Group #10599269 — subgroups

Subgroups — #10599269

Order 640.

146 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 49 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	#65383	C₂	1	1	yes	maximal, characteristic
2	#65370	C₂	1	1	yes	maximal, characteristic
3	#65138	C₂	1	1	yes	maximal, characteristic
4	#65120	C₂	1	1	yes	maximal, characteristic
5	C₅×#332	C₂	1	1	yes	maximal, characteristic
6	#64706	C₂	1	1	yes	maximal, characteristic
7	#64699	C₂	1	1	yes	maximal, characteristic
8	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₀	—	2	1	no	—
10	#4015	C₂²	1	1	yes	characteristic
11	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	#3967	—	2	1	no	—
15	#3967	—	2	1	no	—
16	#3948	—	2	1	no	—
17	#3947	—	2	1	no	—
18	#3946	—	2	1	no	—
19	#3942	—	2	1	no	—
20	#3940	—	2	1	no	—
21	C₄⋊#168	C₂²	1	1	yes	characteristic
22	C₄×#168	C₂²	1	1	yes	characteristic
23	#1700	—	5	1	no	maximal, Sylow
24	C₂×C₅×Q₈	—	2	1	no	—
25	C₂×Dic₁₀	—	2	1	no	—
26	C₂×Dic₁₀	D₄	1	1	yes	characteristic
27	C₂×C₅×C₈	—	2	1	no	—
28	C₂×C₅×C₈	—	2	1	no	—
29	C₅×C₄⋊C₄	—	2	1	no	—
30	C₅×C₄⋊C₄	—	2	1	no	—
31	C₄²×C₅	C₂³	1	1	yes	characteristic
32	C₄⋊Dic₅	—	2	1	no	—
33	C₄⋊Dic₅	—	2	1	no	—
34	C₄⋊Dic₅	D₄	1	1	yes	characteristic
35	#683	—	2	1	no	—
36	C₄×Dic₅	—	2	1	no	—
37	C₂×#168	—	2	1	no	—
38	C₂×#168	D₄	1	1	yes	characteristic
39	C₂×#168	D₄	1	1	yes	characteristic
40	Dic₂₀	—	4	2	no	—
41	#487	—	5	1	no	—
42	#475	—	5	1	no	—
43	#462	—	5	1	no	—
44	#446	—	5	1	no	—
45	#335	—	5	1	no	—
46	#332	—	5	1	no	—
47	#332	D₅	1	1	yes	characteristic
48	C₅×Q₈	—	4	1	no	—
49	C₅×Q₈	—	4	1	no	—
50	C₂×C₄×C₅	—	4	1	no	—
51	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₅	#41	1	1	yes	characteristic
54	C₂×Dic₅	—	2	1	no	—
55	C₂×Dic₅	—	2	1	no	—
56	C₂×Dic₅	—	4	1	no	—
57	Dic₁₀	—	2	1	no	—
58	Dic₁₀	—	2	1	no	—
59	Dic₁₀	—	4	1	no	—
60	Dic₁₀	—	4	1	no	—
61	C₅×C₈	—	4	1	no	—
62	C₅×C₈	—	4	1	no	—
63	#168	—	2	1	no	—
64	#168	—	2	1	no	—
65	#168	—	4	1	no	—
66	C₂×Q₁₆	—	10	1	no	—
67	C₄⋊Q₈	—	5	1	no	—
68	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
69	C₄×Q₈	—	5	1	no	—
70	#106	—	10	1	no	—
71	C₄⋊C₈	—	5	1	no	—
72	C₄⋊C₈	—	10	1	no	—
73	C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
74	C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
75	#103	—	10	1	no	—
76	#103	—	10	1	no	—
77	#103	—	10	1	no	—
78	#103	—	10	1	no	—
79	#97	—	10	1	no	—
80	C₄×C₈	—	5	1	no	—
81	C₂²×C₅	#121	1	1	yes	characteristic
82	C₄×C₅	—	2	1	no	—
83	C₄×C₅	—	8	1	no	—
84	C₄×C₅	#135	1	1	yes	characteristic
85	C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₄×C₅	#137	1	1	yes	characteristic
87	C₄×C₅	#137	1	1	yes	characteristic
88	Dic₅	—	4	1	no	—
89	Dic₅	—	4	1	no	—
90	Dic₅	—	8	1	no	—
91	C₂×Q₈	—	2	1	no	—
92	C₂×Q₈	—	5	1	no	—
93	C₂×Q₈	—	10	1	no	—
94	Q₁₆	—	20	2	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	1	no	—
97	C₂×C₈	—	5	1	no	—
98	C₂×C₈	—	5	1	no	—
99	C₂×C₈	—	10	1	no	—
100	C₄⋊C₄	—	2	1	no	—
101	C₄⋊C₄	—	2	1	no	—
102	C₄⋊C₄	—	5	1	no	—
103	C₄⋊C₄	—	10	1	no	—
104	C₄⋊C₄	—	10	1	no	—
105	C₄⋊C₄	—	10	1	no	—
106	C₄²	—	10	1	no	—
107	C₄²	C₂²×D₅	1	1	yes	characteristic
108	C₂×C₅	#464	1	1	yes	characteristic
109	C₂×C₅	#468	1	1	yes	characteristic
110	C₂×C₅	#473	1	1	yes	characteristic
111	Q₈	—	4	1	no	—
112	Q₈	—	4	1	no	—
113	Q₈	—	10	1	no	—
114	Q₈	—	10	1	no	—
115	Q₈	—	20	1	no	—
116	Q₈	—	20	1	no	—
117	C₂×C₄	—	4	1	no	—
118	C₂×C₄	—	10	1	no	—
119	C₂×C₄	—	10	1	no	—
120	C₂×C₄	—	20	1	no	—
121	C₂×C₄	#709	1	1	yes	characteristic
122	C₂×C₄	D₄×D₅	1	1	yes	characteristic
123	C₂×C₄	D₄×D₅	1	1	yes	characteristic
124	C₈	—	4	1	no	—
125	C₈	—	4	1	no	—
126	C₈	—	10	1	no	—
127	C₈	—	10	1	no	—
128	C₈	—	20	1	no	—
129	C₅	#1700	1	1	yes	characteristic, complemented, Sylow
130	C₂²	#4030	1	1	yes	characteristic
131	C₄	—	2	1	no	—
132	C₄	—	8	1	no	—
133	C₄	—	20	1	no	—
134	C₄	—	20	1	no	—
135	C₄	—	40	1	no	—
136	C₄	#4058	1	1	yes	characteristic
137	C₄	#4060	1	1	yes	characteristic
138	C₄	#4061	1	1	yes	characteristic
139	C₄	#4064	1	1	yes	characteristic
140	C₂	#65044	1	1	yes	characteristic
141	C₂	#65056	1	1	yes	characteristic
142	C₂	#65101	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#65383

