Group #18087682 — subgroups

Subgroups — #18087682

Order 4864.

372 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 59 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⋊#1304	C₂	1	3	yes	maximal
2	C₁₉⋊#1304	C₂	1	3	yes	maximal
3	C₁₉×#1304	C₂	1	1	yes	maximal, characteristic
4	#11926400	C₂²	1	1	yes	characteristic
5	#11926400	C₂²	1	3	yes	—
6	C₁₉×#379	C₂²	1	3	yes	—
7	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
8	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
9	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
10	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
11	C₂×C₂²⋊Dic₁₉	—	2	3	no	—
12	C₂×C₂²⋊Dic₁₉	—	2	3	no	—
13	C₂×C₂²⋊Dic₁₉	—	2	3	no	—
14	C₂×C₂²⋊Dic₁₉	—	2	3	no	—
15	C₂⁴×C₁₉	—	8	3	no	—
16	C₂⁴×C₁₉	#41	1	3	yes	—
17	C₂⁴×C₁₉	#41	1	3	yes	—
18	C₂⁴×C₁₉	#41	1	1	yes	characteristic
19	C₂²×C₄×C₁₉	—	4	3	no	—
20	C₂²×Dic₁₉	—	4	1	no	—
21	C₂²×Dic₁₉	—	4	3	no	—
22	C₂²⋊C₄×C₁₉	—	8	3	no	—
23	C₂²⋊C₄×C₁₉	—	8	3	no	—
24	C₂²⋊C₄×C₁₉	—	8	3	no	—
25	C₂²⋊Dic₁₉	—	8	3	no	—
26	C₂²⋊Dic₁₉	—	8	3	no	—
27	C₂²⋊Dic₁₉	—	8	3	no	—
28	C₂²⋊Dic₁₉	—	8	3	no	—
29	#10690	—	19	1	no	maximal, Sylow
30	C₂³×C₁₉	—	4	3	no	—
31	C₂³×C₁₉	—	4	3	no	—
32	C₂³×C₁₉	—	4	3	no	—
33	C₂³×C₁₉	—	4	3	no	—
34	C₂³×C₁₉	—	4	3	no	—
35	C₂³×C₁₉	—	4	3	no	—
36	C₂³×C₁₉	—	4	3	no	—
37	C₂³×C₁₉	—	8	8	no	—
38	C₂³×C₁₉	#126	1	1	yes	characteristic
39	C₂³×C₁₉	#126	1	3	yes	—
40	C₂³×C₁₉	#126	1	3	yes	—
41	C₂×C₄×C₁₉	—	8	3	no	—
42	C₂×C₄×C₁₉	—	8	3	no	—
43	C₂×C₄×C₁₉	—	8	3	no	—
44	C₂×Dic₁₉	—	8	3	no	—
45	C₂×Dic₁₉	—	8	3	no	—
46	C₂×Dic₁₉	—	8	3	no	—
47	C₂×Dic₁₉	—	8	3	no	—
48	#1304	—	19	3	no	—
49	#1304	—	19	3	no	—
50	#1304	D₁₉	1	1	yes	characteristic
51	C₂²×C₁₉	—	2	3	no	—
52	C₂²×C₁₉	—	2	3	no	—
53	C₂²×C₁₉	—	2	3	no	—
54	C₂²×C₁₉	—	2	3	no	—
55	C₂²×C₁₉	—	2	3	no	—
56	C₂²×C₁₉	—	2	3	no	—
57	C₂²×C₁₉	—	2	3	no	—
58	C₂²×C₁₉	—	8	2	no	—
59	C₂²×C₁₉	—	8	6	no	—
60	C₂²×C₁₉	—	8	6	no	—
61	C₂²×C₁₉	#401	1	1	yes	characteristic
62	C₄×C₁₉	—	16	3	no	—
63	Dic₁₉	—	16	1	no	—
64	Dic₁₉	—	16	3	no	—
65	#379	—	19	1	no	—
66	#379	—	19	3	no	—
67	#379	C₂×D₁₉	1	3	yes	—
68	C₂×C₁₉	—	4	1	no	—
69	C₂×C₁₉	—	4	3	no	—
70	C₂×C₁₉	—	4	3	no	—
71	C₂×C₁₉	#2104	1	3	yes	—
72	C₂⁵	C₂²×D₁₉	1	1	yes	characteristic
73	C₂×C₂²⋊C₄	—	2	3	no	—
74	C₂×C₂²⋊C₄	—	2	3	no	—
75	C₂×C₂²⋊C₄	—	2	3	no	—
76	C₂×C₂²⋊C₄	—	38	3	no	—
77	C₂×C₂²⋊C₄	—	38	3	no	—
78	C₂×C₂²⋊C₄	—	38	3	no	—
79	C₂×C₂²⋊C₄	—	38	3	no	—
80	C₁₉	#10690	1	1	yes	characteristic, complemented, Sylow
81	C₂⁴	—	8	3	no	—
82	C₂⁴	#64541	1	3	yes	—
83	C₂⁴	#64543	1	3	yes	—
84	C₂⁴	#64545	1	1	yes	characteristic
85	C₂²×C₄	—	4	3	no	—
86	C₂²×C₄	—	76	1	no	—
87	C₂²×C₄	—	76	3	no	—
88	C₂²⋊C₄	—	8	3	no	—
89	C₂²⋊C₄	—	8	3	no	—
90	C₂²⋊C₄	—	8	3	no	—
91	C₂²⋊C₄	—	152	3	no	—
92	C₂²⋊C₄	—	152	3	no	—
93	C₂²⋊C₄	—	152	3	no	—
94	C₂²⋊C₄	—	152	3	no	—
95	C₂³	—	4	3	no	—
96	C₂³	—	4	3	no	—
97	C₂³	—	4	3	no	—
98	C₂³	—	4	3	no	—
99	C₂³	—	4	3	no	—
100	C₂³	—	4	3	no	—
101	C₂³	—	4	3	no	—
102	C₂³	—	8	8	no	—
103	C₂³	#10597322	1	1	yes	characteristic
104	C₂³	#10597325	1	3	yes	—
105	C₂³	#10597344	1	3	yes	—
106	C₂×C₄	—	8	3	no	—
107	C₂×C₄	—	8	3	no	—
108	C₂×C₄	—	8	3	no	—
109	C₂×C₄	—	152	3	no	—
110	C₂×C₄	—	152	3	no	—
111	C₂×C₄	—	152	3	no	—
112	C₂×C₄	—	152	3	no	—
113	C₂²	—	2	3	no	—
114	C₂²	—	2	3	no	—
115	C₂²	—	2	3	no	—
116	C₂²	—	2	3	no	—
117	C₂²	—	2	3	no	—
118	C₂²	—	2	3	no	—
119	C₂²	—	2	3	no	—
120	C₂²	—	8	6	no	—
121	C₂²	—	8	6	no	—
122	C₂²	—	8	2	no	—
123	C₂²	C₁₉⋊#401	1	1	yes	characteristic
124	C₄	—	16	3	no	—
125	C₄	—	304	1	no	—
126	C₄	—	304	3	no	—
127	C₂	—	4	3	no	—
128	C₂	—	4	1	no	—
129	C₂	—	4	3	no	—
130	C₂	C₁₉⋊#2104	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉⋊#1304

