Group #18013200 — subgroups

Subgroups — C₁₉×#7241 #18013200

Order 4864.

206 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 110 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×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1567	C₂	1	2	yes	maximal
3	C₂²×C₁₆×C₁₉	C₄	1	2	yes	—
4	C₁₉×#423	—	2	2	no	—
5	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₁₉×C₄⋊C₁₆	—	2	2	no	—
7	C₁₉×#335	—	2	2	no	—
8	C₁₉×#335	C₄	1	4	yes	—
9	C₂×M₁₆×C₁₉	—	4	2	no	—
10	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₉	Q₈	1	1	yes	characteristic
12	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₁₉	—	2	2	no	—
14	C₂×C₁₆×C₁₉	—	4	2	no	—
15	C₁₉×C₄⋊C₈	—	2	4	no	—
16	C₁₉×C₄⋊C₈	—	4	2	no	—
17	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₁₉	D₄	1	2	yes	—
19	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	D₈	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	Q₁₆	1	1	yes	characteristic
22	M₁₆×C₁₉	—	8	2	no	—
23	M₁₆×C₁₉	—	8	2	no	—
24	C₂×C₈×C₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	—	4	1	no	—
27	C₂×C₈×C₁₉	—	4	4	no	—
28	C₂×C₈×C₁₉	C₄²	1	1	yes	characteristic
29	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₉	C₄⋊C₄	1	2	yes	—
31	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
32	C₄²×C₁₉	SD₁₆	1	2	yes	—
33	C₁₆×C₁₉	—	4	2	no	—
34	#7241	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂³×C₁₉	#107	1	1	yes	characteristic
36	C₂×C₄×C₁₉	—	2	1	no	—
37	C₂×C₄×C₁₉	—	2	1	no	—
38	C₂×C₄×C₁₉	—	4	1	no	—
39	C₂×C₄×C₁₉	#95	1	1	yes	characteristic
40	C₂×C₄×C₁₉	#102	1	2	yes	—
41	C₂×C₄×C₁₉	#103	1	2	yes	—
42	C₂×C₄×C₁₉	#106	1	1	yes	characteristic
43	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
44	C₂×C₄×C₁₉	SD₃₂	1	2	yes	—
45	C₂×C₄×C₁₉	Q₃₂	1	1	yes	characteristic
46	C₈×C₁₉	—	2	2	no	—
47	C₈×C₁₉	—	2	1	no	—
48	C₈×C₁₉	—	8	4	no	—
49	C₈×C₁₉	#100	1	1	yes	characteristic
50	C₈×C₁₉	#101	1	1	yes	characteristic
51	C₂×C₄⋊C₁₆	C₂×C₁₉	1	1	yes	characteristic
52	#1567	C₂×C₁₉	1	2	yes	—
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	2	1	no	—
55	C₂²×C₁₉	#340	1	1	yes	characteristic
56	C₂²×C₁₉	#366	1	1	yes	characteristic
57	C₂²×C₁₉	#367	1	1	yes	characteristic
58	C₄×C₁₉	—	2	1	no	—
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	#338	1	1	yes	characteristic
61	C₄×C₁₉	#343	1	1	yes	characteristic
62	C₄×C₁₉	#357	1	2	yes	—
63	C₄×C₁₉	#358	1	2	yes	—
64	C₂²×C₁₆	C₄×C₁₉	1	2	yes	—
65	#423	—	2	2	no	—
66	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
67	C₄⋊C₁₆	—	2	2	no	—
68	#335	—	2	2	no	—
69	#335	C₄×C₁₉	1	4	yes	—
70	C₂×C₁₉	—	2	1	no	—
71	C₂×C₁₉	—	2	1	no	—
72	C₂×C₁₉	#1292	1	1	yes	characteristic
73	C₂×C₁₉	#1380	1	1	yes	characteristic
74	C₂×C₁₉	#1385	1	1	yes	characteristic
75	C₂×M₁₆	—	4	2	no	—
76	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
77	C₂²×C₈	Q₈×C₁₉	1	1	yes	characteristic
78	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
79	C₂×C₁₆	—	2	2	no	—
80	C₂×C₁₆	—	4	2	no	—
81	C₄⋊C₈	—	2	4	no	—
82	C₄⋊C₈	—	4	2	no	—
83	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
84	C₄×C₈	D₄×C₁₉	1	2	yes	—
85	C₁₉	#7241	1	1	yes	characteristic, direct product factor, Sylow
86	C₂²×C₄	C₄⋊C₄×C₁₉	1	1	yes	characteristic
87	C₂²×C₄	D₈×C₁₉	1	1	yes	characteristic
88	C₂²×C₄	Q₁₆×C₁₉	1	1	yes	characteristic
89	M₁₆	—	8	2	no	—
90	M₁₆	—	8	2	no	—
91	C₂×C₈	—	2	1	no	—
92	C₂×C₈	—	2	1	no	—
93	C₂×C₈	—	4	1	no	—
94	C₂×C₈	—	4	4	no	—
95	C₂×C₈	C₄²×C₁₉	1	1	yes	characteristic
96	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
97	C₂×C₈	C₄⋊C₄×C₁₉	1	2	yes	—
98	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
99	C₄²	SD₁₆×C₁₉	1	2	yes	—
100	C₁₆	—	4	2	no	—
101	C₂³	C₁₉×#107	1	1	yes	characteristic
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	C₁₉×#95	1	1	yes	characteristic
106	C₂×C₄	C₁₉×#102	1	2	yes	—
107	C₂×C₄	C₁₉×#103	1	2	yes	—
108	C₂×C₄	C₁₉×#106	1	1	yes	characteristic
109	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
110	C₂×C₄	C₁₉×SD₃₂	1	2	yes	—
111	C₂×C₄	C₁₉×Q₃₂	1	1	yes	characteristic
112	C₈	—	2	1	no	—
113	C₈	—	2	2	no	—
114	C₈	—	8	4	no	—
115	C₈	C₁₉×#100	1	1	yes	characteristic
116	C₈	C₁₉×#101	1	1	yes	characteristic
117	C₂²	—	2	1	no	—
118	C₂²	—	2	1	no	—
119	C₂²	C₁₉×#340	1	1	yes	characteristic
120	C₂²	C₁₉×#366	1	1	yes	characteristic
121	C₂²	C₁₉×#367	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	2	1	no	—
124	C₄	C₁₉×#338	1	1	yes	characteristic
125	C₄	C₁₉×#343	1	1	yes	characteristic
126	C₄	C₁₉×#357	1	2	yes	—
127	C₄	C₁₉×#358	1	2	yes	—
128	C₂	—	2	1	no	—
129	C₂	—	2	1	no	—
130	C₂	C₁₉×#1292	1	1	yes	characteristic
131	C₂	C₁₉×#1380	1	1	yes	characteristic
132	C₂	C₁₉×#1385	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₁₉×#1567

