Group #18019679 — subgroups

Subgroups — C₁₉×#13720 #18019679

Order 4864.

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

normal subgroups only

This group has 182 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
2	C₁₉×#2247	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1416	C₂	1	4	yes	maximal
4	C₄×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×Q₃₂	—	2	1	no	—
6	C₂×C₁₉×Q₃₂	C₂²	1	2	yes	—
7	C₁₉×#500	—	2	1	no	—
8	C₁₉×#494	—	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×Q₁₆×C₁₉	—	2	2	no	—
14	C₂×Q₁₆×C₁₉	—	4	1	no	—
15	C₁₉×C₄⋊Q₈	—	4	1	no	—
16	C₁₉×C₄⋊Q₈	—	4	1	no	—
17	C₁₉×Q₃₂	—	2	4	no	—
18	C₁₉×Q₃₂	—	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	—	4	2	no	—
26	C₂×Q₈×C₁₉	—	8	1	no	—
27	Q₁₆×C₁₉	—	4	2	no	—
28	Q₁₆×C₁₉	—	4	2	no	—
29	Q₁₆×C₁₉	—	8	2	no	—
30	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
31	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
32	C₄⋊C₄×C₁₉	—	4	2	no	—
33	C₄⋊C₄×C₁₉	—	8	1	no	—
34	C₄⋊C₄×C₁₉	—	8	1	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	#13720	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	Q₈×C₁₉	—	8	2	no	—
41	Q₈×C₁₉	—	8	2	no	—
42	Q₈×C₁₉	—	16	2	no	—
43	C₂×C₄×C₁₉	—	8	2	no	—
44	C₂×C₄×C₁₉	—	8	2	no	—
45	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
46	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
48	C₈×C₁₉	SD₃₂	1	2	yes	—
49	C₈×C₁₉	#124	1	1	yes	characteristic
50	C₈×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
51	#2252	C₂×C₁₉	1	1	yes	characteristic
52	#2247	C₂×C₁₉	1	1	yes	characteristic
53	#1416	C₂×C₁₉	1	4	yes	—
54	C₄×C₃₂	C₂×C₁₉	1	1	yes	characteristic
55	C₂²×C₁₉	C₂×D₁₆	1	1	yes	characteristic
56	C₄×C₁₉	—	16	2	no	—
57	C₄×C₁₉	—	16	2	no	—
58	C₄×C₁₉	SD₆₄	1	2	yes	—
59	C₄×C₁₉	Q₆₄	1	2	yes	—
60	C₄×C₁₉	#486	1	1	yes	characteristic
61	C₄×C₁₉	C₂×SD₃₂	1	1	yes	characteristic
62	C₂×Q₃₂	—	2	1	no	—
63	C₂×Q₃₂	C₂²×C₁₉	1	2	yes	—
64	#500	—	2	1	no	—
65	#494	—	2	1	no	—
66	C₂×C₃₂	C₂²×C₁₉	1	2	yes	—
67	#366	—	2	1	no	—
68	#366	C₂²×C₁₉	1	2	yes	—
69	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
70	C₂×C₁₉	#2240	1	1	yes	characteristic
71	C₂×C₁₉	C₂×SD₆₄	1	1	yes	characteristic
72	C₂×C₁₉	C₂×Q₆₄	1	1	yes	characteristic
73	C₂×Q₁₆	—	2	2	no	—
74	C₂×Q₁₆	—	4	1	no	—
75	C₄⋊Q₈	—	4	1	no	—
76	C₄⋊Q₈	—	4	1	no	—
77	Q₃₂	—	2	4	no	—
78	Q₃₂	—	4	2	no	—
79	C₂×C₁₆	D₄×C₁₉	1	1	yes	characteristic
80	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
81	#107	—	2	2	no	—
82	#107	—	4	1	no	—
83	C₄×C₈	D₄×C₁₉	1	1	yes	characteristic
84	C₃₂	—	2	2	no	—
85	C₁₉	#13720	1	1	yes	characteristic, direct product factor, Sylow
86	C₂×Q₈	—	4	2	no	—
87	C₂×Q₈	—	8	1	no	—
88	Q₁₆	—	4	2	no	—
89	Q₁₆	—	4	2	no	—
90	Q₁₆	—	8	2	no	—
91	C₂×C₈	D₈×C₁₉	1	1	yes	characteristic
92	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
93	C₄⋊C₄	—	4	2	no	—
94	C₄⋊C₄	—	8	1	no	—
95	C₄⋊C₄	—	8	1	no	—
96	C₄⋊C₄	—	8	1	no	—
97	C₄²	D₈×C₁₉	1	1	yes	characteristic
98	C₁₆	SD₁₆×C₁₉	1	2	yes	—
99	C₁₆	#41×C₁₉	1	2	yes	—
100	Q₈	—	8	2	no	—
101	Q₈	—	8	2	no	—
102	Q₈	—	16	2	no	—
103	C₂×C₄	—	8	2	no	—
104	C₂×C₄	—	8	2	no	—
105	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
106	C₂×C₄	C₁₉×D₁₆	1	1	yes	characteristic
107	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
108	C₈	C₁₉×SD₃₂	1	2	yes	—
109	C₈	C₁₉×#124	1	1	yes	characteristic
110	C₈	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
111	C₂²	C₂×C₁₉×D₁₆	1	1	yes	characteristic
112	C₄	—	16	2	no	—
113	C₄	—	16	2	no	—
114	C₄	C₁₉×SD₆₄	1	2	yes	—
115	C₄	C₁₉×Q₆₄	1	2	yes	—
116	C₄	C₁₉×#486	1	1	yes	characteristic
117	C₄	C₂×C₁₉×SD₃₂	1	1	yes	characteristic
118	C₂	C₁₉×#2240	1	1	yes	characteristic
119	C₂	C₂×C₁₉×SD₆₄	1	1	yes	characteristic
120	C₂	C₂×C₁₉×Q₆₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2252

