Group #18013405 — subgroups

Subgroups — C₁₉×#7446 #18013405

Order 4864.

136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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×#2249	C₂	1	1	yes	maximal, characteristic
2	C₁₉×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1372	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×Q₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₉×SD₃₂	—	2	1	no	—
6	C₂×C₁₉×D₁₆	C₄	1	1	yes	characteristic
7	C₁₉×#495	—	2	1	no	—
8	C₂×C₁₉×C₃₂	—	2	1	no	—
9	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#335	—	2	1	no	—
11	C₂×Q₁₆×C₁₉	—	2	1	no	—
12	C₂×SD₁₆×C₁₉	—	4	1	no	—
13	C₂×D₈×C₁₉	—	2	1	no	—
14	C₁₉×#124	—	4	1	no	—
15	C₁₉×Q₃₂	—	4	1	no	—
16	C₁₉×SD₃₂	—	4	1	no	—
17	C₁₉×SD₃₂	—	4	1	no	—
18	C₁₉×D₁₆	—	4	1	no	—
19	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
21	C₁₉×C₄⋊C₈	—	4	1	no	—
22	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₁₉×C₃₂	—	4	1	no	—
24	C₂×Q₈×C₁₉	—	4	1	no	—
25	C₂×D₄×C₁₉	—	4	1	no	—
26	Q₁₆×C₁₉	—	4	1	no	—
27	Q₁₆×C₁₉	—	4	1	no	—
28	SD₁₆×C₁₉	—	8	2	no	—
29	D₈×C₁₉	—	4	1	no	—
30	D₈×C₁₉	—	4	1	no	—
31	C₂×C₈×C₁₉	—	8	1	no	—
32	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
34	C₂²⋊C₄×C₁₉	—	8	1	no	—
35	C₂²⋊C₄×C₁₉	—	8	1	no	—
36	C₄²×C₁₉	D₈	1	1	yes	characteristic
37	C₁₆×C₁₉	—	2	1	no	—
38	C₁₆×C₁₉	D₈	1	1	yes	characteristic
39	C₁₆×C₁₉	SD₁₆	1	1	yes	characteristic
40	#7446	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂³×C₁₉	—	8	1	no	—
42	Q₈×C₁₉	—	8	1	no	—
43	Q₈×C₁₉	—	8	1	no	—
44	D₄×C₁₉	—	8	1	no	—
45	D₄×C₁₉	—	8	1	no	—
46	C₂×C₄×C₁₉	—	8	1	no	—
47	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
48	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
50	C₈×C₁₉	—	2	1	no	—
51	C₈×C₁₉	—	16	1	no	—
52	C₈×C₁₉	#100	1	1	yes	characteristic
53	C₈×C₁₉	#102	1	1	yes	characteristic
54	#2249	C₂×C₁₉	1	1	yes	characteristic
55	C₄⋊C₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
56	#1372	C₂×C₁₉	1	1	yes	characteristic, complemented
57	C₂²×C₁₉	—	16	1	no	—
58	C₂²×C₁₉	—	16	1	no	—
59	C₂²×C₁₉	—	16	1	no	—
60	C₂²×C₁₉	#357	1	1	yes	characteristic
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	2	1	no	—
63	C₄×C₁₉	—	16	1	no	—
64	C₄×C₁₉	#331	1	1	yes	characteristic
65	C₄×C₁₉	#361	1	1	yes	characteristic
66	C₂×Q₃₂	C₄×C₁₉	1	1	yes	characteristic
67	C₂×SD₃₂	—	2	1	no	—
68	C₂×D₁₆	C₄×C₁₉	1	1	yes	characteristic
69	#495	—	2	1	no	—
70	C₂×C₃₂	—	2	1	no	—
71	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
72	#335	—	2	1	no	—
73	C₂×C₁₉	—	32	1	no	—
74	C₂×C₁₉	#1361	1	1	yes	characteristic
75	C₂×C₁₉	#1417	1	1	yes	characteristic
76	C₂×C₁₉	#1418	1	1	yes	characteristic
77	C₂×Q₁₆	—	2	1	no	—
78	C₂×SD₁₆	—	4	1	no	—
79	C₂×D₈	—	2	1	no	—
80	#124	—	4	1	no	—
81	Q₃₂	—	4	1	no	—
82	SD₃₂	—	4	1	no	—
83	SD₃₂	—	4	1	no	—
84	D₁₆	—	4	1	no	—
85	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
86	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
87	C₄⋊C₈	—	4	1	no	—
88	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
89	C₃₂	—	4	1	no	—
90	C₁₉	#7446	1	1	yes	characteristic, direct product factor, Sylow
91	C₂×Q₈	—	4	1	no	—
92	C₂×D₄	—	4	1	no	—
93	Q₁₆	—	4	1	no	—
94	Q₁₆	—	4	1	no	—
95	SD₁₆	—	8	2	no	—
96	D₈	—	4	1	no	—
97	D₈	—	4	1	no	—
98	C₂×C₈	—	8	1	no	—
99	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
100	C₂×C₈	SD₁₆×C₁₉	1	1	yes	characteristic
101	C₂²⋊C₄	—	8	1	no	—
102	C₂²⋊C₄	—	8	1	no	—
103	C₄²	D₈×C₁₉	1	1	yes	characteristic
104	C₁₆	—	2	1	no	—
105	C₁₆	D₈×C₁₉	1	1	yes	characteristic
106	C₁₆	SD₁₆×C₁₉	1	1	yes	characteristic
107	C₂³	—	8	1	no	—
108	Q₈	—	8	1	no	—
109	Q₈	—	8	1	no	—
110	D₄	—	8	1	no	—
111	D₄	—	8	1	no	—
112	C₂×C₄	—	8	1	no	—
113	C₂×C₄	C₁₉×#102	1	1	yes	characteristic
114	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
115	C₂×C₄	C₁₉×SD₃₂	1	1	yes	characteristic
116	C₈	—	2	1	no	—
117	C₈	—	16	1	no	—
118	C₈	C₁₉×#100	1	1	yes	characteristic
119	C₈	C₁₉×#102	1	1	yes	characteristic
120	C₂²	—	16	1	no	—
121	C₂²	—	16	1	no	—
122	C₂²	—	16	1	no	—
123	C₂²	C₁₉×#357	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	2	1	no	—
126	C₄	—	16	1	no	—
127	C₄	C₁₉×#331	1	1	yes	characteristic
128	C₄	C₁₉×#361	1	1	yes	characteristic
129	C₂	—	32	1	no	—
130	C₂	C₁₉×#1361	1	1	yes	characteristic
131	C₂	C₁₉×#1417	1	1	yes	characteristic
132	C₂	C₁₉×#1418	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2249

