Group #10602835 — subgroups

Subgroups — #10602835

Order 640.

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

normal subgroups only

This group has 296 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×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#3965	C₂	1	2	yes	maximal, complemented
3	#65504	C₂	1	2	yes	maximal, complemented
4	#65391	C₂	1	1	yes	maximal, characteristic, complemented
5	#64772	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₅×D₄	C₂²	1	2	yes	—
7	C₂×C₅×D₈	—	2	4	no	—
8	C₂×C₅×D₈	—	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	#3965	—	2	4	no	—
14	#3964	—	2	4	no	—
15	#3946	—	2	2	no	—
16	#2045	—	5	1	no	maximal, Sylow
17	C₂⁴×C₅	—	2	2	no	—
18	C₂×C₅×D₄	—	2	2	no	—
19	C₂×C₅×D₄	—	2	2	no	—
20	C₂×C₅×D₄	—	2	2	no	—
21	C₂×C₅×D₄	—	2	2	no	—
22	C₂×C₅×D₄	—	2	2	no	—
23	C₂×C₅×D₄	D₄	1	4	yes	—
24	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₅×D₈	—	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×D₈	D₅	1	1	yes	characteristic
37	#424	—	5	1	no	—
38	#418	—	5	2	no	—
39	C₂×#100	—	5	2	no	—
40	#341	—	5	1	no	—
41	C₂³×C₅	—	2	4	no	—
42	C₂³×C₅	—	4	2	no	—
43	C₂³×C₅	—	4	2	no	—
44	C₂³×C₅	—	8	4	no	—
45	C₂³×C₅	#41	1	1	yes	characteristic
46	C₅×D₄	—	2	4	no	—
47	C₅×D₄	—	2	4	no	—
48	C₅×D₄	—	4	2	no	—
49	C₅×D₄	—	4	2	no	—
50	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
51	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
52	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×C₅	#41	1	2	yes	—
54	C₂×Dic₅	—	2	2	no	—
55	C₅×C₈	—	2	2	no	—
56	#168	—	4	1	no	—
57	#168	—	4	2	no	—
58	C₂²×D₄	C₂×D₅	1	2	yes	—
59	C₂×D₈	—	2	4	no	—
60	C₂×D₈	—	2	2	no	—
61	C₂×M₁₆	—	5	2	no	—
62	C₂×M₁₆	—	5	1	no	—
63	C₂²×C₈	C₂×D₅	1	1	yes	characteristic
64	#117	—	5	1	no	—
65	C₄⋊C₈	—	10	2	no	—
66	#102	—	10	4	no	—
67	#100	—	10	4	no	—
68	C₂²×C₅	—	2	2	no	—
69	C₂²×C₅	—	4	4	no	—
70	C₂²×C₅	—	8	4	no	—
71	C₂²×C₅	—	8	4	no	—
72	C₂²×C₅	—	8	4	no	—
73	C₂²×C₅	#121	1	1	yes	characteristic
74	C₂²×C₅	#123	1	2	yes	—
75	C₄×C₅	#120	1	1	yes	characteristic
76	C₄×C₅	#121	1	2	yes	—
77	C₄×C₅	#124	1	1	yes	characteristic
78	Dic₅	—	4	2	no	—
79	C₂⁴	—	2	2	no	—
80	C₂×D₄	—	2	2	no	—
81	C₂×D₄	—	2	2	no	—
82	C₂×D₄	—	2	2	no	—
83	C₂×D₄	—	2	2	no	—
84	C₂×D₄	—	2	2	no	—
85	C₂×D₄	C₂²⋊D₅	1	4	yes	—
86	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
87	D₈	—	2	8	no	—
88	M₁₆	—	10	2	no	—
89	M₁₆	—	10	2	no	—
90	M₁₆	—	10	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	10	2	no	—
93	C₂×C₈	—	10	1	no	—
94	C₂×C₈	C₂²⋊D₅	1	2	yes	—
95	C₄⋊C₄	—	5	2	no	—
96	C₂²⋊C₄	—	10	1	no	—
97	C₄²	—	10	1	no	—
98	C₂×C₅	—	2	2	no	—
99	C₂×C₅	—	8	4	no	—
100	C₂×C₅	#394	1	1	yes	characteristic
101	C₂×C₅	#472	1	2	yes	—
102	C₂³	—	2	4	no	—
103	C₂³	—	4	2	no	—
104	C₂³	—	4	2	no	—
105	C₂³	—	8	4	no	—
106	C₂³	#711	1	1	yes	characteristic
107	D₄	—	2	4	no	—
108	D₄	—	2	4	no	—
109	D₄	—	4	2	no	—
110	D₄	—	4	2	no	—
111	C₂×C₄	—	10	2	no	—
112	C₂×C₄	D₄×D₅	1	1	yes	characteristic
113	C₂×C₄	#711	1	2	yes	—
114	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
115	C₂×C₄	C₂×C₂²⋊D₅	1	2	yes	—
116	C₈	—	2	2	no	—
117	C₈	—	20	1	no	—
118	C₈	—	20	2	no	—
119	C₅	#2045	1	1	yes	characteristic, complemented, Sylow
120	C₂²	—	2	2	no	—
121	C₂²	—	4	4	no	—
122	C₂²	—	8	4	no	—
123	C₂²	—	8	4	no	—
124	C₂²	—	8	4	no	—
125	C₂²	#4081	1	2	yes	—
126	C₂²	#4084	1	1	yes	characteristic
127	C₄	—	20	2	no	—
128	C₄	#4082	1	1	yes	characteristic
129	C₄	#4085	1	2	yes	—
130	C₄	#4099	1	1	yes	characteristic
131	C₂	—	2	2	no	—
132	C₂	—	8	4	no	—
133	C₂	#65449	1	2	yes	—
134	C₂	#65511	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₅×D₈

