Group #18013307 — subgroups

Subgroups — C₁₉×#7348 #18013307

Order 4864.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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×#1820	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1317	C₂	1	2	yes	maximal
3	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
4	C₁₉×#381	C₄	1	1	yes	characteristic
5	C₁₉×#381	C₂²	1	1	yes	characteristic
6	C₁₉×#342	—	2	2	no	—
7	C₁₉×#323	—	2	2	no	—
8	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
9	C₁₉×#117	—	4	1	no	—
10	C₁₉×#117	—	4	1	no	—
11	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
12	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
14	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
15	C₂×C₄²×C₁₉	C₈	1	2	yes	complemented
16	C₁₉×C₂²⋊C₈	—	4	2	no	—
17	C₁₉×#95	—	4	1	no	—
18	C₁₉×#95	—	4	1	no	—
19	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄×C₁₉	—	2	1	no	—
22	C₂²×C₄×C₁₉	—	2	2	no	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	—	4	2	no	—
25	C₂²×C₄×C₁₉	—	4	1	no	—
26	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
27	C₂²×C₄×C₁₉	M₁₆	1	1	yes	characteristic
28	C₂×C₈×C₁₉	—	8	2	no	—
29	C₄⋊C₄×C₁₉	—	4	2	no	—
30	C₂²⋊C₄×C₁₉	—	4	1	no	—
31	C₂²⋊C₄×C₁₉	—	4	1	no	—
32	C₂²⋊C₄×C₁₉	—	4	2	no	—
33	C₂²⋊C₄×C₁₉	—	4	2	no	—
34	C₄²×C₁₉	—	4	2	no	—
35	#7348	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂³×C₁₉	—	2	2	no	—
37	C₂³×C₁₉	—	8	1	no	—
38	C₂³×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₂³×C₁₉	#99	1	1	yes	characteristic
40	C₂³×C₁₉	#100	1	1	yes	characteristic
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	4	2	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	—	4	1	no	—
46	C₂×C₄×C₁₉	—	4	1	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	8	2	no	—
50	C₂×C₄×C₁₉	—	8	2	no	—
51	C₂×C₄×C₁₉	—	8	1	no	—
52	C₂×C₄×C₁₉	—	8	2	no	—
53	C₈×C₁₉	—	16	2	no	—
54	#1820	C₂×C₁₉	1	1	yes	characteristic
55	#1317	C₂×C₁₉	1	2	yes	—
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	2	1	no	—
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	—	4	1	no	—
60	C₂²×C₁₉	—	4	1	no	—
61	C₂²×C₁₉	—	8	2	no	—
62	C₂²×C₁₉	#323	1	1	yes	characteristic
63	C₂²×C₁₉	#352	1	2	yes	—
64	C₄×C₁₉	—	4	1	no	—
65	C₄×C₁₉	—	4	1	no	—
66	C₄×C₁₉	—	8	2	no	—
67	C₄×C₁₉	—	8	2	no	—
68	C₄×C₁₉	—	16	1	no	—
69	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
70	#381	C₄×C₁₉	1	1	yes	characteristic
71	#381	C₂²×C₁₉	1	1	yes	characteristic
72	#342	—	2	2	no	—
73	#323	—	2	2	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	—	2	2	no	—
76	C₂×C₁₉	—	4	1	no	—
77	C₂×C₁₉	—	4	1	no	—
78	C₂×C₁₉	#1317	1	1	yes	characteristic
79	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
80	#117	—	4	1	no	—
81	#117	—	4	1	no	—
82	C₂×C₄⋊C₄	—	2	1	no	—
83	C₂×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
86	C₂×C₄²	C₈×C₁₉	1	2	yes	complemented
87	C₂²⋊C₈	—	4	2	no	—
88	#95	—	4	1	no	—
89	#95	—	4	1	no	—
90	C₁₉	#7348	1	1	yes	characteristic, direct product factor, Sylow
91	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
92	C₂²×C₄	—	2	1	no	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	—	2	2	no	—
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	—	4	2	no	—
97	C₂²×C₄	—	4	1	no	—
98	C₂²×C₄	C₂×C₈×C₁₉	1	1	yes	characteristic
99	C₂²×C₄	M₁₆×C₁₉	1	1	yes	characteristic
100	C₂×C₈	—	8	2	no	—
101	C₄⋊C₄	—	4	2	no	—
102	C₂²⋊C₄	—	4	1	no	—
103	C₂²⋊C₄	—	4	1	no	—
104	C₂²⋊C₄	—	4	2	no	—
105	C₂²⋊C₄	—	4	2	no	—
106	C₄²	—	4	2	no	—
107	C₂³	—	2	2	no	—
108	C₂³	—	8	1	no	—
109	C₂³	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
110	C₂³	C₁₉×#99	1	1	yes	characteristic
111	C₂³	C₁₉×#100	1	1	yes	characteristic
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	1	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	2	no	—
116	C₂×C₄	—	4	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	—	4	2	no	—
120	C₂×C₄	—	8	2	no	—
121	C₂×C₄	—	8	2	no	—
122	C₂×C₄	—	8	1	no	—
123	C₂×C₄	—	8	2	no	—
124	C₈	—	16	2	no	—
125	C₂²	—	2	1	no	—
126	C₂²	—	2	1	no	—
127	C₂²	—	4	1	no	—
128	C₂²	—	4	1	no	—
129	C₂²	—	4	1	no	—
130	C₂²	—	8	2	no	—
131	C₂²	C₁₉×#323	1	1	yes	characteristic
132	C₂²	C₁₉×#352	1	2	yes	—
133	C₄	—	4	1	no	—
134	C₄	—	4	1	no	—
135	C₄	—	8	2	no	—
136	C₄	—	8	2	no	—
137	C₄	—	16	1	no	—
138	C₂	—	2	1	no	—
139	C₂	—	2	2	no	—
140	C₂	—	4	1	no	—
141	C₂	—	4	1	no	—
142	C₂	C₁₉×#1317	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1820

