Group #14279270 — subgroups

Subgroups — #14279270

Order 1920.

148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 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	C₂×#90936	C₂	1	1	yes	maximal, characteristic
2	#11746748	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64877	C₂	1	1	yes	maximal, characteristic, complemented
4	#10598657	—	3	1	no	maximal, Hall
5	C₂×C₈×D₁₅	C₄	1	1	yes	characteristic
6	C₂×C₅×C₃⋊C₁₆	C₄	1	1	yes	characteristic
7	C₂×C₃×#672	C₂²	1	1	yes	characteristic
8	#90936	—	2	1	no	—
9	#90936	—	2	1	no	—
10	C₃⋊#3928	—	2	1	no	—
11	C₃×#3928	—	2	1	no	—
12	#67602	—	5	1	no	maximal, Hall
13	C₂×#3930	—	3	1	no	—
14	#64877	—	3	1	no	—
15	#64877	D₃	1	1	yes	characteristic, complemented
16	C₂×C₄×D₁₅	C₈	1	1	yes	characteristic
17	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃⋊#168	C₈	1	1	yes	characteristic
19	C₈×D₁₅	—	2	1	no	—
20	C₈×D₁₅	—	2	1	no	—
21	C₃×#672	D₄	1	1	yes	characteristic
22	C₃×#672	D₄	1	1	yes	characteristic
23	C₅×C₃⋊C₁₆	—	2	1	no	—
24	C₂×#798	—	5	1	no	—
25	C₃×M₆₄	—	5	1	no	—
26	#4499	—	5	1	no	—
27	C₂×C₈×D₅	—	3	1	no	—
28	C₂×C₅×C₁₆	—	3	1	no	—
29	C₂×#672	C₂×D₃	1	1	yes	characteristic
30	#3930	—	6	1	no	—
31	#3930	—	6	1	no	—
32	#3928	—	2	1	no	—
33	#3928	—	6	1	no	—
34	#1400	—	15	1	no	Sylow
35	C₂²×D₁₅	C₁₆	1	1	yes	characteristic
36	C₂×C₃×C₄×C₅	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₁₅	C₁₆	1	1	yes	characteristic
38	C₄×D₁₅	—	2	1	no	—
39	C₄×D₁₅	—	2	1	no	—
40	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
41	C₃×C₅×C₈	M₁₆	1	1	yes	characteristic
42	C₃⋊#168	—	2	1	no	—
43	C₂×D₃×C₈	—	5	1	no	—
44	C₂×C₃×C₁₆	—	5	1	no	—
45	C₂×C₃⋊C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic
46	#798	—	10	1	no	—
47	#798	—	10	1	no	—
48	C₃×C₃₂	—	10	1	no	—
49	C₃⋊C₃₂	—	10	1	no	—
50	C₂×C₄×D₅	—	3	1	no	—
51	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
52	C₂×#168	—	3	1	no	—
53	C₈×D₅	—	6	1	no	—
54	C₈×D₅	—	6	1	no	—
55	C₅×C₁₆	—	6	1	no	—
56	#672	D₁₂	1	1	yes	characteristic
57	#672	#67	1	1	yes	characteristic
58	C₂×M₃₂	—	15	1	no	—
59	M₆₄	—	5	1	no	—
60	M₆₄	—	15	1	no	—
61	C₂²×C₃×C₅	C₂×C₁₆	1	1	yes	characteristic
62	C₂×D₁₅	—	2	1	no	—
63	C₂×D₁₅	—	4	1	no	—
64	C₃×C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
65	C₃×C₄×C₅	M₃₂	1	1	yes	characteristic
66	Dic₁₅	—	2	1	no	—
67	C₂×C₄×D₃	—	5	1	no	—
68	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
69	C₂×C₃⋊C₈	—	5	1	no	—
70	D₃×C₈	—	10	1	no	—
71	D₃×C₈	—	10	1	no	—
72	C₃×C₁₆	—	5	1	no	—
73	C₃×C₁₆	—	5	1	no	—
74	C₃⋊C₁₆	—	2	1	no	—
75	C₂²×D₅	—	3	1	no	—
76	C₂×C₄×C₅	D₃×C₈	1	1	yes	characteristic
77	C₂×Dic₅	—	3	1	no	—
78	C₄×D₅	—	6	1	no	—
79	C₄×D₅	—	6	1	no	—
80	C₅×C₈	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
81	C₅×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
82	#168	—	6	1	no	—
83	C₂²×C₈	—	15	1	no	—
84	M₃₂	—	30	1	no	—
85	M₃₂	—	30	1	no	—
86	C₂×C₁₆	—	3	1	no	—
87	C₂×C₁₆	—	5	1	no	—
88	C₃₂	—	10	1	no	—
89	C₃₂	—	30	1	no	—
90	C₂×C₃×C₅	—	2	1	no	—
91	C₂×C₃×C₅	C₂²⋊C₁₆	1	1	yes	characteristic
92	D₁₅	—	4	1	no	—
93	C₂²×D₃	—	5	1	no	—
94	C₂×C₃×C₄	D₅⋊C₈	1	1	yes	characteristic
95	C₂×Dic₃	—	5	1	no	—
96	C₄×D₃	—	10	1	no	—
97	C₄×D₃	—	10	1	no	—
98	C₃×C₈	#700	1	1	yes	characteristic
99	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
100	C₃⋊C₈	—	10	1	no	—
101	C₂²×C₅	D₃×C₁₆	1	1	yes	characteristic
102	C₂×D₅	—	6	1	no	—
103	C₂×D₅	—	12	1	no	—
104	C₄×C₅	#798	1	1	yes	characteristic
105	C₄×C₅	(C₂×D₃)⋊C₈	1	1	yes	characteristic
106	Dic₅	—	6	1	no	—
107	C₂²×C₄	—	15	1	no	—
108	C₂×C₈	—	15	1	no	—
109	C₂×C₈	—	30	1	no	—
110	C₂×C₈	—	30	1	no	—
111	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
112	C₁₆	—	5	1	no	—
113	C₁₆	—	5	1	no	—
114	C₁₆	—	6	1	no	—
115	C₃×C₅	#1400	1	1	yes	characteristic, complemented, Hall
116	C₂²×C₃	D₅⋊C₁₆	1	1	yes	characteristic
117	C₂×D₃	—	10	1	no	—
118	C₂×D₃	—	20	1	no	—
119	C₃×C₄	#3990	1	1	yes	characteristic
120	C₃×C₄	#4003	1	1	yes	characteristic
121	Dic₃	—	10	1	no	—
122	C₂×C₅	—	2	1	no	—
123	C₂×C₅	(C₂×D₃)⋊C₁₆	1	1	yes	characteristic
124	D₅	—	12	1	no	—
125	C₂³	—	15	1	no	—
126	C₂×C₄	—	15	1	no	—
127	C₂×C₄	—	30	1	no	—
128	C₂×C₄	—	30	1	no	—
129	C₂×C₄	#6738	1	1	yes	characteristic
130	C₈	—	30	1	no	—
131	C₈	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
132	C₈	#6740	1	1	yes	characteristic
133	C₂×C₃	—	2	1	no	—
134	C₂×C₃	#64887	1	1	yes	characteristic
135	D₃	—	20	1	no	—
136	C₅	#67602	1	1	yes	characteristic, complemented, Sylow
137	C₂²	—	30	1	no	—
138	C₂²	—	60	1	no	—
139	C₂²	#91164	1	1	yes	characteristic
140	C₄	—	30	1	no	—
141	C₄	#91166	1	1	yes	characteristic
142	C₄	#91171	1	1	yes	characteristic
143	C₃	#10598657	1	1	yes	characteristic, complemented, Sylow
144	C₂	—	2	1	no	—
145	C₂	—	60	1	no	—
146	C₂	#11746547	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#90936

