Subgroups — C₁₃×#10624839 #23744990

Order 9477.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#732	C₃	1	3	yes	maximal, complemented
2	C₁₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#6879	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₃×H(3,𝔽₃)	—	3	3	no	—
5	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
6	C₁₃×#732	—	3	6	no	—
7	C₁₃×#732	C₃²	1	9	yes	complemented
8	C₁₃×C₉⋊C₉	—	3	2	no	—
9	C₁₃×C₃²⋊C₉	—	3	1	no	—
10	C₉²×C₁₃	C₃²	1	3	yes	complemented
11	#10624839	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	9	3	no	—
13	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₁₃×H(3,𝔽₃)	—	3	9	no	—
15	C₁₃×H(3,𝔽₃)	—	9	6	no	—
16	C₃×C₉×C₁₃	—	3	3	no	—
17	C₃×C₉×C₁₃	—	3	3	no	—
18	C₃×C₉×C₁₃	H(3,𝔽₃)	1	2	yes	—
19	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
20	C₃×#732	C₃×C₁₃	1	3	yes	complemented
21	#6887	C₃×C₁₃	1	1	yes	characteristic, complemented
22	#6879	C₃×C₁₃	1	9	yes	complemented
23	C₃²×C₁₃	—	9	1	no	—
24	C₃²×C₁₃	—	9	9	no	—
25	C₃²×C₁₃	—	27	9	no	—
26	C₃²×C₁₃	#732	1	3	yes	—
27	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₉×C₁₃	—	3	2	no	—
29	C₉×C₁₃	—	3	1	no	—
30	C₉×C₁₃	—	9	3	no	—
31	C₃×H(3,𝔽₃)	—	3	3	no	—
32	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
33	#732	—	3	6	no	—
34	#732	C₃²×C₁₃	1	9	yes	complemented
35	C₉⋊C₉	—	3	2	no	—
36	C₃²⋊C₉	—	3	1	no	—
37	C₉²	C₃²×C₁₃	1	3	yes	complemented
38	C₃×C₁₃	—	3	1	no	—
39	C₃×C₁₃	—	3	3	no	—
40	C₃×C₁₃	—	27	9	no	—
41	C₃×C₁₃	C₃×#732	1	1	yes	characteristic
42	C₃³	—	9	3	no	—
43	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
44	H(3,𝔽₃)	—	3	9	no	—
45	H(3,𝔽₃)	—	9	6	no	—
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	C₁₃×H(3,𝔽₃)	1	2	yes	—
49	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
50	C₁₃	#10624839	1	1	yes	characteristic, direct product factor, Sylow
51	C₃²	—	9	1	no	—
52	C₃²	—	9	9	no	—
53	C₃²	—	27	9	no	—
54	C₃²	C₁₃×#732	1	3	yes	—
55	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
56	C₉	—	3	2	no	—
57	C₉	—	3	1	no	—
58	C₉	—	9	3	no	—
59	C₃	—	3	1	no	—
60	C₃	—	3	3	no	—
61	C₃	—	27	9	no	—
62	C₃	C₃×C₁₃×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₃	C₃×#732
commutator, Frattini, cosocle	C₃×C₉	C₃³×C₁₃
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₃ ◁ C₃³×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×#732	C₃	semidirect
2. C₁₃×#6887	C₃	semidirect
3. C₁₃×#6879	C₃	semidirect
7. C₁₃×#732	C₃²	semidirect
10. C₉²×C₁₃	C₃²	semidirect
11. #10624839	C₁₃	direct (N × H)
20. C₃×#732	C₃×C₁₃	semidirect
21. #6887	C₃×C₁₃	semidirect
22. #6879	C₃×C₁₃	semidirect
34. #732	C₃²×C₁₃	semidirect
37. C₉²	C₃²×C₁₃	semidirect
50. C₁₃	#10624839	direct (N × H)

Subgroups — C13×#10624839 #23744990

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624839 #23744990