C₂

yes

maximal, characteristic

C₁₉×#2247

C₂

yes

maximal, characteristic

C₁₉×#1416

C₂

yes

maximal

C₄×C₁₉×C₃₂

C₂

yes

maximal, characteristic

C₂×C₁₉×Q₃₂

—

C₂×C₁₉×Q₃₂

C₂²

yes

—

C₁₉×#500

—

C₁₉×#494

—

C₂×C₁₉×C₃₂

C₂²

yes

—

C₁₉×#366

—

C₁₉×#366

C₂²

yes

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×Q₃₂

—

C₁₉×Q₃₂

—

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×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

D₈

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₁₆×C₁₉

SD₁₆

yes

—

C₁₆×C₁₉

#41

yes

—

#13720

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×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

#2247

C₂×C₁₉

yes

characteristic

#1416

C₂×C₁₉

yes

—

C₄×C₃₂

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

C₂×D₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

SD₆₄

yes

—

C₄×C₁₉

Q₆₄

yes

—

C₄×C₁₉

#486

yes

characteristic

C₄×C₁₉

C₂×SD₃₂

yes

characteristic

C₂×Q₃₂

—

C₂×Q₃₂

C₂²×C₁₉

yes

—

#500

—

#494

—

C₂×C₃₂

C₂²×C₁₉

yes

—

#366

—

#366

C₂²×C₁₉

yes

—

C₄×C₁₆

C₂²×C₁₉

yes

characteristic

C₂×C₁₉

#2240

yes

characteristic

C₂×C₁₉

C₂×SD₆₄

yes

characteristic

C₂×C₁₉

C₂×Q₆₄

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

D₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂³×C₁₉

yes

characteristic

#107

—

#107

—

C₄×C₈

D₄×C₁₉

yes

characteristic

C₃₂

—

C₁₉

#13720

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₈×C₁₉

yes

characteristic

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₈×C₁₉

yes

characteristic

C₁₆

SD₁₆×C₁₉

yes

—

C₁₆

#41×C₁₉

yes

—

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₁₉×D₁₆

yes

characteristic

106

C₂×C₄

C₁₉×D₁₆

yes

characteristic

107

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

108

C₈

C₁₉×SD₃₂

yes

—

109

C₈

C₁₉×#124

yes

characteristic

110

C₈

C₂×SD₁₆×C₁₉

yes

characteristic

111

C₂²

C₂×C₁₉×D₁₆

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

C₁₉×SD₆₄

yes

—

115

C₄

C₁₉×Q₆₄

yes

—

116

C₄

C₁₉×#486

yes

characteristic

117

C₄

C₂×C₁₉×SD₃₂

yes

characteristic

118

C₂

C₁₉×#2240

yes

characteristic

119

C₂

C₂×C₁₉×SD₆₄

yes

characteristic

120

C₂

C₂×C₁₉×Q₆₄

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₉
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, prime radical

C₂²×C₁₉

C₂×D₁₆

commutator, Frattini, cosocle

C₂×C₁₆

C₂³×C₁₉

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
39. #13720	C₁₉	direct (N × H)
85. C₁₉	#13720	direct (N × H)

H ≅ G/N

type

39. #13720

C₁₉

direct (N × H)

85. C₁₉

#13720

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×#2247	2
C₁₉×#1416	2
C₄×C₁₉×C₃₂	2
#13720	19

subgroup

index

C₁₉×#2252

C₁₉×#2247

C₁₉×#1416

C₄×C₁₉×C₃₂

#13720

Subgroups — C₁₉×#13720 #18019679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#13720 #18019679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13720 #18019679