Group #18070380 — subgroups

Subgroups — #18070380

Order 4864.

158 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14562927	C₂	1	1	yes	maximal, characteristic
2	#14561806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1355	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927292	C₄	1	1	yes	characteristic, complemented
5	#11926931	—	2	1	no	—
6	#11926337	—	2	1	no	—
7	#11926286	C₄	1	1	yes	characteristic, complemented
8	#11926283	—	2	1	no	—
9	C₁₉×#490	C₂²	1	1	yes	characteristic
10	C₁₉×#347	—	2	1	no	—
11	C₁₉×#127	D₄	1	1	yes	characteristic
12	C₁₉×#125	C₂×C₄	1	1	yes	characteristic
13	C₂×#64526	—	4	1	no	—
14	C₂×#64525	—	4	1	no	—
15	#10597342	—	4	1	no	—
16	#10597341	—	4	1	no	—
17	#10597340	—	4	1	no	—
18	#10597321	—	2	1	no	—
19	C₁₉×M₃₂	—	4	1	no	—
20	C₁₉×#102	—	4	1	no	—
21	C₁₉×#97	D₄	1	1	yes	characteristic
22	#10597291	—	4	1	no	—
23	#10597260	—	2	1	no	—
24	C₂×D₄×C₁₉	—	2	1	no	—
25	C₂×D₄×C₁₉	—	4	1	no	—
26	C₂×D₇₆	—	2	1	no	—
27	C₂×D₇₆	—	4	1	no	—
28	C₂×C₄×D₁₉	—	4	1	no	—
29	C₂×Dic₃₈	—	2	1	no	—
30	C₂×C₈×C₁₉	—	2	1	no	—
31	C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₄⋊C₄×C₁₉	—	4	1	no	—
33	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²⋊Dic₁₉	—	8	1	no	—
35	#64526	—	8	2	no	—
36	#64525	—	8	2	no	—
37	(C₂×D₁₉)⋊C₄	—	4	1	no	—
38	(C₂×D₁₉)⋊C₄	—	4	1	no	—
39	(C₂×D₁₉)⋊C₄	—	4	1	no	—
40	Dic₁₉⋊C₄	—	4	1	no	—
41	C₂×C₁₉⋊C₈	—	4	1	no	—
42	C₁₆×C₁₉	—	4	2	no	—
43	#7523	—	19	1	no	maximal, Sylow
44	C₂³×C₁₉	—	4	1	no	—
45	C₂²×D₁₉	—	4	1	no	—
46	D₄×C₁₉	—	8	1	no	—
47	D₄×C₁₉	—	8	1	no	—
48	D₄×C₁₉	—	8	1	no	—
49	C₂×C₄×C₁₉	—	2	1	no	—
50	C₂×C₄×C₁₉	—	4	1	no	—
51	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
52	C₂×Dic₁₉	—	4	1	no	—
53	C₂×Dic₁₉	—	16	1	no	—
54	D₇₆	—	8	1	no	—
55	D₇₆	—	16	1	no	—
56	C₄×D₁₉	—	16	1	no	—
57	Dic₃₈	—	8	1	no	—
58	C₈×C₁₉	—	4	1	no	—
59	C₁₉⋊C₈	—	4	2	no	—
60	#1656	—	19	1	no	—
61	#1412	—	19	1	no	—
62	#1355	D₁₉	1	1	yes	characteristic, complemented
63	C₂²×C₁₉	—	8	1	no	—
64	C₂²×C₁₉	—	16	1	no	—
65	C₂²×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
66	C₂×D₁₉	—	8	1	no	—
67	C₂×D₁₉	—	8	1	no	—
68	C₂×D₁₉	—	8	1	no	—
69	C₄×C₁₉	—	2	1	no	—
70	C₄×C₁₉	—	4	1	no	—
71	C₄×C₁₉	—	8	1	no	—
72	Dic₁₉	—	8	1	no	—
73	Dic₁₉	—	32	1	no	—
74	#562	—	19	1	no	—
75	#496	—	38	1	no	—
76	#490	C₂×D₁₉	1	1	yes	characteristic
77	#353	—	38	1	no	—
78	#347	—	2	1	no	—
79	#330	—	19	1	no	—
80	#329	—	38	1	no	—
81	C₂×C₁₉	—	2	1	no	—
82	C₂×C₁₉	—	16	1	no	—
83	C₂×C₁₉	#1404	1	1	yes	characteristic
84	D₁₉	—	16	1	no	—
85	C₂×SD₁₆	—	76	1	no	—
86	C₂×D₈	—	76	1	no	—
87	#127	D₇₆	1	1	yes	characteristic
88	#125	C₄×D₁₉	1	1	yes	characteristic
89	#124	—	38	1	no	—
90	#123	—	76	1	no	—
91	C₂²⋊Q₈	—	76	1	no	—
92	#121	—	76	1	no	—
93	M₃₂	—	4	1	no	—
94	#102	—	4	1	no	—
95	#99	—	76	1	no	—
96	#97	—	38	1	no	—
97	#97	C₂²⋊D₁₉	1	1	yes	characteristic
98	C₁₉	#7523	1	1	yes	characteristic, complemented, Sylow
99	C₂×Q₈	—	38	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	4	1	no	—
102	C₂×D₄	—	38	1	no	—
103	C₂×D₄	—	76	1	no	—
104	C₂²×C₄	—	76	1	no	—
105	SD₁₆	—	152	2	no	—
106	D₈	—	152	2	no	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	76	1	no	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	4	1	no	—
111	C₄⋊C₄	—	76	1	no	—
112	C₂²⋊C₄	—	76	1	no	—
113	C₂²⋊C₄	—	76	1	no	—
114	C₂²⋊C₄	—	76	1	no	—
115	C₂²⋊C₄	—	152	1	no	—
116	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
117	C₁₆	—	4	2	no	—
118	C₂³	—	4	1	no	—
119	C₂³	—	76	1	no	—
120	Q₈	—	152	1	no	—
121	D₄	—	8	1	no	—
122	D₄	—	8	1	no	—
123	D₄	—	8	1	no	—
124	D₄	—	304	1	no	—
125	D₄	—	152	1	no	—
126	C₂×C₄	—	2	1	no	—
127	C₂×C₄	—	4	1	no	—
128	C₂×C₄	—	304	1	no	—
129	C₂×C₄	—	304	1	no	—
130	C₂×C₄	—	76	1	no	—
131	C₂×C₄	#10597263	1	1	yes	characteristic
132	C₈	—	4	1	no	—
133	C₈	—	76	2	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	16	1	no	—
136	C₂²	—	152	1	no	—
137	C₂²	—	152	1	no	—
138	C₂²	—	152	1	no	—
139	C₂²	#11926332	1	1	yes	characteristic
140	C₄	—	2	1	no	—
141	C₄	—	4	1	no	—
142	C₄	—	8	1	no	—
143	C₄	—	608	1	no	—
144	C₄	—	152	1	no	—
145	C₂	—	2	1	no	—
146	C₂	—	16	1	no	—
147	C₂	—	304	1	no	—
148	C₂	#14561787	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14562927

