Group #18069065 — subgroups

Subgroups — C₁₉⋊#7014 #18069065

Order 4864.

338 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 159 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	#14563381	C₂	1	2	yes	maximal
2	C₁₉×#1744	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₉⋊C₈	C₄	1	4	yes	—
4	#11926299	—	2	2	no	—
5	#11926299	—	2	2	no	—
6	C₂×C₄×C₈×C₁₉	C₄	1	2	yes	—
7	C₄³×C₁₉	C₂²	1	1	yes	characteristic
8	C₁₉×#336	—	2	2	no	—
9	C₂²×C₈×C₁₉	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	D₄	1	2	yes	—
14	C₂×C₄²×C₁₉	Q₈	1	1	yes	characteristic
15	C₂²×C₁₉⋊C₈	—	2	4	no	—
16	C₄×C₈×C₁₉	—	2	2	no	—
17	C₄×C₈×C₁₉	C₈	1	4	yes	complemented
18	C₄×C₁₉⋊C₈	—	2	4	no	—
19	C₄×C₁₉⋊C₈	C₈	1	8	yes	complemented
20	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
22	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₄⋊C₄	1	2	yes	—
24	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	4	no	—
26	C₂×C₈×C₁₉	—	4	4	no	—
27	C₄²×C₁₉	—	4	1	no	—
28	C₄²×C₁₉	—	4	2	no	—
29	C₄²×C₁₉	—	4	1	no	—
30	C₄²×C₁₉	C₂×C₈	1	4	yes	—
31	C₄²×C₁₉	C₂×C₈	1	2	yes	—
32	C₄²×C₁₉	M₁₆	1	4	yes	—
33	C₄²×C₁₉	M₁₆	1	2	yes	—
34	C₂×C₁₉⋊C₈	—	2	8	no	—
35	C₂×C₁₉⋊C₈	—	4	4	no	—
36	C₂×C₁₉⋊C₈	—	4	4	no	—
37	#7014	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	#95	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	2	no	—
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	2	no	—
42	C₂×C₄×C₁₉	—	2	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	2	2	no	—
45	C₂×C₄×C₁₉	—	2	1	no	—
46	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₄×C₈	1	2	yes	—
48	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#97	1	2	yes	—
50	C₂×C₄×C₁₉	C₂²⋊C₈	1	4	yes	—
51	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
52	C₂×C₄×C₁₉	C₄⋊C₈	1	2	yes	—
53	C₂×C₄×C₁₉	C₄⋊C₈	1	4	yes	—
54	C₈×C₁₉	—	4	4	no	—
55	C₁₉⋊C₈	—	4	8	no	—
56	#1744	—	19	2	no	—
57	#1744	D₁₉	1	1	yes	characteristic
58	C₂²×C₁₉	#336	1	2	yes	—
59	C₂²×C₁₉	#336	1	1	yes	characteristic
60	C₂²×C₁₉	H(3,ℤ/4)	1	2	yes	—
61	C₂²×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
62	C₂²×C₁₉	#338	1	1	yes	characteristic
63	C₄×C₁₉	—	2	4	no	—
64	C₄×C₁₉	—	2	2	no	—
65	C₄×C₁₉	—	2	4	no	—
66	C₄×C₁₉	—	2	2	no	—
67	C₄×C₁₉	C₈²	1	1	yes	characteristic
68	C₄×C₁₉	#322	1	1	yes	characteristic
69	C₄×C₁₉	#322	1	2	yes	—
70	C₂×C₄×C₈	—	19	4	no	—
71	C₂×C₄×C₈	Dic₁₉	1	2	yes	—
72	C₄³	C₂×D₁₉	1	1	yes	characteristic
73	#336	—	2	2	no	—
74	#336	—	38	2	no	—
75	#336	—	38	2	no	—
76	C₂×C₁₉	#1273	1	1	yes	characteristic
77	C₂×C₁₉	#1274	1	2	yes	—
78	C₂×C₁₉	#1274	1	1	yes	characteristic
79	C₂×C₁₉	#1275	1	2	yes	—
80	C₂×C₁₉	#1275	1	1	yes	characteristic
81	C₂²×C₈	—	2	2	no	—
82	C₂²×C₈	—	38	4	no	—
83	C₂×C₄²	Dic₃₈	1	1	yes	characteristic
84	C₂×C₄²	C₄×D₁₉	1	2	yes	—
85	C₂×C₄²	D₇₆	1	1	yes	characteristic
86	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
87	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
88	C₄×C₈	—	2	2	no	—
89	C₄×C₈	—	19	8	no	—
90	C₄×C₈	—	38	4	no	—
91	C₄×C₈	C₁₉⋊C₈	1	4	yes	complemented
92	C₁₉	#7014	1	1	yes	characteristic, complemented, Sylow
93	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
94	C₂²×C₄	Dic₁₉⋊C₄	1	2	yes	—
95	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
96	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
97	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
98	C₂×C₈	—	2	4	no	—
99	C₂×C₈	—	4	4	no	—
100	C₂×C₈	—	38	8	no	—
101	C₂×C₈	—	76	4	no	—
102	C₂×C₈	—	76	4	no	—
103	C₄²	—	4	1	no	—
104	C₄²	—	4	1	no	—
105	C₄²	—	4	2	no	—
106	C₄²	C₈×D₁₉	1	4	yes	—
107	C₄²	#64515	1	4	yes	—
108	C₄²	C₂×C₁₉⋊C₈	1	2	yes	—
109	C₄²	#64520	1	2	yes	—
110	C₂³	C₁₉⋊#95	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	2	1	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
119	C₂×C₄	#10597260	1	1	yes	characteristic
120	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	2	yes	—
121	C₂×C₄	C₈×Dic₁₉	1	2	yes	—
122	C₂×C₄	Dic₁₉⋊C₈	1	4	yes	—
123	C₂×C₄	#10597272	1	2	yes	—
124	C₂×C₄	(C₂×D₁₉)⋊C₈	1	4	yes	—
125	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
126	C₈	—	4	4	no	—
127	C₈	—	76	8	no	—
128	C₂²	#11926298	1	2	yes	—
129	C₂²	#11926299	1	1	yes	characteristic
130	C₂²	#11926300	1	2	yes	—
131	C₂²	#11926301	1	1	yes	characteristic
132	C₂²	C₁₉⋊#338	1	1	yes	characteristic
133	C₄	—	2	4	no	—
134	C₄	—	2	2	no	—
135	C₄	—	2	4	no	—
136	C₄	—	2	2	no	—
137	C₄	C₈×C₁₉⋊C₈	1	1	yes	characteristic
138	C₄	#11926265	1	1	yes	characteristic
139	C₄	#11926266	1	2	yes	—
140	C₂	C₁₉⋊#1273	1	1	yes	characteristic
141	C₂	#14561463	1	2	yes	—
142	C₂	#14561464	1	1	yes	characteristic
143	C₂	#14561465	1	2	yes	—
144	C₂	#14561466	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563381

