Group #18019678 — subgroups

Subgroups — C₁₉×#13719 #18019678

Order 4864.

202 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 86 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×#2252	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2246	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1415	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉×D₁₆	—	2	1	no	—
6	C₂×C₁₉×D₁₆	C₂²	1	2	yes	—
7	C₁₉×#500	—	2	1	no	—
8	C₁₉×#493	—	2	1	no	—
9	C₂×C₁₉×C₃₂	C₂²	1	2	yes	—
10	C₁₉×#366	—	2	1	no	—
11	C₁₉×#366	C₂²	1	2	yes	—
12	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×D₈×C₁₉	—	2	2	no	—
14	C₂×D₈×C₁₉	—	4	1	no	—
15	C₁₉×C₄⋊Q₈	—	4	1	no	—
16	C₁₉×#127	—	4	1	no	—
17	C₁₉×D₁₆	—	2	4	no	—
18	C₁₉×D₁₆	—	4	2	no	—
19	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
21	C₁₉×#107	—	2	2	no	—
22	C₁₉×#107	—	4	1	no	—
23	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₁₉×C₃₂	—	2	2	no	—
25	C₂×Q₈×C₁₉	—	8	1	no	—
26	C₂×D₄×C₁₉	—	4	2	no	—
27	C₂×D₄×C₁₉	—	8	1	no	—
28	C₂×D₄×C₁₉	—	8	1	no	—
29	D₈×C₁₉	—	4	2	no	—
30	D₈×C₁₉	—	4	2	no	—
31	D₈×C₁₉	—	8	2	no	—
32	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
33	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₄⋊C₄×C₁₉	—	4	2	no	—
35	C₄⋊C₄×C₁₉	—	8	1	no	—
36	C₄²×C₁₉	D₈	1	1	yes	characteristic
37	C₁₆×C₁₉	SD₁₆	1	2	yes	—
38	C₁₆×C₁₉	#41	1	2	yes	—
39	#13719	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂³×C₁₉	—	8	2	no	—
41	Q₈×C₁₉	—	16	2	no	—
42	D₄×C₁₉	—	8	2	no	—
43	D₄×C₁₉	—	8	2	no	—
44	D₄×C₁₉	—	16	2	no	—
45	D₄×C₁₉	—	16	2	no	—
46	C₂×C₄×C₁₉	—	8	2	no	—
47	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
50	C₈×C₁₉	SD₃₂	1	2	yes	—
51	C₈×C₁₉	#124	1	1	yes	characteristic
52	C₈×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
53	#2252	C₂×C₁₉	1	1	yes	characteristic, complemented
54	#2246	C₂×C₁₉	1	1	yes	characteristic
55	#1415	C₂×C₁₉	1	4	yes	complemented
56	C₄×C₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
57	C₂²×C₁₉	—	16	2	no	—
58	C₂²×C₁₉	—	16	2	no	—
59	C₂²×C₁₉	—	16	2	no	—
60	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
61	C₄×C₁₉	—	16	2	no	—
62	C₄×C₁₉	D₃₂	1	2	yes	—
63	C₄×C₁₉	SD₆₄	1	2	yes	—
64	C₄×C₁₉	#486	1	1	yes	characteristic
65	C₄×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
66	C₂×D₁₆	—	2	1	no	—
67	C₂×D₁₆	C₂²×C₁₉	1	2	yes	—
68	#500	—	2	1	no	—
69	#493	—	2	1	no	—
70	C₂×C₃₂	C₂²×C₁₉	1	2	yes	—
71	#366	—	2	1	no	—
72	#366	C₂²×C₁₉	1	2	yes	—
73	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
74	C₂×C₁₉	—	32	2	no	—
75	C₂×C₁₉	#2240	1	1	yes	characteristic
76	C₂×C₁₉	C₂×D₃₂	1	1	yes	characteristic
77	C₂×C₁₉	C₂×SD₆₄	1	1	yes	characteristic
78	C₂×D₈	—	2	2	no	—
79	C₂×D₈	—	4	1	no	—
80	C₄⋊Q₈	—	4	1	no	—
81	#127	—	4	1	no	—
82	D₁₆	—	2	4	no	—
83	D₁₆	—	4	2	no	—
84	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
85	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
86	#107	—	2	2	no	—
87	#107	—	4	1	no	—
88	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
89	C₃₂	—	2	2	no	—
90	C₁₉	#13719	1	1	yes	characteristic, direct product factor, Sylow
91	C₂×Q₈	—	8	1	no	—
92	C₂×D₄	—	4	2	no	—
93	C₂×D₄	—	8	1	no	—
94	C₂×D₄	—	8	1	no	—
95	D₈	—	4	2	no	—
96	D₈	—	4	2	no	—
97	D₈	—	8	2	no	—
98	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
99	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
100	C₄⋊C₄	—	4	2	no	—
101	C₄⋊C₄	—	8	1	no	—
102	C₄²	D₈×C₁₉	1	1	yes	characteristic
103	C₁₆	SD₁₆×C₁₉	1	2	yes	—
104	C₁₆	#41×C₁₉	1	2	yes	—
105	C₂³	—	8	2	no	—
106	Q₈	—	16	2	no	—
107	D₄	—	8	2	no	—
108	D₄	—	8	2	no	—
109	D₄	—	16	2	no	—
110	D₄	—	16	2	no	—
111	C₂×C₄	—	8	2	no	—
112	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
113	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
114	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
115	C₈	C₁₉×SD₃₂	1	2	yes	—
116	C₈	C₁₉×#124	1	1	yes	characteristic
117	C₈	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
118	C₂²	—	16	2	no	—
119	C₂²	—	16	2	no	—
120	C₂²	—	16	2	no	—
121	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
122	C₄	—	16	2	no	—
123	C₄	C₁₉×D₃₂	1	2	yes	—
124	C₄	C₁₉×SD₆₄	1	2	yes	—
125	C₄	C₁₉×#486	1	1	yes	characteristic
126	C₄	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
127	C₂	—	32	2	no	—
128	C₂	C₁₉×#2240	1	1	yes	characteristic
129	C₂	C₂×C₁₉×D₃₂	1	1	yes	characteristic
130	C₂	C₂×C₁₉×SD₆₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2252