C₂

yes

maximal, characteristic

#14561806

C₂

yes

maximal, characteristic, complemented

C₁₉×#1355

C₂

yes

maximal, characteristic, complemented

#11927292

C₄

yes

characteristic, complemented

#11926931

—

#11926337

—

#11926286

C₄

yes

characteristic, complemented

#11926283

—

C₁₉×#490

C₂²

yes

characteristic

C₁₉×#347

—

C₁₉×#127

D₄

yes

characteristic

C₁₉×#125

C₂×C₄

yes

—

—

—

—

—

—

C₁₉×M₃₂

—

C₁₉×#102

—

C₁₉×#97

D₄

yes

characteristic

#10597291

—

#10597260

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

#64526

—

#64525

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

#7523

—

maximal, Sylow

C₂³×C₁₉

—

C₂²×D₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1656

—

#1412

—

#1355

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#562

—

#496

—

#490

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1404

yes

characteristic

D₁₉

—

C₂×SD₁₆

—

C₂×D₈

—

#127

D₇₆

yes

characteristic

#125

C₄×D₁₉

yes

characteristic

#124

—

#123

—

C₂²⋊Q₈

—

#121

—

M₃₂

—

—

—

—

C₂²⋊D₁₉

yes

characteristic

C₁₉

#7523

yes

characteristic, complemented, Sylow

C₂×Q₈

—

100

C₂×D₄

—

101

C₂×D₄

—

102

C₂×D₄

—

103

C₂×D₄

—

104

C₂²×C₄

—

105

SD₁₆

—

152

—

106

D₈

—

152

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

112

C₂²⋊C₄

—

113

C₂²⋊C₄

—

114

C₂²⋊C₄

—

115

C₂²⋊C₄

—

152

—

116

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

117

C₁₆

—

118

C₂³

—

119

C₂³

—

120

Q₈

—

152

—

121

D₄

—

122

D₄

—

123

D₄

—

124

D₄

—

304

—

125

D₄

—

152

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

304

—

129

C₂×C₄

—

304

—

130

C₂×C₄

—

131

C₂×C₄

#10597263

yes

characteristic

132

C₈

—

133

C₈

—

134

C₂²

—

135

C₂²

—

136

C₂²

—

152

—

137

C₂²

—

152

—

138

C₂²

—

152

—

139

C₂²

#11926332

yes

characteristic

140

C₄

—

141

C₄

—

142

C₄

—

143

C₄

—

608

—

144

C₄

—

152

—

145

C₂

—

146

C₂

—

147

C₂

—

304

—

148

C₂

#14561787

yes

characteristic

	subgroup	G/H
center	C₂	#14561787
commutator	C₁₉×#125	C₂×C₄
Frattini	#490	C₂×D₁₉
Fitting	C₁₉×#1355	C₂
socle	C₂×C₁₉	#1404
prime radical	#14562927	C₂
cosocle	C₁₉×#490	C₂²
hypercenter	#1355	D₁₉
hypocenter	C₁₉	#7523
LCS	G ▷ C₁₉×#125 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #490 ◁ #1355

subgroup

G/H

center

C₂

#14561787

commutator

C₁₉×#125

C₂×C₄

Frattini

#490

C₂×D₁₉

Fitting

C₁₉×#1355

C₂

C₂×C₁₉

C₂

C₁₉×#490

C₂²

D₁₉

C₁₉

G ▷ C₁₉×#125 ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #490 ◁ #1355

N	H ≅ G/N	type
2. #14561806	C₂	semidirect
3. C₁₉×#1355	C₂	semidirect
4. #11927292	C₄	semidirect
7. #11926286	C₄	semidirect
62. #1355	D₁₉	semidirect
98. C₁₉	#7523	semidirect

H ≅ G/N

type

2. #14561806

C₂

semidirect

3. C₁₉×#1355

C₂

semidirect

4. #11927292

C₄

semidirect

7. #11926286

C₄

semidirect

62. #1355

D₁₉

semidirect

98. C₁₉

#7523

semidirect

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

subgroup	index
#14562927	2
#14561806	2
C₁₉×#1355	2
#7523	19

subgroup

index

#14562927

#14561806

C₁₉×#1355

#7523

Subgroups — #18070380

Conjugacy classes of subgroups

Complements

Maximal subgroups