Group #14559809 — subgroups

Subgroups — C₁₉×#1952 #14559809

Order 2432.

196 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 112 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	C₂×C₁₉×#108	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#428	C₂	1	2	yes	maximal
3	C₂×C₁₉×#107	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#405	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#343	C₂	1	2	yes	maximal
6	C₂×M₁₆×C₁₉	C₂²	1	2	yes	—
7	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#108	C₄	1	4	yes	complemented
12	C₁₉×#107	—	2	1	no	—
13	C₁₉×#107	—	2	1	no	—
14	C₁₉×#107	—	2	2	no	—
15	C₁₉×#106	—	2	2	no	—
16	C₁₉×#97	—	2	1	no	—
17	C₄×C₈×C₁₉	—	2	1	no	—
18	C₂²×C₄×C₁₉	—	2	2	no	—
19	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
20	M₁₆×C₁₉	—	2	2	no	—
21	M₁₆×C₁₉	—	2	1	no	—
22	M₁₆×C₁₉	C₂×C₄	1	4	yes	—
23	M₁₆×C₁₉	Q₈	1	2	yes	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	—	2	2	no	—
26	C₂×C₈×C₁₉	C₂×C₄	1	2	yes	—
27	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₈×C₁₉	Q₈	1	2	yes	—
30	C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
34	C₂²⋊C₄×C₁₉	—	2	1	no	—
35	C₄²×C₁₉	—	2	1	no	—
36	C₂³×C₁₉	#41	1	1	yes	characteristic
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	4	2	no	—
40	C₂×C₄×C₁₉	—	8	2	no	—
41	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₁₉	#41	1	1	yes	characteristic
47	C₈×C₁₉	—	2	4	no	—
48	C₈×C₁₉	—	2	2	no	—
49	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
50	C₈×C₁₉	C₄⋊C₄	1	2	yes	—
51	#1952	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
52	C₂²×C₁₉	—	2	1	no	—
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	C₄×Q₈	1	1	yes	characteristic
55	C₂²×C₁₉	#121	1	1	yes	characteristic
56	C₂²×C₁₉	#125	1	1	yes	characteristic
57	C₄×C₁₉	—	4	1	no	—
58	C₄×C₁₉	—	4	1	no	—
59	C₄×C₁₉	—	8	2	no	—
60	C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
62	C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
63	C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
64	C₂×#108	C₂×C₁₉	1	1	yes	characteristic
65	#428	C₂×C₁₉	1	2	yes	—
66	C₂×#107	C₂×C₁₉	1	1	yes	characteristic
67	#405	C₂×C₁₉	1	1	yes	characteristic
68	#343	C₂×C₁₉	1	2	yes	—
69	C₂×C₁₉	—	2	1	no	—
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	#389	1	1	yes	characteristic
72	C₂×C₁₉	#472	1	1	yes	characteristic
73	C₂×C₁₉	#473	1	1	yes	characteristic
74	C₂×M₁₆	C₂²×C₁₉	1	2	yes	—
75	C₂×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
76	C₂²×C₈	C₂²×C₁₉	1	1	yes	characteristic
77	#117	C₂²×C₁₉	1	1	yes	characteristic
78	C₂×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
79	#108	C₄×C₁₉	1	4	yes	complemented
80	#107	—	2	1	no	—
81	#107	—	2	1	no	—
82	#107	—	2	2	no	—
83	#106	—	2	2	no	—
84	#97	—	2	1	no	—
85	C₄×C₈	—	2	1	no	—
86	C₁₉	#1952	1	1	yes	characteristic, direct product factor, Sylow
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	C₂³×C₁₉	1	1	yes	characteristic
89	M₁₆	—	2	2	no	—
90	M₁₆	—	2	1	no	—
91	M₁₆	C₂×C₄×C₁₉	1	4	yes	—
92	M₁₆	Q₈×C₁₉	1	2	yes	—
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	2	2	no	—
95	C₂×C₈	C₂×C₄×C₁₉	1	2	yes	—
96	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
97	C₂×C₈	D₄×C₁₉	1	1	yes	characteristic
98	C₂×C₈	Q₈×C₁₉	1	2	yes	—
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	2	2	no	—
101	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
102	C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
103	C₂²⋊C₄	—	2	1	no	—
104	C₄²	—	2	1	no	—
105	C₂³	#41×C₁₉	1	1	yes	characteristic
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	8	2	no	—
110	C₂×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
111	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
112	C₂×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
113	C₂×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
114	C₂×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
115	C₂×C₄	#41×C₁₉	1	1	yes	characteristic
116	C₈	—	2	4	no	—
117	C₈	—	2	2	no	—
118	C₈	C₄⋊C₄×C₁₉	1	2	yes	—
119	C₈	C₄⋊C₄×C₁₉	1	2	yes	—
120	C₂²	—	2	1	no	—
121	C₂²	—	2	1	no	—
122	C₂²	C₄×Q₈×C₁₉	1	1	yes	characteristic
123	C₂²	C₁₉×#121	1	1	yes	characteristic
124	C₂²	C₁₉×#125	1	1	yes	characteristic
125	C₄	—	4	1	no	—
126	C₄	—	4	1	no	—
127	C₄	—	8	2	no	—
128	C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
129	C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
130	C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
131	C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	2	1	no	—
134	C₂	C₁₉×#389	1	1	yes	characteristic
135	C₂	C₁₉×#472	1	1	yes	characteristic
136	C₂	C₁₉×#473	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#108

