Subgroups — C₁₉×#10624656 #28352852

Order 13851.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#6891	C₃	1	2	yes	maximal, complemented
2	C₁₉×C₃²⋊H(3,𝔽₃)	C₃	1	2	yes	maximal, complemented
3	C₁₉×#6856	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×H(3,𝔽₃)	—	3	2	no	—
7	C₃×C₁₉×H(3,𝔽₃)	—	3	2	no	—
8	C₃×C₁₉×H(3,𝔽₃)	—	3	2	no	—
9	C₃×C₁₉×H(3,𝔽₃)	C₃²	1	6	yes	—
10	C₁₉×C₃²⋊C₉	—	3	2	no	—
11	C₁₉×C₃²⋊C₉	—	3	2	no	—
12	C₁₉×C₃²⋊C₉	C₃²	1	6	yes	—
13	#10624656	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₉	—	3	6	no	—
15	C₃³×C₁₉	—	9	2	no	—
16	C₃³×C₁₉	—	9	2	no	—
17	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃³×C₁₉	H(3,𝔽₃)	1	2	yes	—
19	C₃³×C₁₉	C₃³	1	1	yes	characteristic
20	C₁₉×3₋¹⁺²	—	9	6	no	—
21	C₁₉×H(3,𝔽₃)	—	9	6	no	—
22	C₁₉×H(3,𝔽₃)	—	9	6	no	—
23	C₁₉×H(3,𝔽₃)	—	9	6	no	—
24	C₁₉×H(3,𝔽₃)	—	9	6	no	—
25	C₃×C₉×C₁₉	—	3	6	no	—
26	#6891	C₃×C₁₉	1	2	yes	complemented
27	C₃²⋊H(3,𝔽₃)	C₃×C₁₉	1	2	yes	complemented
28	#6856	C₃×C₁₉	1	9	yes	complemented
29	C₃²×C₁₉	—	3	2	no	—
30	C₃²×C₁₉	—	3	2	no	—
31	C₃²×C₁₉	—	3	2	no	—
32	C₃²×C₁₉	—	3	2	no	—
33	C₃²×C₁₉	—	3	2	no	—
34	C₃²×C₁₉	—	3	2	no	—
35	C₃²×C₁₉	—	3	2	no	—
36	C₃²×C₁₉	—	3	2	no	—
37	C₃²×C₁₉	—	9	9	no	—
38	C₃²×C₁₉	—	9	6	no	—
39	C₃²×C₁₉	—	9	6	no	—
40	C₃²×C₁₉	—	9	6	no	—
41	C₃²×C₁₉	—	9	6	no	—
42	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₉×C₁₉	—	9	6	no	—
44	C₃⁴	C₃²×C₁₉	1	1	yes	characteristic
45	C₃×3₋¹⁺²	—	3	2	no	—
46	C₃×H(3,𝔽₃)	—	3	2	no	—
47	C₃×H(3,𝔽₃)	—	3	2	no	—
48	C₃×H(3,𝔽₃)	—	3	2	no	—
49	C₃×H(3,𝔽₃)	C₃²×C₁₉	1	6	yes	—
50	C₃²⋊C₉	—	3	2	no	—
51	C₃²⋊C₉	—	3	2	no	—
52	C₃²⋊C₉	C₃²×C₁₉	1	6	yes	—
53	C₃×C₁₉	—	9	2	no	—
54	C₃×C₁₉	—	9	1	no	—
55	C₃×C₁₉	—	9	1	no	—
56	C₃×C₁₉	—	27	6	no	—
57	C₃×C₁₉	#6909	1	2	yes	—
58	C₃×C₁₉	#6911	1	2	yes	—
59	C₃³	—	3	6	no	—
60	C₃³	—	9	2	no	—
61	C₃³	—	9	2	no	—
62	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
63	C₃³	C₁₉×H(3,𝔽₃)	1	2	yes	—
64	C₃³	C₃³×C₁₉	1	1	yes	characteristic
65	3₋¹⁺²	—	9	6	no	—
66	H(3,𝔽₃)	—	9	6	no	—
67	H(3,𝔽₃)	—	9	6	no	—
68	H(3,𝔽₃)	—	9	6	no	—
69	H(3,𝔽₃)	—	9	6	no	—
70	C₃×C₉	—	3	6	no	—
71	C₁₉	#10624656	1	1	yes	characteristic, direct product factor, Sylow
72	C₃²	—	3	2	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	3	2	no	—
75	C₃²	—	3	2	no	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	2	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	9	9	no	—
81	C₃²	—	9	6	no	—
82	C₃²	—	9	6	no	—
83	C₃²	—	9	6	no	—
84	C₃²	—	9	6	no	—
85	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
86	C₉	—	9	6	no	—
87	C₃	—	9	2	no	—
88	C₃	—	9	1	no	—
89	C₃	—	9	1	no	—
90	C₃	—	27	6	no	—
91	C₃	C₁₉×#6909	1	2	yes	—
92	C₃	C₁₉×#6911	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₉	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₉
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
1. C₁₉×#6891	C₃	semidirect
2. C₁₉×C₃²⋊H(3,𝔽₃)	C₃	semidirect
3. C₁₉×#6856	C₃	semidirect
13. #10624656	C₁₉	direct (N × H)
26. #6891	C₃×C₁₉	semidirect
27. C₃²⋊H(3,𝔽₃)	C₃×C₁₉	semidirect
28. #6856	C₃×C₁₉	semidirect
71. C₁₉	#10624656	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×C₃²⋊H(3,𝔽₃)	3
C₁₉×#6856	3
#10624656	19

Subgroups — C19×#10624656 #28352852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624656 #28352852