Group #18018025 — subgroups

Subgroups — C₁₉×#12066 #18018025

Order 4864.

214 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2176	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1579	C₂	1	2	yes	maximal
3	C₁₉×#1368	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1334	C₂	1	2	yes	maximal
5	C₁₉×#1313	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×Q₃₂	C₄	1	1	yes	characteristic
7	C₈×Q₈×C₁₉	—	2	2	no	—
8	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	—
9	C₁₉×#367	C₄	1	1	yes	characteristic
10	C₁₉×#358	C₄	1	2	yes	—
11	C₁₉×#346	C₂²	1	1	yes	characteristic
12	C₁₉×#346	C₂²	1	1	yes	characteristic
13	C₁₉×#334	C₂²	1	2	yes	—
14	C₁₉×Q₈⋊C₈	—	2	2	no	—
15	C₁₉×#322	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
17	C₄×Q₈×C₁₉	—	2	2	no	—
18	C₁₉×Q₃₂	C₈	1	4	yes	complemented
19	C₂×C₁₆×C₁₉	—	2	1	no	—
20	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₁₉×#107	C₂×C₄	1	2	yes	—
23	C₁₉×C₄⋊C₈	—	2	2	no	—
24	C₁₉×C₄⋊C₈	—	4	2	no	—
25	C₁₉×#103	—	2	2	no	—
26	C₄×C₈×C₁₉	—	4	2	no	—
27	C₄×C₈×C₁₉	D₄	1	2	yes	—
28	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
29	C₂×Q₈×C₁₉	—	2	2	no	—
30	Q₁₆×C₁₉	—	2	2	no	—
31	Q₁₆×C₁₉	C₂×C₈	1	4	yes	—
32	C₂×C₈×C₁₉	—	2	2	no	—
33	C₂×C₈×C₁₉	—	4	2	no	—
34	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
36	C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₄⋊C₄×C₁₉	—	4	2	no	—
38	C₄²×C₁₉	—	4	2	no	—
39	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
40	C₁₆×C₁₉	—	2	1	no	—
41	C₁₆×C₁₉	—	4	1	no	—
42	C₁₆×C₁₉	C₂×C₈	1	2	yes	—
43	#12066	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	Q₈×C₁₉	—	2	4	no	—
45	Q₈×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	4	2	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
49	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
50	C₈×C₁₉	—	2	1	no	—
51	C₈×C₁₉	—	4	2	no	—
52	C₈×C₁₉	—	8	2	no	—
53	C₈×C₁₉	C₂²×C₈	1	1	yes	characteristic
54	C₈×C₁₉	#131	1	1	yes	characteristic
55	#2176	C₂×C₁₉	1	1	yes	characteristic
56	#1579	C₂×C₁₉	1	2	yes	—
57	#1368	C₂×C₁₉	1	1	yes	characteristic
58	#1334	C₂×C₁₉	1	2	yes	—
59	#1313	C₂×C₁₉	1	1	yes	characteristic
60	C₂²×C₁₉	#442	1	1	yes	characteristic
61	C₄×C₁₉	—	2	2	no	—
62	C₄×C₁₉	—	4	4	no	—
63	C₄×C₁₉	—	8	2	no	—
64	C₄×C₁₉	C₈×D₄	1	1	yes	characteristic
65	C₄×C₁₉	#444	1	1	yes	characteristic
66	C₂×Q₃₂	C₄×C₁₉	1	1	yes	characteristic
67	C₈×Q₈	—	2	2	no	—
68	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	—
69	#367	C₄×C₁₉	1	1	yes	characteristic
70	#358	C₄×C₁₉	1	2	yes	—
71	#346	C₂²×C₁₉	1	1	yes	characteristic
72	#346	C₂²×C₁₉	1	1	yes	characteristic
73	#334	C₂²×C₁₉	1	2	yes	—
74	Q₈⋊C₈	—	2	2	no	—
75	#322	C₂²×C₁₉	1	1	yes	characteristic
76	C₂×C₁₉	#1580	1	1	yes	characteristic
77	C₂×C₁₉	#2180	1	2	yes	—
78	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
79	C₄×Q₈	—	2	2	no	—
80	Q₃₂	C₈×C₁₉	1	4	yes	complemented
81	C₂×C₁₆	—	2	1	no	—
82	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
83	C₂×C₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
84	#107	C₂×C₄×C₁₉	1	2	yes	—
85	C₄⋊C₈	—	2	2	no	—
86	C₄⋊C₈	—	4	2	no	—
87	#103	—	2	2	no	—
88	C₄×C₈	—	4	2	no	—
89	C₄×C₈	D₄×C₁₉	1	2	yes	—
90	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
91	C₁₉	#12066	1	1	yes	characteristic, direct product factor, Sylow
92	C₂×Q₈	—	2	2	no	—
93	Q₁₆	—	2	2	no	—
94	Q₁₆	C₂×C₈×C₁₉	1	4	yes	—
95	C₂×C₈	—	2	2	no	—
96	C₂×C₈	—	4	2	no	—
97	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
98	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
99	C₄⋊C₄	—	2	2	no	—
100	C₄⋊C₄	—	4	2	no	—
101	C₄²	—	4	2	no	—
102	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
103	C₁₆	—	2	1	no	—
104	C₁₆	—	4	1	no	—
105	C₁₆	C₂×C₈×C₁₉	1	2	yes	—
106	Q₈	—	2	4	no	—
107	Q₈	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	4	2	no	—
110	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
111	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
112	C₈	—	2	1	no	—
113	C₈	—	4	2	no	—
114	C₈	—	8	2	no	—
115	C₈	C₂²×C₈×C₁₉	1	1	yes	characteristic
116	C₈	C₁₉×#131	1	1	yes	characteristic
117	C₂²	C₁₉×#442	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	4	4	no	—
120	C₄	—	8	2	no	—
121	C₄	C₈×D₄×C₁₉	1	1	yes	characteristic
122	C₄	C₁₉×#444	1	1	yes	characteristic
123	C₂	C₁₉×#1580	1	1	yes	characteristic
124	C₂	C₁₉×#2180	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2176

