Group #18072959 — subgroups

Subgroups — #18072959

Order 4864.

520 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 151 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	#14572267	C₂	1	3	yes	maximal
2	C₁₉⋊#1309	C₂	1	3	yes	maximal, complemented
3	C₁₉×#1309	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
5	#11926600	—	2	6	no	—
6	#11926596	—	2	6	no	—
7	#11926568	C₂²	1	3	yes	—
8	#11926507	C₄	1	6	yes	—
9	M₁₆×Dic₁₉	C₄	1	6	yes	—
10	C₁₉×#423	C₂²	1	3	yes	—
11	C₂²×C₄×D₁₉	C₂×C₄	1	3	yes	—
12	C₂×M₁₆×C₁₉	C₂×C₄	1	6	yes	—
13	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
14	C₂×C₄×Dic₁₉	C₂×C₄	1	3	yes	—
15	C₂×#64520	C₂×C₄	1	6	yes	—
16	C₄²×D₁₉	D₄	1	6	yes	—
17	C₄²×D₁₉	Q₈	1	2	yes	—
18	C₁₉×C₄⋊C₈	—	2	6	no	—
19	(C₂×D₁₉)⋊C₈	—	2	12	no	—
20	#10597272	—	2	6	no	—
21	C₈×Dic₁₉	—	2	6	no	—
22	C₄⋊(C₁₉⋊C₈)	—	2	6	no	—
23	C₂³×D₁₉	C₄²	1	1	yes	characteristic
24	C₂²×C₄×C₁₉	C₂²×C₄	1	3	yes	—
25	C₂²×Dic₁₉	C₄²	1	3	yes	—
26	C₂×C₄×D₁₉	—	4	3	no	—
27	C₂×C₄×D₁₉	—	4	3	no	—
28	C₂×C₄×D₁₉	C₂²⋊C₄	1	6	yes	—
29	C₂×C₄×D₁₉	C₄⋊C₄	1	6	yes	—
30	M₁₆×C₁₉	—	4	6	no	—
31	C₂×C₈×C₁₉	—	2	6	no	—
32	C₄²×C₁₉	C₂×D₄	1	3	yes	—
33	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
34	C₄×Dic₁₉	C₂²⋊C₄	1	3	yes	—
35	C₄×Dic₁₉	C₂²⋊C₄	1	3	yes	—
36	C₄×Dic₁₉	C₄⋊C₄	1	6	yes	—
37	#64520	—	4	6	no	—
38	C₂×C₁₉⋊C₈	—	2	6	no	—
39	#8130	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
41	C₂²×D₁₉	—	4	3	no	—
42	C₂²×D₁₉	#95	1	2	yes	—
43	C₂×C₄×C₁₉	—	2	3	no	—
44	C₂×C₄×C₁₉	—	2	3	no	—
45	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	3	yes	—
46	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	3	yes	—
47	C₂×Dic₁₉	—	4	3	no	—
48	C₂×Dic₁₉	#95	1	6	yes	—
49	C₄×D₁₉	—	2	6	no	—
50	C₄×D₁₉	—	2	6	no	—
51	C₄×D₁₉	—	4	6	no	—
52	C₈×C₁₉	—	4	6	no	—
53	C₁₉⋊C₈	—	4	6	no	—
54	#2920	—	19	3	no	—
55	#1309	—	19	3	no	—
56	#1309	D₁₉	1	1	yes	characteristic, complemented
57	C₂²×C₁₉	—	2	3	no	—
58	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
59	C₂×D₁₉	—	2	6	no	—
60	C₂×D₁₉	—	4	4	no	—
61	C₄×C₁₉	—	2	3	no	—
62	C₄×C₁₉	#413	1	3	yes	—
63	C₄×C₁₉	#413	1	3	yes	—
64	Dic₁₉	—	2	6	no	—
65	C₂²×C₄²	—	19	1	no	—
66	#432	—	38	6	no	—
67	#431	—	38	6	no	—
68	#423	—	19	3	no	—
69	#423	C₂×D₁₉	1	3	yes	—
70	#407	—	19	6	no	—
71	C₄×M₁₆	—	19	6	no	—
72	C₂×C₁₉	—	4	1	no	—
73	C₂×C₁₉	#1742	1	3	yes	—
74	D₁₉	—	4	2	no	—
75	C₂³×C₄	—	19	3	no	—
76	C₂×M₁₆	—	19	6	no	—
77	C₂×M₁₆	C₄×D₁₉	1	6	yes	—
78	C₂×C₄²	—	19	3	no	—
79	C₂×C₄²	—	19	6	no	—
80	C₂×C₄²	—	19	2	no	—
81	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
82	C₄⋊C₈	—	2	6	no	—
83	C₄⋊C₈	—	38	6	no	—
84	C₂²⋊C₈	—	38	12	no	—
85	#97	—	38	6	no	—
86	C₄×C₈	—	38	6	no	—
87	C₁₉	#8130	1	1	yes	characteristic, complemented, Sylow
88	C₂⁴	—	19	1	no	—
89	C₂²×C₄	—	19	3	no	—
90	C₂²×C₄	—	19	6	no	—
91	C₂²×C₄	—	19	6	no	—
92	C₂²×C₄	—	76	3	no	—
93	C₂²×C₄	—	76	3	no	—
94	C₂²×C₄	C₂×C₄×D₁₉	1	3	yes	—
95	M₁₆	—	4	6	no	—
96	M₁₆	—	76	6	no	—
97	C₂×C₈	—	2	6	no	—
98	C₂×C₈	—	38	6	no	—
99	C₄²	—	19	3	no	—
100	C₄²	—	19	3	no	—
101	C₄²	—	19	6	no	—
102	C₄²	D₄×D₁₉	1	3	yes	—
103	C₄²	Q₈×D₁₉	1	1	yes	characteristic
104	C₂³	—	19	2	no	—
105	C₂³	—	76	3	no	—
106	C₂³	C₄²×D₁₉	1	1	yes	characteristic
107	C₂×C₄	—	2	3	no	—
108	C₂×C₄	—	2	3	no	—
109	C₂×C₄	—	19	6	no	—
110	C₂×C₄	—	38	6	no	—
111	C₂×C₄	—	38	6	no	—
112	C₂×C₄	—	76	6	no	—
113	C₂×C₄	—	76	3	no	—
114	C₂×C₄	C₂²⋊C₄×D₁₉	1	3	yes	—
115	C₂×C₄	C₄⋊C₄×D₁₉	1	3	yes	—
116	C₈	—	4	6	no	—
117	C₈	—	76	6	no	—
118	C₂²	—	2	3	no	—
119	C₂²	—	38	6	no	—
120	C₂²	—	76	4	no	—
121	C₂²	#95×D₁₉	1	1	yes	characteristic
122	C₄	—	2	3	no	—
123	C₄	—	38	6	no	—
124	C₄	#11926525	1	3	yes	—
125	C₄	#11926527	1	3	yes	—
126	C₂	—	4	1	no	—
127	C₂	—	76	2	no	—
128	C₂	#14563372	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572267

