Group #18069390 — subgroups

Subgroups — #18069390

Order 4864.

210 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14565438	C₂	1	2	yes	maximal
2	C₂×C₁₉×#322	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉⋊C₁₆)	—	2	2	no	—
4	C₂²⋊(C₁₉⋊C₁₆)	—	2	2	no	—
5	#11926320	C₄	1	4	yes	—
6	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₉	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#322	—	2	2	no	—
10	C₂²×C₈×C₁₉	—	2	1	no	—
11	C₂²×C₈×C₁₉	C₈	1	2	yes	—
12	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
14	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₄×C₈×C₁₉	—	2	1	no	—
16	C₄×C₈×C₁₉	—	2	1	no	—
17	C₄×C₈×C₁₉	—	2	1	no	—
18	C₄×C₈×C₁₉	C₈	1	2	yes	—
19	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₄×C₈×C₁₉	D₄	1	2	yes	—
21	C₂×C₁₉⋊C₁₆	—	2	4	no	—
22	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
25	C₂×C₈×C₁₉	—	2	4	no	—
26	C₂×C₈×C₁₉	—	2	2	no	—
27	C₂×C₈×C₁₉	—	2	2	no	—
28	C₂×C₈×C₁₉	—	4	1	no	—
29	C₂×C₈×C₁₉	—	4	1	no	—
30	C₂×C₈×C₁₉	—	4	2	no	—
31	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
32	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
33	C₄²×C₁₉	C₄²	1	1	yes	characteristic
34	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
36	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
37	C₁₉⋊C₁₆	—	4	4	no	—
38	#7146	—	19	1	no	maximal, Sylow
39	C₂³×C₁₉	C₄⋊C₈	1	1	yes	characteristic
40	C₂×C₄×C₁₉	—	2	2	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	2	no	—
44	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₄×C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#97	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₄⋊C₈	1	1	yes	characteristic
50	C₈×C₁₉	—	2	4	no	—
51	C₈×C₁₉	—	2	2	no	—
52	C₈×C₁₉	—	2	2	no	—
53	C₈×C₁₉	—	4	2	no	—
54	#2163	—	19	2	no	—
55	C₂×#322	D₁₉	1	1	yes	characteristic
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	#336	1	1	yes	characteristic
59	C₂²×C₁₉	#364	1	2	yes	—
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	2	1	no	—
64	C₄×C₁₉	H(3,ℤ/4)	1	1	yes	characteristic
65	C₄×C₁₉	#338	1	1	yes	characteristic
66	C₄×C₁₉	#349	1	2	yes	—
67	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
68	C₂×C₄×C₈	Dic₁₉	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
70	C₄⋊C₁₆	—	38	2	no	—
71	C₂²⋊C₁₆	—	38	2	no	—
72	#346	—	19	4	no	—
73	#322	—	2	2	no	—
74	C₂×C₁₉	—	2	2	no	—
75	C₂×C₁₉	#1275	1	1	yes	characteristic
76	C₂×C₁₉	#1376	1	1	yes	characteristic
77	C₂×C₁₉	#1377	1	1	yes	characteristic
78	C₂²×C₈	—	2	1	no	—
79	C₂²×C₈	C₁₉⋊C₈	1	2	yes	—
80	C₂²×C₈	Dic₃₈	1	1	yes	characteristic
81	C₂²×C₈	D₇₆	1	1	yes	characteristic
82	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
83	C₂×C₁₆	—	38	4	no	—
84	C₄×C₈	—	2	1	no	—
85	C₄×C₈	—	2	1	no	—
86	C₄×C₈	—	2	1	no	—
87	C₄×C₈	C₁₉⋊C₈	1	2	yes	—
88	C₄×C₈	C₄×D₁₉	1	2	yes	—
89	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
90	C₁₉	#7146	1	1	yes	characteristic, complemented, Sylow
91	C₂²×C₄	C₂×C₁₉⋊C₈	1	1	yes	characteristic
92	C₂²×C₄	#64520	1	1	yes	characteristic
93	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
94	C₂×C₈	—	2	4	no	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	—	4	1	no	—
98	C₂×C₈	—	4	1	no	—
99	C₂×C₈	—	4	2	no	—
100	C₂×C₈	Dic₁₉⋊C₄	1	2	yes	—
101	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
102	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
103	C₄²	#64520	1	1	yes	characteristic
104	C₄²	C₄×Dic₁₉	1	1	yes	characteristic
105	C₄²	C₂²⋊Dic₁₉	1	1	yes	characteristic
106	C₁₆	—	76	4	no	—
107	C₂³	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
108	C₂×C₄	—	2	2	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	2	1	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	C₄×C₁₉⋊C₈	1	1	yes	characteristic
113	C₂×C₄	#10597260	1	1	yes	characteristic
114	C₂×C₄	C₄⋊(C₁₉⋊C₈)	1	1	yes	characteristic
115	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
116	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
117	C₂×C₄	C₁₉⋊#95	1	1	yes	characteristic
118	C₈	—	2	4	no	—
119	C₈	—	2	2	no	—
120	C₈	—	2	2	no	—
121	C₈	—	4	2	no	—
122	C₂²	—	2	1	no	—
123	C₂²	—	2	1	no	—
124	C₂²	#11926299	1	1	yes	characteristic
125	C₂²	#11926365	1	2	yes	—
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	2	1	no	—
129	C₄	—	2	1	no	—
130	C₄	#11926301	1	1	yes	characteristic
131	C₄	C₁₉⋊#338	1	1	yes	characteristic
132	C₄	#11926326	1	2	yes	—
133	C₂	—	2	2	no	—
134	C₂	#14561466	1	1	yes	characteristic
135	C₂	#14561717	1	1	yes	characteristic
136	C₂	#14561719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565438

