Subgroups — C₁₃×#10624773 #23744924

Order 9477.

464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6891	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6866	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	3	yes	—
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
7	C₃×C₁₃×H(3,𝔽₃)	—	3	2	no	—
8	C₃×C₁₃×H(3,𝔽₃)	—	3	1	no	—
9	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
10	C₁₃×C₃²⋊C₉	—	3	6	no	—
11	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
12	#10624773	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	—	3	3	no	—
14	C₃³×C₁₃	—	3	6	no	—
15	C₃³×C₁₃	—	3	3	no	—
16	C₃³×C₁₃	—	9	3	no	—
17	C₃³×C₁₃	—	9	9	no	—
18	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
19	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃³×C₁₃	3₋¹⁺²	1	9	yes	complemented
21	C₃³×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	9	9	no	—
23	C₁₃×H(3,𝔽₃)	—	3	18	no	—
24	C₁₃×H(3,𝔽₃)	—	3	9	no	—
25	C₃×C₉×C₁₃	—	3	9	no	—
26	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
27	#6891	C₃×C₁₃	1	3	yes	complemented
28	#6866	C₃×C₁₃	1	9	yes	complemented
29	C₃²×C₁₃	—	3	3	no	—
30	C₃²×C₁₃	—	3	2	no	—
31	C₃²×C₁₃	—	3	1	no	—
32	C₃²×C₁₃	—	3	9	no	—
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	—	3	6	no	—
35	C₃²×C₁₃	—	9	9	no	—
36	C₃²×C₁₃	—	9	9	no	—
37	C₃²×C₁₃	—	9	18	no	—
38	C₃²×C₁₃	—	9	9	no	—
39	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
41	C₉×C₁₃	—	9	9	no	—
42	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
43	C₃⁴	C₃²×C₁₃	1	3	yes	—
44	C₃×3₋¹⁺²	—	3	3	no	—
45	C₃×H(3,𝔽₃)	—	3	2	no	—
46	C₃×H(3,𝔽₃)	—	3	1	no	—
47	C₃×H(3,𝔽₃)	—	3	9	no	—
48	C₃²⋊C₉	—	3	6	no	—
49	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
50	C₃×C₁₃	—	3	3	no	—
51	C₃×C₁₃	—	9	1	no	—
52	C₃×C₁₃	—	9	2	no	—
53	C₃×C₁₃	—	9	9	no	—
54	C₃×C₁₃	#6891	1	1	yes	characteristic
55	C₃×C₁₃	#6909	1	3	yes	—
56	C₃³	—	3	3	no	—
57	C₃³	—	3	3	no	—
58	C₃³	—	3	6	no	—
59	C₃³	—	9	3	no	—
60	C₃³	—	9	9	no	—
61	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
62	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
63	C₃³	C₁₃×3₋¹⁺²	1	9	yes	complemented
64	C₃³	C₃³×C₁₃	1	1	yes	characteristic
65	3₋¹⁺²	—	9	9	no	—
66	H(3,𝔽₃)	—	3	18	no	—
67	H(3,𝔽₃)	—	3	9	no	—
68	C₃×C₉	—	3	9	no	—
69	C₁₃	#10624773	1	1	yes	characteristic, direct product factor, Sylow
70	C₃²	—	3	3	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	3	9	no	—
74	C₃²	—	3	3	no	—
75	C₃²	—	3	6	no	—
76	C₃²	—	9	9	no	—
77	C₃²	—	9	9	no	—
78	C₃²	—	9	18	no	—
79	C₃²	—	9	9	no	—
80	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
81	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
82	C₉	—	9	9	no	—
83	C₃	—	3	3	no	—
84	C₃	—	9	1	no	—
85	C₃	—	9	2	no	—
86	C₃	—	9	9	no	—
87	C₃	C₁₃×#6891	1	1	yes	characteristic
88	C₃	C₁₃×#6909	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
LCS	G ▷ C₃³ ▷ 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
2. C₁₃×#6891	C₃	semidirect
3. C₁₃×#6866	C₃	semidirect
12. #10624773	C₁₃	direct (N × H)
20. C₃³×C₁₃	3₋¹⁺²	semidirect
27. #6891	C₃×C₁₃	semidirect
28. #6866	C₃×C₁₃	semidirect
63. C₃³	C₁₃×3₋¹⁺²	semidirect
69. C₁₃	#10624773	direct (N × H)

Subgroups — C13×#10624773 #23744924

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624773 #23744924