Group #10600464 — subgroups

Subgroups — #10600464

Order 640.

222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 81 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	C₅×#391	C₂	1	1	yes	maximal, characteristic
2	C₂×#3967	C₂	1	2	yes	maximal
3	#65225	C₂	1	1	yes	maximal, characteristic
4	#64749	C₂	1	2	yes	maximal
5	#64744	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅×Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₅	C₂²	1	2	yes	—
10	C₂²×#168	C₂²	1	2	yes	—
11	C₅×#95	—	2	2	no	—
12	#3967	—	2	4	no	—
13	#3963	—	2	2	no	—
14	#2074	—	5	1	no	maximal, Sylow
15	C₂×C₅×Q₈	—	2	1	no	—
16	C₂×C₅×Q₈	—	2	2	no	—
17	C₂×C₅×Q₈	—	2	2	no	—
18	C₂×C₅×Q₈	D₄	1	2	yes	—
19	C₂²×C₄×C₅	—	2	1	no	—
20	C₂²×C₄×C₅	—	2	1	no	—
21	C₂²×C₄×C₅	D₄	1	2	yes	—
22	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂²×Dic₅	—	2	2	no	—
24	C₅×C₄⋊C₄	—	2	2	no	—
25	C₄²×C₅	—	2	2	no	—
26	C₄⋊Dic₅	—	2	2	no	—
27	C₄⋊Dic₅	—	2	2	no	—
28	C₂×#168	—	2	2	no	—
29	C₂×#168	—	2	2	no	—
30	C₂×#168	—	2	2	no	—
31	C₂×#103	—	5	2	no	—
32	#391	D₅	1	1	yes	characteristic
33	#382	—	5	1	no	—
34	#340	—	5	2	no	—
35	#336	—	5	1	no	—
36	C₂³×C₅	C₂×D₄	1	1	yes	characteristic
37	C₅×Q₈	—	2	4	no	—
38	C₅×Q₈	—	4	2	no	—
39	C₂×C₄×C₅	—	2	2	no	—
40	C₂×C₄×C₅	—	2	2	no	—
41	C₂×C₄×C₅	—	2	2	no	—
42	C₂×C₄×C₅	—	2	2	no	—
43	C₂×C₄×C₅	—	4	1	no	—
44	C₂×C₄×C₅	—	4	1	no	—
45	C₂×C₄×C₅	—	4	1	no	—
46	C₂×C₄×C₅	—	4	2	no	—
47	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₅	#41	1	1	yes	characteristic
49	C₂×C₄×C₅	#41	1	2	yes	—
50	C₂×C₄×C₅	#41	1	2	yes	—
51	C₂×Dic₅	—	4	2	no	—
52	C₂×Dic₅	—	4	2	no	—
53	C₂×Dic₅	—	4	2	no	—
54	#168	—	4	2	no	—
55	C₂²×Q₈	C₂×D₅	1	1	yes	characteristic
56	C₂²×C₈	—	5	2	no	—
57	C₂×C₄⋊C₄	—	5	2	no	—
58	C₂×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
59	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
60	#103	—	10	4	no	—
61	#95	—	2	2	no	—
62	#95	—	10	2	no	—
63	C₂²×C₅	#121	1	1	yes	characteristic
64	C₂²×C₅	#123	1	1	yes	characteristic
65	C₂²×C₅	#124	1	1	yes	characteristic
66	C₂²×C₅	#135	1	2	yes	—
67	C₂²×C₅	#137	1	2	yes	—
68	C₄×C₅	—	4	2	no	—
69	C₄×C₅	—	4	2	no	—
70	C₄×C₅	—	8	1	no	—
71	C₄×C₅	#123	1	2	yes	—
72	C₄×C₅	#126	1	2	yes	—
73	Dic₅	—	8	2	no	—
74	C₂×Q₈	—	2	1	no	—
75	C₂×Q₈	—	2	2	no	—
76	C₂×Q₈	—	2	2	no	—
77	C₂×Q₈	D₂₀	1	2	yes	—
78	C₂²×C₄	—	2	1	no	—
79	C₂²×C₄	—	2	1	no	—
80	C₂²×C₄	—	10	2	no	—
81	C₂²×C₄	C₂²⋊D₅	1	2	yes	—
82	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
83	C₂×C₈	—	10	2	no	—
84	C₂×C₈	—	10	2	no	—
85	C₂×C₈	—	10	2	no	—
86	C₄⋊C₄	—	2	2	no	—
87	C₄⋊C₄	—	10	2	no	—
88	C₄⋊C₄	—	10	2	no	—
89	C₄²	—	2	2	no	—
90	C₂×C₅	#397	1	1	yes	characteristic
91	C₂×C₅	#464	1	2	yes	—
92	C₂×C₅	#485	1	2	yes	—
93	C₂×C₅	#488	1	1	yes	characteristic
94	C₂×C₅	#491	1	1	yes	characteristic
95	C₂³	C₂×C₂²⋊D₅	1	1	yes	characteristic
96	Q₈	—	2	4	no	—
97	Q₈	—	4	2	no	—
98	C₂×C₄	—	2	2	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	4	1	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	20	2	no	—
107	C₂×C₄	—	20	2	no	—
108	C₂×C₄	—	20	2	no	—
109	C₂×C₄	C₂×D₂₀	1	1	yes	characteristic
110	C₂×C₄	#709	1	1	yes	characteristic
111	C₂×C₄	#711	1	2	yes	—
112	C₂×C₄	#711	1	2	yes	—
113	C₈	—	20	2	no	—
114	C₅	#2074	1	1	yes	characteristic, complemented, Sylow
115	C₂²	#4076	1	1	yes	characteristic
116	C₂²	#4081	1	1	yes	characteristic
117	C₂²	#4082	1	1	yes	characteristic
118	C₂²	#4088	1	2	yes	—
119	C₂²	#4096	1	2	yes	—
120	C₄	—	4	2	no	—
121	C₄	—	4	2	no	—
122	C₄	—	8	1	no	—
123	C₄	—	40	2	no	—
124	C₄	#4025	1	2	yes	—
125	C₄	#4032	1	2	yes	—
126	C₂	#65242	1	1	yes	characteristic
127	C₂	#65317	1	2	yes	—
128	C₂	#65334	1	2	yes	—
129	C₂	#65345	1	1	yes	characteristic
130	C₂	#65371	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#391

