Group #18019663 — subgroups

Subgroups — C₁₉×#13704 #18019663

Order 4864.

164 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2252	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1424	C₂	1	2	yes	maximal
4	C₁₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1416	C₂	1	2	yes	maximal
6	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
7	C₁₉×#500	—	2	1	no	—
8	C₄×Q₁₆×C₁₉	—	2	1	no	—
9	C₂×C₁₉×C₃₂	C₂²	1	2	yes	—
10	C₁₉×#366	—	2	1	no	—
11	C₁₉×#366	C₂²	1	1	yes	characteristic
12	C₁₉×#366	C₂²	1	2	yes	—
13	C₁₉×#358	—	2	1	no	—
14	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆×C₁₉	—	2	1	no	—
16	C₁₉×C₄⋊Q₈	—	4	1	no	—
17	C₄×Q₈×C₁₉	—	4	1	no	—
18	C₁₉×Q₃₂	—	2	1	no	—
19	C₁₉×Q₃₂	Q₈	1	2	yes	complemented
20	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
22	C₁₉×#107	—	2	1	no	—
23	C₁₉×#107	—	2	2	no	—
24	C₁₉×#107	—	4	1	no	—
25	C₁₉×#103	—	4	1	no	—
26	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
27	C₁₉×C₃₂	—	2	2	no	—
28	C₂×Q₈×C₁₉	—	4	1	no	—
29	C₂×Q₈×C₁₉	—	8	1	no	—
30	Q₁₆×C₁₉	—	2	2	no	—
31	Q₁₆×C₁₉	—	4	1	no	—
32	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₄⋊C₄×C₁₉	—	4	1	no	—
35	C₄⋊C₄×C₁₉	—	4	2	no	—
36	C₄⋊C₄×C₁₉	—	8	1	no	—
37	C₄⋊C₄×C₁₉	—	8	1	no	—
38	C₄²×C₁₉	—	8	1	no	—
39	C₄²×C₁₉	D₈	1	1	yes	characteristic
40	C₁₆×C₁₉	—	2	1	no	—
41	C₁₆×C₁₉	C₂×Q₈	1	1	yes	characteristic
42	C₁₆×C₁₉	#41	1	1	yes	characteristic
43	#13704	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	Q₈×C₁₉	—	4	2	no	—
45	Q₈×C₁₉	—	8	1	no	—
46	Q₈×C₁₉	—	16	2	no	—
47	C₂×C₄×C₁₉	—	8	1	no	—
48	C₂×C₄×C₁₉	—	8	1	no	—
49	C₂×C₄×C₁₉	—	8	2	no	—
50	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
52	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
53	C₈×C₁₉	—	2	1	no	—
54	C₈×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
55	C₈×C₁₉	#137	1	1	yes	characteristic
56	#2252	C₂×C₁₉	1	1	yes	characteristic
57	C₄×Q₃₂	C₂×C₁₉	1	1	yes	characteristic
58	#1424	C₂×C₁₉	1	2	yes	—
59	C₄⋊C₃₂	C₂×C₁₉	1	1	yes	characteristic
60	#1416	C₂×C₁₉	1	2	yes	—
61	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	8	2	no	—
64	C₄×C₁₉	—	16	2	no	—
65	C₄×C₁₉	—	16	1	no	—
66	C₄×C₁₉	SD₆₄	1	2	yes	—
67	C₄×C₁₉	#474	1	1	yes	characteristic
68	C₄×C₁₉	#510	1	1	yes	characteristic
69	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
70	#500	—	2	1	no	—
71	C₄×Q₁₆	—	2	1	no	—
72	C₂×C₃₂	C₂²×C₁₉	1	2	yes	—
73	#366	—	2	1	no	—
74	#366	C₂²×C₁₉	1	1	yes	characteristic
75	#366	C₂²×C₁₉	1	2	yes	—
76	#358	—	2	1	no	—
77	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
78	C₂×C₁₉	#2224	1	1	yes	characteristic
79	C₂×C₁₉	C₂×SD₆₄	1	1	yes	characteristic
80	C₂×C₁₉	#2264	1	1	yes	characteristic
81	C₂×Q₁₆	—	2	1	no	—
82	C₄⋊Q₈	—	4	1	no	—
83	C₄×Q₈	—	4	1	no	—
84	Q₃₂	—	2	1	no	—
85	Q₃₂	Q₈×C₁₉	1	2	yes	complemented
86	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
87	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
88	#107	—	2	1	no	—
89	#107	—	2	2	no	—
90	#107	—	4	1	no	—
91	#103	—	4	1	no	—
92	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
93	C₃₂	—	2	2	no	—
94	C₁₉	#13704	1	1	yes	characteristic, direct product factor, Sylow
95	C₂×Q₈	—	4	1	no	—
96	C₂×Q₈	—	8	1	no	—
97	Q₁₆	—	2	2	no	—
98	Q₁₆	—	4	1	no	—
99	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
100	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
101	C₄⋊C₄	—	4	1	no	—
102	C₄⋊C₄	—	4	2	no	—
103	C₄⋊C₄	—	8	1	no	—
104	C₄⋊C₄	—	8	1	no	—
105	C₄²	—	8	1	no	—
106	C₄²	D₈×C₁₉	1	1	yes	characteristic
107	C₁₆	—	2	1	no	—
108	C₁₆	C₂×Q₈×C₁₉	1	1	yes	characteristic
109	C₁₆	#41×C₁₉	1	1	yes	characteristic
110	Q₈	—	4	2	no	—
111	Q₈	—	8	1	no	—
112	Q₈	—	16	2	no	—
113	C₂×C₄	—	8	1	no	—
114	C₂×C₄	—	8	1	no	—
115	C₂×C₄	—	8	2	no	—
116	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
117	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
118	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
119	C₈	—	2	1	no	—
120	C₈	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
121	C₈	C₁₉×#137	1	1	yes	characteristic
122	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
123	C₄	—	2	1	no	—
124	C₄	—	8	2	no	—
125	C₄	—	16	2	no	—
126	C₄	—	16	1	no	—
127	C₄	C₁₉×SD₆₄	1	2	yes	—
128	C₄	C₁₉×#474	1	1	yes	characteristic
129	C₄	C₁₉×#510	1	1	yes	characteristic
130	C₂	C₁₉×#2224	1	1	yes	characteristic
131	C₂	C₂×C₁₉×SD₆₄	1	1	yes	characteristic
132	C₂	C₁₉×#2264	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2252

