Subgroups — C₃×#11760439 #15691640

Order 3159.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66851	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃²⋊(C₁₃⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₁₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	#11760439	C₃	1	9	yes	maximal, direct product factor
5	C₃×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₁₃	C₃²	1	1	yes	characteristic
7	C₃²×C₁₃⋊C₃	—	3	1	no	—
8	C₁₃×3₋¹⁺²	—	3	2	no	—
9	C₁₃×3₋¹⁺²	C₃²	1	3	yes	complemented
10	C₃×C₉×C₁₃	—	3	1	no	—
11	C₃²⋊(C₁₃⋊C₃)	—	3	2	no	—
12	C₃²⋊(C₁₃⋊C₃)	C₃²	1	3	yes	—
13	#66851	—	3	2	no	—
14	#66851	C₃²	1	3	yes	complemented
15	C₃×C₁₃⋊C₉	—	3	2	no	—
16	C₃×C₁₃⋊C₉	—	3	1	no	—
17	C₃×C₁₃⋊C₉	—	3	1	no	—
18	C₃×C₁₃⋊C₉	C₃²	1	3	yes	complemented
19	C₃×#731	—	13	1	no	maximal, Sylow
20	C₃²×C₁₃	—	3	3	no	—
21	C₃²×C₁₃	H(3,𝔽₃)	1	2	yes	—
22	C₃²×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃²×C₁₃	C₃³	1	1	yes	characteristic
24	C₃×C₁₃⋊C₃	—	3	3	no	—
25	C₃×C₁₃⋊C₃	—	9	3	no	—
26	C₉×C₁₃	—	3	3	no	—
27	C₁₃⋊C₉	—	3	3	no	—
28	C₁₃⋊C₉	—	3	3	no	—
29	C₃×3₋¹⁺²	—	13	1	no	—
30	C₃×3₋¹⁺²	C₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₃×H(3,𝔽₃)	—	13	1	no	—
32	C₃²×C₉	—	13	1	no	—
33	#731	—	13	9	no	—
34	C₃×C₁₃	—	3	2	no	—
35	C₃×C₁₃	—	3	1	no	—
36	C₃×C₁₃	#731	1	3	yes	complemented
37	C₃×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₁₃⋊C₃	—	9	3	no	—
39	C₃³	—	39	1	no	—
40	C₃³	C₃×C₁₃⋊C₃	1	1	yes	characteristic
41	3₋¹⁺²	—	3	2	no	—
42	3₋¹⁺²	—	13	3	no	—
43	3₋¹⁺²	—	39	2	no	—
44	3₋¹⁺²	C₃×C₁₃⋊C₃	1	3	yes	complemented
45	H(3,𝔽₃)	—	13	3	no	—
46	H(3,𝔽₃)	—	39	2	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	—	13	3	no	—
49	C₃×C₉	—	39	2	no	—
50	C₃×C₉	—	39	1	no	—
51	C₃×C₉	—	39	1	no	—
52	C₁₃	C₃×#731	1	1	yes	characteristic, complemented, Sylow
53	C₃²	—	3	3	no	—
54	C₃²	—	39	3	no	—
55	C₃²	—	117	3	no	—
56	C₃²	C₃²⋊(C₁₃⋊C₃)	1	2	yes	—
57	C₃²	C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
58	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
59	C₉	—	3	3	no	—
60	C₉	—	39	3	no	—
61	C₉	—	39	3	no	—
62	C₃	—	3	2	no	—
63	C₃	—	3	1	no	—
64	C₃	—	117	3	no	—
65	C₃	#11760439	1	3	yes	direct product factor
66	C₃	C₃×C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₁₃⋊C₃)
commutator, cosocle	C₃²×C₁₃	C₃³
Frattini	C₃²	C₃²×C₁₃⋊C₃
Fitting	C₃×C₁₃×3₋¹⁺²	C₃
socle	C₃²×C₁₃	H(3,𝔽₃)
prime radical	C₃×C₃²⋊(C₁₃⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#731
LCS	G ▷ C₃²×C₁₃ ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. C₃×#66851	C₃	semidirect
3. C₃²×C₁₃⋊C₉	C₃	semidirect
4. #11760439	C₃	direct (N × H)
5. C₃×C₁₃×3₋¹⁺²	C₃	semidirect
9. C₁₃×3₋¹⁺²	C₃²	semidirect
14. #66851	C₃²	semidirect
18. C₃×C₁₃⋊C₉	C₃²	semidirect
30. C₃×3₋¹⁺²	C₁₃⋊C₃	semidirect
36. C₃×C₁₃	#731	semidirect
44. 3₋¹⁺²	C₃×C₁₃⋊C₃	semidirect
52. C₁₃	C₃×#731	semidirect
65. C₃	#11760439	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#66851	3
C₃×C₃²⋊(C₁₃⋊C₃)	3
C₃²×C₁₃⋊C₉	3
#11760439	3
C₃×C₁₃×3₋¹⁺²	3
C₃×#731	13

Subgroups — C3×#11760439 #15691640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#11760439 #15691640