Group #18016278 — subgroups

Subgroups — C₁₉×#10319 #18016278

Order 4864.

538 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 162 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×#487	C₂	1	3	yes	maximal
2	C₁₉×#1990	C₂	1	3	yes	maximal
3	C₁₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×C₄⋊Q₈	C₂²	1	3	yes	—
5	C₁₉×#487	—	2	6	no	—
6	C₁₉×#487	—	2	6	no	—
7	C₂×C₁₉×#103	—	2	6	no	—
8	C₂×C₄×C₈×C₁₉	C₂²	1	3	yes	—
9	C₁₉×#384	C₂²	1	1	yes	characteristic
10	C₁₉×#340	—	2	6	no	—
11	C₂²×Q₈×C₁₉	—	2	3	no	—
12	C₂²×C₈×C₁₉	D₄	1	6	yes	—
13	C₁₉×C₄⋊Q₈	—	2	3	no	—
14	C₁₉×C₄⋊Q₈	—	2	3	no	—
15	C₁₉×C₄⋊Q₈	—	2	3	no	—
16	C₁₉×C₄⋊Q₈	D₄	1	6	yes	—
17	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	C₁₉×#103	—	2	24	no	—
22	C₄×C₈×C₁₉	—	2	3	no	—
23	C₄×C₈×C₁₉	—	2	3	no	—
24	C₂×Q₈×C₁₉	—	2	6	no	—
25	C₂×Q₈×C₁₉	—	4	3	no	—
26	C₂×Q₈×C₁₉	—	4	6	no	—
27	C₂×Q₈×C₁₉	—	4	6	no	—
28	C₂²×C₄×C₁₉	—	4	3	no	—
29	C₂²×C₄×C₁₉	—	4	1	no	—
30	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
31	C₂×C₈×C₁₉	—	2	6	no	—
32	C₂×C₈×C₁₉	—	2	6	no	—
33	C₂×C₈×C₁₉	—	2	6	no	—
34	C₄⋊C₄×C₁₉	—	2	6	no	—
35	C₄⋊C₄×C₁₉	—	2	6	no	—
36	C₄⋊C₄×C₁₉	—	4	3	no	—
37	C₄⋊C₄×C₁₉	—	4	3	no	—
38	C₄⋊C₄×C₁₉	—	4	6	no	—
39	C₄²×C₁₉	C₂×D₄	1	3	yes	—
40	C₄²×C₁₉	#41	1	1	yes	characteristic
41	#10319	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂³×C₁₉	#127	1	1	yes	characteristic
43	Q₈×C₁₉	—	4	12	no	—
44	Q₈×C₁₉	—	8	6	no	—
45	C₂×C₄×C₁₉	—	4	6	no	—
46	C₂×C₄×C₁₉	—	8	3	no	—
47	C₂×C₄×C₁₉	—	8	3	no	—
48	C₂×C₄×C₁₉	—	8	3	no	—
49	C₂×C₄×C₁₉	#120	1	3	yes	—
50	C₂×C₄×C₁₉	#121	1	3	yes	—
51	C₂×C₄×C₁₉	#135	1	6	yes	—
52	C₂×C₄×C₁₉	#137	1	6	yes	—
53	C₈×C₁₉	—	4	6	no	—
54	C₂×#487	C₂×C₁₉	1	3	yes	—
55	#1990	C₂×C₁₉	1	3	yes	—
56	#1273	C₂×C₁₉	1	1	yes	characteristic
57	C₂²×C₁₉	#392	1	1	yes	characteristic
58	C₂²×C₁₉	#495	1	3	yes	—
59	C₂²×C₁₉	#497	1	3	yes	—
60	C₄×C₁₉	—	8	6	no	—
61	C₄×C₁₉	—	16	1	no	—
62	C₄×C₁₉	#452	1	6	yes	—
63	C₄×C₁₉	#464	1	6	yes	—
64	C₂×C₄⋊Q₈	C₂²×C₁₉	1	3	yes	—
65	#487	—	2	6	no	—
66	#487	—	2	6	no	—
67	C₂×#103	—	2	6	no	—
68	C₂×C₄×C₈	C₂²×C₁₉	1	3	yes	—
69	#384	C₂²×C₁₉	1	1	yes	characteristic
70	#340	—	2	6	no	—
71	C₂×C₁₉	#1711	1	1	yes	characteristic
72	C₂×C₁₉	#1718	1	3	yes	—
73	C₂×C₁₉	#2015	1	3	yes	—
74	C₂²×Q₈	—	2	3	no	—
75	C₂²×C₈	D₄×C₁₉	1	6	yes	—
76	C₄⋊Q₈	—	2	3	no	—
77	C₄⋊Q₈	—	2	3	no	—
78	C₄⋊Q₈	—	2	3	no	—
79	C₄⋊Q₈	D₄×C₁₉	1	6	yes	—
80	C₂×C₄⋊C₄	—	2	3	no	—
81	C₂×C₄⋊C₄	—	2	3	no	—
82	C₂×C₄⋊C₄	—	2	3	no	—
83	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
84	#103	—	2	24	no	—
85	C₄×C₈	—	2	3	no	—
86	C₄×C₈	—	2	3	no	—
87	C₁₉	#10319	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×Q₈	—	2	6	no	—
89	C₂×Q₈	—	4	3	no	—
90	C₂×Q₈	—	4	6	no	—
91	C₂×Q₈	—	4	6	no	—
92	C₂²×C₄	—	4	3	no	—
93	C₂²×C₄	—	4	1	no	—
94	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
95	C₂×C₈	—	2	6	no	—
96	C₂×C₈	—	2	6	no	—
97	C₂×C₈	—	2	6	no	—
98	C₄⋊C₄	—	2	6	no	—
99	C₄⋊C₄	—	2	6	no	—
100	C₄⋊C₄	—	4	3	no	—
101	C₄⋊C₄	—	4	3	no	—
102	C₄⋊C₄	—	4	6	no	—
103	C₄²	C₂×D₄×C₁₉	1	3	yes	—
104	C₄²	#41×C₁₉	1	1	yes	characteristic
105	C₂³	C₁₉×#127	1	1	yes	characteristic
106	Q₈	—	4	12	no	—
107	Q₈	—	8	6	no	—
108	C₂×C₄	—	4	6	no	—
109	C₂×C₄	—	8	3	no	—
110	C₂×C₄	—	8	3	no	—
111	C₂×C₄	—	8	3	no	—
112	C₂×C₄	C₁₉×#120	1	3	yes	—
113	C₂×C₄	C₁₉×#121	1	3	yes	—
114	C₂×C₄	C₁₉×#135	1	6	yes	—
115	C₂×C₄	C₁₉×#137	1	6	yes	—
116	C₈	—	4	6	no	—
117	C₂²	C₁₉×#392	1	1	yes	characteristic
118	C₂²	C₁₉×#495	1	3	yes	—
119	C₂²	C₁₉×#497	1	3	yes	—
120	C₄	—	8	6	no	—
121	C₄	—	16	1	no	—
122	C₄	C₁₉×#452	1	6	yes	—
123	C₄	C₁₉×#464	1	6	yes	—
124	C₂	C₁₉×#1711	1	1	yes	characteristic
125	C₂	C₁₉×#1718	1	3	yes	—
126	C₂	C₁₉×#2015	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#487

