Group #10602863 — subgroups

Subgroups — #10602863

Order 640.

256 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 71 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	C₂²×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#3968	C₂	1	2	yes	maximal
3	#65514	C₂	1	2	yes	maximal
4	#65391	C₂	1	1	yes	maximal, characteristic
5	#64772	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅×Q₈	C₂²	1	2	yes	—
7	C₂×C₅×Q₁₆	—	2	4	no	—
8	C₂×C₅×Q₁₆	—	2	2	no	—
9	C₂²×C₅×C₈	C₂²	1	1	yes	characteristic
10	#4072	C₂²	1	1	yes	characteristic
11	C₂×#681	C₂²	1	2	yes	—
12	C₂×#681	C₂²	1	1	yes	characteristic
13	#3968	—	2	4	no	—
14	#3967	—	2	4	no	—
15	#3946	—	2	2	no	—
16	#2047	—	5	1	no	maximal, Sylow
17	C₂×C₅×Q₈	—	2	2	no	—
18	C₂×C₅×Q₈	—	2	2	no	—
19	C₂×C₅×Q₈	—	2	2	no	—
20	C₂×C₅×Q₈	—	2	2	no	—
21	C₂×C₅×Q₈	—	2	2	no	—
22	C₂×C₅×Q₈	D₄	1	4	yes	—
23	C₂²×C₄×C₅	—	2	2	no	—
24	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₅×Q₁₆	—	2	8	no	—
26	C₂×C₅×C₈	—	2	2	no	—
27	C₂×C₅×C₈	D₄	1	2	yes	—
28	C₂²⋊Dic₅	—	2	1	no	—
29	C₄⋊Dic₅	D₄	1	2	yes	—
30	C₄×Dic₅	—	2	1	no	—
31	#681	—	2	2	no	—
32	#681	—	2	2	no	—
33	#681	—	2	2	no	—
34	C₂×#168	—	2	1	no	—
35	C₂×#168	—	2	2	no	—
36	C₂²×Q₁₆	D₅	1	1	yes	characteristic
37	#424	—	5	1	no	—
38	#419	—	5	2	no	—
39	C₂×#101	—	5	2	no	—
40	#341	—	5	1	no	—
41	C₂³×C₅	#41	1	1	yes	characteristic
42	C₅×Q₈	—	2	4	no	—
43	C₅×Q₈	—	2	4	no	—
44	C₅×Q₈	—	4	2	no	—
45	C₅×Q₈	—	4	2	no	—
46	C₂×C₄×C₅	—	2	4	no	—
47	C₂×C₄×C₅	—	4	2	no	—
48	C₂×C₄×C₅	—	4	2	no	—
49	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₅	#41	1	2	yes	—
53	C₂×Dic₅	—	2	2	no	—
54	C₅×C₈	—	2	2	no	—
55	#168	—	4	1	no	—
56	#168	—	4	2	no	—
57	C₂²×Q₈	C₂×D₅	1	2	yes	—
58	C₂×Q₁₆	—	2	4	no	—
59	C₂×Q₁₆	—	2	2	no	—
60	C₂×M₁₆	—	5	2	no	—
61	C₂×M₁₆	—	5	1	no	—
62	C₂²×C₈	C₂×D₅	1	1	yes	characteristic
63	#117	—	5	1	no	—
64	C₄⋊C₈	—	10	2	no	—
65	#103	—	10	4	no	—
66	#101	—	10	4	no	—
67	C₂²×C₅	—	2	2	no	—
68	C₂²×C₅	#121	1	1	yes	characteristic
69	C₂²×C₅	#123	1	2	yes	—
70	C₄×C₅	—	4	4	no	—
71	C₄×C₅	#120	1	1	yes	characteristic
72	C₄×C₅	#121	1	2	yes	—
73	C₄×C₅	#124	1	1	yes	characteristic
74	Dic₅	—	4	2	no	—
75	C₂×Q₈	—	2	2	no	—
76	C₂×Q₈	—	2	2	no	—
77	C₂×Q₈	—	2	2	no	—
78	C₂×Q₈	—	2	2	no	—
79	C₂×Q₈	—	2	2	no	—
80	C₂×Q₈	C₂²⋊D₅	1	4	yes	—
81	C₂²×C₄	—	2	2	no	—
82	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
83	Q₁₆	—	2	8	no	—
84	M₁₆	—	10	2	no	—
85	M₁₆	—	10	2	no	—
86	M₁₆	—	10	2	no	—
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	10	2	no	—
89	C₂×C₈	—	10	1	no	—
90	C₂×C₈	C₂²⋊D₅	1	2	yes	—
91	C₄⋊C₄	—	5	2	no	—
92	C₂²⋊C₄	—	10	1	no	—
93	C₄²	—	10	1	no	—
94	C₂×C₅	—	2	2	no	—
95	C₂×C₅	#394	1	1	yes	characteristic
96	C₂×C₅	#473	1	2	yes	—
97	C₂³	#711	1	1	yes	characteristic
98	Q₈	—	2	4	no	—
99	Q₈	—	2	4	no	—
100	Q₈	—	4	2	no	—
101	Q₈	—	4	2	no	—
102	C₂×C₄	—	2	4	no	—
103	C₂×C₄	—	4	2	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	10	2	no	—
106	C₂×C₄	D₄×D₅	1	1	yes	characteristic
107	C₂×C₄	#711	1	2	yes	—
108	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
109	C₂×C₄	C₂×C₂²⋊D₅	1	2	yes	—
110	C₈	—	2	2	no	—
111	C₈	—	20	1	no	—
112	C₈	—	20	2	no	—
113	C₅	#2047	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	2	2	no	—
115	C₂²	#4081	1	2	yes	—
116	C₂²	#4084	1	1	yes	characteristic
117	C₄	—	4	4	no	—
118	C₄	—	20	2	no	—
119	C₄	#4082	1	1	yes	characteristic
120	C₄	#4085	1	2	yes	—
121	C₄	#4099	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	#65481	1	2	yes	—
124	C₂	#65511	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₅×Q₁₆

