Group #10601255 — subgroups

Subgroups — #10601255

Order 640.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#3950	C₂	1	1	yes	maximal, characteristic
3	#65217	C₂	1	2	yes	maximal
4	#64771	C₂	1	2	yes	maximal
5	#64771	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₅	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₅	C₂²	1	2	yes	—
11	C₂×#683	—	2	2	no	—
12	C₅×C₄⋊C₈	—	2	2	no	—
13	#3963	—	2	2	no	—
14	#3950	—	2	2	no	—
15	#2086	—	5	1	no	maximal, Sylow
16	C₂²×C₄×C₅	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₅	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂²×Dic₅	—	2	2	no	—
20	C₂²×Dic₅	—	2	2	no	—
21	C₂×C₅×C₈	—	2	2	no	—
22	C₂×C₅×C₈	—	2	1	no	—
23	C₂×C₅×C₈	—	2	2	no	—
24	C₂×C₅×C₈	D₄	1	2	yes	—
25	C₄²×C₅	—	2	1	no	—
26	C₄²×C₅	—	2	1	no	—
27	C₄⋊Dic₅	—	2	2	no	—
28	C₄⋊Dic₅	—	2	2	no	—
29	C₄⋊Dic₅	—	2	2	no	—
30	C₄⋊Dic₅	Q₈	1	4	yes	—
31	#683	—	4	4	no	—
32	C₂×#107	—	5	1	no	—
33	C₂×C₄⋊C₈	D₅	1	1	yes	characteristic
34	#389	—	5	2	no	—
35	#340	—	5	1	no	—
36	#340	—	5	2	no	—
37	C₂³×C₅	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₅	—	2	1	no	—
39	C₂×C₄×C₅	—	2	1	no	—
40	C₂×C₄×C₅	—	2	1	no	—
41	C₂×C₄×C₅	—	2	2	no	—
42	C₂×C₄×C₅	D₈	1	2	yes	—
43	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₅	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₅	#41	1	1	yes	characteristic
46	C₂×C₄×C₅	#41	1	2	yes	—
47	C₂×Dic₅	—	2	4	no	—
48	C₂×Dic₅	—	4	2	no	—
49	C₂×Dic₅	—	4	2	no	—
50	C₂×Dic₅	—	4	2	no	—
51	C₂×Dic₅	—	4	2	no	—
52	C₂×Dic₅	—	4	2	no	—
53	C₅×C₈	—	2	2	no	—
54	C₅×C₈	—	4	1	no	—
55	C₂²×C₈	C₂×D₅	1	1	yes	characteristic
56	C₂²×C₈	C₂×D₅	1	1	yes	characteristic
57	C₂×C₄⋊C₄	—	5	2	no	—
58	C₂×C₄⋊C₄	—	5	2	no	—
59	C₂×C₄⋊C₄	—	10	2	no	—
60	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
61	#107	—	10	2	no	—
62	C₄⋊C₈	—	2	2	no	—
63	#95	—	10	2	no	—
64	C₂²×C₅	#121	1	1	yes	characteristic
65	C₂²×C₅	C₂²⋊Q₈	1	2	yes	—
66	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
67	C₂²×C₅	#135	1	1	yes	characteristic
68	C₂²×C₅	#137	1	2	yes	—
69	C₄×C₅	—	2	2	no	—
70	C₄×C₅	—	4	1	no	—
71	C₄×C₅	#123	1	1	yes	characteristic
72	C₄×C₅	#125	1	2	yes	—
73	C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
74	Dic₅	—	4	4	no	—
75	Dic₅	—	8	2	no	—
76	C₂²×C₄	—	10	2	no	—
77	C₂²×C₄	—	10	2	no	—
78	C₂²×C₄	D₂₀	1	1	yes	characteristic
79	C₂²×C₄	D₂₀	1	1	yes	characteristic
80	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	C₂²⋊D₅	1	2	yes	—
85	C₄⋊C₄	—	5	4	no	—
86	C₄⋊C₄	—	10	2	no	—
87	C₄⋊C₄	—	10	2	no	—
88	C₄⋊C₄	—	10	2	no	—
89	C₄⋊C₄	—	20	4	no	—
90	C₄²	—	2	1	no	—
91	C₄²	—	2	1	no	—
92	C₂×C₅	#398	1	1	yes	characteristic
93	C₂×C₅	#466	1	1	yes	characteristic
94	C₂×C₅	#470	1	1	yes	characteristic
95	C₂×C₅	#474	1	2	yes	—
96	C₂×C₅	#479	1	2	yes	—
97	C₂³	C₂×D₂₀	1	1	yes	characteristic
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	10	4	no	—
103	C₂×C₄	—	20	2	no	—
104	C₂×C₄	—	20	2	no	—
105	C₂×C₄	—	20	2	no	—
106	C₂×C₄	—	20	2	no	—
107	C₂×C₄	—	20	2	no	—
108	C₂×C₄	D₄₀	1	2	yes	—
109	C₂×C₄	#709	1	1	yes	characteristic
110	C₂×C₄	#711	1	2	yes	—
111	C₂×C₄	Q₈×D₅	1	2	yes	—
112	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	4	1	no	—
115	C₅	#2086	1	1	yes	characteristic, complemented, Sylow
116	C₂²	#4043	1	2	yes	—
117	C₂²	C₂×D₄₀	1	1	yes	characteristic
118	C₂²	#4050	1	1	yes	characteristic
119	C₂²	#4055	1	2	yes	—
120	C₂²	#4076	1	1	yes	characteristic
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	20	4	no	—
124	C₄	—	40	2	no	—
125	C₄	#4035	1	2	yes	—
126	C₄	#4081	1	1	yes	characteristic
127	C₄	#4090	1	1	yes	characteristic
128	C₂	#65118	1	2	yes	—
129	C₂	#65135	1	2	yes	—
130	C₂	#65272	1	1	yes	characteristic
131	C₂	#65404	1	1	yes	characteristic
132	C₂	#65426	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#3950