C₂

yes

maximal, characteristic

#65370

C₂

yes

maximal, characteristic

#65138

C₂

yes

maximal, characteristic

#65120

C₂

yes

maximal, characteristic

C₅×#332

C₂

yes

maximal, characteristic

#64706

C₂

yes

maximal, characteristic

#64699

C₂

yes

maximal, characteristic

C₅×C₄⋊Q₈

C₂²

yes

characteristic

C₂×Dic₂₀

—

#4015

C₂²

yes

characteristic

C₄×Dic₁₀

C₂²

yes

characteristic

C₅×C₄⋊C₈

C₂²

yes

characteristic

C₅×C₄⋊C₈

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

C₄×#168

C₂²

yes

characteristic

#1700

—

maximal, Sylow

C₂×C₅×Q₈

—

C₂×Dic₁₀

—

C₂×Dic₁₀

D₄

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂³

yes

characteristic

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₄⋊Dic₅

D₄

yes

characteristic

#683

—

C₄×Dic₅

—

C₂×#168

—

C₂×#168

D₄

yes

characteristic

C₂×#168

D₄

yes

characteristic

Dic₂₀

—

—

—

—

—

—

—

D₅

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

#41

yes

characteristic

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

Dic₁₀

—

Dic₁₀

—

Dic₁₀

—

Dic₁₀

—

C₅×C₈

—

C₅×C₈

—

#168

—

#168

—

#168

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₅

yes

characteristic

C₄×Q₈

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₅

yes

characteristic

C₄⋊C₈

C₂×D₅

yes

—

—

—

—

—

C₄×C₈

—

C₂²×C₅

#121

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

yes

C₄×C₅

yes

Dic₅

—

Dic₅

—

Dic₅

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄²

—

107

C₄²

C₂²×D₅

yes

characteristic

108

C₂×C₅

#464

yes

characteristic

109

C₂×C₅

#468

yes

characteristic

110

C₂×C₅

#473

yes

characteristic

111

Q₈

—

112

Q₈

—

113

Q₈

—

114

Q₈

—

115

Q₈

—

116

Q₈

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

#709

yes

characteristic

122

C₂×C₄

D₄×D₅

yes

characteristic

123

C₂×C₄

D₄×D₅

yes

characteristic

124

C₈

—

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₅

#1700

yes

characteristic, complemented, Sylow

130

C₂²

#4030

yes

characteristic

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#4058

yes

characteristic

137

C₄

#4060

yes

characteristic

138

C₄

#4061

yes

characteristic

139

C₄

#4064

yes

characteristic

140

C₂

#65044

yes

characteristic

141

C₂

#65056

yes

characteristic

142

C₂

#65101

yes

characteristic

	subgroup	G/H
center	C₂²	#4030
commutator, cosocle	C₄²×C₅	C₂³
Frattini	C₄²	C₂²×D₅
Fitting	C₅×#332	C₂
socle, prime radical	C₂²×C₅	#121
hypercenter	#332	D₅
hypocenter	C₅	#1700
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #332

subgroup

G/H

center

C₂²

#4030

commutator, cosocle

C₄²×C₅

C₂³

Frattini

C₄²

C₂²×D₅

C₂

C₂²×C₅

D₅

C₅

G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #332

N	H ≅ G/N	type
129. C₅	#1700	semidirect

H ≅ G/N

type

129. C₅

#1700

semidirect

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

subgroup	index
#65383	2
#65370	2
#65138	2
#65120	2
C₅×#332	2
#64706	2
#64699	2
#1700	5

subgroup

index

Subgroups — #10599269

Conjugacy classes of subgroups

Complements

Maximal subgroups