C₂

yes

maximal, characteristic, complemented

C₁₉×#2246

C₂

yes

maximal, characteristic

C₁₉×#1415

C₂

yes

maximal, complemented

C₄×C₁₉×C₃₂

C₂

yes

maximal, characteristic, complemented

C₂×C₁₉×D₁₆

—

C₂×C₁₉×D₁₆

C₂²

yes

—

C₁₉×#500

—

C₁₉×#493

—

C₂×C₁₉×C₃₂

C₂²

yes

—

C₁₉×#366

—

C₁₉×#366

C₂²

yes

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×D₈×C₁₉

—

C₂×D₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×#127

—

C₁₉×D₁₆

—

C₁₉×D₁₆

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#107

—

C₄×C₈×C₁₉

D₄

yes

characteristic

C₁₉×C₃₂

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

D₈×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

—

C₁₆×C₁₉

#41

yes

—

#13719

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₈×C₁₉

SD₃₂

yes

—

C₈×C₁₉

#124

yes

characteristic

C₈×C₁₉

C₂×SD₁₆

yes

characteristic

#2252

C₂×C₁₉

yes

characteristic, complemented

#2246

C₂×C₁₉

yes

characteristic

#1415

C₂×C₁₉

yes

complemented

C₄×C₃₂

C₂×C₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

D₃₂

yes

—

C₄×C₁₉

SD₆₄

yes

—

C₄×C₁₉

#486

yes

characteristic

C₄×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×D₁₆

—

C₂×D₁₆

C₂²×C₁₉

yes

—

#500

—

#493

—

C₂×C₃₂

C₂²×C₁₉

yes

—

#366

—

#366

C₂²×C₁₉

yes

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#2240

yes

characteristic

C₂×C₁₉

C₂×D₃₂

yes

characteristic

C₂×C₁₉

C₂×SD₆₄

yes

characteristic

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

D₁₆

—

D₁₆

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

#107

—

#107

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#13719

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

C₂×C₈

D₈×C₁₉

yes

characteristic

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄²

D₈×C₁₉

yes

characteristic

103

C₁₆

SD₁₆×C₁₉

yes

—

104

C₁₆

#41×C₁₉

yes

—

105

C₂³

—

106

Q₈

—

107

D₄

—

108

D₄

—

109

D₄

—

110

D₄

—

111

C₂×C₄

—

112

C₂×C₄

C₁₉×D₁₆

yes

characteristic

113

C₂×C₄

C₁₉×D₁₆

yes

characteristic

114

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

115

C₈

C₁₉×SD₃₂

yes

—

116

C₈

C₁₉×#124

yes

characteristic

117

C₈

C₂×SD₁₆×C₁₉

yes

characteristic

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

122

C₄

—

123

C₄

C₁₉×D₃₂

yes

—

124

C₄

C₁₉×SD₆₄

yes

—

125

C₄

C₁₉×#486

yes

characteristic

126

C₄

C₂×C₁₉×SD₃₂

yes

characteristic

127

C₂

—

128

C₂

C₁₉×#2240

yes

characteristic

129

C₂

C₂×C₁₉×D₃₂

yes

characteristic

130

C₂

C₂×C₁₉×SD₆₄

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
prime radical	C₁₉×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

prime radical

C₁₉×#2246

C₂

LCS

G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

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

N	H ≅ G/N	type
1. C₁₉×#2252	C₂	semidirect
3. C₁₉×#1415	C₂	semidirect
4. C₄×C₁₉×C₃₂	C₂	semidirect
39. #13719	C₁₉	direct (N × H)
53. #2252	C₂×C₁₉	semidirect
55. #1415	C₂×C₁₉	semidirect
56. C₄×C₃₂	C₂×C₁₉	semidirect
90. C₁₉	#13719	direct (N × H)

H ≅ G/N

type

1. C₁₉×#2252

C₂

semidirect

3. C₁₉×#1415

C₂

semidirect

4. C₄×C₁₉×C₃₂

C₂

semidirect

39. #13719

C₁₉

direct (N × H)

53. #2252

C₂×C₁₉

semidirect

55. #1415

C₂×C₁₉

semidirect

56. C₄×C₃₂

C₂×C₁₉

semidirect

90. C₁₉

#13719

direct (N × H)

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

subgroup	index
C₁₉×#2252	2
C₁₉×#2246	2
C₁₉×#1415	2
C₄×C₁₉×C₃₂	2
#13719	19

subgroup

index

C₁₉×#2252

C₁₉×#2246

C₁₉×#1415

C₄×C₁₉×C₃₂

#13719

Subgroups — C₁₉×#13719 #18019678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13719 #18019678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13719 #18019678