C₂

yes

maximal, characteristic

C₂×#3968

C₂

yes

maximal

#65514

C₂

yes

maximal

#65391

C₂

yes

maximal, characteristic

#64772

C₂

yes

maximal, characteristic

C₂²×C₅×Q₈

C₂²

yes

—

C₂×C₅×Q₁₆

—

C₂×C₅×Q₁₆

—

C₂²×C₅×C₈

C₂²

yes

characteristic

#4072

C₂²

yes

characteristic

C₂×#681

C₂²

yes

—

C₂×#681

C₂²

yes

—

—

—

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

D₄

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂³

yes

characteristic

C₅×Q₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

D₄

yes

—

C₂²⋊Dic₅

—

C₄⋊Dic₅

D₄

yes

—

C₄×Dic₅

—

—

—

—

—

—

C₂²×Q₁₆

D₅

yes

—

—

—

—

C₂³×C₅

#41

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

#41

yes

—

C₂×Dic₅

—

C₅×C₈

—

#168

—

#168

—

C₂²×Q₈

C₂×D₅

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₅

yes

characteristic

#117

—

C₄⋊C₈

—

#103

—

#101

—

C₂²×C₅

—

C₂²×C₅

#121

yes

characteristic

C₂²×C₅

#123

yes

—

C₄×C₅

—

C₄×C₅

#120

yes

characteristic

C₄×C₅

#121

yes

—

C₄×C₅

#124

yes

characteristic

Dic₅

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²⋊D₅

yes

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₅

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂×C₅

—

C₂×C₅

#394

yes

characteristic

C₂×C₅

#473

yes

—

C₂³

#711

yes

characteristic

Q₈

—

Q₈

—

100

Q₈

—

101

Q₈

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

D₄×D₅

yes

characteristic

107

C₂×C₄

#711

yes

—

108

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

109

C₂×C₄

C₂×C₂²⋊D₅

yes

—

110

C₈

—

111

C₈

—

112

C₈

—

113

C₅

#2047

yes

characteristic, complemented, Sylow

114

C₂²

—

115

C₂²

#4081

yes

—

116

C₂²

#4084

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

#4082

yes

characteristic

120

C₄

#4085

yes

—

121

C₄

#4099

yes

characteristic

122

C₂

—

123

C₂

#65481

yes

—

124

C₂

#65511

yes

characteristic

	subgroup	G/H
center	C₂²	#4084
commutator, cosocle	C₂²×C₄×C₅	C₂³
Frattini	C₂²×C₄	C₂²×D₅
Fitting	C₂²×C₅×Q₁₆	C₂
socle	C₂²×C₅	#121
prime radical	C₂³×C₅	#41
hypercenter	C₂²×Q₁₆	D₅
hypocenter	C₅	#2047
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

subgroup

G/H

center

C₂²

#4084

commutator, cosocle

C₂²×C₄×C₅

C₂³

Frattini

C₂²×C₄

C₂²×D₅

Fitting

C₂²×C₅×Q₁₆

C₂

C₂²×C₅

C₂³×C₅

C₂²×Q₁₆

D₅

hypocenter

C₅

#2047

LCS

G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×Q₁₆

N	H ≅ G/N	type
113. C₅	#2047	semidirect

H ≅ G/N

type

113. C₅

#2047

semidirect

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

subgroup	index
C₂²×C₅×Q₁₆	2
C₂×#3968	2
#65514	2
#65391	2
#64772	2
#2047	5

subgroup

index

C₂²×C₅×Q₁₆

Subgroups — #10602863

Conjugacy classes of subgroups

Complements

Maximal subgroups