Group #18019660 — subgroups

Subgroups — C₁₉×#13701 #18019660

Order 4864.

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

normal subgroups only

This group has 180 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	C₂×C₁₉×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2258	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2222	C₂	1	2	yes	maximal
4	C₁₉×#1425	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1420	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×Q₃₂	C₂²	1	2	yes	—
7	C₁₉×#504	C₂²	1	1	yes	characteristic
8	C₁₉×#473	—	2	2	no	—
9	C₁₉×Q₆₄	—	2	1	no	—
10	C₁₉×Q₆₄	—	2	1	no	—
11	C₁₉×M₆₄	—	2	1	no	—
12	C₁₉×M₆₄	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₃₂	—	2	1	no	—
14	C₂×C₁₉×C₃₂	C₂²	1	1	yes	characteristic
15	C₁₉×#368	C₂²	1	2	yes	—
16	C₁₉×#362	—	2	2	no	—
17	C₁₉×#137	—	4	2	no	—
18	C₂×Q₁₆×C₁₉	—	2	2	no	—
19	C₁₉×#131	D₄	1	1	yes	characteristic
20	C₁₉×Q₃₂	—	2	2	no	—
21	C₁₉×Q₃₂	—	2	2	no	—
22	C₁₉×M₃₂	—	2	1	no	—
23	C₁₉×M₃₂	D₄	1	1	yes	characteristic
24	C₂×C₁₆×C₁₉	—	2	1	no	—
25	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
26	C₁₉×#108	—	2	2	no	—
27	C₁₉×#101	—	4	2	no	—
28	C₁₉×C₃₂	—	2	1	no	—
29	C₁₉×C₃₂	D₄	1	1	yes	characteristic
30	C₁₉×C₃₂	D₄	1	1	yes	characteristic
31	#41×C₁₉	D₈	1	1	yes	characteristic
32	C₂×Q₈×C₁₉	—	4	2	no	—
33	Q₁₆×C₁₉	—	4	2	no	—
34	Q₁₆×C₁₉	—	4	2	no	—
35	Q₁₆×C₁₉	—	8	2	no	—
36	SD₁₆×C₁₉	—	8	2	no	—
37	M₁₆×C₁₉	—	2	1	no	—
38	M₁₆×C₁₉	—	4	2	no	—
39	M₁₆×C₁₉	D₈	1	1	yes	characteristic
40	C₂×C₈×C₁₉	—	2	1	no	—
41	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
42	C₁₆×C₁₉	—	2	1	no	—
43	C₁₆×C₁₉	C₂×D₄	1	1	yes	characteristic
44	C₁₆×C₁₉	#41	1	1	yes	characteristic
45	#13701	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	Q₈×C₁₉	—	8	2	no	—
47	Q₈×C₁₉	—	8	2	no	—
48	Q₈×C₁₉	D₁₆	1	1	yes	characteristic
49	D₄×C₁₉	—	2	1	no	—
50	D₄×C₁₉	D₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₉	—	2	1	no	—
52	C₂×C₄×C₁₉	—	8	2	no	—
53	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
54	C₈×C₁₉	—	2	1	no	—
55	C₈×C₁₉	—	8	2	no	—
56	C₈×C₁₉	#121	1	1	yes	characteristic
57	C₈×C₁₉	#135	1	1	yes	characteristic
58	C₂×Q₆₄	C₂×C₁₉	1	1	yes	characteristic, complemented
