Subgroups — C₃×#11760453 #15691692

Order 3159.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11760453	C₃	1	27	yes	maximal, direct product factor
2	C₃×#66851	C₃	1	2	yes	maximal, complemented
3	C₃×#66848	C₃	1	3	yes	maximal, complemented
4	C₃×#66849	C₃	1	3	yes	maximal, complemented
5	C₃×C₃²⋊(C₁₃⋊C₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×C₁₃⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₃²×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃³×C₁₃	C₃²	1	1	yes	characteristic
9	C₃²×C₁₃⋊C₃	C₃²	1	3	yes	—
10	C₃×C₉×C₁₃	C₃²	1	1	yes	characteristic
11	C₃×C₉×C₁₃	C₃²	1	1	yes	characteristic
12	C₃×C₉×C₁₃	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₁₃	C₃²	1	9	yes	complemented
14	C₃²⋊(C₁₃⋊C₃)	C₃²	1	9	yes	—
15	#66851	C₃²	1	18	yes	complemented
16	C₃×C₁₃⋊C₉	C₃²	1	6	yes	—
17	#66849	C₃²	1	27	yes	complemented
18	#66848	C₃²	1	27	yes	complemented
19	C₉×C₁₃⋊C₃	C₃²	1	27	yes	complemented
20	C₃×#737	—	13	1	no	maximal, Sylow
21	C₃²×C₁₃	—	3	3	no	—
22	C₃²×C₁₃	C₃³	1	3	yes	—
23	C₃²×C₁₃	C₃³	1	1	yes	characteristic
24	C₃×C₁₃⋊C₃	—	3	9	no	—
25	C₃×C₁₃⋊C₃	C₃³	1	9	yes	—
26	C₉×C₁₃	C₃³	1	3	yes	—
27	C₉×C₁₃	C₃³	1	3	yes	—
28	C₉×C₁₃	C₃³	1	3	yes	—
29	C₁₃⋊C₉	C₃³	1	18	yes	—
30	#737	—	13	27	no	—
31	C₃×3₋¹⁺²	—	13	2	no	—
32	C₃×3₋¹⁺²	—	13	3	no	—
33	C₃×3₋¹⁺²	—	13	3	no	—
34	C₃×H(3,𝔽₃)	—	13	1	no	—
35	C₃²×C₉	—	13	3	no	—
36	C₃²×C₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
37	C₃×C₁₃	—	3	3	no	—
38	C₃×C₁₃	#737	1	3	yes	complemented
39	C₃×C₁₃	C₃⁴	1	1	yes	characteristic
40	C₁₃⋊C₃	—	3	9	no	—
41	C₃³	—	13	3	no	—
42	C₃³	C₃×C₁₃⋊C₃	1	1	yes	characteristic
43	3₋¹⁺²	—	13	18	no	—
44	3₋¹⁺²	—	13	27	no	—
45	3₋¹⁺²	—	13	27	no	—
46	H(3,𝔽₃)	—	13	9	no	—
47	C₃×C₉	—	13	6	no	—
48	C₃×C₉	—	13	27	no	—
49	C₃×C₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic
50	C₃×C₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic
51	C₃×C₉	C₃×C₁₃⋊C₃	1	1	yes	characteristic
52	C₃×C₉	C₃×C₁₃⋊C₃	1	9	yes	complemented
53	C₁₃	C₃×#737	1	1	yes	characteristic, complemented, Sylow
54	C₃²	—	3	3	no	—
55	C₃²	—	13	9	no	—
56	C₃²	—	39	9	no	—
57	C₃²	C₃²×C₁₃⋊C₃	1	3	yes	—
58	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
59	C₉	—	13	18	no	—
60	C₉	C₃²×C₁₃⋊C₃	1	3	yes	—
61	C₉	C₃²×C₁₃⋊C₃	1	3	yes	—
62	C₉	C₃²×C₁₃⋊C₃	1	3	yes	—
63	C₃	—	3	3	no	—
64	C₃	—	39	9	no	—
65	C₃	#11760453	1	3	yes	direct product factor
66	C₃	C₃³×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁴
Frattini	C₃	C₃³×C₁₃⋊C₃
Fitting	C₃²×C₉×C₁₃	C₃
socle	C₃²×C₁₃	C₃³
prime radical	C₃×C₃²⋊(C₁₃⋊C₃)	C₃
hypercenter	C₃²×C₉	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#737
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #11760453	C₃	direct (N × H)
2. C₃×#66851	C₃	semidirect
3. C₃×#66848	C₃	semidirect
4. C₃×#66849	C₃	semidirect
6. C₃×C₉×C₁₃⋊C₃	C₃	semidirect
7. C₃²×C₉×C₁₃	C₃	semidirect
13. C₃×C₉×C₁₃	C₃²	semidirect
15. #66851	C₃²	semidirect
17. #66849	C₃²	semidirect
18. #66848	C₃²	semidirect
19. C₉×C₁₃⋊C₃	C₃²	semidirect
36. C₃²×C₉	C₁₃⋊C₃	semidirect
38. C₃×C₁₃	#737	semidirect
52. C₃×C₉	C₃×C₁₃⋊C₃	semidirect
53. C₁₃	C₃×#737	semidirect
65. C₃	#11760453	direct (N × H)

Maximal subgroups

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

subgroup	index
#11760453	3
C₃×#66851	3
C₃×#66848	3
C₃×#66849	3
C₃×C₃²⋊(C₁₃⋊C₃)	3
C₃×C₉×C₁₃⋊C₃	3
C₃²×C₉×C₁₃	3
C₃×#737	13

Subgroups — C3×#11760453 #15691692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#11760453 #15691692