Group #18085791 — subgroups

Subgroups — #18085791

Order 4864.

542 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 77 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	#14563707	C₂	1	3	yes	maximal
2	C₁₉⋊#1304	C₂	1	3	yes	maximal
3	C₁₉×#2840	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
5	#11926400	C₂²	1	3	yes	—
6	#11926310	—	2	6	no	—
7	C₁₉×#393	—	2	6	no	—
8	C₁₉×#379	C₂²	1	3	yes	—
9	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
10	C₂²×Q₈×C₁₉	—	2	2	no	—
11	C₂³×Dic₁₉	Q₈	1	2	yes	complemented
12	C₂×C₂²⋊C₄×C₁₉	—	2	6	no	—
13	C₂×C₂²⋊C₄×C₁₉	D₄	1	6	yes	—
14	C₂×C₂²⋊Dic₁₉	—	2	3	no	—
15	C₂×C₂²⋊Dic₁₉	—	2	3	no	—
16	C₂×C₂²⋊Dic₁₉	—	2	3	no	—
17	C₂×C₂²⋊Dic₁₉	—	2	6	no	—
18	C₁₉×#95	—	2	6	no	—
19	C₂⁴×C₁₉	—	4	2	no	—
20	C₂⁴×C₁₉	—	8	2	no	—
21	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
22	C₂⁴×C₁₉	C₂×Q₈	1	1	yes	characteristic
23	C₂⁴×C₁₉	#41	1	3	yes	—
24	C₂×Q₈×C₁₉	—	8	4	no	—
25	C₂×Q₈×C₁₉	—	8	2	no	—
26	C₂²×C₄×C₁₉	—	2	6	no	—
27	C₂²×Dic₁₉	—	2	6	no	—
28	C₂²×Dic₁₉	—	4	3	no	—
29	C₂²×Dic₁₉	—	8	2	no	—
30	C₂²⋊C₄×C₁₉	—	4	6	no	—
31	C₂²⋊C₄×C₁₉	—	8	6	no	—
32	C₂²⋊Dic₁₉	—	4	1	no	—
33	C₂²⋊Dic₁₉	—	4	3	no	—
34	C₂²⋊Dic₁₉	—	4	6	no	—
35	C₂²⋊Dic₁₉	—	8	6	no	—
36	#10391	—	19	1	no	maximal, Sylow
37	C₂³×C₁₉	—	2	6	no	—
38	C₂³×C₁₉	—	4	2	no	—
39	C₂³×C₁₉	—	4	1	no	—
40	C₂³×C₁₉	—	4	6	no	—
41	C₂³×C₁₉	—	4	6	no	—
42	C₂³×C₁₉	—	4	3	no	—
43	C₂³×C₁₉	—	8	8	no	—
44	C₂³×C₁₉	#120	1	1	yes	characteristic
45	C₂³×C₁₉	C₂²⋊Q₈	1	3	yes	—
46	C₂³×C₁₉	#124	1	3	yes	—
47	Q₈×C₁₉	—	8	8	no	—
48	C₂×C₄×C₁₉	—	4	12	no	—
49	C₂×C₄×C₁₉	—	4	6	no	—
50	C₂×Dic₁₉	—	4	2	no	—
51	C₂×Dic₁₉	—	8	6	no	—
52	C₂×Dic₁₉	—	8	3	no	—
53	C₂×Dic₁₉	—	8	6	no	—
54	#2840	D₁₉	1	1	yes	characteristic
55	#1819	—	19	3	no	—
56	#1304	—	19	3	no	—
57	C₂²×C₁₉	—	2	2	no	—
58	C₂²×C₁₉	—	2	3	no	—
59	C₂²×C₁₉	—	2	3	no	—
60	C₂²×C₁₉	—	2	6	no	—
61	C₂²×C₁₉	—	2	6	no	—
62	C₂²×C₁₉	—	4	4	no	—
63	C₂²×C₁₉	—	8	6	no	—
64	C₂²×C₁₉	—	8	6	no	—
