Subgroups — C₃²×C₃²⋊(C₁₃⋊C₃) #15691685

Order 3159.

900 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₃³	C₃×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁴
Frattini	C₃	C₃³×C₁₃⋊C₃
Fitting	C₃⁴×C₁₃	C₃
socle	C₃³×C₁₃	C₃²
hypercenter	C₃⁴	C₁₃⋊C₃
hypocenter	C₁₃	C₃²×H(3,𝔽₃)
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃³ ◁ C₃⁴

Complements

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

N	H ≅ G/N	type
1. C₃³×C₁₃⋊C₃	C₃	semidirect
2. C₃×C₃²⋊(C₁₃⋊C₃)	C₃	direct (N × H)
3. C₃⁴×C₁₃	C₃	semidirect
6. C₃³×C₁₃	C₃²	semidirect
8. C₃²×C₁₃⋊C₃	C₃²	semidirect
9. C₃²⋊(C₁₃⋊C₃)	C₃²	direct (N × H)
12. C₃²×C₁₃	H(3,𝔽₃)	semidirect
14. C₃²×C₁₃	C₃³	semidirect
16. C₃×C₁₃⋊C₃	C₃³	semidirect
18. C₃⁴	C₁₃⋊C₃	semidirect
21. C₃×C₁₃	C₃×H(3,𝔽₃)	semidirect
28. C₃³	C₃×C₁₃⋊C₃	semidirect
30. C₁₃	C₃²×H(3,𝔽₃)	semidirect
34. C₃²	C₃²⋊(C₁₃⋊C₃)	direct (N × H)
36. C₃²	C₃²×C₁₃⋊C₃	semidirect
39. C₃	C₃×C₃²⋊(C₁₃⋊C₃)	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃³×C₁₃⋊C₃	3
C₃×C₃²⋊(C₁₃⋊C₃)	3
C₃⁴×C₁₃	3
C₃²×H(3,𝔽₃)	13

Subgroups — C32×C32⋊(C13⋊C3) #15691685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₃²⋊(C₁₃⋊C₃) #15691685