Subgroups — C₁₃×#10624918 #23745069

Order 9477.

828 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#737	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6903	C₃	1	27	yes	maximal, complemented
3	C₃×C₁₃×C₂₇⋊C₃	C₃	1	12	yes	maximal, complemented
4	C₁₃×#737	C₉	1	18	yes	—
5	C₁₃×#737	C₃²	1	9	yes	—
6	C₃×C₁₃×3₋¹⁺²	C₉	1	8	yes	—
7	C₃×C₁₃×H(3,𝔽₃)	C₉	1	1	yes	characteristic
8	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
9	C₁₃×C₂₇⋊C₃	C₃²	1	9	yes	—
10	C₁₃×C₂₇⋊C₃	C₃²	1	72	yes	complemented
11	C₃×C₁₃×C₂₇	C₃²	1	36	yes	complemented
12	#10624918	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₃	C₃×C₉	1	4	yes	—
14	C₁₃×3₋¹⁺²	C₃×C₉	1	72	yes	—
15	C₁₃×H(3,𝔽₃)	C₃×C₉	1	9	yes	—
16	C₃×C₉×C₁₃	C₃×C₉	1	8	yes	—
17	C₃×C₉×C₁₃	C₃×C₉	1	24	yes	—
18	C₃×C₉×C₁₃	C₃³	1	12	yes	—
19	C₃×C₉×C₁₃	C₃³	1	1	yes	characteristic
20	C₁₃×C₂₇	C₃³	1	27	yes	—
21	C₃×#737	C₃×C₁₃	1	1	yes	characteristic
22	#6903	C₃×C₁₃	1	27	yes	complemented
23	C₃×C₂₇⋊C₃	C₃×C₁₃	1	12	yes	complemented
24	C₃²×C₁₃	—	9	4	no	—
25	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
26	C₃²×C₁₃	C₃²×C₉	1	12	yes	—
27	C₉×C₁₃	C₃²×C₉	1	2	yes	—
28	C₉×C₁₃	C₃²×C₉	1	24	yes	—
29	C₉×C₁₃	C₃⁴	1	1	yes	characteristic
30	#737	C₉×C₁₃	1	18	yes	—
31	#737	C₃²×C₁₃	1	9	yes	—
32	C₃×3₋¹⁺²	C₉×C₁₃	1	8	yes	—
33	C₃×H(3,𝔽₃)	C₉×C₁₃	1	1	yes	characteristic
34	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
35	C₂₇⋊C₃	C₃²×C₁₃	1	9	yes	—
36	C₂₇⋊C₃	C₃²×C₁₃	1	72	yes	complemented
37	C₃×C₂₇	C₃²×C₁₃	1	36	yes	complemented
38	C₃×C₁₃	—	3	1	no	—
39	C₃×C₁₃	—	3	12	no	—
40	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
41	C₃³	C₃×C₉×C₁₃	1	4	yes	—
42	3₋¹⁺²	C₃×C₉×C₁₃	1	72	yes	—
43	H(3,𝔽₃)	C₃×C₉×C₁₃	1	9	yes	—
44	C₃×C₉	C₃×C₉×C₁₃	1	8	yes	—
45	C₃×C₉	C₃×C₉×C₁₃	1	24	yes	—
46	C₃×C₉	C₃³×C₁₃	1	12	yes	—
47	C₃×C₉	C₃³×C₁₃	1	1	yes	characteristic
48	C₂₇	C₃³×C₁₃	1	27	yes	—
49	C₁₃	#10624918	1	1	yes	characteristic, direct product factor, Sylow
50	C₃²	—	9	4	no	—
51	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
52	C₃²	C₃²×C₉×C₁₃	1	12	yes	—
53	C₉	C₃²×C₉×C₁₃	1	2	yes	—
54	C₉	C₃²×C₉×C₁₃	1	24	yes	—
55	C₉	C₃⁴×C₁₃	1	1	yes	characteristic
56	C₃	—	3	1	no	—
57	C₃	—	3	12	no	—
58	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₉×C₁₃	C₃⁴
commutator	C₃	C₃³×C₉×C₁₃
Frattini, cosocle	C₉	C₃⁴×C₁₃
socle	C₃×C₁₃	C₃³×C₉
prime radical	C₃×C₁₃×H(3,𝔽₃)	C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#6903	C₃	semidirect
3. C₃×C₁₃×C₂₇⋊C₃	C₃	semidirect
10. C₁₃×C₂₇⋊C₃	C₃²	semidirect
11. C₃×C₁₃×C₂₇	C₃²	semidirect
12. #10624918	C₁₃	direct (N × H)
22. #6903	C₃×C₁₃	semidirect
23. C₃×C₂₇⋊C₃	C₃×C₁₃	semidirect
36. C₂₇⋊C₃	C₃²×C₁₃	semidirect
37. C₃×C₂₇	C₃²×C₁₃	semidirect
49. C₁₃	#10624918	direct (N × H)

Subgroups — C13×#10624918 #23745069

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624918 #23745069