Group #10602063 — subgroups

Subgroups — #10602063

Order 640.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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	#66047	C₂	1	1	yes	maximal, characteristic
2	C₅×#492	C₂	1	1	yes	maximal, characteristic
3	#65380	C₂	1	2	yes	maximal, complemented
4	#64764	C₂	1	1	yes	maximal, characteristic
5	#64676	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×SD₁₆	—	2	2	no	—
7	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₅×#127	C₂²	1	1	yes	characteristic
9	#4082	—	2	2	no	—
10	#4081	—	2	2	no	—
11	D₄×Dic₅	—	2	2	no	—
12	C₄×Dic₁₀	C₂²	1	2	yes	—
13	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	#3942	—	2	2	no	—
15	#3939	—	2	2	no	—
16	C₄⋊#168	C₂²	1	2	yes	—
17	#1630	—	5	1	no	maximal, Sylow
18	C₂×C₅×Q₈	—	2	1	no	—
19	C₂×C₅×D₄	—	2	2	no	—
20	C₂×C₅×D₄	D₄	1	2	yes	—
21	C₂²×Dic₅	—	2	2	no	—
22	C₂×Dic₁₀	D₄	1	2	yes	—
23	C₅×SD₁₆	—	4	4	no	—
24	C₂×C₅×C₈	—	2	1	no	—
25	C₅×C₄⋊C₄	—	2	2	no	—
26	C₄²×C₅	C₂³	1	1	yes	characteristic
27	C₂²⋊Dic₅	—	2	4	no	—
28	C₂²⋊Dic₅	—	2	2	no	—
29	C₄⋊Dic₅	D₄	1	2	yes	—
30	#683	—	2	2	no	—
31	C₄×Dic₅	—	2	2	no	—
32	C₂×#168	—	2	2	no	—
33	#559	—	5	1	no	—
34	#492	D₅	1	1	yes	characteristic
35	#477	—	5	2	no	—
36	#331	—	5	1	no	—
37	Q₈⋊C₈	—	5	2	no	—
38	C₂³×C₅	—	2	2	no	—
39	C₅×Q₈	—	4	2	no	—
40	C₅×D₄	—	4	2	no	—
41	C₅×D₄	—	4	2	no	—
42	C₅×D₄	—	4	2	no	—
43	C₂×C₄×C₅	—	4	1	no	—
44	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₅	—	2	2	no	—
47	C₂×Dic₅	—	2	2	no	—
48	C₂×Dic₅	—	8	2	no	—
49	Dic₁₀	—	2	2	no	—
50	Dic₁₀	—	2	2	no	—
51	C₅×C₈	—	2	2	no	—
52	#168	—	4	2	no	—
53	C₂×SD₁₆	—	2	2	no	—
54	C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
55	#127	C₂×D₅	1	1	yes	characteristic
56	#124	—	10	2	no	—
57	#123	—	10	2	no	—
58	C₄×Q₈	—	5	2	no	—
59	C₄×D₄	—	10	2	no	—
60	#107	—	10	2	no	—
61	C₄⋊C₈	—	5	2	no	—
62	#103	—	10	2	no	—
63	C₄×C₈	C₂×D₅	1	1	yes	characteristic
64	C₂²×C₅	—	4	4	no	—
65	C₂²×C₅	—	4	2	no	—
66	C₂²×C₅	#120	1	1	yes	characteristic
67	C₄×C₅	—	2	1	no	—
68	C₄×C₅	—	8	1	no	—
69	C₄×C₅	#135	1	2	yes	—
70	C₄×C₅	#137	1	2	yes	—
71	Dic₅	—	4	2	no	—
72	Dic₅	—	4	2	no	—
73	C₂×Q₈	—	2	1	no	—
74	C₂×Q₈	—	5	2	no	—
75	C₂×D₄	—	2	2	no	—
76	C₂×D₄	C₂²⋊D₅	1	2	yes	—
77	C₂²×C₄	—	10	2	no	—
78	SD₁₆	—	4	4	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	10	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	5	2	no	—
83	C₄⋊C₄	—	10	2	no	—
84	C₂²⋊C₄	—	10	4	no	—
85	C₂²⋊C₄	—	10	2	no	—
86	C₄²	—	10	2	no	—
87	C₄²	C₂²×D₅	1	1	yes	characteristic
88	C₂×C₅	—	8	2	no	—
89	C₂×C₅	#452	1	2	yes	—
90	C₂×C₅	#453	1	1	yes	characteristic
91	C₂³	—	2	2	no	—
92	Q₈	—	4	2	no	—
93	Q₈	—	10	2	no	—
94	Q₈	—	10	2	no	—
95	D₄	—	4	2	no	—
96	D₄	—	4	2	no	—
97	D₄	—	4	2	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	10	2	no	—
100	C₂×C₄	—	10	2	no	—
101	C₂×C₄	—	40	2	no	—
102	C₂×C₄	D₄×D₅	1	2	yes	—
103	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
104	C₈	—	2	2	no	—
105	C₈	—	20	2	no	—
106	C₅	#1630	1	1	yes	characteristic, complemented, Sylow
107	C₂²	—	4	2	no	—
108	C₂²	—	4	4	no	—
109	C₂²	#4083	1	1	yes	characteristic
110	C₄	—	2	1	no	—
111	C₄	—	8	1	no	—
112	C₄	—	20	2	no	—
113	C₄	—	20	2	no	—
114	C₄	#4061	1	2	yes	—
115	C₄	#4062	1	2	yes	—
116	C₂	—	8	2	no	—
117	C₂	#65366	1	1	yes	characteristic
118	C₂	#65462	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#66047

