Subgroups — C₃×#11760454 #15691693

Order 3159.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11760454	C₃	1	27	yes	maximal, direct product factor
2	C₃×#66851	C₃	1	1	yes	maximal, characteristic, 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	C₃²×C₁₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×C₁₃⋊C₃	C₃	1	3	yes	maximal, complemented
8	C₃×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
9	C₃³×C₁₃	C₃²	1	1	yes	characteristic
10	C₃²×C₁₃⋊C₃	C₃²	1	3	yes	—
11	C₁₃×3₋¹⁺²	C₃²	1	9	yes	complemented
12	C₃×C₉×C₁₃	C₃²	1	3	yes	—
13	C₃²⋊(C₁₃⋊C₃)	C₃²	1	9	yes	—
14	#66851	C₃²	1	9	yes	complemented
15	C₃×C₁₃⋊C₉	C₃²	1	1	yes	characteristic
16	C₃×C₁₃⋊C₉	C₃²	1	3	yes	—
17	C₃×C₁₃⋊C₉	C₃²	1	1	yes	characteristic
18	C₃×C₁₃⋊C₉	C₃²	1	1	yes	characteristic
19	C₃×C₁₃⋊C₉	C₃²	1	9	yes	complemented
20	#66849	C₃²	1	27	yes	complemented
21	#66848	C₃²	1	27	yes	complemented
22	C₉×C₁₃⋊C₃	C₃²	1	27	yes	complemented
23	C₃×#737	—	13	1	no	maximal, Sylow
24	C₃²×C₁₃	—	3	3	no	—
25	C₃²×C₁₃	C₃³	1	3	yes	—
26	C₃²×C₁₃	C₃³	1	1	yes	characteristic
27	C₃×C₁₃⋊C₃	—	3	9	no	—
28	C₃×C₁₃⋊C₃	C₃³	1	9	yes	—
29	C₉×C₁₃	C₃³	1	9	yes	—
30	C₁₃⋊C₉	C₃³	1	3	yes	—
31	C₁₃⋊C₉	C₃³	1	9	yes	—
32	C₁₃⋊C₉	C₃³	1	3	yes	—
33	C₁₃⋊C₉	C₃³	1	3	yes	—
34	#737	—	13	27	no	—
35	C₃×3₋¹⁺²	—	13	1	no	—
36	C₃×3₋¹⁺²	—	13	3	no	—
37	C₃×3₋¹⁺²	—	13	3	no	—
38	C₃×3₋¹⁺²	C₁₃⋊C₃	1	1	yes	characteristic, complemented
39	C₃×H(3,𝔽₃)	—	13	1	no	—
40	C₃²×C₉	—	13	1	no	—
41	C₃²×C₉	—	13	3	no	—
42	C₃×C₁₃	—	3	3	no	—
43	C₃×C₁₃	#737	1	3	yes	complemented
44	C₃×C₁₃	C₃⁴	1	1	yes	characteristic
45	C₁₃⋊C₃	—	3	9	no	—
46	C₃³	—	13	3	no	—
47	C₃³	C₃×C₁₃⋊C₃	1	1	yes	characteristic
48	3₋¹⁺²	—	13	9	no	—
49	3₋¹⁺²	—	13	27	no	—
50	3₋¹⁺²	—	13	27	no	—
51	3₋¹⁺²	C₃×C₁₃⋊C₃	1	9	yes	complemented
52	H(3,𝔽₃)	—	13	9	no	—
53	C₃×C₉	—	13	9	no	—
54	C₃×C₉	—	13	1	no	—
55	C₃×C₉	—	13	3	no	—
56	C₃×C₉	—	13	1	no	—
57	C₃×C₉	—	13	1	no	—
58	C₃×C₉	—	13	27	no	—
59	C₃×C₉	C₃×C₁₃⋊C₃	1	3	yes	—
60	C₁₃	C₃×#737	1	1	yes	characteristic, complemented, Sylow
61	C₃²	—	3	3	no	—
62	C₃²	—	13	9	no	—
63	C₃²	—	39	9	no	—
64	C₃²	C₃²×C₁₃⋊C₃	1	3	yes	—
65	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
66	C₉	—	13	3	no	—
67	C₉	—	13	3	no	—
68	C₉	—	13	3	no	—
69	C₉	—	13	9	no	—
70	C₉	C₃²×C₁₃⋊C₃	1	9	yes	—
71	C₃	—	3	3	no	—
72	C₃	—	39	9	no	—
73	C₃	#11760454	1	3	yes	direct product factor
74	C₃	C₃³×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²×C₁₃⋊C₃
commutator, cosocle	C₃×C₁₃	C₃⁴
Frattini	C₃	C₃³×C₁₃⋊C₃
Fitting	C₃×C₁₃×3₋¹⁺²	C₃
socle	C₃²×C₁₃	C₃³
prime radical	C₃×C₃²⋊(C₁₃⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#737
LCS	G ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #11760454	C₃	direct (N × H)
2. C₃×#66851	C₃	semidirect
3. C₃×#66848	C₃	semidirect
4. C₃×#66849	C₃	semidirect
6. C₃²×C₁₃⋊C₉	C₃	semidirect
7. C₃×C₉×C₁₃⋊C₃	C₃	semidirect
8. C₃×C₁₃×3₋¹⁺²	C₃	semidirect
11. C₁₃×3₋¹⁺²	C₃²	semidirect
14. #66851	C₃²	semidirect
19. C₃×C₁₃⋊C₉	C₃²	semidirect
20. #66849	C₃²	semidirect
21. #66848	C₃²	semidirect
22. C₉×C₁₃⋊C₃	C₃²	semidirect
38. C₃×3₋¹⁺²	C₁₃⋊C₃	semidirect
43. C₃×C₁₃	#737	semidirect
51. 3₋¹⁺²	C₃×C₁₃⋊C₃	semidirect
60. C₁₃	C₃×#737	semidirect
73. C₃	#11760454	direct (N × H)

Maximal subgroups

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

subgroup	index
#11760454	3
C₃×#66851	3
C₃×#66848	3
C₃×#66849	3
C₃×C₃²⋊(C₁₃⋊C₃)	3
C₃²×C₁₃⋊C₉	3
C₃×C₉×C₁₃⋊C₃	3
C₃×C₁₃×3₋¹⁺²	3
C₃×#737	13

Subgroups — C3×#11760454 #15691693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#11760454 #15691693