C₂

yes

maximal

C₁₉⋊#1304

C₂

yes

maximal

C₁₉×#1304

C₂

yes

maximal, characteristic

#11926400

C₂²

yes

characteristic

#11926400

C₂²

yes

—

C₁₉×#379

C₂²

yes

—

C₂⁵×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

#41

yes

—

C₂⁴×C₁₉

#41

yes

—

C₂⁴×C₁₉

#41

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#10690

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#126

yes

characteristic

C₂³×C₁₉

#126

yes

—

C₂³×C₁₉

#126

yes

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#1304

—

#1304

—

#1304

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#401

yes

characteristic

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#379

—

#379

—

#379

C₂×D₁₉

yes

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2104

yes

—

C₂⁵

C₂²×D₁₉

yes

characteristic

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₁₉

#10690

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

#64541

yes

—

C₂⁴

#64543

yes

—

C₂⁴

#64545

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

152

—

C₂²⋊C₄

—

152

—

C₂²⋊C₄

—

152

—

C₂²⋊C₄

—

152

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

#10597322

yes

characteristic

104

C₂³

#10597325

yes

—

105

C₂³

#10597344

yes

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

152

—

110

C₂×C₄

—

152

—

111

C₂×C₄

—

152

—

112

C₂×C₄

—

152

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

C₁₉⋊#401

yes

characteristic

124

C₄

—

125

C₄

—

304

—

126

C₄

—

304

—

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

C₁₉⋊#2104

yes

—

	subgroup	G/H
center	C₂²	C₁₉⋊#401
commutator, prime radical, cosocle	C₂⁵×C₁₉	C₂³
Frattini	C₂⁵	C₂²×D₁₉
Fitting	C₁₉×#1304	C₂
socle	C₂²×C₁₉	#401
hypercenter	#1304	D₁₉
hypocenter	C₁₉	#10690
LCS	G ▷ C₂⁵×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #1304

subgroup

G/H

center

C₂²

C₁₉⋊#401

commutator, prime radical, cosocle

C₂⁵×C₁₉

C₂³

Frattini

C₂⁵

C₂²×D₁₉

Fitting

C₁₉×#1304

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂⁵×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂⁵ ◁ #1304

N	H ≅ G/N	type
80. C₁₉	#10690	semidirect

H ≅ G/N

type

80. C₁₉

#10690

semidirect

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

subgroup	index
C₁₉⋊#1304	2
C₁₉×#1304	2
#10690	19

subgroup

index

C₁₉⋊#1304

C₁₉×#1304

#10690

Subgroups — #18087682

Conjugacy classes of subgroups

Complements

Maximal subgroups