Group #14563710 — subgroups

Subgroups — #14563710

Order 2432.

300 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 85 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×#10597372	C₂	1	1	yes	maximal, characteristic
2	#11926407	C₂	1	1	yes	maximal, characteristic
3	#11926310	C₂	1	4	yes	maximal
4	C₁₉×#381	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
7	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
8	C₂×C₂²⋊Dic₁₉	C₂²	1	2	yes	—
9	#10597372	—	2	2	no	—
10	#10597372	—	2	2	no	—
11	C₂×C₄⋊Dic₁₉	C₄	1	2	yes	complemented
12	C₂×C₄×Dic₁₉	C₄	1	2	yes	complemented
13	C₁₉×#95	—	2	2	no	—
14	C₁₉⋊#95	—	2	2	no	—
15	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
16	C₂²×C₄×C₁₉	—	2	4	no	—
17	C₂²×C₄×C₁₉	—	2	2	no	—
18	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₁₉	D₄	1	2	yes	—
21	C₂²×C₄×C₁₉	D₄	1	2	yes	—
22	C₂²×Dic₁₉	—	2	2	no	—
23	C₂²×Dic₁₉	C₂×C₄	1	4	yes	—
24	C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₂²⋊Dic₁₉	—	2	2	no	—
26	C₂²⋊Dic₁₉	—	2	2	no	—
27	C₂²⋊Dic₁₉	—	2	4	no	—
28	C₄⋊Dic₁₉	—	2	4	no	—
29	C₄×Dic₁₉	—	2	4	no	—
30	C₂³×C₁₉	—	4	2	no	—
31	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
32	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
33	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂³×C₁₉	#41	1	4	yes	—
35	C₂×C₄×C₁₉	—	2	2	no	—
36	C₂×C₄×C₁₉	—	2	2	no	—
37	C₂×C₄×C₁₉	—	2	4	no	—
38	C₂×C₄×C₁₉	—	2	4	no	—
39	C₂×C₄×C₁₉	—	4	4	no	—
40	C₂×C₄×C₁₉	—	4	2	no	—
41	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
43	C₂×Dic₁₉	—	2	4	no	—
44	C₂×Dic₁₉	—	4	4	no	—
45	C₂×Dic₁₉	—	4	4	no	—
46	C₂×Dic₁₉	—	4	2	no	—
47	#1820	—	19	1	no	maximal, Sylow
48	C₂²×C₁₉	—	2	2	no	—
49	C₂²×C₁₉	—	2	2	no	—
50	C₂²×C₁₉	—	2	2	no	—
51	C₂²×C₁₉	—	4	4	no	—
52	C₂²×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₁₉	#117	1	2	yes	—
54	C₂²×C₁₉	#123	1	2	yes	—
55	C₂²×C₁₉	#123	1	2	yes	—
56	C₄×C₁₉	—	2	2	no	—
57	C₄×C₁₉	—	2	2	no	—
58	C₄×C₁₉	—	8	2	no	—
59	Dic₁₉	—	4	4	no	—
60	Dic₁₉	—	8	2	no	—
61	C₂×#117	—	19	1	no	—
62	#381	—	19	1	no	—
63	#381	D₁₉	1	1	yes	characteristic
64	#342	—	19	4	no	—
65	C₂×C₁₉	—	2	2	no	—
66	C₂×C₁₉	—	2	2	no	—
67	C₂×C₁₉	—	2	2	no	—
68	C₂×C₁₉	#381	1	1	yes	characteristic
69	C₂×C₁₉	#410	1	2	yes	—
70	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
71	#117	—	38	2	no	—
72	#117	—	38	2	no	—
73	C₂×C₄⋊C₄	—	19	2	no	—
74	C₂×C₂²⋊C₄	—	19	2	no	—
75	C₂×C₂²⋊C₄	—	19	2	no	—
76	C₂×C₂²⋊C₄	C₂×D₁₉	1	2	yes	—
77	C₂×C₄²	—	19	2	no	—
78	#95	—	2	2	no	—
79	#95	—	38	2	no	—
80	C₁₉	#1820	1	1	yes	characteristic, complemented, Sylow
81	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
82	C₂²×C₄	—	2	4	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	19	4	no	—
85	C₂²×C₄	—	38	2	no	—
86	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
87	C₂²×C₄	C₄×D₁₉	1	1	yes	characteristic
88	C₂²×C₄	D₇₆	1	2	yes	—
89	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
90	C₄⋊C₄	—	38	4	no	—
91	C₂²⋊C₄	—	2	4	no	—
92	C₂²⋊C₄	—	38	2	no	—
93	C₂²⋊C₄	—	38	2	no	—
94	C₂²⋊C₄	—	38	4	no	—
95	C₄²	—	38	4	no	—
96	C₂³	—	4	2	no	—
97	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
98	C₂³	C₂×D₇₆	1	1	yes	characteristic
99	C₂³	#64543	1	4	yes	—
100	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	4	4	no	—
106	C₂×C₄	—	4	2	no	—
107	C₂×C₄	—	38	4	no	—
108	C₂×C₄	—	76	4	no	—
109	C₂×C₄	—	76	4	no	—
110	C₂×C₄	—	76	2	no	—
111	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
112	C₂×C₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
113	C₂²	—	2	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	4	4	no	—
117	C₂²	#10597323	1	2	yes	—
118	C₂²	#10597332	1	2	yes	—
119	C₂²	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
120	C₂²	#10597381	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	2	2	no	—
123	C₄	—	8	2	no	—
124	C₄	—	76	4	no	—
125	C₄	—	152	2	no	—
126	C₂	—	2	2	no	—
127	C₂	—	2	2	no	—
128	C₂	—	2	2	no	—
129	C₂	#11926405	1	1	yes	characteristic
130	C₂	#11926517	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597372

