Subgroups — C₁₃×#10624732 #23744883

Order 9477.

644 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×#732	C₃	1	9	yes	maximal, complemented
3	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
6	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
7	C₃²×C₉×C₁₃	—	3	3	no	—
8	C₃²×C₉×C₁₃	—	3	9	no	—
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₁₃×#732	—	3	27	no	—
11	#10624732	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	9	no	—
13	C₃³×C₁₃	—	3	3	no	—
14	C₃³×C₁₃	—	3	9	no	—
15	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₁₃×H(3,𝔽₃)	—	3	27	no	—
18	C₁₃×H(3,𝔽₃)	—	9	27	no	—
19	C₃×C₉×C₁₃	—	3	27	no	—
20	C₃×C₉×C₁₃	—	3	6	no	—
21	C₃×C₉×C₁₃	—	3	3	no	—
22	C₃×C₉×C₁₃	H(3,𝔽₃)	1	9	yes	complemented
23	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic, complemented
24	C₃×#732	C₃×C₁₃	1	9	yes	complemented
25	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	3	yes	complemented
26	C₃²×C₁₃	—	3	27	no	—
27	C₃²×C₁₃	—	3	3	no	—
28	C₃²×C₁₃	—	3	6	no	—
29	C₃²×C₁₃	—	3	3	no	—
30	C₃²×C₁₃	—	9	9	no	—
31	C₃²×C₁₃	—	9	27	no	—
32	C₃²×C₁₃	#732	1	9	yes	complemented
33	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
34	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₉×C₁₃	—	3	9	no	—
36	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
37	C₃×H(3,𝔽₃)	—	3	9	no	—
38	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	9	yes	—
39	C₃²×C₉	—	3	3	no	—
40	C₃²×C₉	—	3	9	no	—
41	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
42	#732	—	3	27	no	—
43	C₃×C₁₃	—	3	9	no	—
44	C₃×C₁₃	—	3	3	no	—
45	C₃×C₁₃	—	27	9	no	—
46	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
47	C₃×C₁₃	C₃×#732	1	3	yes	—
48	C₃³	—	3	9	no	—
49	C₃³	—	3	3	no	—
50	C₃³	—	3	9	no	—
51	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
52	C₃³	C₃³×C₁₃	1	1	yes	characteristic
53	H(3,𝔽₃)	—	3	27	no	—
54	H(3,𝔽₃)	—	9	27	no	—
55	C₃×C₉	—	3	27	no	—
56	C₃×C₉	—	3	6	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	C₁₃×H(3,𝔽₃)	1	9	yes	complemented
59	C₁₃	#10624732	1	1	yes	characteristic, direct product factor, Sylow
60	C₃²	—	3	27	no	—
61	C₃²	—	3	3	no	—
62	C₃²	—	3	6	no	—
63	C₃²	—	3	3	no	—
64	C₃²	—	9	9	no	—
65	C₃²	—	9	27	no	—
66	C₃²	C₁₃×#732	1	9	yes	complemented
67	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
68	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
69	C₉	—	3	9	no	—
70	C₃	—	3	9	no	—
71	C₃	—	3	3	no	—
72	C₃	—	27	9	no	—
73	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
74	C₃	C₃×C₁₃×#732	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
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
1. C₃³×C₉×C₁₃	C₃	semidirect
2. C₃×C₁₃×#732	C₃	semidirect
3. C₁₃×C₃²⋊H(3,𝔽₃)	C₃	semidirect
11. #10624732	C₁₃	direct (N × H)
22. C₃×C₉×C₁₃	H(3,𝔽₃)	semidirect
23. C₃³×C₉	C₃×C₁₃	semidirect
24. C₃×#732	C₃×C₁₃	semidirect
25. C₃²⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
32. C₃²×C₁₃	#732	semidirect
58. C₃×C₉	C₁₃×H(3,𝔽₃)	semidirect
59. C₁₃	#10624732	direct (N × H)
66. C₃²	C₁₃×#732	semidirect

Subgroups — C13×#10624732 #23744883

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624732 #23744883