C₂

yes

maximal, characteristic

C₂×#3965

C₂

yes

maximal, complemented

#65504

C₂

yes

maximal, complemented

#65391

C₂

yes

maximal, characteristic, complemented

#64772

C₂

yes

maximal, characteristic, complemented

C₂²×C₅×D₄

C₂²

yes

—

C₂×C₅×D₈

—

C₂×C₅×D₈

—

C₂²×C₅×C₈

C₂²

yes

characteristic

#4072

C₂²

yes

characteristic

C₂×#681

C₂²

yes

—

C₂×#681

C₂²

yes

—

—

—

—

C₂⁴×C₅

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

D₄

yes

—

C₂²×C₄×C₅

C₂³

yes

characteristic

C₅×D₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

D₄

yes

—

C₂²⋊Dic₅

—

C₄⋊Dic₅

D₄

yes

—

C₄×Dic₅

—

—

—

—

—

—

C₂²×D₈

D₅

yes

—

—

—

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#41

yes

characteristic

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

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×D₄

C₂×D₅

yes

—

C₂×D₈

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₅

yes

characteristic

#117

—

C₄⋊C₈

—

#102

—

#100

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

#121

yes

characteristic

C₂²×C₅

#123

yes

—

C₄×C₅

#120

yes

characteristic

C₄×C₅

#121

yes

—

C₄×C₅

#124

yes

characteristic

Dic₅

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂²⋊D₅

yes

—

C₂²×C₄

C₂²×D₅

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₅

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂×C₅

—

C₂×C₅

—

100

C₂×C₅

#394

yes

characteristic

101

C₂×C₅

#472

yes

—

102

C₂³

—

103

C₂³

—

104

C₂³

—

105

C₂³

—

106

C₂³

#711

yes

characteristic

107

D₄

—

108

D₄

—

109

D₄

—

110

D₄

—

111

C₂×C₄

—

112

C₂×C₄

D₄×D₅

yes

characteristic

113

C₂×C₄

#711

yes

—

114

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

115

C₂×C₄

C₂×C₂²⋊D₅

yes

—

116

C₈

—

117

C₈

—

118

C₈

—

119

C₅

#2045

yes

characteristic, complemented, Sylow

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

—

125

C₂²

#4081

yes

—

126

C₂²

#4084

yes

characteristic

127

C₄

—

128

C₄

#4082

yes

characteristic

129

C₄

#4085

yes

—

130

C₄

#4099

yes

characteristic

131

C₂

—

132

C₂

—

133

C₂

#65449

yes

—

134

C₂

#65511

yes

characteristic

	subgroup	G/H
center	C₂²	#4084
commutator, cosocle	C₂²×C₄×C₅	C₂³
Frattini	C₂²×C₄	C₂²×D₅
Fitting, prime radical	C₂²×C₅×D₈	C₂
socle	C₂²×C₅	#121
hypercenter	C₂²×D₈	D₅
hypocenter	C₅	#2045
LCS	G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₈

subgroup

G/H

center

C₂²

#4084

commutator, cosocle

C₂²×C₄×C₅

C₂³

Frattini

C₂²×C₄

C₂²×D₅

Fitting, prime radical

C₂²×C₅×D₈

C₂

socle

C₂²×C₅

#121

hypercenter

C₂²×D₈

D₅

hypocenter

C₅

#2045

LCS

G ▷ C₂²×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₈

N	H ≅ G/N	type
2. C₂×#3965	C₂	semidirect
3. #65504	C₂	semidirect
4. #65391	C₂	semidirect
5. #64772	C₂	semidirect
119. C₅	#2045	semidirect

H ≅ G/N

type

2. C₂×#3965

C₂

semidirect

3. #65504

C₂

semidirect

4. #65391

C₂

semidirect

5. #64772

C₂

semidirect

119. C₅

#2045

semidirect

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

subgroup	index
C₂²×C₅×D₈	2
C₂×#3965	2
#65504	2
#65391	2
#64772	2
#2045	5

subgroup

index

C₂²×C₅×D₈

Subgroups — #10602835

Conjugacy classes of subgroups

Complements

Maximal subgroups