Subgroups — C₃×#17987519 #28356576

Order 13851.

980 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587025	C₃	1	3	yes	maximal
2	#17987519	C₃	1	27	yes	maximal, direct product factor
3	C₃×#13095322	C₃	1	9	yes	maximal, complemented
4	C₃²×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
5	C₃×#10587025	—	3	6	no	—
6	C₃×#10587025	—	3	18	no	—
7	C₃×#10587025	C₃²	1	9	yes	—
8	C₃×#10587025	C₃²	1	27	yes	—
9	C₃²×#4294	—	3	3	no	—
10	#13095322	C₃²	1	81	yes	complemented
11	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
12	C₃×C₁₉×3₋¹⁺²	—	3	3	no	—
13	C₃×C₁₉×3₋¹⁺²	—	3	6	no	—
14	C₃×C₁₉×3₋¹⁺²	C₃²	1	9	yes	—
15	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
16	C₃×#6912	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	—	9	3	no	—
18	C₃³×C₁₉	H(3,𝔽₃)	1	3	yes	—
19	C₃³×C₁₉	H(3,𝔽₃)	1	6	yes	—
20	C₃³×C₁₉	C₃³	1	1	yes	characteristic
21	C₃³×C₁₉	C₃³	1	3	yes	—
22	C₁₉×3₋¹⁺²	—	3	27	no	—
23	C₃×C₉×C₁₉	—	3	6	no	—
24	C₃×C₉×C₁₉	—	3	3	no	—
25	C₃×C₉×C₁₉	C₃³	1	9	yes	—
26	#10587025	—	3	54	no	—
27	#10587025	—	3	18	no	—
28	#10587025	C₃³	1	27	yes	—
29	C₃×#4294	—	3	27	no	—
30	C₃×#4294	—	3	9	no	—
31	C₃²×3₋¹⁺²	—	19	3	no	—
32	C₃²×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
33	#6912	—	19	27	no	—
34	C₃×#733	—	19	9	no	—
35	C₃²×C₁₉	—	3	9	no	—
36	C₃²×C₁₉	—	3	3	no	—
37	C₃²×C₁₉	—	9	6	no	—
38	C₃²×C₁₉	—	9	3	no	—
39	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	9	yes	—
40	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	2	yes	—
41	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
43	C₉×C₁₉	—	3	9	no	—
44	#4294	—	3	27	no	—
45	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
46	C₃×3₋¹⁺²	—	3	6	no	—
47	C₃×3₋¹⁺²	—	3	3	no	—
48	C₃×3₋¹⁺²	—	19	27	no	—
49	C₃×3₋¹⁺²	—	19	9	no	—
50	C₃×3₋¹⁺²	—	57	18	no	—
51	C₃×3₋¹⁺²	—	57	6	no	—
52	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	9	yes	—
53	C₃²×C₉	—	57	3	no	—
54	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
55	#733	—	19	81	no	—
56	C₃×C₁₉	—	3	9	no	—
57	C₃×C₁₉	—	3	2	no	—
58	C₃×C₁₉	—	3	1	no	—
59	C₃×C₁₉	#6912	1	3	yes	complemented
60	C₃×C₁₉	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
61	C₃³	—	9	3	no	—
62	C₃³	C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
63	C₃³	C₃²⋊(C₁₉⋊C₃)	1	6	yes	—
64	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
65	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
66	3₋¹⁺²	—	3	27	no	—
67	3₋¹⁺²	—	19	27	no	—
68	3₋¹⁺²	—	57	18	no	—
69	3₋¹⁺²	—	57	54	no	—
70	C₃×C₉	—	3	6	no	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	57	27	no	—
73	C₃×C₉	—	57	9	no	—
74	C₃×C₉	C₃²×C₁₉⋊C₃	1	9	yes	—
75	C₁₉	C₃×#6912	1	1	yes	characteristic, complemented, Sylow
76	C₃²	—	3	9	no	—
77	C₃²	—	3	3	no	—
78	C₃²	—	9	6	no	—
79	C₃²	—	9	3	no	—
80	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	2	yes	—
81	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	9	yes	—
82	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
83	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
84	C₉	—	3	9	no	—
85	C₉	—	57	27	no	—
86	C₃	—	3	9	no	—
87	C₃	—	3	2	no	—
88	C₃	—	3	1	no	—
89	C₃	#17987519	1	3	yes	direct product factor
90	C₃	C₃²×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₃²×C₁₉×3₋¹⁺²	C₃
socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
prime radical	C₃⁴×C₁₉	C₃²
hypercenter	C₃²×3₋¹⁺²	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6912
LCS	G ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #17987519	C₃	direct (N × H)
3. C₃×#13095322	C₃	semidirect
10. #13095322	C₃²	semidirect
59. C₃×C₁₉	#6912	semidirect
75. C₁₉	C₃×#6912	semidirect
89. C₃	#17987519	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#10587025	3
#17987519	3
C₃×#13095322	3
C₃²×C₁₉×3₋¹⁺²	3
C₃×#6912	19

Subgroups — C3×#17987519 #28356576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987519 #28356576