Subgroups — C₁₉×#10624663 #28352859

Order 13851.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#6891	C₃	1	2	yes	maximal
2	C₁₉×#6891	C₃	1	2	yes	maximal
3	C₁₉×#6860	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
5	C₃×C₁₉×3₋¹⁺²	—	3	2	no	—
6	C₃×C₁₉×3₋¹⁺²	C₃²	1	6	yes	—
7	C₁₉×C₃²⋊C₉	—	3	2	no	—
8	C₁₉×C₃²⋊C₉	—	3	4	no	—
9	C₁₉×C₃²⋊C₉	—	3	2	no	—
10	C₁₉×C₃²⋊C₉	—	3	2	no	—
11	C₁₉×C₃²⋊C₉	C₃²	1	6	yes	—
12	#10624663	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³×C₁₉	—	9	2	no	—
14	C₃³×C₁₉	—	9	2	no	—
15	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃³×C₁₉	H(3,𝔽₃)	1	2	yes	—
17	C₃³×C₁₉	C₃³	1	1	yes	characteristic
18	C₁₉×3₋¹⁺²	—	9	6	no	—
19	C₁₉×3₋¹⁺²	—	9	6	no	—
20	C₃×C₉×C₁₉	—	3	6	no	—
21	C₃×C₉×C₁₉	—	3	6	no	—
22	#6891	C₃×C₁₉	1	2	yes	—
23	#6891	C₃×C₁₉	1	2	yes	—
24	#6860	C₃×C₁₉	1	9	yes	complemented
25	C₃²×C₁₉	—	3	2	no	—
26	C₃²×C₁₉	—	3	4	no	—
27	C₃²×C₁₉	—	3	2	no	—
28	C₃²×C₁₉	—	3	2	no	—
29	C₃²×C₁₉	—	3	2	no	—
30	C₃²×C₁₉	—	3	2	no	—
31	C₃²×C₁₉	—	3	2	no	—
32	C₃²×C₁₉	—	9	9	no	—
33	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₉×C₁₉	—	9	6	no	—
35	C₉×C₁₉	—	9	6	no	—
36	C₃⁴	C₃²×C₁₉	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	3	2	no	—
38	C₃×3₋¹⁺²	C₃²×C₁₉	1	6	yes	—
39	C₃²⋊C₉	—	3	2	no	—
40	C₃²⋊C₉	—	3	4	no	—
41	C₃²⋊C₉	—	3	2	no	—
42	C₃²⋊C₉	—	3	2	no	—
43	C₃²⋊C₉	C₃²×C₁₉	1	6	yes	—
44	C₃×C₁₉	—	9	2	no	—
45	C₃×C₁₉	—	9	1	no	—
46	C₃×C₁₉	—	9	1	no	—
47	C₃×C₁₉	#6909	1	2	yes	—
48	C₃×C₁₉	#6912	1	2	yes	—
49	C₃³	—	9	2	no	—
50	C₃³	—	9	2	no	—
51	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
52	C₃³	C₁₉×H(3,𝔽₃)	1	2	yes	—
53	C₃³	C₃³×C₁₉	1	1	yes	characteristic
54	3₋¹⁺²	—	9	6	no	—
55	3₋¹⁺²	—	9	6	no	—
56	C₃×C₉	—	3	6	no	—
57	C₃×C₉	—	3	6	no	—
58	C₁₉	#10624663	1	1	yes	characteristic, direct product factor, Sylow
59	C₃²	—	3	2	no	—
60	C₃²	—	3	2	no	—
61	C₃²	—	3	2	no	—
62	C₃²	—	3	2	no	—
63	C₃²	—	3	2	no	—
64	C₃²	—	3	4	no	—
65	C₃²	—	3	2	no	—
66	C₃²	—	9	9	no	—
67	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
68	C₉	—	9	6	no	—
69	C₉	—	9	6	no	—
70	C₃	—	9	2	no	—
71	C₃	—	9	1	no	—
72	C₃	—	9	1	no	—
73	C₃	C₁₉×#6909	1	2	yes	—
74	C₃	C₁₉×#6912	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₉
prime radical	C₃⁴×C₁₉	C₃²
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₉ ◁ C₃⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#6860	C₃	semidirect
12. #10624663	C₁₉	direct (N × H)
24. #6860	C₃×C₁₉	semidirect
58. C₁₉	#10624663	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#6891	3
C₁₉×#6860	3
#10624663	19

Subgroups — C19×#10624663 #28352859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624663 #28352859