C₂

yes

maximal

C₂²×C₁₆×C₁₉

C₄

yes

—

C₁₉×#423

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×#335

—

C₁₉×#335

C₄

yes

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

D₈

yes

characteristic

C₂²×C₄×C₁₉

Q₁₆

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₄²

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₄⋊C₄

yes

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

SD₁₆

yes

—

C₁₆×C₁₉

—

#7241

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#107

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#95

yes

characteristic

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

#103

yes

—

C₂×C₄×C₁₉

#106

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

—

C₂×C₄×C₁₉

Q₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₄⋊C₁₆

C₂×C₁₉

yes

characteristic

#1567

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₄×C₁₉

#358

yes

—

C₂²×C₁₆

C₄×C₁₉

yes

—

#423

—

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₁₆

—

#335

—

#335

C₄×C₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×M₁₆

—

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

C₂²×C₈

Q₈×C₁₉

yes

characteristic

C₂×C₄²

D₄×C₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

C₂×C₄×C₁₉

yes

—

C₄×C₈

D₄×C₁₉

yes

—

C₁₉

#7241

yes

characteristic, direct product factor, Sylow

C₂²×C₄

C₄⋊C₄×C₁₉

yes

characteristic

C₂²×C₄

D₈×C₁₉

yes

characteristic

C₂²×C₄

Q₁₆×C₁₉

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₁₉

yes

characteristic

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

C₂×C₈

C₄⋊C₄×C₁₉

yes

—

C₄²

C₂²⋊C₄×C₁₉

yes

—

C₄²

SD₁₆×C₁₉

yes

—

100

C₁₆

—

101

C₂³

C₁₉×#107

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₁₉×#95

yes

characteristic

106

C₂×C₄

C₁₉×#102

yes

—

107

C₂×C₄

C₁₉×#103

yes

—

108

C₂×C₄

C₁₉×#106

yes

characteristic

109

C₂×C₄

C₁₉×D₁₆

yes

characteristic

110

C₂×C₄

C₁₉×SD₃₂

yes

—

111

C₂×C₄

C₁₉×Q₃₂

yes

characteristic

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

C₁₉×#100

yes

characteristic

116

C₈

C₁₉×#101

yes

characteristic

117

C₂²

—

118

C₂²

—

119

C₂²

C₁₉×#340

yes

characteristic

120

C₂²

C₁₉×#366

yes

characteristic

121

C₂²

C₁₉×#367

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

C₁₉×#338

yes

characteristic

125

C₄

C₁₉×#343

yes

characteristic

126

C₄

C₁₉×#357

yes

—

127

C₄

C₁₉×#358

yes

—

128

C₂

—

129

C₂

—

130

C₂

C₁₉×#1292

yes

characteristic

131

C₂

C₁₉×#1380

yes

characteristic

132

C₂

C₁₉×#1385

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#340
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
prime radical	C₂³×C₁₉	#107
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#340

commutator

C₂×C₈

C₄²×C₁₉

Frattini, cosocle

C₂×C₄×C₈

C₂²×C₁₉

prime radical

C₂³×C₁₉

#107

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
34. #7241	C₁₉	direct (N × H)
85. C₁₉	#7241	direct (N × H)

H ≅ G/N

type

34. #7241

C₁₉

direct (N × H)

85. C₁₉

#7241

direct (N × H)

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

subgroup	index
C₂×C₁₉×C₄⋊C₁₆	2
C₁₉×#1567	2
#7241	19

subgroup

index

C₂×C₁₉×C₄⋊C₁₆

C₁₉×#1567

#7241

Subgroups — C₁₉×#7241 #18013200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7241 #18013200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7241 #18013200