C₂

yes

maximal, characteristic

#11746748

C₂

yes

maximal, characteristic, complemented

C₃×#64877

C₂

yes

maximal, characteristic, complemented

#10598657

—

maximal, Hall

C₂×C₈×D₁₅

C₄

yes

characteristic

C₂×C₅×C₃⋊C₁₆

C₄

yes

characteristic

C₂×C₃×#672

C₂²

yes

—

—

—

—

—

—

—

D₃

yes

characteristic, complemented

C₂×C₄×D₁₅

C₈

yes

characteristic

C₂×C₃×C₅×C₈

C₂×C₄

yes

characteristic

C₂×C₃⋊#168

C₈

yes

characteristic

C₈×D₁₅

—

C₈×D₁₅

—

C₃×#672

D₄

yes

characteristic

C₃×#672

D₄

yes

characteristic

C₅×C₃⋊C₁₆

—

C₂×#798

—

C₃×M₆₄

—

#4499

—

C₂×C₈×D₅

—

C₂×C₅×C₁₆

—

C₂×#672

C₂×D₃

yes

—

—

—

—

—

C₂²×D₁₅

C₁₆

yes

characteristic

C₂×C₃×C₄×C₅

C₂×C₈

yes

characteristic

C₂×Dic₁₅

C₁₆

yes

characteristic

C₄×D₁₅

—

C₄×D₁₅

—

C₃×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₃×C₅×C₈

M₁₆

yes

characteristic

C₃⋊#168

—

C₂×D₃×C₈

—

C₂×C₃×C₁₆

—

C₂×C₃⋊C₁₆

yes

—

—

C₃×C₃₂

—

C₃⋊C₃₂

—

C₂×C₄×D₅

—

C₂×C₅×C₈

C₄×D₃

yes

characteristic

C₂×#168

—

C₈×D₅

—

C₈×D₅

—

C₅×C₁₆

—

#672

D₁₂

yes

yes

C₂×M₃₂

—

M₆₄

—

M₆₄

—

C₂²×C₃×C₅

C₂×C₁₆

yes

characteristic

C₂×D₁₅

—

C₂×D₁₅

—

C₃×C₄×C₅

C₂²⋊C₈

yes

characteristic

C₃×C₄×C₅

M₃₂

yes

characteristic

Dic₁₅

—

C₂×C₄×D₃

—

C₂×C₃×C₈

C₂×AGL(1,𝔽₅)