C₂

yes

maximal, characteristic

C₁₉×#428

C₂

yes

maximal

C₂×C₁₉×#107

C₂

yes

maximal, characteristic

C₁₉×#405

C₂

yes

maximal, characteristic

C₁₉×#343

C₂

yes

maximal

C₂×M₁₆×C₁₉

C₂²

yes

—

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

C₂²×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#117

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₁₉×#108

C₄

yes

complemented

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#107

—

C₁₉×#106

—

C₁₉×#97

—

C₄×C₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

C₂×C₄

yes

—

M₁₆×C₁₉

Q₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×C₄

yes

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

Q₈

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₄⋊C₄×C₁₉

D₄

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₂³×C₁₉

#41

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₉

#41

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₄⋊C₄

yes

—

C₈×C₁₉

C₄⋊C₄

yes

—

#1952

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₄×Q₈

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₉

C₄×D₄

yes

characteristic

C₄×C₁₉

C₂²⋊Q₈

yes

characteristic

C₄×C₁₉

C₄⋊Q₈

yes

characteristic

C₂×#108

C₂×C₁₉

yes

characteristic

#428

C₂×C₁₉

yes

—

C₂×#107

C₂×C₁₉

yes

characteristic

#405

C₂×C₁₉

yes

characteristic

#343

C₂×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

C₂²×C₁₉

yes

—

C₂×M₁₆

C₂²×C₁₉

yes

characteristic

C₂²×C₈

C₂²×C₁₉

yes

characteristic

#117

C₂²×C₁₉

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₁₉

yes

—

#108

C₄×C₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₁₉

#1952

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

C₂³×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

C₂×C₄×C₁₉

yes

—

M₁₆

Q₈×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×C₄×C₁₉

yes

—

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

D₄×C₁₉

yes

characteristic

C₂×C₈

Q₈×C₁₉

yes

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

D₄×C₁₉

yes

characteristic

102

C₄⋊C₄

D₄×C₁₉

yes

characteristic

103

C₂²⋊C₄

—

104

C₄²

—

105

C₂³

#41×C₁₉

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₂²×C₄×C₁₉

yes

characteristic

111

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

112

C₂×C₄

C₂×D₄×C₁₉

yes

characteristic

113

C₂×C₄

C₂×Q₈×C₁₉

yes

characteristic

114

C₂×C₄

C₂×Q₈×C₁₉

yes

characteristic

115

C₂×C₄

#41×C₁₉

yes

characteristic

116

C₈

—

117

C₈

—

118

C₈

C₄⋊C₄×C₁₉

yes

—

119

C₈

C₄⋊C₄×C₁₉

yes

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₄×Q₈×C₁₉

yes

characteristic

123

C₂²

C₁₉×#121

yes

characteristic

124

C₂²

C₁₉×#125

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

C₂×C₄⋊C₄×C₁₉

yes

characteristic

129

C₄

C₄×D₄×C₁₉

yes

characteristic

130

C₄

C₁₉×C₂²⋊Q₈

yes

characteristic

131

C₄

C₁₉×C₄⋊Q₈

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

C₁₉×#389

yes

characteristic

135

C₂

C₁₉×#472

yes

characteristic

136

C₂

C₁₉×#473

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#121
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂³×C₁₉	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#121

commutator

C₂×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂²×C₄

C₂³×C₁₉

C₂³×C₁₉

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
11. C₁₉×#108	C₄	semidirect
51. #1952	C₁₉	direct (N × H)
79. #108	C₄×C₁₉	semidirect
86. C₁₉	#1952	direct (N × H)

H ≅ G/N

type

11. C₁₉×#108

C₄

semidirect

51. #1952

C₁₉

direct (N × H)

79. #108

C₄×C₁₉

semidirect

86. C₁₉

#1952

direct (N × H)

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

subgroup	index
C₂×C₁₉×#108	2
C₁₉×#428	2
C₂×C₁₉×#107	2
C₁₉×#405	2
C₁₉×#343	2
#1952	19

subgroup

index

C₂×C₁₉×#108

C₁₉×#428

C₂×C₁₉×#107

C₁₉×#405

C₁₉×#343

#1952

Subgroups — C₁₉×#1952 #14559809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#1952 #14559809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#1952 #14559809