Subgroups — C₁₃×#10624933 #23745084

Order 9477.

936 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×3₋¹⁺⁴	C₃	1	3	yes	maximal
2	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6912	C₃	1	24	yes	maximal, complemented
4	C₃×C₁₃×#733	C₃	1	12	yes	maximal, complemented
5	C₁₃×#737	—	3	9	no	—
6	C₁₃×#737	—	3	27	no	—
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	36	yes	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	8	yes	—
9	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
11	C₁₃×#733	C₃²	1	9	yes	—
12	C₁₃×#733	C₃²	1	72	yes	—
13	#10624933	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	C₃³	1	4	yes	—
15	C₁₃×3₋¹⁺²	—	3	72	no	—
16	C₁₃×3₋¹⁺²	—	3	24	no	—
17	C₁₃×3₋¹⁺²	C₃³	1	27	yes	—
18	C₁₃×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
19	C₃×C₉×C₁₃	—	3	12	no	—
20	C₃×C₉×C₁₃	—	3	36	no	—
21	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
22	C₃×C₉×C₁₃	C₃³	1	8	yes	—
23	3₋¹⁺⁴	C₃×C₁₃	1	3	yes	—
24	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
25	#6912	C₃×C₁₃	1	24	yes	complemented
26	C₃×#733	C₃×C₁₃	1	12	yes	complemented
27	C₃²×C₁₃	—	9	4	no	—
28	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
29	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
30	C₉×C₁₃	—	3	1	no	—
31	C₉×C₁₃	—	3	27	no	—
32	C₉×C₁₃	—	3	8	no	—
33	#737	—	3	9	no	—
34	#737	—	3	27	no	—
35	C₃×3₋¹⁺²	C₃²×C₁₃	1	36	yes	—
36	C₃×3₋¹⁺²	C₃²×C₁₃	1	8	yes	—
37	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	1	yes	characteristic
38	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
39	#733	C₃²×C₁₃	1	72	yes	—
40	#733	C₃²×C₁₃	1	9	yes	—
41	C₃×C₁₃	—	3	1	no	—
42	C₃×C₁₃	—	3	12	no	—
43	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
44	C₃³	C₃³×C₁₃	1	4	yes	—
45	3₋¹⁺²	—	3	72	no	—
46	3₋¹⁺²	—	3	24	no	—
47	3₋¹⁺²	C₃³×C₁₃	1	27	yes	—
48	H(3,𝔽₃)	C₁₃×H(3,𝔽₃)	1	9	yes	—
49	C₃×C₉	—	3	12	no	—
50	C₃×C₉	—	3	36	no	—
51	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
52	C₃×C₉	C₃³×C₁₃	1	8	yes	—
53	C₁₃	#10624933	1	1	yes	characteristic, direct product factor, Sylow
54	C₃²	—	9	4	no	—
55	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
56	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
57	C₉	—	3	1	no	—
58	C₉	—	3	27	no	—
59	C₉	—	3	8	no	—
60	C₃	—	3	1	no	—
61	C₃	—	3	12	no	—
62	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
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₃²
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
3. C₁₃×#6912	C₃	semidirect
4. C₃×C₁₃×#733	C₃	semidirect
13. #10624933	C₁₃	direct (N × H)
25. #6912	C₃×C₁₃	semidirect
26. C₃×#733	C₃×C₁₃	semidirect
53. C₁₃	#10624933	direct (N × H)

Subgroups — C13×#10624933 #23745084

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624933 #23745084