59	#2258	C₂×C₁₉	1	1	yes	characteristic
60	#2222	C₂×C₁₉	1	2	yes	—
61	#1425	C₂×C₁₉	1	1	yes	characteristic, complemented
62	#1420	C₂×C₁₉	1	2	yes	complemented
63	C₂²×C₁₉	—	2	1	no	—
64	C₂²×C₁₉	#508	1	1	yes	characteristic
65	C₄×C₁₉	—	2	1	no	—
66	C₄×C₁₉	—	16	2	no	—
67	C₄×C₁₉	#466	1	1	yes	characteristic
68	C₄×C₁₉	C₂×D₁₆	1	1	yes	characteristic
69	C₂×Q₃₂	C₂²×C₁₉	1	2	yes	—
70	#504	C₂²×C₁₉	1	1	yes	characteristic
71	#473	—	2	2	no	—
72	Q₆₄	—	2	1	no	—
73	Q₆₄	—	2	1	no	—
74	M₆₄	—	2	1	no	—
75	M₆₄	C₂²×C₁₉	1	1	yes	characteristic
76	C₂×C₃₂	—	2	1	no	—
77	C₂×C₃₂	C₂²×C₁₉	1	1	yes	characteristic
78	#368	C₂²×C₁₉	1	2	yes	—
79	#362	—	2	2	no	—
80	C₂×C₁₉	—	2	1	no	—
81	C₂×C₁₉	—	4	1	no	—
82	C₂×C₁₉	#2215	1	1	yes	characteristic
83	#137	—	4	2	no	—
84	C₂×Q₁₆	—	2	2	no	—
85	#131	D₄×C₁₉	1	1	yes	characteristic
86	Q₃₂	—	2	2	no	—
87	Q₃₂	—	2	2	no	—
88	M₃₂	—	2	1	no	—
89	M₃₂	D₄×C₁₉	1	1	yes	characteristic
90	C₂×C₁₆	—	2	1	no	—
91	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
92	#108	—	2	2	no	—
93	#101	—	4	2	no	—
94	C₃₂	—	2	1	no	—
95	C₃₂	D₄×C₁₉	1	1	yes	characteristic
96	C₃₂	D₄×C₁₉	1	1	yes	characteristic
97	C₁₉	#13701	1	1	yes	characteristic, direct product factor, Sylow
98	#41	D₈×C₁₉	1	1	yes	characteristic
99	C₂×Q₈	—	4	2	no	—
100	Q₁₆	—	4	2	no	—
101	Q₁₆	—	4	2	no	—
102	Q₁₆	—	8	2	no	—
103	SD₁₆	—	8	2	no	—
104	M₁₆	—	2	1	no	—
105	M₁₆	—	4	2	no	—
106	M₁₆	D₈×C₁₉	1	1	yes	characteristic
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
109	C₁₆	—	2	1	no	—
110	C₁₆	C₂×D₄×C₁₉	1	1	yes	characteristic
111	C₁₆	#41×C₁₉	1	1	yes	characteristic
112	Q₈	—	8	2	no	—
113	Q₈	—	8	2	no	—
114	Q₈	C₁₉×D₁₆	1	1	yes	characteristic
115	D₄	—	2	1	no	—
116	D₄	C₁₉×D₁₆	1	1	yes	characteristic
117	C₂×C₄	—	2	1	no	—
118	C₂×C₄	—	8	2	no	—
119	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
120	C₈	—	2	1	no	—
121	C₈	—	8	2	no	—
122	C₈	C₁₉×#121	1	1	yes	characteristic
123	C₈	C₁₉×#135	1	1	yes	characteristic
124	C₂²	—	2	1	no	—
125	C₂²	C₁₉×#508	1	1	yes	characteristic
126	C₄	—	2	1	no	—
127	C₄	—	16	2	no	—
128	C₄	C₁₉×#466	1	1	yes	characteristic
129	C₄	C₂×C₁₉×D₁₆	1	1	yes	characteristic
130	C₂	—	2	1	no	—
131	C₂	—	4	1	no	—
132	C₂	C₁₉×#2215	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×Q₆₄

