Subgroups — C₁₃×#10624880 #23745031

Order 9477.

1718 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	4	yes	maximal, complemented
2	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	36	yes	maximal, complemented
3	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
4	C₃⁴×C₁₃	C₃²	1	12	yes	complemented
5	C₃×C₁₃×H(3,𝔽₃)	—	3	36	no	—
6	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	36	yes	complemented
7	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	81	yes	complemented
8	#10624880	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃³×C₁₃	—	3	36	no	—
10	C₃³×C₁₃	—	9	3	no	—
11	C₃³×C₁₃	—	9	36	no	—
12	C₃³×C₁₃	H(3,𝔽₃)	1	9	yes	complemented
13	C₃³×C₁₃	C₃³	1	36	yes	—
14	C₃³×C₁₃	C₃³	1	4	yes	—
15	C₁₃×H(3,𝔽₃)	—	3	108	no	—
16	C₁₃×H(3,𝔽₃)	—	9	81	no	—
17	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	4	yes	complemented
18	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	36	yes	complemented
19	C₃²×C₁₃	—	3	12	no	—
20	C₃²×C₁₃	—	3	36	no	—
21	C₃²×C₁₃	—	3	108	no	—
22	C₃²×C₁₃	—	9	9	no	—
23	C₃²×C₁₃	—	9	108	no	—
24	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	12	yes	—
25	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
26	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
27	C₃⁴	C₃²×C₁₃	1	12	yes	complemented
28	C₃×H(3,𝔽₃)	—	3	36	no	—
29	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	36	yes	complemented
30	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	81	yes	complemented
31	C₃×C₁₃	—	3	12	no	—
32	C₃×C₁₃	—	9	36	no	—
33	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
34	C₃×C₁₃	H(5,𝔽₃)	1	3	yes	—
35	C₃³	—	3	36	no	—
36	C₃³	—	9	3	no	—
37	C₃³	—	9	36	no	—
38	C₃³	C₁₃×H(3,𝔽₃)	1	9	yes	complemented
39	C₃³	C₃³×C₁₃	1	36	yes	—
40	C₃³	C₃³×C₁₃	1	4	yes	—
41	H(3,𝔽₃)	—	3	108	no	—
42	H(3,𝔽₃)	—	9	81	no	—
43	C₁₃	#10624880	1	1	yes	characteristic, direct product factor, Sylow
44	C₃²	—	3	12	no	—
45	C₃²	—	3	36	no	—
46	C₃²	—	3	108	no	—
47	C₃²	—	9	9	no	—
48	C₃²	—	9	108	no	—
49	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	12	yes	—
50	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
51	C₃	—	3	12	no	—
52	C₃	—	9	36	no	—
53	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
54	C₃	C₁₃×H(5,𝔽₃)	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×H(3,𝔽₃)	C₃	semidirect
2. C₁₃×C₃²⋊H(3,𝔽₃)	C₃	semidirect
4. C₃⁴×C₁₃	C₃²	semidirect
6. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
7. C₃×C₁₃×H(3,𝔽₃)	C₃²	semidirect
8. #10624880	C₁₃	direct (N × H)
12. C₃³×C₁₃	H(3,𝔽₃)	semidirect
17. C₃²×H(3,𝔽₃)	C₃×C₁₃	semidirect
18. C₃²⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
27. C₃⁴	C₃²×C₁₃	semidirect
29. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
30. C₃×H(3,𝔽₃)	C₃²×C₁₃	semidirect
38. C₃³	C₁₃×H(3,𝔽₃)	semidirect
43. C₁₃	#10624880	direct (N × H)

Subgroups — C13×#10624880 #23745031

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624880 #23745031