C₂

yes

maximal, characteristic

#11926407

C₂

yes

maximal, characteristic

#11926310

C₂

yes

maximal

C₁₉×#381

C₂

yes

maximal, characteristic

C₂³×C₄×C₁₉

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

#10597372

—

#10597372

—

C₂×C₄⋊Dic₁₉

C₄

yes

complemented

C₂×C₄×Dic₁₉

C₄

yes

complemented

C₁₉×#95

—

C₁₉⋊#95

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

C₂×C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂²×C₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

C₂×D₄

yes

characteristic

C₂³×C₁₉

#41

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#1820

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₁₉

#117

yes

—

C₂²×C₁₉

#123

yes

—

C₂²×C₁₉

#123

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂×#117

—

#381

—

#381

D₁₉

yes

characteristic

#342

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#381

yes

characteristic

C₂×C₁₉

#410

yes

—

C₂³×C₄

C₂×D₁₉

yes

characteristic

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

#95

—

#95

—

C₁₉

#1820

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

C₄×D₁₉

yes

characteristic

C₂²×C₄

D₇₆

yes

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₂×C₄×D₁₉

yes

characteristic

C₂³

C₂×D₇₆

yes

characteristic

C₂³

#64543

yes

—

100

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

112

C₂×C₄

(C₂×D₁₉)⋊C₄

yes

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

#10597323

yes

—

118

C₂²

#10597332

yes

—

119

C₂²

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

120

C₂²

#10597381

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

152

—

126

C₂

—

127

C₂

—

128

C₂

—

129

C₂

#11926405

yes

characteristic

130

C₂

#11926517

yes

—

	subgroup	G/H
center	C₂²	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂³×C₁₉	C₂²×C₄
Frattini	C₂⁴	C₂²×D₁₉
Fitting	C₁₉×#381	C₂
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical, cosocle	C₂⁴×C₁₉	C₂³
hypercenter	#381	D₁₉
hypocenter	C₁₉	#1820
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

subgroup

G/H

center

C₂²

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂³×C₁₉

C₂²×C₄

Frattini

C₂⁴

C₂²×D₁₉

Fitting

C₁₉×#381

C₂

socle

C₂²×C₁₉

C₂×C₂²⋊C₄

prime radical, cosocle

C₂⁴×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #381

N	H ≅ G/N	type
11. C₂×C₄⋊Dic₁₉	C₄	semidirect
12. C₂×C₄×Dic₁₉	C₄	semidirect
80. C₁₉	#1820	semidirect

H ≅ G/N

type

11. C₂×C₄⋊Dic₁₉

C₄

semidirect

12. C₂×C₄×Dic₁₉

C₄

semidirect

80. C₁₉

#1820

semidirect

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

subgroup	index
C₂×#10597372	2
#11926407	2
#11926310	2
C₁₉×#381	2
#1820	19

subgroup

index

C₁₉×#381

Subgroups — #14563710

Conjugacy classes of subgroups

Complements

Maximal subgroups