yes

characteristic

C₂×C₃⋊C₈

—

D₃×C₈

—

D₃×C₈

—

C₃×C₁₆

—

C₃×C₁₆

—

C₃⋊C₁₆

—

C₂²×D₅

—

C₂×C₄×C₅

D₃×C₈

yes

characteristic

C₂×Dic₅

—

C₄×D₅

—

C₄×D₅

—

C₅×C₈

ΓL(1,𝔽₂₅)

yes

characteristic

C₅×C₈

(C₂×D₃)⋊C₄

yes

characteristic

#168

—

C₂²×C₈

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₃₂

—

C₃₂

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₂²⋊C₁₆

yes

characteristic

D₁₅

—

C₂²×D₃

—

C₂×C₃×C₄

D₅⋊C₈

yes

characteristic

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₃×C₈

#700

yes

characteristic

C₃×C₈

C₂²⋊AGL(1,𝔽₅)

yes

characteristic

100

C₃⋊C₈

—

101

C₂²×C₅

D₃×C₁₆

yes

characteristic

102

C₂×D₅

—

103

C₂×D₅

—

104

C₄×C₅

#798

yes

characteristic

105

C₄×C₅

(C₂×D₃)⋊C₈

yes

characteristic

106

Dic₅

—

107

C₂²×C₄

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

D₃×AGL(1,𝔽₅)

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

115

C₃×C₅

#1400

yes

characteristic, complemented, Hall

116

C₂²×C₃

D₅⋊C₁₆

yes

characteristic

117

C₂×D₃

—

118

C₂×D₃

—

119

C₃×C₄

#3990

yes

characteristic

120

C₃×C₄

#4003

yes

characteristic

121

Dic₃

—

122

C₂×C₅

—

123

C₂×C₅

(C₂×D₃)⋊C₁₆

yes

characteristic

124

D₅

—

125

C₂³

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

#6738

yes

characteristic

130

C₈

—

131

C₈

(C₂×D₃)⋊AGL(1,𝔽₅)

yes

characteristic

132

C₈

#6740

yes

characteristic

133

C₂×C₃

—

134

C₂×C₃

#64887

yes

characteristic

135

D₃

—

136

C₅

#67602

yes

characteristic, complemented, Sylow

137

C₂²

—

138

C₂²

—

139

C₂²

#91164

yes

characteristic

140

C₄

—

141

C₄

#91166

yes

characteristic

142

C₄

#91171

yes

characteristic

143

C₃

#10598657

yes

characteristic, complemented, Sylow

144

C₂

—

145

C₂

—

146

C₂

#11746547

yes

characteristic

	subgroup	G/H
center	C₈	(C₂×D₃)⋊AGL(1,𝔽₅)
commutator	C₂²×C₃×C₅	C₂×C₁₆
Frattini, hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂×C₃×C₅	C₂²⋊C₁₆
prime radical	C₂²×D₁₅	C₁₆
cosocle	C₂×C₃×#672	C₂²
hypocenter	C₃×C₅	#1400
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ C₂×C₈

subgroup

G/H

center

C₈

(C₂×D₃)⋊AGL(1,𝔽₅)

commutator

C₂²×C₃×C₅

C₂×C₁₆

Frattini, hypercenter

C₂×C₈

D₃×AGL(1,𝔽₅)

Fitting

C₂×C₃×C₅×C₈

C₂×C₄

socle

C₂×C₃×C₅

C₂²⋊C₁₆

prime radical

C₂²×D₁₅

C₁₆

cosocle

C₂×C₃×#672

C₂²

hypocenter

C₃×C₅

#1400

LCS

G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₈ ◁ C₂×C₈

N	H ≅ G/N	type
2. #11746748	C₂	semidirect
3. C₃×#64877	C₂	semidirect
15. #64877	D₃	semidirect
115. C₃×C₅	#1400	semidirect
136. C₅	#67602	semidirect
143. C₃	#10598657	semidirect

H ≅ G/N

type

2. #11746748

C₂

semidirect

3. C₃×#64877

C₂

semidirect

15. #64877

D₃

semidirect

115. C₃×C₅

#1400

semidirect

136. C₅

#67602

semidirect

143. C₃

#10598657

semidirect

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

subgroup	index
C₂×#90936	2
#11746748	2
C₃×#64877	2
#10598657	3
#67602	5

subgroup

index

Subgroups — #14279270

Conjugacy classes of subgroups

Complements

Maximal subgroups