Group #18013093 — subgroups

Subgroups — C₁₉×#7134 #18013093

Order 4864.

230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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×#1994	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1276	C₂	1	2	yes	maximal
3	C₁₉×#533	C₄	1	1	yes	characteristic
4	C₁₉×#431	—	2	2	no	—
5	C₁₉×#423	C₄	1	1	yes	characteristic
6	C₄³×C₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×#339	—	2	2	no	—
8	C₂×M₁₆×C₁₉	—	2	1	no	—
9	C₁₉×C₄⋊Q₈	—	2	1	no	—
10	C₁₉×#125	C₈	1	2	yes	complemented
11	C₁₉×C₂²⋊Q₈	—	4	1	no	—
12	C₄×Q₈×C₁₉	—	4	1	no	—
13	C₁₉×#117	—	2	1	no	—
14	C₂×C₄²×C₁₉	—	4	1	no	—
15	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₉	D₄	1	2	yes	—
17	C₁₉×C₄⋊C₈	—	2	4	no	—
18	C₁₉×C₄⋊C₈	—	4	1	no	—
19	C₁₉×C₂²⋊C₈	—	4	2	no	—
20	C₄×C₈×C₁₉	—	4	2	no	—
21	C₂×Q₈×C₁₉	—	4	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	—	2	2	no	—
24	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	M₁₆×C₁₉	—	4	2	no	—
26	C₂×C₈×C₁₉	—	4	4	no	—
27	C₂×C₈×C₁₉	—	4	1	no	—
28	C₄⋊C₄×C₁₉	—	2	2	no	—
29	C₄⋊C₄×C₁₉	—	4	2	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₂²⋊C₄×C₁₉	—	4	1	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	—	2	2	no	—
34	C₄²×C₁₉	—	4	4	no	—
35	C₄²×C₁₉	—	4	1	no	—
36	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
37	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
38	C₄²×C₁₉	SD₁₆	1	2	yes	—
39	C₄²×C₁₉	Q₁₆	1	2	yes	—
40	#7134	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂³×C₁₉	#99	1	1	yes	characteristic
42	Q₈×C₁₉	—	8	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	—	2	2	no	—
47	C₂×C₄×C₁₉	—	4	4	no	—
48	C₂×C₄×C₁₉	—	4	2	no	—
49	C₂×C₄×C₁₉	—	4	2	no	—
50	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
51	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
52	C₂×C₄×C₁₉	#103	1	2	yes	—
53	C₂×C₄×C₁₉	#104	1	2	yes	—
54	C₈×C₁₉	—	8	4	no	—
55	C₈×C₁₉	—	8	1	no	—
56	#1994	C₂×C₁₉	1	1	yes	characteristic
57	#1276	C₂×C₁₉	1	2	yes	—
58	C₂²×C₁₉	—	4	1	no	—
59	C₂²×C₁₉	#323	1	1	yes	characteristic
60	C₂²×C₁₉	#328	1	2	yes	—
61	C₄×C₁₉	—	2	4	no	—
62	C₄×C₁₉	—	2	2	no	—
63	C₄×C₁₉	—	4	1	no	—
64	C₄×C₁₉	—	4	2	no	—
65	C₄×C₁₉	—	8	2	no	—
66	C₄×C₁₉	Q₈⋊C₈	1	2	yes	—
67	C₄×C₁₉	#329	1	1	yes	characteristic
68	C₄×C₁₉	#333	1	1	yes	characteristic
69	#533	C₄×C₁₉	1	1	yes	characteristic
70	#431	—	2	2	no	—
71	#423	C₄×C₁₉	1	1	yes	characteristic
72	C₄³	C₂²×C₁₉	1	1	yes	characteristic
73	#339	—	2	2	no	—
74	C₂×C₁₉	—	2	1	no	—
75	C₂×C₁₉	—	2	2	no	—
76	C₂×C₁₉	#1272	1	1	yes	characteristic
77	C₂×M₁₆	—	2	1	no	—
78	C₄⋊Q₈	—	2	1	no	—
79	#125	C₈×C₁₉	1	2	yes	complemented
80	C₂²⋊Q₈	—	4	1	no	—
81	C₄×Q₈	—	4	1	no	—
82	#117	—	2	1	no	—
83	C₂×C₄²	—	4	1	no	—
84	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
85	C₂×C₄²	D₄×C₁₉	1	2	yes	—
86	C₄⋊C₈	—	2	4	no	—
87	C₄⋊C₈	—	4	1	no	—
88	C₂²⋊C₈	—	4	2	no	—
89	C₄×C₈	—	4	2	no	—
90	C₁₉	#7134	1	1	yes	characteristic, direct product factor, Sylow
91	C₂×Q₈	—	4	1	no	—
92	C₂²×C₄	—	2	2	no	—
93	C₂²×C₄	—	2	1	no	—
94	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
95	M₁₆	—	4	2	no	—
96	C₂×C₈	—	4	4	no	—
97	C₂×C₈	—	4	1	no	—
98	C₄⋊C₄	—	2	2	no	—
99	C₄⋊C₄	—	4	2	no	—
100	C₄⋊C₄	—	4	1	no	—
101	C₂²⋊C₄	—	4	1	no	—
102	C₄²	—	2	1	no	—
103	C₄²	—	2	2	no	—
104	C₄²	—	4	4	no	—
105	C₄²	—	4	1	no	—
106	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
107	C₄²	M₁₆×C₁₉	1	1	yes	characteristic
108	C₄²	SD₁₆×C₁₉	1	2	yes	—
109	C₄²	Q₁₆×C₁₉	1	2	yes	—
110	C₂³	C₁₉×#99	1	1	yes	characteristic
111	Q₈	—	8	2	no	—
112	C₂×C₄	—	2	1	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	1	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	4	4	no	—
117	C₂×C₄	—	4	2	no	—
118	C₂×C₄	—	4	2	no	—
119	C₂×C₄	C₁₉×C₂²⋊C₈	1	1	yes	characteristic
120	C₂×C₄	C₁₉×#100	1	1	yes	characteristic
121	C₂×C₄	C₁₉×#103	1	2	yes	—
122	C₂×C₄	C₁₉×#104	1	2	yes	—
123	C₈	—	8	4	no	—
124	C₈	—	8	1	no	—
125	C₂²	—	4	1	no	—
126	C₂²	C₁₉×#323	1	1	yes	characteristic
127	C₂²	C₁₉×#328	1	2	yes	—
128	C₄	—	2	4	no	—
129	C₄	—	2	2	no	—
130	C₄	—	4	1	no	—
131	C₄	—	4	2	no	—
132	C₄	—	8	2	no	—
133	C₄	C₁₉×Q₈⋊C₈	1	2	yes	—
134	C₄	C₁₉×#329	1	1	yes	characteristic
135	C₄	C₁₉×#333	1	1	yes	characteristic
136	C₂	—	2	1	no	—
137	C₂	—	2	2	no	—
138	C₂	C₁₉×#1272	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#1994

