Group #10601262 — subgroups

Subgroups — #10601262

Order 640.

248 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 109 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×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#3946	C₂	1	2	yes	maximal
3	C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#3935	C₂	1	1	yes	maximal, characteristic
5	#64770	C₂	1	2	yes	maximal
6	C₂²×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₅	C₄	1	2	yes	—
9	C₂×C₄×Dic₅	C₂²	1	2	yes	—
10	C₂²×#168	C₂²	1	1	yes	characteristic
11	C₂²×#168	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₈	—	2	2	no	—
13	#3963	C₄	1	1	yes	characteristic
14	#3963	C₄	1	1	yes	characteristic
15	#3946	—	2	4	no	—
16	#3935	—	2	2	no	—
17	#1940	—	5	1	no	maximal, Sylow
18	C₂²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
21	C₂²×Dic₅	C₂×C₄	1	2	yes	—
22	C₂²×Dic₅	C₂×C₄	1	2	yes	—
23	C₂×C₅×C₈	—	2	2	no	—
24	C₂×C₅×C₈	—	2	2	no	—
25	C₂×C₅×C₈	—	2	2	no	—
26	C₄²×C₅	D₄	1	2	yes	—
27	C₄²×C₅	Q₈	1	2	yes	—
28	C₄⋊Dic₅	—	2	4	no	—
29	C₄×Dic₅	—	2	2	no	—
30	C₄×Dic₅	—	2	2	no	—
31	C₂×#168	—	2	1	no	—
32	C₂×#168	—	2	1	no	—
33	C₂×#168	—	2	1	no	—
34	C₂×#168	—	2	1	no	—
35	C₂×#168	D₄	1	2	yes	—
36	C₂×#168	Q₈	1	2	yes	—
37	C₂×C₄⋊C₈	—	5	2	no	—
38	C₂×C₄⋊C₈	D₅	1	1	yes	characteristic
39	C₂×#97	—	5	1	no	—
40	C₄×C₄⋊C₄	—	5	1	no	—
41	#336	—	5	2	no	—
42	C₂³×C₅	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₄×C₅	—	2	2	no	—
44	C₂×C₄×C₅	—	2	2	no	—
45	C₂×C₄×C₅	C₄⋊C₄	1	2	yes	—
46	C₂×C₄×C₅	C₄⋊C₄	1	2	yes	—
47	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄×C₅	#41	1	1	yes	characteristic
52	C₂×C₄×C₅	#41	1	1	yes	characteristic
53	C₂×Dic₅	—	2	2	no	—
54	C₂×Dic₅	—	2	2	no	—
55	C₂×Dic₅	—	2	2	no	—
56	C₂×Dic₅	—	2	2	no	—
57	C₂×Dic₅	—	2	2	no	—
58	C₂×Dic₅	M₁₆	1	4	yes	—
59	C₅×C₈	—	4	2	no	—
60	#168	—	2	2	no	—
61	#168	—	2	2	no	—
62	C₂²×C₈	—	5	1	no	—
63	C₂²×C₈	—	5	1	no	—
64	C₂²×C₈	C₂×D₅	1	2	yes	—
65	C₂×C₄⋊C₄	—	5	2	no	—
66	C₂×C₄²	—	5	2	no	—
67	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
68	C₄⋊C₈	—	2	2	no	—
69	C₄⋊C₈	—	10	4	no	—
70	#97	—	10	2	no	—
71	#95	—	5	1	no	—
72	#95	—	5	1	no	—
73	C₂²×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₅	C₄×D₄	1	1	yes	characteristic