C₂

yes

maximal, characteristic

C₂×#3967

C₂

yes

maximal

#65225

C₂

yes

maximal, characteristic

#64749

C₂

yes

maximal

#64744

C₂

yes

maximal, characteristic

C₂²×C₅×Q₈

C₂²

yes

characteristic

C₂×C₅×C₄⋊C₄

C₂²

yes

characteristic

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄⋊Dic₅

C₂²

yes

—

C₂²×#168

C₂²

yes

—

C₅×#95

—

—

—

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

D₄

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

D₄

yes

—

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

—

C₅×C₄⋊C₄

—

C₄²×C₅

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

—

—

—

—

D₅

yes

—

—

—

C₂³×C₅

C₂×D₄

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₄

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

#41

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

#168

—

C₂²×Q₈

C₂×D₅

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅

yes

characteristic

C₂×C₄²

C₂×D₅

yes

—

—

—

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

—

C₂²×C₅

#137

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#123

yes

—

C₄×C₅

#126

yes

—

Dic₅

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

D₂₀

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₅

yes

—

C₂²×C₄

C₂²×D₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₂×C₅

#397

yes

characteristic

C₂×C₅

#464

yes

—

C₂×C₅

#485

yes

—

C₂×C₅

yes

C₂×C₅

yes

C₂³

C₂×C₂²⋊D₅

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂×D₂₀

yes

characteristic

110

C₂×C₄

#709

yes

characteristic

111

C₂×C₄

#711

yes

—

112

C₂×C₄

#711

yes

—

113

C₈

—

114

C₅

#2074

yes

characteristic, complemented, Sylow

115

C₂²

#4076

yes

characteristic

116

C₂²

#4081

yes

characteristic

117

C₂²

#4082

yes

characteristic

118

C₂²

#4088

yes

—

119

C₂²

#4096

yes

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#4025

yes

—

125

C₄

#4032

yes

—

126

C₂

#65242

yes

characteristic

127

C₂

#65317

yes

—

128

C₂

#65334

yes

—

129

C₂

#65345

yes

characteristic

130

C₂

#65371

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₅
commutator, cosocle	C₂²×C₄×C₅	C₂³
Frattini	C₂²×C₄	C₂²×D₅
Fitting	C₅×#391	C₂
socle, prime radical	C₂³×C₅	C₂×D₄
hypercenter	#391	D₅
hypocenter	C₅	#2074
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₅

commutator, cosocle

C₂²×C₄×C₅

C₂³

Frattini

C₂²×C₄

C₂²×D₅

Fitting

C₅×#391

C₂

socle, prime radical

C₂³×C₅

C₂×D₄

D₅

C₅

G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #391

N	H ≅ G/N	type
114. C₅	#2074	semidirect

H ≅ G/N

type

114. C₅

#2074

semidirect

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

subgroup	index
C₅×#391	2
C₂×#3967	2
#65225	2
#64749	2
#64744	2
#2074	5

subgroup

index

Subgroups — #10600464

Conjugacy classes of subgroups

Complements

Maximal subgroups