C₂

yes

maximal

C₁₉×#1990

C₂

yes

maximal

C₁₉×#1273

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#487

—

C₁₉×#487

—

C₂×C₁₉×#103

—

C₂×C₄×C₈×C₁₉

C₂²

yes

—

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#340

—

C₂²×Q₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

#10319

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#127

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#135

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

C₂×#487

C₂×C₁₉

yes

—

#1990

C₂×C₁₉

yes

—

#1273

C₂×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#497

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#452

yes

—

C₄×C₁₉

#464

yes

—

C₂×C₄⋊Q₈

C₂²×C₁₉

yes

—

#487

—

#487

—

C₂×#103

—

C₂×C₄×C₈

C₂²×C₁₉

yes

—

#384

C₂²×C₁₉

yes

characteristic

#340

—

C₂×C₁₉

#1711

yes

characteristic

C₂×C₁₉

#1718

yes

—

C₂×C₁₉

#2015

yes

—

C₂²×Q₈

—

C₂²×C₈

D₄×C₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

D₄×C₁₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂³×C₁₉

yes

characteristic

#103

—

C₄×C₈

—

C₄×C₈

—

C₁₉

#10319

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄²

C₂×D₄×C₁₉

yes

—

104

C₄²

#41×C₁₉

yes

characteristic

105

C₂³

C₁₉×#127

yes

characteristic

106

Q₈

—

107

Q₈

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

C₁₉×#120

yes

—

113

C₂×C₄

C₁₉×#121

yes

—

114

C₂×C₄

C₁₉×#135

yes

—

115

C₂×C₄

C₁₉×#137

yes

—

116

C₈

—

117

C₂²

C₁₉×#392

yes

characteristic

118

C₂²

C₁₉×#495

yes

—

119

C₂²

C₁₉×#497

yes

—

120

C₄

—

121

C₄

—

122

C₄

C₁₉×#452

yes

—

123

C₄

C₁₉×#464

yes

—

124

C₂

C₁₉×#1711

yes

characteristic

125

C₂

C₁₉×#1718

yes

—

126

C₂

C₁₉×#2015

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₁₉

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
41. #10319	C₁₉	direct (N × H)
87. C₁₉	#10319	direct (N × H)

H ≅ G/N

type

41. #10319

C₁₉

direct (N × H)

87. C₁₉

#10319

direct (N × H)

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

subgroup	index
C₂×C₁₉×#487	2
C₁₉×#1990	2
C₁₉×#1273	2
#10319	19

subgroup

index

C₂×C₁₉×#487

C₁₉×#1990

C₁₉×#1273

#10319

Subgroups — C₁₉×#10319 #18016278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10319 #18016278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10319 #18016278