75	C₂²×C₅	C₄×Q₈	1	1	yes	characteristic
76	C₂²×C₅	C₂×M₁₆	1	2	yes	—
77	C₂²×C₅	#131	1	2	yes	—
78	C₄×C₅	—	2	2	no	—
79	C₄×C₅	—	2	2	no	—
80	C₄×C₅	#121	1	1	yes	characteristic
81	C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
82	C₄×C₅	#125	1	1	yes	characteristic
83	C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
84	Dic₅	—	2	4	no	—
85	Dic₅	—	4	2	no	—
86	C₂²×C₄	—	5	2	no	—
87	C₂²×C₄	—	5	2	no	—
88	C₂²×C₄	C₄×D₅	1	1	yes	characteristic
89	C₂²×C₄	C₄×D₅	1	1	yes	characteristic
90	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	5	2	no	—
95	C₂×C₈	—	5	2	no	—
96	C₂×C₈	—	10	1	no	—
97	C₂×C₈	—	10	1	no	—
98	C₂×C₈	—	10	1	no	—
99	C₂×C₈	—	10	1	no	—
100	C₄⋊C₄	—	10	4	no	—
101	C₄²	—	10	2	no	—
102	C₄²	—	10	2	no	—
103	C₄²	Dic₁₀	1	2	yes	—
104	C₄²	C₂²⋊D₅	1	2	yes	—
105	C₂×C₅	#389	1	1	yes	characteristic
106	C₂×C₅	#423	1	1	yes	characteristic
107	C₂×C₅	#424	1	1	yes	characteristic
108	C₂×C₅	#435	1	2	yes	—
109	C₂×C₅	#446	1	2	yes	—
110	C₂³	C₂×C₄×D₅	1	1	yes	characteristic
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	5	4	no	—
114	C₂×C₄	—	10	2	no	—
115	C₂×C₄	—	10	2	no	—
116	C₂×C₄	—	10	2	no	—
117	C₂×C₄	—	10	2	no	—
118	C₂×C₄	—	10	2	no	—
119	C₂×C₄	#683	1	2	yes	—
120	C₂×C₄	#683	1	2	yes	—
121	C₂×C₄	C₂×Dic₁₀	1	1	yes	characteristic
122	C₂×C₄	D₄×D₅	1	1	yes	characteristic
123	C₂×C₄	#711	1	1	yes	characteristic
124	C₂×C₄	Q₈×D₅	1	1	yes	characteristic
125	C₂×C₄	#713	1	1	yes	characteristic
126	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
127	C₈	—	4	2	no	—
128	C₈	—	10	2	no	—
129	C₈	—	10	2	no	—
130	C₅	#1940	1	1	yes	characteristic, complemented, Sylow
131	C₂²	#4033	1	1	yes	characteristic
132	C₂²	#4039	1	1	yes	characteristic
133	C₂²	#4047	1	2	yes	—
134	C₂²	D₅×M₁₆	1	2	yes	—
135	C₂²	C₂×#683	1	1	yes	characteristic
136	C₄	—	2	2	no	—
137	C₄	—	2	2	no	—
138	C₄	—	10	4	no	—
139	C₄	—	20	2	no	—
140	C₄	#4034	1	1	yes	characteristic
141	C₄	#4036	1	1	yes	characteristic
142	C₄	#4084	1	1	yes	characteristic
143	C₄	#4092	1	1	yes	characteristic
144	C₂	#65117	1	2	yes	—
145	C₂	#65125	1	2	yes	—
146	C₂	#65262	1	1	yes	characteristic
147	C₂	#65391	1	1	yes	characteristic
148	C₂	#65407	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#3946

