Subgroups — C₁₉×#10624662 #28352858

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	4	no	—
8	C₁₉×C₃²⋊C₉	—	3	2	no	—
9	C₁₉×C₃²⋊C₉	—	3	4	no	—
10	C₁₉×C₃²⋊C₉	C₃²	1	6	yes	—
11	#10624662	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₉	—	9	2	no	—
13	C₃³×C₁₉	—	9	2	no	—
14	C₃³×C₁₉	H(3,𝔽₃)	1	2	yes	—
15	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃³×C₁₉	C₃³	1	1	yes	characteristic
17	C₁₉×3₋¹⁺²	—	9	6	no	—
18	C₁₉×3₋¹⁺²	—	9	6	no	—
19	C₃×C₉×C₁₉	—	3	6	no	—
20	C₃×C₉×C₁₉	—	3	6	no	—
21	#6891	C₃×C₁₉	1	2	yes	—
22	#6891	C₃×C₁₉	1	2	yes	—
23	#6860	C₃×C₁₉	1	9	yes	complemented
24	C₃²×C₁₉	—	3	4	no	—
25	C₃²×C₁₉	—	3	2	no	—
26	C₃²×C₁₉	—	3	2	no	—
27	C₃²×C₁₉	—	3	2	no	—
28	C₃²×C₁₉	—	3	2	no	—
29	C₃²×C₁₉	—	3	4	no	—
30	C₃²×C₁₉	—	9	9	no	—
31	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
32	C₉×C₁₉	—	9	6	no	—
33	C₉×C₁₉	—	9	6	no	—
34	C₃⁴	C₃²×C₁₉	1	1	yes	characteristic
35	C₃×3₋¹⁺²	—	3	2	no	—
36	C₃×3₋¹⁺²	C₃²×C₁₉	1	6	yes	—
37	C₃²⋊C₉	—	3	4	no	—
38	C₃²⋊C₉	—	3	2	no	—
39	C₃²⋊C₉	—	3	4	no	—
40	C₃²⋊C₉	C₃²×C₁₉	1	6	yes	—
41	C₃×C₁₉	—	9	1	no	—
42	C₃×C₁₉	—	9	2	no	—
43	C₃×C₁₉	—	9	1	no	—
44	C₃×C₁₉	#6909	1	2	yes	—
45	C₃×C₁₉	#6912	1	2	yes	—
46	C₃³	—	9	2	no	—
47	C₃³	—	9	2	no	—
48	C₃³	C₁₉×H(3,𝔽₃)	1	2	yes	—
49	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
50	C₃³	C₃³×C₁₉	1	1	yes	characteristic
51	3₋¹⁺²	—	9	6	no	—
52	3₋¹⁺²	—	9	6	no	—
53	C₃×C₉	—	3	6	no	—
54	C₃×C₉	—	3	6	no	—
55	C₁₉	#10624662	1	1	yes	characteristic, direct product factor, Sylow
56	C₃²	—	3	2	no	—
57	C₃²	—	3	2	no	—
58	C₃²	—	3	4	no	—
59	C₃²	—	3	4	no	—
60	C₃²	—	3	2	no	—
61	C₃²	—	3	2	no	—
62	C₃²	—	9	9	no	—
63	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
64	C₉	—	9	6	no	—
65	C₉	—	9	6	no	—
66	C₃	—	9	1	no	—
67	C₃	—	9	1	no	—
68	C₃	—	9	2	no	—
69	C₃	C₁₉×#6909	1	2	yes	—
70	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
11. #10624662	C₁₉	direct (N × H)
23. #6860	C₃×C₁₉	semidirect
55. C₁₉	#10624662	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
#10624662	19

Subgroups — C19×#10624662 #28352858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624662 #28352858