Group #18069930 — subgroups

Subgroups — #18069930

Order 4864.

180 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14561581	C₂	1	2	yes	maximal
2	C₁₉×#1992	C₂	1	1	yes	maximal, characteristic
3	#11926270	—	2	2	no	—
4	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#97	C₄	1	1	yes	characteristic
6	C₁₉×#384	C₂²	1	1	yes	characteristic
7	C₁₉×#340	—	2	2	no	—
8	C₂²×C₈×C₁₉	—	2	1	no	—
9	C₁₉×#125	—	2	1	no	—
10	C₁₉×#125	—	4	1	no	—
11	C₁₉×#125	C₈	1	2	yes	complemented
12	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
13	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
14	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
15	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×#97	—	4	1	no	—
18	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
19	C₂²×C₄×C₁₉	—	2	1	no	—
20	C₂²×C₄×C₁₉	—	2	2	no	—
21	C₂²×C₄×C₁₉	—	4	1	no	—
22	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₉	—	2	2	no	—
24	C₂×C₈×C₁₉	—	4	1	no	—
25	C₂×C₈×C₁₉	—	4	1	no	—
26	C₄⋊C₄×C₁₉	—	2	2	no	—
27	C₄⋊C₄×C₁₉	—	4	2	no	—
28	C₄⋊C₄×C₁₉	—	4	2	no	—
29	C₄⋊C₄×C₁₉	—	4	2	no	—
30	C₄⋊C₄×C₁₉	—	4	1	no	—
31	C₄⋊C₄×C₁₉	—	8	2	no	—
32	C₄²×C₁₉	—	2	1	no	—
33	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
34	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
35	C₂×C₁₉⋊C₈	—	8	2	no	—
36	#7358	—	19	1	no	maximal, Sylow
37	C₂³×C₁₉	#99	1	1	yes	characteristic
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	4	1	no	—
43	C₂×C₄×C₁₉	—	4	1	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	8	1	no	—
47	C₂×C₄×C₁₉	—	8	1	no	—
48	C₂×C₄×C₁₉	—	8	2	no	—
49	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
50	C₂×C₄×C₁₉	#100	1	1	yes	characteristic
51	C₈×C₁₉	—	4	2	no	—
52	C₁₉⋊C₈	—	16	2	no	—
53	#1992	D₁₉	1	1	yes	characteristic
54	#1325	—	19	2	no	—
55	C₂²×C₁₉	—	2	1	no	—
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	#323	1	1	yes	characteristic
58	C₂²×C₁₉	#354	1	1	yes	characteristic
59	C₂²×C₁₉	#356	1	1	yes	characteristic
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	2	1	no	—
62	C₄×C₁₉	—	4	1	no	—
63	C₄×C₁₉	—	4	1	no	—
64	C₄×C₁₉	—	8	2	no	—
65	C₄×C₁₉	—	8	2	no	—
66	C₂×#125	Dic₁₉	1	1	yes	characteristic
67	C₂×#97	Dic₁₉	1	1	yes	characteristic
68	#384	C₂×D₁₉	1	1	yes	characteristic
69	#340	—	2	2	no	—
70	#324	—	38	2	no	—
71	C₂×C₁₉	—	2	1	no	—
72	C₂×C₁₉	—	2	1	no	—
73	C₂×C₁₉	#1319	1	1	yes	characteristic
74	C₂×C₁₉	#1412	1	1	yes	characteristic
75	C₂×C₁₉	#1413	1	1	yes	characteristic
76	C₂²×C₈	—	2	1	no	—
77	#125	—	2	1	no	—
78	#125	—	4	1	no	—
79	#125	C₁₉⋊C₈	1	2	yes	complemented
80	C₂×C₄⋊C₄	—	2	1	no	—
81	C₂×C₄⋊C₄	—	4	1	no	—
82	C₂×C₄⋊C₄	—	4	1	no	—
83	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
84	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
85	C₂²⋊C₈	—	76	2	no	—
86	#97	—	4	1	no	—
87	C₁₉	#7358	1	1	yes	characteristic, complemented, Sylow
88	C₂²×C₄	—	2	1	no	—
89	C₂²×C₄	—	2	2	no	—
90	C₂²×C₄	—	4	1	no	—
91	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	4	1	no	—
94	C₂×C₈	—	4	1	no	—
95	C₂×C₈	—	152	2	no	—
96	C₄⋊C₄	—	2	2	no	—
97	C₄⋊C₄	—	4	2	no	—
98	C₄⋊C₄	—	4	2	no	—
99	C₄⋊C₄	—	4	2	no	—
100	C₄⋊C₄	—	4	1	no	—
101	C₄⋊C₄	—	8	2	no	—
102	C₄²	—	2	1	no	—
103	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
104	C₄²	#64520	1	1	yes	characteristic
105	C₂³	#10597291	1	1	yes	characteristic
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	2	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	4	1	no	—
112	C₂×C₄	—	4	2	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	—	8	1	no	—
115	C₂×C₄	—	8	1	no	—
116	C₂×C₄	—	8	2	no	—
117	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
118	C₂×C₄	#10597290	1	1	yes	characteristic
119	C₈	—	4	2	no	—
120	C₈	—	304	2	no	—
121	C₂²	—	2	1	no	—
122	C₂²	—	2	1	no	—
123	C₂²	#11926268	1	1	yes	characteristic
124	C₂²	#11926339	1	1	yes	characteristic
125	C₂²	#11926343	1	1	yes	characteristic
126	C₄	—	2	1	no	—
127	C₄	—	2	1	no	—
128	C₄	—	4	1	no	—
129	C₄	—	4	1	no	—
130	C₄	—	8	2	no	—
131	C₄	—	8	2	no	—
132	C₂	—	2	1	no	—
133	C₂	—	2	1	no	—
134	C₂	#14561569	1	1	yes	characteristic
135	C₂	#14561806	1	1	yes	characteristic
136	C₂	#14561808	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561581