C₂

yes

maximal

C₄×C₄⋊Dic₅

C₂

yes

maximal, characteristic

C₂×#3935

C₂

yes

maximal, characteristic

#64770

C₂

yes

maximal

C₂²×C₅×C₈

C₂²

yes

—

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄⋊Dic₅

C₄

yes

—

C₂×C₄×Dic₅

C₂²

yes

—

C₂²×#168

C₂²

yes

characteristic

C₂²×#168

C₂²

yes

characteristic

C₅×C₄⋊C₈

—

#3963

C₄

yes

characteristic

#3963

C₄

yes

—

—

—

C₂²×C₄×C₅

C₂×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×C₄

yes

characteristic

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

C₂×C₄

yes

—

C₂²×Dic₅

C₂×C₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

D₄

yes

—

C₄²×C₅

Q₈

yes

—

C₄⋊Dic₅

—

C₄×Dic₅

—

C₄×Dic₅

—

—

—

—

—

D₄

yes

—

C₂×#168

Q₈

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₅

yes

characteristic

C₂×#97

—

C₄×C₄⋊C₄

—

#336

—

C₂³×C₅

C₂²×C₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄⋊C₄

yes

—

C₂×C₄×C₅

C₄⋊C₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×Q₈

yes

characteristic

C₂×C₄×C₅

C₂×Q₈

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

M₁₆

yes

—

C₅×C₈

—

#168

—

#168

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×D₅

yes

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#97

—

#95

—

#95

—

C₂²×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₅

C₄×D₄

yes

characteristic

C₂²×C₅

C₄×Q₈

yes

characteristic

C₂²×C₅

C₂×M₁₆

yes

—

C₂²×C₅

#131

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#121

yes

characteristic

C₄×C₅

C₂²⋊Q₈

yes

characteristic

C₄×C₅

#125

yes

characteristic

C₄×C₅

C₄⋊Q₈

yes

characteristic

Dic₅

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₅

yes

characteristic

C₂²×C₄

C₄×D₅

yes

characteristic

C₂²×C₄

C₂²×D₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₄²

—

102

C₄²

—

103

C₄²

Dic₁₀

yes

—

104

C₄²

C₂²⋊D₅

yes

—

105

C₂×C₅

#389

yes

characteristic

106

C₂×C₅

#423

yes

characteristic

107

C₂×C₅

#424

yes

characteristic

108

C₂×C₅

#435

yes

—

109

C₂×C₅

#446

yes

—

110

C₂³

C₂×C₄×D₅

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

#683

yes

—

120

C₂×C₄

#683

yes

—

121

C₂×C₄

C₂×Dic₁₀

yes

characteristic

122

C₂×C₄

D₄×D₅

yes

characteristic

123

C₂×C₄

#711

yes

characteristic

124

C₂×C₄

Q₈×D₅

yes

characteristic

125

C₂×C₄

#713

yes

characteristic

126

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₅

#1940

yes

characteristic, complemented, Sylow

131

C₂²

#4033

yes

characteristic

132

C₂²

#4039

yes

characteristic

133

C₂²

#4047

yes

—

134

C₂²

D₅×M₁₆

yes

—

135

C₂²

C₂×#683

yes

characteristic

136

C₄

—

137

C₄

—

138

C₄

—

139

C₄

—

140

C₄

#4034

yes

characteristic

141

C₄

#4036

yes

characteristic

142

C₄

#4084

yes

characteristic

143

C₄

#4092

yes

characteristic

144

C₂

#65117

yes

—

145

C₂

#65125

yes

—

146

C₂

#65262

yes

characteristic

147

C₂

#65391

yes

characteristic

148

C₂

#65407

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅
commutator, socle, prime radical	C₂³×C₅	C₂²×C₄
Fitting	C₂×C₅×C₄⋊C₈	C₂
cosocle	C₂²×C₄×C₅	C₂³
hypercenter	C₂×C₄⋊C₈	D₅
hypocenter	C₅	#1940
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₅

commutator, socle, prime radical

C₂³×C₅

C₂²×C₄

Fitting

C₂×C₅×C₄⋊C₈

C₂

cosocle

C₂²×C₄×C₅

C₂³

hypercenter

C₂×C₄⋊C₈

D₅

C₅

G ▷ C₂³×C₅ ▷ C₅

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
130. C₅	#1940	semidirect

H ≅ G/N

type

130. C₅

#1940

semidirect

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

subgroup	index
C₂×C₅×C₄⋊C₈	2
C₂×#3946	2
C₄×C₄⋊Dic₅	2
C₂×#3935	2
#64770	2
#1940	5

subgroup

index

C₂×C₅×C₄⋊C₈

C₄×C₄⋊Dic₅

Subgroups — #10601262

Conjugacy classes of subgroups

Complements

Maximal subgroups