Subgroups — C₃×C₁₃×#6893 #23745019

Order 9477.

1232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
2	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#6893	C₃	1	27	yes	maximal, direct product factor
5	C₃×C₁₃×C₃²⋊C₉	C₃	1	9	yes	maximal, complemented
6	C₃⁴×C₁₃	C₃²	1	3	yes	—
7	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
8	C₃×C₁₃×3₋¹⁺²	—	3	18	no	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	18	yes	complemented
10	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
12	C₃²×C₉×C₁₃	—	3	9	no	—
13	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
14	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
15	C₃²×C₉×C₁₃	C₃²	1	9	yes	complemented
16	C₁₃×C₃²⋊C₉	C₃²	1	81	yes	complemented
17	C₃×#6893	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	—	3	9	no	—
19	C₃³×C₁₃	—	3	9	no	—
20	C₃³×C₁₃	—	3	27	no	—
21	C₃³×C₁₃	H(3,𝔽₃)	1	9	yes	—
22	C₃³×C₁₃	C₃³	1	9	yes	—
23	C₃³×C₁₃	C₃³	1	3	yes	—
24	C₃³×C₁₃	C₃³	1	1	yes	characteristic
25	C₁₃×3₋¹⁺²	—	3	54	no	—
26	C₁₃×H(3,𝔽₃)	—	3	27	no	—
27	C₃×C₉×C₁₃	—	3	9	no	—
28	C₃×C₉×C₁₃	—	3	27	no	—
29	C₃×C₉×C₁₃	—	3	18	no	—
30	C₃×C₉×C₁₃	C₃³	1	9	yes	—
31	C₃×C₉×C₁₃	C₃³	1	18	yes	—
32	C₃²×3₋¹⁺²	C₃×C₁₃	1	2	yes	complemented
33	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
34	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
35	#6893	C₃×C₁₃	1	27	yes	direct product factor
36	C₃×C₃²⋊C₉	C₃×C₁₃	1	9	yes	complemented
37	C₃²×C₁₃	—	3	9	no	—
38	C₃²×C₁₃	—	3	27	no	—
39	C₃²×C₁₃	—	3	9	no	—
40	C₃²×C₁₃	—	3	27	no	—
41	C₃²×C₁₃	—	9	27	no	—
42	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	9	yes	—
43	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
44	C₃²×C₁₃	#737	1	9	yes	—
45	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
46	C₉×C₁₃	—	3	9	no	—
47	C₉×C₁₃	—	3	18	no	—
48	C₃⁴	C₃²×C₁₃	1	3	yes	—
49	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
50	C₃×3₋¹⁺²	—	3	18	no	—
51	C₃×3₋¹⁺²	C₃²×C₁₃	1	18	yes	complemented
52	C₃×H(3,𝔽₃)	—	3	9	no	—
53	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	9	yes	—
54	C₃²×C₉	—	3	9	no	—
55	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
56	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
57	C₃²×C₉	C₃²×C₁₃	1	9	yes	complemented
58	C₃²⋊C₉	C₃²×C₁₃	1	81	yes	complemented
59	C₃×C₁₃	—	3	9	no	—
60	C₃×C₁₃	—	9	9	no	—
61	C₃×C₁₃	#6893	1	9	yes	direct product factor
62	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
63	C₃×C₁₃	C₃×#737	1	3	yes	—
64	C₃³	—	3	9	no	—
65	C₃³	—	3	9	no	—
66	C₃³	—	3	27	no	—
67	C₃³	C₁₃×H(3,𝔽₃)	1	9	yes	—
68	C₃³	C₃³×C₁₃	1	9	yes	—
69	C₃³	C₃³×C₁₃	1	3	yes	—
70	C₃³	C₃³×C₁₃	1	1	yes	characteristic
71	3₋¹⁺²	—	3	54	no	—
72	H(3,𝔽₃)	—	3	27	no	—
73	C₃×C₉	—	3	9	no	—
74	C₃×C₉	—	3	27	no	—
75	C₃×C₉	—	3	18	no	—
76	C₃×C₉	C₃³×C₁₃	1	9	yes	—
77	C₃×C₉	C₃³×C₁₃	1	18	yes	—
78	C₁₃	C₃×#6893	1	1	yes	characteristic, direct product factor, Sylow
79	C₃²	—	3	27	no	—
80	C₃²	—	3	9	no	—
81	C₃²	—	3	9	no	—
82	C₃²	—	3	27	no	—
83	C₃²	—	9	27	no	—
84	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	9	yes	—
85	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
86	C₃²	C₁₃×#737	1	9	yes	—
87	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
88	C₉	—	3	9	no	—
89	C₉	—	3	18	no	—
90	C₃	—	3	9	no	—
91	C₃	—	9	9	no	—
92	C₃	C₁₃×#6893	1	9	yes	direct product factor
93	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
94	C₃	C₃×C₁₃×#737	1	3	yes	—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×3₋¹⁺²	C₃	semidirect
3. C₃³×C₉×C₁₃	C₃	semidirect
4. C₁₃×#6893	C₃	direct (N × H)
5. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
9. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
15. C₃²×C₉×C₁₃	C₃²	semidirect
16. C₁₃×C₃²⋊C₉	C₃²	semidirect
17. C₃×#6893	C₁₃	direct (N × H)
32. C₃²×3₋¹⁺²	C₃×C₁₃	semidirect
34. C₃³×C₉	C₃×C₁₃	semidirect
35. #6893	C₃×C₁₃	direct (N × H)
36. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
51. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
57. C₃²×C₉	C₃²×C₁₃	semidirect
58. C₃²⋊C₉	C₃²×C₁₃	semidirect
61. C₃×C₁₃	#6893	direct (N × H)
78. C₁₃	C₃×#6893	direct (N × H)
92. C₃	C₁₃×#6893	direct (N × H)

Subgroups — C3×C13×#6893 #23745019

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6893 #23745019