Subgroups — C₃×#11760440 #15691642

Order 3159.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₁₃⋊C₃)	C₃	1	2	yes	maximal, complemented
2	C₃²×C₁₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#11760440	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₁₃	—	3	1	no	—
6	C₃³×C₁₃	C₃²	1	1	yes	characteristic
7	C₃²×C₁₃⋊C₃	—	3	2	no	—
8	C₁₃×H(3,𝔽₃)	—	3	2	no	—
9	C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	complemented
10	C₃²⋊(C₁₃⋊C₃)	—	3	4	no	—
11	C₃²⋊(C₁₃⋊C₃)	C₃²	1	6	yes	complemented
12	C₃×C₁₃⋊C₉	—	3	2	no	—
13	C₃×C₁₃⋊C₉	—	3	1	no	—
14	C₃×C₁₃⋊C₉	C₃²	1	3	yes	complemented
15	C₃×#732	—	13	1	no	maximal, Sylow
16	C₃²×C₁₃	—	3	3	no	—
17	C₃²×C₁₃	—	3	3	no	—
18	C₃²×C₁₃	—	9	3	no	—
19	C₃²×C₁₃	H(3,𝔽₃)	1	2	yes	—
20	C₃²×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃²×C₁₃	C₃³	1	1	yes	characteristic
22	C₃×C₁₃⋊C₃	—	3	6	no	—
23	C₃×C₁₃⋊C₃	—	9	6	no	—
24	C₁₃⋊C₉	—	3	3	no	—
25	C₃×H(3,𝔽₃)	—	13	2	no	—
26	C₃×H(3,𝔽₃)	C₁₃⋊C₃	1	1	yes	characteristic, complemented
27	C₃²×C₉	—	13	1	no	—
28	#732	—	13	9	no	—
29	C₃×C₁₃	—	3	2	no	—
30	C₃×C₁₃	—	3	1	no	—
31	C₃×C₁₃	—	9	3	no	—
32	C₃×C₁₃	#732	1	3	yes	complemented
33	C₃×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₁₃⋊C₃	—	9	6	no	—
35	C₃³	—	3	1	no	—
36	C₃³	—	39	2	no	—
37	C₃³	C₃×C₁₃⋊C₃	1	1	yes	characteristic
38	H(3,𝔽₃)	—	3	2	no	—
39	H(3,𝔽₃)	—	13	6	no	—
40	H(3,𝔽₃)	—	39	4	no	—
41	H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	3	yes	complemented
42	C₃×C₉	—	13	3	no	—
43	C₃×C₉	—	39	2	no	—
44	C₃×C₉	—	39	1	no	—
45	C₁₃	C₃×#732	1	1	yes	characteristic, complemented, Sylow
46	C₃²	—	3	3	no	—
47	C₃²	—	3	3	no	—
48	C₃²	—	9	3	no	—
49	C₃²	—	39	6	no	—
50	C₃²	—	117	6	no	—
51	C₃²	C₃²⋊(C₁₃⋊C₃)	1	2	yes	—
52	C₃²	C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
53	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
54	C₉	—	39	3	no	—
55	C₃	—	3	2	no	—
56	C₃	—	3	1	no	—
57	C₃	—	9	3	no	—
58	C₃	—	117	6	no	—
59	C₃	#11760440	1	3	yes	direct product factor
60	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×H(3,𝔽₃)	C₃
socle	C₃²×C₁₃	H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#732
LCS	G ▷ C₃²×C₁₃ ▷ C₃×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×C₃²⋊(C₁₃⋊C₃)	C₃	semidirect
2. C₃²×C₁₃⋊C₉	C₃	semidirect
3. #11760440	C₃	direct (N × H)
4. C₃×C₁₃×H(3,𝔽₃)	C₃	semidirect
9. C₁₃×H(3,𝔽₃)	C₃²	semidirect
11. C₃²⋊(C₁₃⋊C₃)	C₃²	semidirect
14. C₃×C₁₃⋊C₉	C₃²	semidirect
26. C₃×H(3,𝔽₃)	C₁₃⋊C₃	semidirect
32. C₃×C₁₃	#732	semidirect
41. H(3,𝔽₃)	C₃×C₁₃⋊C₃	semidirect
45. C₁₃	C₃×#732	semidirect
59. C₃	#11760440	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×C₃²⋊(C₁₃⋊C₃)	3
C₃²×C₁₃⋊C₉	3
#11760440	3
C₃×C₁₃×H(3,𝔽₃)	3
C₃×#732	13

Subgroups — C3×#11760440 #15691642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#11760440 #15691642