Group #14298744 — subgroups

Subgroups — #14298744

Order 1920.

432 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 207 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	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₃⋊#168)	C₂	1	2	yes	maximal
3	#11746345	C₂	1	4	yes	maximal
4	#10600230	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
6	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₃⋊#168	C₂²	1	4	yes	—
8	C₃×C₅×#95	C₄	1	4	yes	—
9	C₄⋊(C₃⋊#168)	—	2	4	no	—
10	#69437	—	5	1	no	maximal, Hall
11	C₅×#376	D₃	1	1	yes	characteristic
12	C₂×C₄⋊#168	—	3	2	no	—
13	#64744	—	3	4	no	—
14	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
15	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
16	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
17	C₃×C₄²×C₅	—	2	4	no	—
18	C₃×C₄²×C₅	D₄	1	2	yes	—
19	C₃×C₄²×C₅	Q₈	1	2	yes	—
20	C₂×C₃⋊#168	—	2	4	no	—
21	C₂×C₃⋊#168	—	2	8	no	—
22	C₃×#376	D₅	1	1	yes	characteristic
23	C₂×C₄⋊(C₃⋊C₈)	—	5	2	no	—
24	#4524	—	5	4	no	—
25	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
26	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
27	C₂²×#168	—	3	4	no	—
28	C₅×#95	Dic₃	1	4	yes	—
29	C₄⋊#168	—	6	4	no	—
30	#1832	—	15	1	no	Sylow
31	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₃×C₄×C₅	—	2	4	no	—
33	C₂×C₃×C₄×C₅	—	2	4	no	—
34	C₂×C₃×C₄×C₅	—	2	8	no	—
35	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
36	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
37	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₃×C₄×C₅	#41	1	4	yes	—
39	C₃⋊#168	—	4	4	no	—
40	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
41	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
42	C₂²×C₃⋊C₈	—	5	4	no	—
43	C₃×#95	Dic₅	1	4	yes	—
44	C₄⋊(C₃⋊C₈)	—	10	4	no	—
45	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	—
46	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
47	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
48	C₄²×C₅	—	2	4	no	—
49	C₄²×C₅	Dic₆	1	2	yes	—
50	C₄²×C₅	D₁₂	1	2	yes	—
51	C₂×#168	—	6	4	no	—
52	C₂×#168	—	6	8	no	—
53	C₂×C₄⋊C₈	—	15	2	no	—
54	#376	D₁₅	1	1	yes	characteristic
55	#336	—	15	4	no	—
56	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₃×C₅	#117	1	2	yes	—
58	C₂²×C₃×C₅	#131	1	4	yes	—
59	C₃×C₄×C₅	—	2	4	no	—
60	C₃×C₄×C₅	—	4	4	no	—
61	C₃×C₄×C₅	#124	1	2	yes	—
62	C₃×C₄×C₅	#125	1	2	yes	—
63	C₂²×C₃×C₄	C₂×Dic₅	1	4	yes	—
64	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
65	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
66	C₃×C₄²	—	2	4	no	—
67	C₃×C₄²	Dic₁₀	1	2	yes	—
68	C₃×C₄²	D₂₀	1	2	yes	—
69	C₂×C₃⋊C₈	—	10	4	no	—
70	C₂×C₃⋊C₈	—	10	8	no	—
71	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
72	C₂×C₄×C₅	—	2	4	no	—
73	C₂×C₄×C₅	—	2	4	no	—
74	C₂×C₄×C₅	—	2	8	no	—
75	C₂×C₄×C₅	C₄⋊Dic₃	1	4	yes	—
76	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
77	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
78	C₂×C₄×C₅	#235	1	4	yes	—
79	#168	—	12	4	no	—
80	C₂²×C₈	—	15	4	no	—
81	C₂×C₄²	C₂×D₁₅	1	2	yes	—
82	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
83	C₄⋊C₈	—	30	4	no	—
84	#95	Dic₁₅	1	4	yes	—
85	C₂×C₃×C₅	#382	1	1	yes	characteristic
86	C₂×C₃×C₅	#424	1	2	yes	—
87	C₂×C₃×C₅	#433	1	4	yes	—
88	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
89	C₂×C₃×C₄	—	2	4	no	—
90	C₂×C₃×C₄	—	2	4	no	—
91	C₂×C₃×C₄	—	2	8	no	—
92	C₂×C₃×C₄	C₄⋊Dic₅	1	4	yes	—
93	C₂×C₃×C₄	C₂×Dic₁₀	1	1	yes	characteristic
94	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
95	C₂×C₃×C₄	#709	1	4	yes	—
96	C₃⋊C₈	—	20	4	no	—
97	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
98	C₂²×C₅	#926	1	2	yes	—
99	C₂²×C₅	#948	1	4	yes	—
100	C₄×C₅	—	2	4	no	—
101	C₄×C₅	—	4	4	no	—
102	C₄×C₅	#870	1	2	yes	—
103	C₄×C₅	#875	1	2	yes	—
104	C₂²×C₄	C₂×Dic₁₅	1	4	yes	—
105	C₂²×C₄	C₂×Dic₁₅	1	2	yes	—
106	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
107	C₂×C₈	—	30	4	no	—
108	C₂×C₈	—	30	8	no	—
109	C₄²	—	2	4	no	—
110	C₄²	Dic₃₀	1	2	yes	—
111	C₄²	D₆₀	1	2	yes	—
112	C₃×C₅	#1832	1	1	yes	characteristic, complemented, Hall
113	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
114	C₂²×C₃	#4072	1	2	yes	—
115	C₂²×C₃	#4094	1	4	yes	—
116	C₃×C₄	—	2	4	no	—
117	C₃×C₄	—	4	4	no	—
118	C₃×C₄	#4016	1	2	yes	—
119	C₃×C₄	#4021	1	2	yes	—
120	C₂×C₅	#4936	1	1	yes	characteristic
121	C₂×C₅	#4999	1	2	yes	—
122	C₂×C₅	#5000	1	4	yes	—
123	C₂³	C₂²×Dic₁₅	1	1	yes	characteristic
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	2	4	no	—
126	C₂×C₄	—	2	8	no	—
127	C₂×C₄	C₄⋊Dic₁₅	1	4	yes	—
128	C₂×C₄	C₂×Dic₃₀	1	1	yes	characteristic
129	C₂×C₄	C₂×D₆₀	1	1	yes	characteristic
130	C₂×C₄	#6817	1	4	yes	—
131	C₈	—	60	4	no	—
132	C₂×C₃	#65225	1	1	yes	characteristic
133	C₂×C₃	#65288	1	2	yes	—
134	C₂×C₃	#65289	1	4	yes	—
135	C₅	#69437	1	1	yes	characteristic, complemented, Sylow
136	C₂²	C₂×C₄⋊Dic₁₅	1	1	yes	characteristic
137	C₂²	#91815	1	2	yes	—
138	C₂²	#91837	1	4	yes	—
139	C₄	—	2	4	no	—
140	C₄	—	4	4	no	—
141	C₄	#91759	1	2	yes	—
142	C₄	#91764	1	2	yes	—
143	C₃	#10600230	1	1	yes	characteristic, complemented, Sylow
144	C₂	#11751037	1	1	yes	characteristic
145	C₂	#11751100	1	2	yes	—
146	C₂	#11751101	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×#376

