Subgroups — C₁₉×#10624643 #28352839

Order 13851.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#6891	C₃	1	1	yes	maximal, characteristic
2	C₁₉×#6891	C₃	1	2	yes	maximal
3	C₃×C₁₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₁₉×#6861	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
6	C₃×C₁₉×3₋¹⁺²	—	3	2	no	—
7	C₃×C₁₉×3₋¹⁺²	—	3	1	no	—
8	C₃²×C₉×C₁₉	—	3	1	no	—
9	C₁₉×C₃²⋊C₉	—	3	2	no	—
10	C₁₉×C₃²⋊C₉	—	3	2	no	—
11	C₁₉×C₃²⋊C₉	—	3	2	no	—
12	C₁₉×C₃²⋊C₉	—	3	2	no	—
13	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	—
15	C₁₉×C₃²⋊C₉	C₃²	1	6	yes	—
16	#10624643	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₉	—	3	3	no	—
18	C₃³×C₁₉	—	9	2	no	—
19	C₃³×C₁₉	—	9	1	no	—
20	C₃³×C₁₉	H(3,𝔽₃)	1	2	yes	—
21	C₃³×C₁₉	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃³×C₁₉	C₃³	1	1	yes	characteristic
23	C₁₉×3₋¹⁺²	—	9	6	no	—
24	C₁₉×3₋¹⁺²	—	9	3	no	—
25	C₃×C₉×C₁₉	—	3	3	no	—
26	C₃×C₉×C₁₉	—	3	3	no	—
27	C₃×C₉×C₁₉	—	3	6	no	—
28	C₃×C₉×C₁₉	—	9	3	no	—
29	#6891	C₃×C₁₉	1	1	yes	characteristic
30	#6891	C₃×C₁₉	1	2	yes	—
31	C₃×C₃²⋊C₉	C₃×C₁₉	1	1	yes	characteristic
32	#6861	C₃×C₁₉	1	9	yes	complemented
33	C₃²×C₁₉	—	3	2	no	—
34	C₃²×C₁₉	—	3	1	no	—
35	C₃²×C₁₉	—	3	4	no	—
36	C₃²×C₁₉	—	3	2	no	—
37	C₃²×C₁₉	—	3	2	no	—
38	C₃²×C₁₉	—	3	1	no	—
39	C₃²×C₁₉	—	3	2	no	—
40	C₃²×C₁₉	—	3	1	no	—
41	C₃²×C₁₉	—	9	9	no	—
42	C₃²×C₁₉	#731	1	3	yes	—
43	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
44	C₉×C₁₉	—	9	3	no	—
45	C₉×C₁₉	—	9	3	no	—
46	C₉×C₁₉	—	9	6	no	—
47	C₃⁴	C₃²×C₁₉	1	1	yes	characteristic
48	C₃×3₋¹⁺²	—	3	2	no	—
49	C₃×3₋¹⁺²	—	3	1	no	—
50	C₃²×C₉	—	3	1	no	—
51	C₃²⋊C₉	—	3	2	no	—
52	C₃²⋊C₉	—	3	2	no	—
53	C₃²⋊C₉	—	3	2	no	—
54	C₃²⋊C₉	—	3	2	no	—
55	C₃²⋊C₉	C₃²×C₁₉	1	3	yes	—
56	C₃²⋊C₉	C₃²×C₁₉	1	3	yes	—
57	C₃²⋊C₉	C₃²×C₁₉	1	6	yes	—
58	C₃×C₁₉	—	3	3	no	—
59	C₃×C₁₉	—	9	2	no	—
60	C₃×C₁₉	—	9	1	no	—
61	C₃×C₁₉	C₃×#731	1	1	yes	characteristic
62	C₃×C₁₉	#6911	1	1	yes	characteristic
63	C₃×C₁₉	#6912	1	2	yes	—
64	C₃³	—	3	3	no	—
65	C₃³	—	9	1	no	—
66	C₃³	—	9	2	no	—
67	C₃³	C₁₉×H(3,𝔽₃)	1	2	yes	—
68	C₃³	C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
69	C₃³	C₃³×C₁₉	1	1	yes	characteristic
70	3₋¹⁺²	—	9	6	no	—
71	3₋¹⁺²	—	9	3	no	—
72	C₃×C₉	—	3	3	no	—
73	C₃×C₉	—	3	3	no	—
74	C₃×C₉	—	3	6	no	—
75	C₃×C₉	—	9	3	no	—
76	C₁₉	#10624643	1	1	yes	characteristic, direct product factor, Sylow
77	C₃²	—	3	1	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	1	no	—
81	C₃²	—	3	2	no	—
82	C₃²	—	3	1	no	—
83	C₃²	—	3	4	no	—
84	C₃²	—	3	2	no	—
85	C₃²	—	9	9	no	—
86	C₃²	C₁₉×#731	1	3	yes	—
87	C₃²	C₃×C₁₉×H(3,𝔽₃)	1	1	yes	characteristic
88	C₉	—	9	3	no	—
89	C₉	—	9	3	no	—
90	C₉	—	9	6	no	—
91	C₃	—	3	3	no	—
92	C₃	—	9	2	no	—
93	C₃	—	9	1	no	—
94	C₃	C₃×C₁₉×#731	1	1	yes	characteristic
95	C₃	C₁₉×#6911	1	1	yes	characteristic
96	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
4. C₁₉×#6861	C₃	semidirect
16. #10624643	C₁₉	direct (N × H)
32. #6861	C₃×C₁₉	semidirect
76. C₁₉	#10624643	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
C₃×C₁₉×C₃²⋊C₉	3
C₁₉×#6861	3
#10624643	19

Subgroups — C19×#10624643 #28352839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10624643 #28352839