	yes	—
12	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
13	C₃²×C₉×C₁₃	—	3	3	no	—
14	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
15	C₁₃×#733	C₃²	1	81	yes	complemented
16	C₃×#6912	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	9	3	no	—
18	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
19	C₃³×C₁₃	H(3,𝔽₃)	1	6	yes	—
20	C₃³×C₁₃	C₃³	1	1	yes	characteristic
21	C₃³×C₁₃	C₃³	1	3	yes	—
22	C₁₃×3₋¹⁺²	—	3	18	no	—
23	C₁₃×3₋¹⁺²	—	3	54	no	—
24	C₁₃×3₋¹⁺²	—	3	27	no	—
25	C₁₃×3₋¹⁺²	C₃³	1	27	yes	—
26	C₃×C₉×C₁₃	—	3	27	no	—
27	C₃×C₉×C₁₃	—	3	6	no	—
28	C₃×C₉×C₁₃	—	3	9	no	—
29	C₃×C₉×C₁₃	—	3	3	no	—
30	C₃×C₉×C₁₃	C₃³	1	9	yes	—
31	C₃²×3₋¹⁺²	C₃×C₁₃	1	3	yes	—
32	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
33	#6912	C₃×C₁₃	1	27	yes	direct product factor
34	C₃×#733	C₃×C₁₃	1	9	yes	complemented
35	C₃²×C₁₃	—	3	9	no	—
36	C₃²×C₁₃	—	3	3	no	—
37	C₃²×C₁₃	—	9	6	no	—
38	C₃²×C₁₃	—	9	3	no	—
39	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	9	yes	—
40	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	2	yes	—
41	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
43	C₉×C₁₃	—	3	27	no	—
44	C₉×C₁₃	—	3	9	no	—
45	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
46	C₃×3₋¹⁺²	—	3	6	no	—
47	C₃×3₋¹⁺²	—	3	18	no	—
48	C₃×3₋¹⁺²	—	3	3	no	—
49	C₃×3₋¹⁺²	—	3	6	no	—
50	C₃×3₋¹⁺²	C₃²×C₁₃	1	27	yes	—
51	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
52	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
53	C₃²×C₉	—	3	3	no	—
54	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
55	#733	C₃²×C₁₃	1	81	yes	complemented
56	C₃×C₁₃	—	3	9	no	—
57	C₃×C₁₃	—	3	2	no	—
58	C₃×C₁₃	—	3	1	no	—
59	C₃×C₁₃	#6912	1	3	yes	direct product factor
60	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
61	C₃³	—	9	3	no	—
62	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
63	C₃³	C₁₃×H(3,𝔽₃)	1	6	yes	—
64	C₃³	C₃³×C₁₃	1	1	yes	characteristic
65	C₃³	C₃³×C₁₃	1	3	yes	—
66	3₋¹⁺²	—	3	54	no	—
67	3₋¹⁺²	—	3	18	no	—
68	3₋¹⁺²	—	3	27	no	—
69	3₋¹⁺²	C₃³×C₁₃	1	27	yes	—
70	C₃×C₉	—	3	27	no	—
71	C₃×C₉	—	3	9	no	—
72	C₃×C₉	—	3	6	no	—
73	C₃×C₉	—	3	3	no	—
74	C₃×C₉	C₃³×C₁₃	1	9	yes	—
75	C₁₃	C₃×#6912	1	1	yes	characteristic, direct product factor, Sylow
76	C₃²	—	3	9	no	—
77	C₃²	—	3	3	no	—
78	C₃²	—	9	6	no	—
79	C₃²	—	9	3	no	—
80	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	9	yes	—
81	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	2	yes	—
82	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
83	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
84	C₉	—	3	27	no	—
85	C₉	—	3	9	no	—
86	C₃	—	3	9	no	—
87	C₃	—	3	2	no	—
88	C₃	—	3	1	no	—
89	C₃	C₁₃×#6912	1	3	yes	direct product factor
90	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6912	C₃	direct (N × H)
4. C₃×C₁₃×#733	C₃	semidirect
15. C₁₃×#733	C₃²	semidirect
16. C₃×#6912	C₁₃	direct (N × H)
33. #6912	C₃×C₁₃	direct (N × H)
34. C₃×#733	C₃×C₁₃	semidirect
55. #733	C₃²×C₁₃	semidirect
59. C₃×C₁₃	#6912	direct (N × H)
75. C₁₃	C₃×#6912	direct (N × H)
89. C₃	C₁₃×#6912	direct (N × H)

Subgroups — C3×C13×#6912 #23745078

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6912 #23745078