C₂

yes

maximal, characteristic

C₁₉×C₄⋊C₃₂

C₂

yes

maximal, characteristic, complemented

C₁₉×#1372

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×Q₃₂

C₄

yes

characteristic

C₂×C₁₉×SD₃₂

—

C₂×C₁₉×D₁₆

C₄

yes

characteristic

C₁₉×#495

—

C₂×C₁₉×C₃₂

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#335

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×#124

—

C₁₉×Q₃₂

—

C₁₉×SD₃₂

—

C₁₉×SD₃₂

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

characteristic

#7446

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic

C₄⋊C₃₂

C₂×C₁₉

yes

characteristic, complemented

#1372

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₂×Q₃₂

C₄×C₁₉

yes

characteristic

C₂×SD₃₂

—

C₂×D₁₆

C₄×C₁₉

yes

characteristic

#495

—

C₂×C₃₂

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

#335

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#124

—

Q₃₂

—

SD₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂×C₄×C₁₉

yes

characteristic

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₄⋊C₈

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#7446

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

Q₁₆

—

SD₁₆

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

100

C₂×C₈

SD₁₆×C₁₉

yes

characteristic

101

C₂²⋊C₄

—

102

C₂²⋊C₄

—

103

C₄²

D₈×C₁₉

yes

characteristic

104

C₁₆

—

105

C₁₆

D₈×C₁₉

yes

characteristic

106

C₁₆

SD₁₆×C₁₉

yes

characteristic

107

C₂³

—

108

Q₈

—

109

Q₈

—

110

D₄

—

111

D₄

—

112

C₂×C₄

—

113

C₂×C₄

C₁₉×#102

yes

characteristic

114

C₂×C₄

C₁₉×D₁₆

yes

characteristic

115

C₂×C₄

C₁₉×SD₃₂

yes

characteristic

116

C₈

—

117

C₈

—

118

C₈

C₁₉×#100

yes

characteristic

119

C₈

C₁₉×#102

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

C₁₉×#357

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

C₁₉×#331

yes

characteristic

128

C₄

C₁₉×#361

yes

characteristic

129

C₂

—

130

C₂

C₁₉×#1361

yes

characteristic

131

C₂

C₁₉×#1417

yes

characteristic

132

C₂

C₁₉×#1418

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₄
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#357

commutator

C₂×C₁₆

C₂×C₄×C₁₉

Frattini, cosocle

C₄×C₁₆

C₂²×C₁₉

prime radical

C₂×C₁₉×D₁₆

C₄

LCS

G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×C₄⋊C₃₂	C₂	semidirect
3. C₁₉×#1372	C₂	semidirect
40. #7446	C₁₉	direct (N × H)
55. C₄⋊C₃₂	C₂×C₁₉	semidirect
56. #1372	C₂×C₁₉	semidirect
90. C₁₉	#7446	direct (N × H)

H ≅ G/N

type

2. C₁₉×C₄⋊C₃₂

C₂

semidirect

3. C₁₉×#1372

C₂

semidirect

40. #7446

C₁₉

direct (N × H)

55. C₄⋊C₃₂

C₂×C₁₉

semidirect

56. #1372

C₂×C₁₉

semidirect

90. C₁₉

#7446

direct (N × H)

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

subgroup	index
C₁₉×#2249	2
C₁₉×C₄⋊C₃₂	2
C₁₉×#1372	2
#7446	19

subgroup

index

C₁₉×#2249

C₁₉×C₄⋊C₃₂

C₁₉×#1372

#7446

Subgroups — C₁₉×#7446 #18013405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#7446 #18013405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#7446 #18013405