C₂

yes

maximal

C₁₉×#1744

C₂

yes

maximal, characteristic

C₂×C₄×C₁₉⋊C₈

C₄

yes

—

#11926299

—

#11926299

—

C₂×C₄×C₈×C₁₉

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

Q₈

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₈

yes

complemented

C₄×C₁₉⋊C₈

—

C₄×C₁₉⋊C₈

C₈

yes

complemented

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

C₂×C₈

yes

—

C₄²×C₁₉

M₁₆

yes

—

C₄²×C₁₉

M₁₆

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

C₄×C₈

yes

—

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

#97

yes

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₂×C₄×C₁₉

C₄⋊C₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1744

—

#1744

D₁₉

yes

characteristic

C₂²×C₁₉

#336

yes

—

C₂²×C₁₉

#336

yes

characteristic

C₂²×C₁₉

H(3,ℤ/4)

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₈²

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

Dic₁₉

yes

—

C₄³

C₂×D₁₉

yes

—

—

—

C₂×C₁₉

#1273

yes

characteristic

C₂×C₁₉

#1274

yes

—

C₂×C₁₉

#1274

yes

characteristic

C₂×C₁₉

#1275

yes

—

C₂×C₁₉

#1275

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

Dic₃₈

yes

characteristic

C₂×C₄²

C₄×D₁₉

yes

—

C₂×C₄²

D₇₆

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₄²

C₂²⋊D₁₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₁₉⋊C₈

yes

complemented

C₁₉

#7014

yes

characteristic, complemented, Sylow

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

C₂²×C₄

Dic₁₉⋊C₄

yes

—

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₈×D₁₉

yes

—

107

C₄²

#64515

yes

—

108

C₄²

C₂×C₁₉⋊C₈

yes

—

109

C₄²

#64520

yes

—

110

C₂³

C₁₉⋊#95

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

C₄×C₁₉⋊C₈

yes

characteristic

119

C₂×C₄

#10597260

yes

characteristic

120

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

—

121

C₂×C₄

C₈×Dic₁₉

yes

—

122

C₂×C₄

Dic₁₉⋊C₈

yes

—

123

C₂×C₄

#10597272

yes

—

124

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

—

125

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

—

126

C₈

—

127

C₈

—

128

C₂²

#11926298

yes

—

129

C₂²

#11926299

yes

characteristic

130

C₂²

#11926300

yes

—

131

C₂²

#11926301

yes

characteristic

132

C₂²

C₁₉⋊#338

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

C₈×C₁₉⋊C₈

yes

characteristic

138

C₄

#11926265

yes

characteristic

139

C₄

#11926266

yes

—

140

C₂

C₁₉⋊#1273

yes

characteristic

141

C₂

#14561463

yes

—

142

C₂

#14561464

yes

characteristic

143

C₂

#14561465

yes

—

144

C₂

#14561466

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₄×Dic₁₉
commutator	C₄×C₁₉	C₈²
Frattini	C₄³	C₂×D₁₉
Fitting	C₁₉×#1744	C₂
socle, prime radical	C₂³×C₁₉	#95
cosocle	C₄³×C₁₉	C₂²
hypercenter	#1744	D₁₉
hypocenter	C₁₉	#7014
LCS	G ▷ C₄×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1744

subgroup

G/H

center

C₂²×C₄

C₄×Dic₁₉

commutator

C₄×C₁₉

C₈²

Frattini

C₄³

C₂×D₁₉

Fitting

C₁₉×#1744

C₂

socle, prime radical

C₂³×C₁₉

#95

cosocle

C₄³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₄×C₁₉ ▷ C₁₉

C₁ ◁ C₂²×C₄ ◁ #1744

N	H ≅ G/N	type
17. C₄×C₈×C₁₉	C₈	semidirect
19. C₄×C₁₉⋊C₈	C₈	semidirect
91. C₄×C₈	C₁₉⋊C₈	semidirect
92. C₁₉	#7014	semidirect

H ≅ G/N

type

17. C₄×C₈×C₁₉

C₈

semidirect

19. C₄×C₁₉⋊C₈

C₈

semidirect

91. C₄×C₈

C₁₉⋊C₈

semidirect

92. C₁₉

#7014

semidirect

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

subgroup	index
#14563381	2
C₁₉×#1744	2
#7014	19

subgroup

index

#14563381

C₁₉×#1744

#7014

Subgroups — C₁₉⋊#7014 #18069065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19⋊#7014 #18069065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉⋊#7014 #18069065