C₂

yes

maximal, characteristic

C₅×#492

C₂

yes

maximal, characteristic

#65380

C₂

yes

maximal, complemented

#64764

C₂

yes

maximal, characteristic

#64676

C₂

yes

maximal, complemented

C₂×C₅×SD₁₆

—

C₅×C₄⋊Q₈

C₂²

yes

characteristic

C₅×#127

C₂²

yes

characteristic

#4082

—

#4081

—

D₄×Dic₅

—

C₄×Dic₁₀

C₂²

yes

—

C₄×C₅×C₈

C₂²

yes

—

—

C₂²

yes

—

#1630

—

maximal, Sylow

C₂×C₅×Q₈

—

C₂×C₅×D₄

—

C₂×C₅×D₄

D₄

yes

—

C₂²×Dic₅

—

C₂×Dic₁₀

D₄

yes

—

C₅×SD₁₆

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂³

yes

characteristic

C₂²⋊Dic₅

—

C₂²⋊Dic₅

—

C₄⋊Dic₅

D₄

yes

—

#683

—

C₄×Dic₅

—

C₂×#168

—

#559

—

#492

D₅

yes

characteristic

#477

—

#331

—

Q₈⋊C₈

—

C₂³×C₅

—

C₅×Q₈

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

Dic₁₀

—

Dic₁₀

—

C₅×C₈

—

#168

—

C₂×SD₁₆

—

C₄⋊Q₈

C₂×D₅

yes

characteristic

#127

C₂×D₅

yes

characteristic

#124

—

#123

—

C₄×Q₈

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

C₂×D₅

yes

characteristic

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#120

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#135

yes

—

C₄×C₅

#137

yes

—

Dic₅

—

Dic₅

—

C₂×Q₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₅

yes

—

C₂²×C₄

—

SD₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²×D₅

yes

characteristic

C₂×C₅

—

C₂×C₅

#452

yes

—

C₂×C₅

#453

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

D₄×D₅

yes

—

103

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

104

C₈

—

105

C₈

—

106

C₅

#1630

yes

characteristic, complemented, Sylow

107

C₂²

—

108

C₂²

—

109

C₂²

#4083

yes

characteristic

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

#4061

yes

—

115

C₄

#4062

yes

—

116

C₂

—

117

C₂

#65366

yes

characteristic

118

C₂

#65462

yes

—

	subgroup	G/H
center	C₂²	#4083
commutator, cosocle	C₄²×C₅	C₂³
Frattini	C₄²	C₂²×D₅
Fitting	C₅×#492	C₂
socle	C₂²×C₅	#120
prime radical	C₅×#127	C₂²
hypercenter	#492	D₅
hypocenter	C₅	#1630
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#4083

commutator, cosocle

C₄²×C₅

C₂³

Frattini

C₄²

C₂²×D₅

C₂

C₂²×C₅

C₂²

D₅

C₅

G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
3. #65380	C₂	semidirect
5. #64676	C₂	semidirect
106. C₅	#1630	semidirect

H ≅ G/N

type

3. #65380

C₂

semidirect

5. #64676

C₂

semidirect

106. C₅

#1630

semidirect

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

subgroup	index
#66047	2
C₅×#492	2
#65380	2
#64764	2
#64676	2
#1630	5

subgroup

index

Subgroups — #10602063

Conjugacy classes of subgroups

Complements

Maximal subgroups