C₂

yes

maximal, characteristic

C₁₉×#1579

C₂

yes

maximal

C₁₉×#1368

C₂

yes

maximal, characteristic

C₁₉×#1334

C₂

yes

maximal

C₁₉×#1313

C₂

yes

maximal, characteristic

C₂×C₁₉×Q₃₂

C₄

yes

characteristic

C₈×Q₈×C₁₉

—

C₄×Q₁₆×C₁₉

C₂²

yes

—

C₁₉×#367

C₄

yes

characteristic

C₁₉×#358

C₄

yes

—

C₁₉×#346

C₂²

yes

characteristic

C₁₉×#346

C₂²

yes

characteristic

C₁₉×#334

C₂²

yes

—

C₁₉×Q₈⋊C₈

—

C₁₉×#322

C₂²

yes

characteristic

C₂×Q₁₆×C₁₉

C₂×C₄

yes

—

C₄×Q₈×C₁₉

—

C₁₉×Q₃₂

C₈

yes

complemented

C₂×C₁₆×C₁₉

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#107

C₂×C₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

C₂×C₈

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₉

#41

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₈

yes

—

#12066

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

C₂²×C₈

yes

C₈×C₁₉

yes

C₂×C₁₉

yes

characteristic

#1579

C₂×C₁₉

yes

—

#1368

C₂×C₁₉

yes

characteristic

#1334

C₂×C₁₉

yes

—

#1313

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

#442

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₈×D₄

yes

characteristic

C₄×C₁₉

#444

yes

characteristic

C₂×Q₃₂

C₄×C₁₉

yes

characteristic

C₈×Q₈

—

C₄×Q₁₆

C₂²×C₁₉

yes

—

#367

C₄×C₁₉

yes

characteristic

#358

C₄×C₁₉

yes

—

#346

C₂²×C₁₉

yes

characteristic

#346

C₂²×C₁₉

yes

characteristic

#334

C₂²×C₁₉

yes

—

Q₈⋊C₈

—

#322

C₂²×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂×Q₁₆

C₂×C₄×C₁₉

yes

—

C₄×Q₈

—

Q₃₂

C₈×C₁₉

yes

complemented

C₂×C₁₆

—

C₂×C₁₆

C₂×C₄×C₁₉

yes

characteristic

C₂×C₁₆

C₂×C₄×C₁₉

yes

characteristic

#107

C₂×C₄×C₁₉

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₄×C₈

D₄×C₁₉

yes

—

C₄×C₈

C₂³×C₁₉

yes

characteristic

C₁₉

#12066

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

C₂×C₈×C₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×C₄×C₁₉

yes

characteristic

C₂×C₈

#41×C₁₉

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄²

—

102

C₄²

C₂×D₄×C₁₉

yes

characteristic

103

C₁₆

—

104

C₁₆

—

105

C₁₆

C₂×C₈×C₁₉

yes

—

106

Q₈

—

107

Q₈

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

C₄×D₄×C₁₉

yes

characteristic

111

C₂×C₄

C₁₉×AGL(1,ℤ/8)

yes

—

112

C₈

—

113

C₈

—

114

C₈

—

115

C₈

C₂²×C₈×C₁₉

yes

characteristic

116

C₈

C₁₉×#131

yes

characteristic

117

C₂²

C₁₉×#442

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₈×D₄×C₁₉

yes

characteristic

122

C₄

C₁₉×#444

yes

characteristic

123

C₂

C₁₉×#1580

yes

characteristic

124

C₂

C₁₉×#2180

yes

—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#442
commutator	C₈	C₂²×C₈×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#322 ◁ G

subgroup

G/H

center, socle, prime radical

C₂²×C₁₉

#442

commutator

C₈

C₂²×C₈×C₁₉

Frattini, cosocle

C₄×C₈

C₂³×C₁₉

LCS

G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#322 ◁ G

N	H ≅ G/N	type
18. C₁₉×Q₃₂	C₈	semidirect
43. #12066	C₁₉	direct (N × H)
80. Q₃₂	C₈×C₁₉	semidirect
91. C₁₉	#12066	direct (N × H)

H ≅ G/N

type

18. C₁₉×Q₃₂

C₈

semidirect

43. #12066

C₁₉

direct (N × H)

80. Q₃₂

C₈×C₁₉

semidirect

91. C₁₉

#12066

direct (N × H)

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

subgroup	index
C₁₉×#2176	2
C₁₉×#1579	2
C₁₉×#1368	2
C₁₉×#1334	2
C₁₉×#1313	2
#12066	19

subgroup

index

C₁₉×#2176

C₁₉×#1579

C₁₉×#1368

C₁₉×#1334

C₁₉×#1313

#12066

Subgroups — C₁₉×#12066 #18018025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12066 #18018025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12066 #18018025