C₂

yes

maximal, characteristic

C₁₉×#1317

C₂

yes

maximal

C₂×C₁₉×#117

C₄

yes

characteristic

C₁₉×#381

C₄

yes

characteristic

C₁₉×#381

C₂²

yes

characteristic

C₁₉×#342

—

C₁₉×#323

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₈

yes

complemented

C₁₉×C₂²⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₁₉

M₁₆

yes

characteristic

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#7348

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²⋊C₈

yes

C₂³×C₁₉

yes

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₈×C₁₉

—

#1820

C₂×C₁₉

yes

characteristic

#1317

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₂²×C₁₉

#352

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#117

C₄×C₁₉

yes

characteristic

#381

C₄×C₁₉

yes

characteristic

#381

C₂²×C₁₉

yes

characteristic

#342

—

#323

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1317

yes

characteristic

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

D₄×C₁₉

yes

—

C₂×C₄²

C₈×C₁₉

yes

complemented

C₂²⋊C₈

—

#95

—

#95

—

C₁₉

#7348

yes

characteristic, direct product factor, Sylow

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₈×C₁₉

yes

characteristic

C₂²×C₄

M₁₆×C₁₉

yes

characteristic

100

C₂×C₈

—

101

C₄⋊C₄

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₄²

—

107

C₂³

—

108

C₂³

—

109

C₂³

C₁₉×C₂²⋊C₈

yes

characteristic

110

C₂³

C₁₉×#99

yes

characteristic

111

C₂³

C₁₉×#100

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₈

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

C₁₉×#323

yes

characteristic

132

C₂²

C₁₉×#352

yes

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

—

137

C₄

—

138

C₂

—

139

C₂

—

140

C₂

—

141

C₂

—

142

C₂

C₁₉×#1317

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#1317
commutator	C₂²×C₄	C₂×C₈×C₁₉
Frattini, cosocle	#381	C₂²×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₁₉×#381 ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#1317

commutator

C₂²×C₄

C₂×C₈×C₁₉

Frattini, cosocle

#381

C₂²×C₁₉

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₁₉×#381 ◁ G

N	H ≅ G/N	type
15. C₂×C₄²×C₁₉	C₈	semidirect
35. #7348	C₁₉	direct (N × H)
86. C₂×C₄²	C₈×C₁₉	semidirect
90. C₁₉	#7348	direct (N × H)

H ≅ G/N

type

15. C₂×C₄²×C₁₉

C₈

semidirect

35. #7348

C₁₉

direct (N × H)

86. C₂×C₄²

C₈×C₁₉

semidirect

90. C₁₉

#7348

direct (N × H)

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

subgroup	index
C₁₉×#1820	2
C₁₉×#1317	2
#7348	19

subgroup

index

C₁₉×#1820

C₁₉×#1317

#7348

Subgroups — C₁₉×#7348 #18013307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7348 #18013307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7348 #18013307