C₂

yes

maximal

C₂×C₁₉×#322

C₂

yes

maximal, characteristic

C₄⋊(C₁₉⋊C₁₆)

—

C₂²⋊(C₁₉⋊C₁₆)

—

#11926320

C₄

yes

—

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₄

yes

characteristic

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₈

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₈

yes

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂×C₁₉⋊C₁₆

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₄²

yes

characteristic

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

#7146

—

maximal, Sylow

C₂³×C₁₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

C₄×C₈

yes

characteristic

C₂×C₄×C₁₉

#97

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₄⋊C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

#2163

—

C₂×#322

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#336

yes

characteristic

C₂²×C₁₉

#364

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂×C₄×C₈

Dic₁₉

yes

characteristic

C₂×C₄×C₈

Dic₁₉

yes

characteristic

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

C₂²×C₈

C₁₉⋊C₈

yes

—

C₂²×C₈

Dic₃₈

yes

characteristic

C₂²×C₈

D₇₆

yes

characteristic

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₁₉⋊C₈

yes

—

C₄×C₈

C₄×D₁₉

yes

—

C₄×C₈

C₂²⋊D₁₉

yes

—

C₁₉

#7146

yes

characteristic, complemented, Sylow

C₂²×C₄

C₂×C₁₉⋊C₈

yes

characteristic

C₂²×C₄

#64520

yes

characteristic

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

Dic₁₉⋊C₄

yes

—

101

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

102

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

103

C₄²

#64520

yes

characteristic

104

C₄²

C₄×Dic₁₉

yes

characteristic

105

C₄²

C₂²⋊Dic₁₉

yes

characteristic

106

C₁₆

—

107

C₂³

C₄⋊(C₁₉⋊C₈)

yes

characteristic

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₄×C₁₉⋊C₈

yes

characteristic

113

C₂×C₄

#10597260

yes

characteristic

114

C₂×C₄

C₄⋊(C₁₉⋊C₈)

yes

characteristic

115

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

116

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

117

C₂×C₄

C₁₉⋊#95

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

—

122

C₂²

—

123

C₂²

—

124

C₂²

#11926299

yes

characteristic

125

C₂²

#11926365

yes

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

#11926301

yes

characteristic

131

C₄

C₁₉⋊#338

yes

characteristic

132

C₄

#11926326

yes

—

133

C₂

—

134

C₂

#14561466

yes

characteristic

135

C₂

#14561717

yes

characteristic

136

C₂

#14561719

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₁₉⋊#95
commutator	C₂×C₄×C₁₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₉
Fitting	C₂×C₁₉×#322	C₂
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₄⋊C₈
cosocle	C₂×C₄×C₈×C₁₉	C₂²
hypercenter	C₂×#322	D₁₉
hypocenter	C₁₉	#7146
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

subgroup

G/H

center

C₂×C₄

C₁₉⋊#95

commutator

C₂×C₄×C₁₉

C₄×C₈

Frattini

C₂×C₄×C₈

C₂×D₁₉

Fitting

C₂×C₁₉×#322

C₂

socle

C₂²×C₁₉

#336

prime radical

C₂³×C₁₉

C₄⋊C₈

cosocle

C₂×C₄×C₈×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

N	H ≅ G/N	type
90. C₁₉	#7146	semidirect

H ≅ G/N

type

90. C₁₉

#7146

semidirect

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

subgroup	index
#14565438	2
C₂×C₁₉×#322	2
#7146	19

subgroup

index

#14565438

C₂×C₁₉×#322

#7146

Subgroups — #18069390

Conjugacy classes of subgroups

Complements

Maximal subgroups