C₂

yes

maximal

C₁₉×#1992

C₂

yes

maximal, characteristic

#11926270

—

C₂×C₁₉×#125

C₄

yes

characteristic

C₂×C₁₉×#97

C₄

yes

characteristic

C₁₉×#384

C₂²

yes

characteristic

C₁₉×#340

—

C₂²×C₈×C₁₉

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×#125

C₈

yes

complemented

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#100

yes

characteristic

C₈×C₁₉

—

C₁₉⋊C₈

—

#1992

D₁₉

yes

characteristic

#1325

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#125

Dic₁₉

yes

characteristic

C₂×#97

Dic₁₉

yes

characteristic

#384

C₂×D₁₉

yes

characteristic

#340

—

#324

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂²×C₈

—

#125

—

#125

—

#125

C₁₉⋊C₈

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

C₂²⋊C₈

—

#97

—

C₁₉

#7358

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

152

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄²

—

103

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

104

C₄²

#64520

yes

characteristic

105

C₂³

#10597291

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

118

C₂×C₄

#10597290

yes

characteristic

119

C₈

—

120

C₈

—

304

—

121

C₂²

—

122

C₂²

—

123

C₂²

#11926268

yes

characteristic

124

C₂²

#11926339

yes

characteristic

125

C₂²

#11926343

yes

characteristic

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₂

—

133

C₂

—

134

C₂

#14561569

yes

characteristic

135

C₂

#14561806

yes

characteristic

136

C₂

#14561808

yes

characteristic

	subgroup	G/H
center	C₂²	#11926339
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#384	C₂×D₁₉
Fitting	C₁₉×#1992	C₂
socle	C₂²×C₁₉	#354
prime radical	C₂³×C₁₉	#99
cosocle	C₁₉×#384	C₂²
hypercenter	#1992	D₁₉
hypocenter	C₁₉	#7358
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1992

subgroup

G/H

center

C₂²

#11926339

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#384

C₂×D₁₉

Fitting

C₁₉×#1992

C₂

C₂²×C₁₉

C₂³×C₁₉

C₁₉×#384

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ #384 ◁ #1992

N	H ≅ G/N	type
11. C₁₉×#125	C₈	semidirect
79. #125	C₁₉⋊C₈	semidirect
87. C₁₉	#7358	semidirect

H ≅ G/N

type

11. C₁₉×#125

C₈

semidirect

79. #125

C₁₉⋊C₈

semidirect

87. C₁₉

#7358

semidirect

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

subgroup	index
#14561581	2
C₁₉×#1992	2
#7358	19

subgroup

index

#14561581

C₁₉×#1992

#7358

Subgroups — #18069930

Conjugacy classes of subgroups

Complements

Maximal subgroups