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₃⋊#168)

C₂

yes

maximal

#11746345

C₂

yes

maximal

#10600230

—

maximal, Hall

C₂×C₃×C₄²×C₅

C₂²

yes

—

C₂×C₃×C₄²×C₅

C₂²

yes

characteristic

C₂²×C₃⋊#168

C₂²

yes

—

C₃×C₅×#95

C₄

yes

—

—

—

D₃

yes

characteristic

C₂×C₄⋊#168

—

#64744

—

C₂²×C₃×C₄×C₅

C₂×C₄

yes

—

C₂²×C₃×C₄×C₅

C₂×C₄

yes

—

C₂²×C₃×C₄×C₅

C₂³

yes

characteristic

C₃×C₄²×C₅

—

C₃×C₄²×C₅

D₄

yes

—

C₃×C₄²×C₅

Q₈

yes

—

C₂×C₃⋊#168

—

C₂×C₃⋊#168

—

C₃×#376

D₅

yes

characteristic

C₂×C₄⋊(C₃⋊C₈)

—

#4524

—

C₂×C₄²×C₅

C₂×D₃

yes

—

C₂×C₄²×C₅

C₂×D₃

yes

characteristic

C₂²×#168

—

C₅×#95

Dic₃

yes

—

C₄⋊#168

—

#1832

—

Sylow

C₂³×C₃×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

—

C₂×C₃×C₄×C₅

C₄⋊C₄

yes

—

C₂×C₃×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×Q₈

yes

characteristic

C₂×C₃×C₄×C₅

#41

yes

—

C₃⋊#168

—

C₂×C₃×C₄²

C₂×D₅

yes

—

C₂×C₃×C₄²

C₂×D₅

yes

characteristic

C₂²×C₃⋊C₈

—

C₃×#95

Dic₅

yes

—

C₄⋊(C₃⋊C₈)

