Subgroups — C₁₃×#10624932 #23745083

Order 9477.

1062 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×H(5,𝔽₃)	C₃	1	3	yes	maximal, complemented
2	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#6911	C₃	1	24	yes	maximal, complemented
4	C₃×C₁₃×#732	C₃	1	12	yes	maximal, complemented
5	C₁₃×#737	—	3	9	no	—
6	C₃×C₁₃×3₋¹⁺²	C₃²	1	8	yes	complemented
7	C₃×C₁₃×H(3,𝔽₃)	—	3	27	no	—
8	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
9	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	36	yes	complemented
10	C₃²×C₉×C₁₃	C₃²	1	4	yes	complemented
11	C₁₃×#732	C₃²	1	9	yes	complemented
12	C₁₃×#732	C₃²	1	72	yes	complemented
13	#10624932	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	—	3	36	no	—
15	C₃³×C₁₃	C₃³	1	4	yes	—
16	C₁₃×3₋¹⁺²	—	3	24	no	—
17	C₁₃×H(3,𝔽₃)	—	3	72	no	—
18	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
19	C₁₃×H(3,𝔽₃)	C₃³	1	27	yes	—
20	C₃×C₉×C₁₃	—	3	12	no	—
21	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
22	C₃×C₉×C₁₃	C₃³	1	8	yes	—
23	H(5,𝔽₃)	C₃×C₁₃	1	3	yes	complemented
24	C₃×#737	C₃×C₁₃	1	1	yes	characteristic, complemented
25	#6911	C₃×C₁₃	1	24	yes	complemented
26	C₃×#732	C₃×C₁₃	1	12	yes	complemented
27	C₃²×C₁₃	—	3	27	no	—
28	C₃²×C₁₃	—	9	4	no	—
29	C₃²×C₁₃	—	27	36	no	—
30	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
31	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
32	C₉×C₁₃	—	3	1	no	—
33	C₉×C₁₃	—	3	8	no	—
34	#737	—	3	9	no	—
35	C₃×3₋¹⁺²	C₃²×C₁₃	1	8	yes	complemented
36	C₃×H(3,𝔽₃)	—	3	27	no	—
37	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
38	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	36	yes	complemented
39	C₃²×C₉	C₃²×C₁₃	1	4	yes	complemented
40	#732	C₃²×C₁₃	1	9	yes	complemented
41	#732	C₃²×C₁₃	1	72	yes	complemented
42	C₃×C₁₃	—	3	1	no	—
43	C₃×C₁₃	—	3	12	no	—
44	C₃×C₁₃	—	9	27	no	—
45	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
46	C₃³	—	3	36	no	—
47	C₃³	C₃³×C₁₃	1	4	yes	—
48	3₋¹⁺²	—	3	24	no	—
49	H(3,𝔽₃)	—	3	72	no	—
50	H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	1	9	yes	—
51	H(3,𝔽₃)	C₃³×C₁₃	1	27	yes	—
52	C₃×C₉	—	3	12	no	—
53	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
54	C₃×C₉	C₃³×C₁₃	1	8	yes	—
55	C₁₃	#10624932	1	1	yes	characteristic, direct product factor, Sylow
56	C₃²	—	3	27	no	—
57	C₃²	—	9	4	no	—
58	C₃²	—	27	36	no	—
59	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
60	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
61	C₉	—	3	1	no	—
62	C₉	—	3	8	no	—
63	C₃	—	3	1	no	—
64	C₃	—	3	12	no	—
65	C₃	—	9	27	no	—
66	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×H(5,𝔽₃)	C₃	semidirect
2. C₃×C₁₃×#737	C₃	semidirect
3. C₁₃×#6911	C₃	semidirect
4. C₃×C₁₃×#732	C₃	semidirect
6. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
9. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
10. C₃²×C₉×C₁₃	C₃²	semidirect
11. C₁₃×#732	C₃²	semidirect
12. C₁₃×#732	C₃²	semidirect
13. #10624932	C₁₃	direct (N × H)
23. H(5,𝔽₃)	C₃×C₁₃	semidirect
24. C₃×#737	C₃×C₁₃	semidirect
25. #6911	C₃×C₁₃	semidirect
26. C₃×#732	C₃×C₁₃	semidirect
35. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
38. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
39. C₃²×C₉	C₃²×C₁₃	semidirect
40. #732	C₃²×C₁₃	semidirect
41. #732	C₃²×C₁₃	semidirect
55. C₁₃	#10624932	direct (N × H)

Subgroups — C13×#10624932 #23745083

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624932 #23745083