C₂

yes

maximal, characteristic

C₁₉×#1276

C₂

yes

maximal

C₁₉×#533

C₄

yes

characteristic

C₁₉×#431

—

C₁₉×#423

C₄

yes

characteristic

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#339

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×#125

C₈

yes

complemented

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

—

C₄²×C₁₉

Q₁₆

yes

—

#7134

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#99

yes

characteristic

Q₈×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

C₂²⋊C₈

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#1994

C₂×C₁₉

yes

characteristic

#1276

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₂²×C₁₉

#328

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

Q₈⋊C₈

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

characteristic

#431

—

#423

C₄×C₁₉

yes

characteristic

C₄³

C₂²×C₁₉

yes

characteristic

#339

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1272

yes

characteristic

C₂×M₁₆

—

C₄⋊Q₈

—

#125

C₈×C₁₉

yes

complemented

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

C₂×C₄²

D₄×C₁₉

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₁₉

#7134

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₂²⋊C₄

—

102

C₄²

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₂×C₈×C₁₉

yes

characteristic

107

C₄²

M₁₆×C₁₉

yes

characteristic

108

C₄²

SD₁₆×C₁₉

yes

—

109

C₄²

Q₁₆×C₁₉

yes

—

110

C₂³

C₁₉×#99

yes

characteristic

111

Q₈

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₁₉×C₂²⋊C₈

yes

characteristic

120

C₂×C₄

C₁₉×#100

yes

characteristic

121

C₂×C₄

C₁₉×#103

yes

—

122

C₂×C₄

C₁₉×#104

yes

—

123

C₈

—

124

C₈

—

125

C₂²

—

126

C₂²

C₁₉×#323

yes

characteristic

127

C₂²

C₁₉×#328

yes

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

C₁₉×Q₈⋊C₈

yes

—

134

C₄

C₁₉×#329

yes

characteristic

135

C₄

C₁₉×#333

yes

characteristic

136

C₂

—

137

C₂

—

138

C₂

C₁₉×#1272

yes

characteristic

	subgroup	G/H
center	C₄×C₁₉	#333
commutator	C₄²	C₂×C₈×C₁₉
Frattini, cosocle	C₄³	C₂²×C₁₉
socle	C₂×C₁₉	#1272
prime radical	C₂³×C₁₉	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₄³×C₁₉ ◁ G

subgroup

G/H

center

C₄×C₁₉

#333

commutator

C₄²

C₂×C₈×C₁₉

Frattini, cosocle

C₄³

C₂²×C₁₉

C₂×C₁₉

C₂³×C₁₉

G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₄³×C₁₉ ◁ G

N	H ≅ G/N	type
10. C₁₉×#125	C₈	semidirect
40. #7134	C₁₉	direct (N × H)
79. #125	C₈×C₁₉	semidirect
90. C₁₉	#7134	direct (N × H)

H ≅ G/N

type

10. C₁₉×#125

C₈

semidirect

40. #7134

C₁₉

direct (N × H)

79. #125

C₈×C₁₉

semidirect

90. C₁₉

#7134

direct (N × H)

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

subgroup	index
C₁₉×#1994	2
C₁₉×#1276	2
#7134	19

subgroup

index

C₁₉×#1994

C₁₉×#1276

#7134

Subgroups — C₁₉×#7134 #18013093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7134 #18013093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7134 #18013093