—

C₂²×C₄×C₅

C₂×Dic₃

yes

—

C₂²×C₄×C₅

C₂×Dic₃

yes

—

C₂²×C₄×C₅

C₂²×D₃

yes

characteristic

C₄²×C₅

—

C₄²×C₅

Dic₆

yes

—

C₄²×C₅

D₁₂

yes

—

C₂×#168

—

C₂×#168

—

C₂×C₄⋊C₈

—

#376

D₁₅

yes

characteristic

#336

—

C₂²×C₃×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃×C₅

#117

yes

—

C₂²×C₃×C₅

#131

yes

—

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

#124

yes

—

C₃×C₄×C₅

#125

yes

—

C₂²×C₃×C₄

C₂×Dic₅

yes

—

C₂²×C₃×C₄

C₂×Dic₅

yes

—

C₂²×C₃×C₄

C₂²×D₅

yes

characteristic

C₃×C₄²

—

C₃×C₄²

Dic₁₀

yes

—

C₃×C₄²

D₂₀

yes

—

C₂×C₃⋊C₈

—

C₂×C₃⋊C₈

—

C₂³×C₅

C₂²×Dic₃

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄⋊Dic₃

yes

—

C₂×C₄×C₅

C₂×Dic₆

yes

characteristic

C₂×C₄×C₅

C₂×D₁₂

yes

characteristic

C₂×C₄×C₅

#235

yes

—

#168

—

C₂²×C₈

—

C₂×C₄²

C₂×D₁₅

yes

—

C₂×C₄²

C₂×D₁₅

yes

characteristic

C₄⋊C₈

—

#95

Dic₁₅

yes

—

C₂×C₃×C₅

#382

yes

characteristic

C₂×C₃×C₅

#424

yes

—

C₂×C₃×C₅

#433

yes

—

C₂³×C₃

C₂²×Dic₅

yes

characteristic

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

—

C₂×C₃×C₄

C₄⋊Dic₅

yes

—

C₂×C₃×C₄

C₂×Dic₁₀

yes

characteristic

C₂×C₃×C₄

C₂×D₂₀

yes

characteristic

C₂×C₃×C₄

#709

yes

—

C₃⋊C₈

—

C₂²×C₅

C₂×C₄⋊Dic₃

yes

characteristic

C₂²×C₅

#926

yes

—

C₂²×C₅

#948

yes

—

100

C₄×C₅

—

101

C₄×C₅

—

102

C₄×C₅

#870

yes

—

103

C₄×C₅

#875

yes

—

104

C₂²×C₄

C₂×Dic₁₅

yes

—

105

C₂²×C₄

C₂×Dic₁₅

yes

—

106

C₂²×C₄

C₂²×D₁₅

yes

characteristic

107

C₂×C₈

—

108

C₂×C₈

—

109

C₄²

—

110

C₄²

Dic₃₀

yes

—

111

C₄²

D₆₀

yes

—

112

C₃×C₅

#1832

yes

characteristic, complemented, Hall

113

C₂²×C₃

C₂×C₄⋊Dic₅

yes

characteristic

114

C₂²×C₃

#4072

yes

—

115

C₂²×C₃

#4094

yes

—

116

C₃×C₄

—

117

C₃×C₄

—

118

C₃×C₄

#4016

yes

—

119

C₃×C₄

#4021

yes

—

120

C₂×C₅

#4936

yes

characteristic

121

C₂×C₅

#4999

yes

—

122

C₂×C₅

#5000

yes

—

123

C₂³

C₂²×Dic₁₅

yes

characteristic

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

C₄⋊Dic₁₅

yes

—

128

C₂×C₄

C₂×Dic₃₀

yes

characteristic

129

C₂×C₄

C₂×D₆₀

yes

characteristic

130

C₂×C₄

#6817

yes

—

131

C₈

—

132

C₂×C₃

#65225

yes

characteristic

133

C₂×C₃

#65288

yes

—

134

C₂×C₃

#65289

yes

—

135

C₅

#69437

yes

characteristic, complemented, Sylow

136

C₂²

C₂×C₄⋊Dic₁₅

yes

characteristic

137

C₂²

#91815

yes

—

138

C₂²

#91837

yes

—

139

C₄

—

140

C₄

—

141

C₄

#91759

yes

—

142

C₄

#91764

yes

—

143

C₃

#10600230

yes

characteristic, complemented, Sylow

144

C₂

#11751037

yes

characteristic

145

C₂

#11751100

yes

—

146

C₂

#11751101

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₅
commutator, socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
Fitting	C₃×C₅×#376	C₂
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#376	D₁₅
hypocenter	C₃×C₅	#1832
LCS	G ▷ C₂³×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₅

commutator, socle, prime radical

C₂³×C₃×C₅

C₂²×C₄

Fitting

C₃×C₅×#376

C₂

cosocle

C₂²×C₃×C₄×C₅

C₂³

D₁₅

C₃×C₅

G ▷ C₂³×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
112. C₃×C₅	#1832	semidirect
135. C₅	#69437	semidirect
143. C₃	#10600230	semidirect

H ≅ G/N

type

112. C₃×C₅

#1832

semidirect

135. C₅

#69437

semidirect

143. C₃

#10600230

semidirect

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

subgroup	index
C₃×C₅×#376	2
C₂×C₄⋊(C₃⋊#168)	2
#11746345	2
#10600230	3
#69437	5

subgroup

index

C₃×C₅×#376

C₂×C₄⋊(C₃⋊#168)

#11746345

#10600230

#69437

Subgroups — #14298744

Conjugacy classes of subgroups

Complements

Maximal subgroups