65	C₂²×C₁₉	#393	1	1	yes	characteristic
66	C₂²×C₁₉	#458	1	2	yes	—
67	C₄×C₁₉	—	8	6	no	—
68	Dic₁₉	—	8	2	no	—
69	Dic₁₉	—	16	3	no	—
70	C₂²×C₂²⋊C₄	—	19	1	no	—
71	#393	—	2	6	no	—
72	#379	—	19	3	no	—
73	#379	C₂×D₁₉	1	3	yes	—
74	#342	—	38	6	no	—
75	C₂×C₁₉	—	2	2	no	—
76	C₂×C₁₉	—	4	3	no	—
77	C₂×C₁₉	—	4	3	no	—
78	C₂×C₁₉	#2030	1	1	yes	characteristic
79	C₂×C₁₉	#2032	1	2	yes	—
80	C₂⁵	C₂²×D₁₉	1	1	yes	characteristic
81	C₂²×Q₈	—	2	2	no	—
82	C₂³×C₄	—	19	2	no	—
83	C₂×C₂²⋊C₄	—	2	6	no	—
84	C₂×C₂²⋊C₄	—	38	3	no	—
85	C₂×C₂²⋊C₄	—	38	3	no	—
86	C₂×C₂²⋊C₄	—	38	3	no	—
87	C₂×C₂²⋊C₄	—	38	6	no	—
88	C₂×C₂²⋊C₄	C₂²⋊D₁₉	1	6	yes	—
89	#95	—	2	6	no	—
90	C₁₉	#10391	1	1	yes	characteristic, complemented, Sylow
91	C₂⁴	—	4	2	no	—
92	C₂⁴	—	8	2	no	—
93	C₂⁴	Q₈×D₁₉	1	1	yes	characteristic
94	C₂⁴	#64545	1	3	yes	—
95	C₂⁴	C₂×C₂²⋊D₁₉	1	3	yes	—
96	C₂×Q₈	—	8	4	no	—
97	C₂×Q₈	—	8	2	no	—
98	C₂²×C₄	—	2	6	no	—
99	C₂²×C₄	—	38	6	no	—
100	C₂²×C₄	—	76	3	no	—
101	C₂²×C₄	—	152	2	no	—
102	C₂²⋊C₄	—	4	6	no	—
103	C₂²⋊C₄	—	8	6	no	—
104	C₂²⋊C₄	—	76	3	no	—
105	C₂²⋊C₄	—	76	1	no	—
106	C₂²⋊C₄	—	76	6	no	—
107	C₂²⋊C₄	—	152	6	no	—
108	C₂³	—	2	6	no	—
109	C₂³	—	4	2	no	—
110	C₂³	—	4	1	no	—
111	C₂³	—	4	6	no	—
112	C₂³	—	4	6	no	—
113	C₂³	—	4	3	no	—
114	C₂³	—	8	8	no	—
115	C₂³	#10597392	1	3	yes	—
116	C₂³	#10597393	1	3	yes	—
117	C₂³	#10597399	1	1	yes	characteristic
118	Q₈	—	8	8	no	—
119	C₂×C₄	—	4	12	no	—
120	C₂×C₄	—	4	6	no	—
121	C₂×C₄	—	76	2	no	—
122	C₂×C₄	—	152	3	no	—
123	C₂×C₄	—	152	6	no	—
124	C₂×C₄	—	152	6	no	—
125	C₂²	—	2	2	no	—
126	C₂²	—	2	3	no	—
127	C₂²	—	2	3	no	—
128	C₂²	—	2	6	no	—
129	C₂²	—	2	6	no	—
130	C₂²	—	4	4	no	—
131	C₂²	—	8	6	no	—
132	C₂²	—	8	6	no	—
133	C₂²	#11926455	1	1	yes	characteristic
134	C₂²	#11926734	1	2	yes	—
135	C₄	—	8	6	no	—
136	C₄	—	304	3	no	—
137	C₄	—	152	2	no	—
138	C₂	—	2	2	no	—
139	C₂	—	4	3	no	—
140	C₂	—	4	3	no	—
141	C₂	#14564801	1	1	yes	characteristic
142	C₂	#14564811	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563707