C₂

yes

maximal, characteristic, complemented

C₁₉×#2258

C₂

yes

maximal, characteristic

C₁₉×#2222

C₂

yes

maximal

C₁₉×#1425

C₂

yes

maximal, characteristic, complemented

C₁₉×#1420

C₂

yes

maximal, complemented

C₂×C₁₉×Q₃₂

C₂²

yes

—

C₁₉×#504

C₂²

yes

characteristic

C₁₉×#473

—

C₁₉×Q₆₄

—

C₁₉×Q₆₄

—

C₁₉×M₆₄

—

C₁₉×M₆₄

C₂²

yes

characteristic

C₂×C₁₉×C₃₂

—

C₂×C₁₉×C₃₂

C₂²

yes

characteristic

C₁₉×#368

C₂²

yes

—

C₁₉×#362

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₁₉×#131

D₄

yes

characteristic

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

C₁₉×M₃₂

—

C₁₉×M₃₂

D₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#108

—

C₁₉×#101

—

C₁₉×C₃₂

—

C₁₉×C₃₂

D₄

yes

characteristic

C₁₉×C₃₂

D₄

yes

characteristic

#41×C₁₉

D₈

yes

characteristic

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×D₄

yes

C₁₆×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

D₁₆

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₂×Q₆₄

C₂×C₁₉

yes

characteristic, complemented

#2258

C₂×C₁₉

yes

characteristic

#2222

C₂×C₁₉

yes

—

#1425

C₂×C₁₉

yes

characteristic, complemented

#1420

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

#508

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#466

yes

characteristic

C₄×C₁₉

C₂×D₁₆

yes

characteristic

C₂×Q₃₂

C₂²×C₁₉

yes

—

#504

C₂²×C₁₉

yes

characteristic

#473

—

Q₆₄

—

Q₆₄

—

M₆₄

—

M₆₄

C₂²×C₁₉

yes

characteristic

C₂×C₃₂

—

C₂×C₃₂

C₂²×C₁₉

yes

characteristic

#368

C₂²×C₁₉

yes

—

#362

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2215

yes

characteristic

#137

—

C₂×Q₁₆

—

#131

D₄×C₁₉

yes

characteristic

Q₃₂

—

Q₃₂

—

M₃₂

—

M₃₂

D₄×C₁₉

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

#108

—

#101

—

C₃₂

—

C₃₂

D₄×C₁₉

yes

characteristic

C₃₂

D₄×C₁₉

yes

characteristic

C₁₉

#13701

yes

characteristic, direct product factor, Sylow

#41

D₈×C₁₉

yes

characteristic

C₂×Q₈

—

100

Q₁₆

—

101

Q₁₆

—

102

Q₁₆

—

103

SD₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

D₈×C₁₉

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

109

C₁₆

—

110

C₁₆

C₂×D₄×C₁₉

yes

characteristic

111

C₁₆

#41×C₁₉

yes

characteristic

112

Q₈

—

113

Q₈

—

114

Q₈

C₁₉×D₁₆

yes

characteristic

115

D₄

—

116

D₄

C₁₉×D₁₆

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

120

C₈

—

121

C₈

—

122

C₈

C₁₉×#121

yes

characteristic

123

C₈

C₁₉×#135

yes

characteristic

124

C₂²

—

125

C₂²

C₁₉×#508

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

C₁₉×#466

yes

characteristic

129

C₄

C₂×C₁₉×D₁₆

yes

characteristic

130

C₂

—

131

C₂

—

132

C₂

C₁₉×#2215

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2215
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	#41×C₁₉	D₈
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ C₁₉×#504 ◁ G

subgroup

G/H

center, socle

C₂×C₁₉

#2215

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

prime radical

#41×C₁₉

D₈

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#131 ◁ C₁₉×#504 ◁ G

N	H ≅ G/N	type
1. C₂×C₁₉×Q₆₄	C₂	semidirect
4. C₁₉×#1425	C₂	semidirect
5. C₁₉×#1420	C₂	semidirect
45. #13701	C₁₉	direct (N × H)
58. C₂×Q₆₄	C₂×C₁₉	semidirect
61. #1425	C₂×C₁₉	semidirect
62. #1420	C₂×C₁₉	semidirect
97. C₁₉	#13701	direct (N × H)

H ≅ G/N

type

1. C₂×C₁₉×Q₆₄

C₂

semidirect

4. C₁₉×#1425

C₂

semidirect

5. C₁₉×#1420

C₂

semidirect

45. #13701

C₁₉

direct (N × H)

58. C₂×Q₆₄

C₂×C₁₉

semidirect

61. #1425

C₂×C₁₉

semidirect

62. #1420

C₂×C₁₉

semidirect

97. C₁₉

#13701

direct (N × H)

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

subgroup	index
C₂×C₁₉×Q₆₄	2
C₁₉×#2258	2
C₁₉×#2222	2
C₁₉×#1425	2
C₁₉×#1420	2
#13701	19

subgroup

index

C₂×C₁₉×Q₆₄

C₁₉×#2258

C₁₉×#2222

C₁₉×#1425

C₁₉×#1420

#13701

Subgroups — C₁₉×#13701 #18019660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13701 #18019660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13701 #18019660