C₂

yes

maximal, characteristic

C₄×C₁₉×Q₃₂

C₂

yes

maximal, characteristic

C₁₉×#1424

C₂

yes

maximal

C₁₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic

C₁₉×#1416

C₂

yes

maximal

C₂×C₁₉×Q₃₂

C₂²

yes

characteristic

C₁₉×#500

—

C₄×Q₁₆×C₁₉

—

C₂×C₁₉×C₃₂

C₂²

yes

—

C₁₉×#366

—

C₁₉×#366

C₂²

yes

characteristic

C₁₉×#366

C₂²

yes

—

C₁₉×#358

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

Q₈

yes

complemented

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#103

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×Q₈

yes

C₁₆×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊Q₈

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic

C₄×Q₃₂

C₂×C₁₉

yes

characteristic

#1424

C₂×C₁₉

yes

—

C₄⋊C₃₂

C₂×C₁₉

yes

characteristic

#1416

C₂×C₁₉

yes

—

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

SD₆₄

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

C₂²×C₁₉

yes

characteristic

#500

—

C₄×Q₁₆

—

C₂×C₃₂

C₂²×C₁₉

yes

—

#366

—

#366

C₂²×C₁₉

yes

characteristic

#366

C₂²×C₁₉

yes

—

#358

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

#2224

yes

characteristic

C₂×C₁₉

C₂×SD₆₄

yes

characteristic

C₂×C₁₉

#2264

yes

characteristic

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

Q₈×C₁₉

yes

complemented

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂³×C₁₉

yes

—

—

—

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#13704

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₈×C₁₉

yes

characteristic

100

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄²

—

106

C₄²

D₈×C₁₉

yes

characteristic

107

C₁₆

—

108

C₁₆

C₂×Q₈×C₁₉

yes

characteristic

109

C₁₆

#41×C₁₉

yes

characteristic

110

Q₈

—

111

Q₈

—

112

Q₈

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₁₉×D₁₆

yes

characteristic

117

C₂×C₄

C₁₉×D₁₆

yes

characteristic

118

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

119

C₈

—

120

C₈

C₁₉×C₂²⋊Q₈

yes

characteristic

121

C₈

C₁₉×#137

yes

characteristic

122

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

C₁₉×SD₆₄

yes

—

128

C₄

C₁₉×#474

yes

characteristic

129

C₄

C₁₉×#510

yes

characteristic

130

C₂

C₁₉×#2224

yes

characteristic

131

C₂

C₂×C₁₉×SD₆₄

yes

characteristic

132

C₂

C₁₉×#2264

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
19. C₁₉×Q₃₂	Q₈	semidirect
43. #13704	C₁₉	direct (N × H)
85. Q₃₂	Q₈×C₁₉	semidirect
94. C₁₉	#13704	direct (N × H)

H ≅ G/N

type

19. C₁₉×Q₃₂

Q₈

semidirect

43. #13704

C₁₉

direct (N × H)

85. Q₃₂

Q₈×C₁₉

semidirect

94. C₁₉

#13704

direct (N × H)

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

subgroup	index
C₁₉×#2252	2
C₄×C₁₉×Q₃₂	2
C₁₉×#1424	2
C₁₉×C₄⋊C₃₂	2
C₁₉×#1416	2
#13704	19

subgroup

index

C₁₉×#2252

C₄×C₁₉×Q₃₂

C₁₉×#1424

C₁₉×C₄⋊C₃₂

C₁₉×#1416

#13704

Subgroups — C₁₉×#13704 #18019663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13704 #18019663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13704 #18019663