C₂

yes

maximal, characteristic

#65217

C₂

yes

maximal

#64771

C₂

yes

maximal

#64771

C₂

yes

maximal, characteristic

C₂²×C₅×C₈

C₂²

yes

characteristic

C₂²×C₅×C₈

C₂²

yes

characteristic

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄⋊Dic₅

C₂²

yes

—

C₂×C₄⋊Dic₅

C₂²

yes

—

C₂×#683

—

C₅×C₄⋊C₈

—

—

—

—

C₂²×C₄×C₅

D₄

yes

characteristic

C₂²×C₄×C₅

D₄

yes

characteristic

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

—

C₂²×Dic₅

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

D₄

yes

—

C₄²×C₅

—

C₄²×C₅

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₄⋊Dic₅

Q₈

yes

—

#683

—

C₂×#107

—

C₂×C₄⋊C₈

D₅

yes

—

—

—

C₂³×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

D₈

yes

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×Q₈

yes

—

C₂×C₄×C₅

#41

yes

characteristic

C₂×C₄×C₅

#41

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₅×C₈

—

C₅×C₈

—

C₂²×C₈

C₂×D₅

yes

characteristic

C₂²×C₈

C₂×D₅

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₅

yes

characteristic

#107

—

C₄⋊C₈

—

#95

—

C₂²×C₅

#121

yes

characteristic

C₂²×C₅

C₂²⋊Q₈

yes

—

C₂²×C₅

C₂×D₈

yes

C₂²×C₅

yes

C₂²×C₅

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#123

yes

characteristic

C₄×C₅

#125

yes

—

C₄×C₅

C₄⋊Q₈

yes

characteristic

Dic₅

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₂₀

yes

characteristic

C₂²×C₄

D₂₀

yes

characteristic

C₂²×C₄

C₂²×D₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₅

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂×C₅

yes

C₂×C₅

yes

C₂×C₅

yes

C₂×C₅

yes

—

C₂×C₅

#479

yes

—

C₂³

C₂×D₂₀

yes

characteristic

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

D₄₀

yes

—

109

C₂×C₄

#709

yes

characteristic

110

C₂×C₄

#711

yes

—

111

C₂×C₄

Q₈×D₅

yes

—

112

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

113

C₈

—

114

C₈

—

115

C₅

#2086

yes

characteristic, complemented, Sylow

116

C₂²

#4043

yes

—

117

C₂²

C₂×D₄₀

yes

characteristic

118

C₂²

#4050

yes

characteristic

119

C₂²

#4055

yes

—

120

C₂²

#4076

yes

characteristic

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

#4035

yes

—

126

C₄

#4081

yes

characteristic

127

C₄

#4090

yes

characteristic

128

C₂

#65118

yes

—

129

C₂

#65135

yes

—

130

C₂

#65272

yes

characteristic

131

C₂

#65404

yes

characteristic

132

C₂

#65426

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₂₀
commutator, cosocle	C₂²×C₄×C₅	C₂³
Frattini	C₂²×C₄	C₂²×D₅
Fitting	C₂×C₅×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₅	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₅
hypocenter	C₅	#2086
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₂₀

commutator, cosocle

C₂²×C₄×C₅

C₂³

Frattini

C₂²×C₄

C₂²×D₅

Fitting

C₂×C₅×C₄⋊C₈

C₂

socle, prime radical

C₂³×C₅

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₅

hypocenter

C₅

#2086

LCS

G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
115. C₅	#2086	semidirect

H ≅ G/N

type

115. C₅

#2086

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×#3950	2
#65217	2
#64771	2
#2086	5

subgroup

index

C₂×C₅×C₄⋊C₈

Subgroups — #10601255

Conjugacy classes of subgroups

Complements

Maximal subgroups