C₂

yes

maximal

C₁₉⋊#1304

C₂

yes

maximal

C₁₉×#2840

C₂

yes

maximal, characteristic

C₂²×C₂²⋊Dic₁₉

C₂²

yes

characteristic

#11926400

C₂²

yes

—

#11926310

—

C₁₉×#393

—

C₁₉×#379

C₂²

yes

—

C₂⁵×C₁₉

C₂³

yes

characteristic

C₂²×Q₈×C₁₉

—

C₂³×Dic₁₉

Q₈

yes

complemented

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₂×C₂²⋊Dic₁₉

—

C₁₉×#95

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

—

C₂⁴×C₁₉

C₂×D₄

yes

—

C₂⁴×C₁₉

C₂×Q₈

yes

characteristic

C₂⁴×C₁₉

#41

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

#10391

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

C₂³×C₁₉

C₂²⋊Q₈

yes

—

C₂³×C₁₉

#124

yes

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

#2840

D₁₉

yes

characteristic

#1819

—

#1304

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#393

yes

characteristic

C₂²×C₁₉

#458

yes

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

C₂²×C₂²⋊C₄

—

#393

—

#379

—

#379

C₂×D₁₉

yes

—

#342

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#2030

yes

characteristic

C₂×C₁₉

#2032

yes

—

C₂⁵

C₂²×D₁₉

yes

characteristic

C₂²×Q₈

—

C₂³×C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂²⋊D₁₉

yes

—

#95

—

C₁₉

#10391

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

—

C₂⁴

Q₈×D₁₉

yes

characteristic

C₂⁴

#64545

yes

—

C₂⁴

C₂×C₂²⋊D₁₉

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

152

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₂²⋊C₄

—

105

C₂²⋊C₄

—

106

C₂²⋊C₄

—

107

C₂²⋊C₄

—

152

—

108

C₂³

—

109

C₂³

—

110

C₂³

—

111

C₂³

—

112

C₂³

—

113

C₂³

—

114

C₂³

—

115

C₂³

#10597392

yes

—

116

C₂³

#10597393

yes

—

117

C₂³

#10597399

yes

characteristic

118

Q₈

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

152

—

123

C₂×C₄

—

152

—

124

C₂×C₄

—

152

—

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₂²

—

129

C₂²

—

130

C₂²

—

131

C₂²

—

132

C₂²

—

133

C₂²

#11926455

yes

characteristic

134

C₂²

#11926734

yes

—

135

C₄

—

136

C₄

—

304

—

137

C₄

—

152

—

138

C₂

—

139

C₂

—

140

C₂

—

141

C₂

#14564801

yes

characteristic

142

C₂

#14564811

yes

—

	subgroup	G/H
center	C₂²	#11926455
commutator, prime radical, cosocle	C₂⁵×C₁₉	C₂³
Frattini	C₂⁵	C₂²×D₁₉
Fitting	C₁₉×#2840	C₂
socle	C₂²×C₁₉	#393
hypercenter	#2840	D₁₉
hypocenter	C₁₉	#10391
LCS	G ▷ C₂⁵×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #2840

subgroup

G/H

center

C₂²

#11926455

commutator, prime radical, cosocle

C₂⁵×C₁₉

C₂³

Frattini

C₂⁵

C₂²×D₁₉

Fitting

C₁₉×#2840

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂⁵×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂⁵ ◁ #2840

N	H ≅ G/N	type
11. C₂³×Dic₁₉	Q₈	semidirect
90. C₁₉	#10391	semidirect

H ≅ G/N

type

11. C₂³×Dic₁₉

Q₈

semidirect

90. C₁₉

#10391

semidirect

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

subgroup	index
#14563707	2
C₁₉⋊#1304	2
C₁₉×#2840	2
#10391	19

subgroup

index

#14563707

C₁₉⋊#1304

C₁₉×#2840

#10391

Subgroups — #18085791

Conjugacy classes of subgroups

Complements

Maximal subgroups