C₂

yes

maximal

C₁₉⋊#1309

C₂

yes

maximal, complemented

C₁₉×#1309

C₂

yes

maximal, characteristic, complemented

C₂×C₄²×D₁₉

C₂²

yes

—

—

C₂²

yes

—

#11926507

C₄

yes

—

M₁₆×Dic₁₉

C₄

yes

—

C₁₉×#423

C₂²

yes

—

C₂²×C₄×D₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

C₂×C₄

yes

—

C₂×#64520

C₂×C₄

yes

—

C₄²×D₁₉

D₄

yes

—

C₄²×D₁₉

Q₈

yes

—

C₁₉×C₄⋊C₈

—

(C₂×D₁₉)⋊C₈

—

#10597272

—

C₈×Dic₁₉

—

C₄⋊(C₁₉⋊C₈)

—

C₂³×D₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

—

C₂²×Dic₁₉

C₄²

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

C₂²⋊C₄

yes

—

C₂×C₄×D₁₉

C₄⋊C₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄×Dic₁₉

C₂²⋊C₄

yes

—

C₄×Dic₁₉

C₂²⋊C₄

yes

—

C₄×Dic₁₉

C₄⋊C₄

yes

—

#64520

—

C₂×C₁₉⋊C₈

—

#8130

—

maximal, Sylow

C₂³×C₁₉

C₂×C₄²

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

#95

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

#95

yes

—

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#2920

—

#1309

—

#1309

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

C₂×#95

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#413

yes

—

C₄×C₁₉

#413

yes

—

Dic₁₉

—

C₂²×C₄²

—

—

—

—

C₂×D₁₉

yes

—

#407

—

C₄×M₁₆

—

C₂×C₁₉

—

C₂×C₁₉

#1742

yes

—

D₁₉

—

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₁₉

#8130

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₁₉

yes

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

D₄×D₁₉

yes

—

103

C₄²

Q₈×D₁₉

yes

characteristic

104

C₂³

—

105

C₂³

—

106

C₂³

C₄²×D₁₉

yes

characteristic

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

C₂²⋊C₄×D₁₉

yes

—

115

C₂×C₄

C₄⋊C₄×D₁₉

yes

—

116

C₈

—

117

C₈

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

#95×D₁₉

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

#11926525

yes

—

125

C₄

#11926527

yes

—

126

C₂

—

127

C₂

—

128

C₂

#14563372

yes

—

	subgroup	G/H
center	C₂²	#95×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1309	C₂
socle	C₂²×C₁₉	C₂×#95
prime radical	C₂³×D₁₉	C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1309	D₁₉
hypocenter	C₁₉	#8130
LCS	G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

subgroup

G/H

center

C₂²

#95×D₁₉

commutator

C₂³×C₁₉

C₂×C₄²

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1309

C₂

socle

C₂²×C₁₉

C₂×#95

prime radical

C₂³×D₁₉

C₄²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1309

N	H ≅ G/N	type
2. C₁₉⋊#1309	C₂	semidirect
3. C₁₉×#1309	C₂	semidirect
56. #1309	D₁₉	semidirect
87. C₁₉	#8130	semidirect

H ≅ G/N

type

2. C₁₉⋊#1309

C₂

semidirect

3. C₁₉×#1309

C₂

semidirect

56. #1309

D₁₉

semidirect

87. C₁₉

#8130

semidirect

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

subgroup	index
#14572267	2
C₁₉⋊#1309	2
C₁₉×#1309	2
#8130	19

subgroup

index

#14572267

C₁₉⋊#1309

C₁₉×#1309

#8130

Subgroups — #18072959

Conjugacy classes of subgroups

Complements

Maximal subgroups