Group #10614787 — subgroups

Subgroups — #10614787

Order 640.

472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 181 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×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×#4016	C₂	1	1	yes	maximal, characteristic
3	#65266	C₂	1	2	yes	maximal
4	#65265	C₂	1	2	yes	maximal
5	#65261	C₂	1	8	yes	maximal
6	C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
7	C₅×#125	—	2	4	no	—
8	C₂×C₅×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₅	C₂²	1	2	yes	—
12	C₂×#683	C₂²	1	4	yes	—
13	C₂×#683	C₂²	1	8	yes	—
14	C₂×C₄×Dic₅	C₂²	1	4	yes	—
15	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₅	C₂²	1	1	yes	characteristic
17	#4016	—	2	4	no	—
18	#3963	C₂²	1	8	yes	—
19	#2859	—	5	1	no	maximal, Sylow
20	C₂²×C₄×C₅	C₂³	1	4	yes	—
21	C₂²×C₄×C₅	C₂³	1	2	yes	—
22	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂²×Dic₅	C₂³	1	4	yes	—
24	C₂²×Dic₅	C₂³	1	2	yes	—
25	C₂²×Dic₅	C₂³	1	2	yes	—
26	C₅×C₄⋊C₄	—	2	8	no	—
27	C₅×C₄⋊C₄	—	2	4	no	—
28	C₄²×C₅	D₄	1	4	yes	—
29	C₄⋊Dic₅	—	2	4	no	—
30	#683	—	2	8	no	—
31	#683	—	2	16	no	—
32	C₄×Dic₅	—	2	8	no	—
33	C₄×Dic₅	Q₈	1	4	yes	—
34	C₄×Dic₅	Q₈	1	4	yes	—
35	C₂×#125	—	5	1	no	—
36	C₂×#125	D₅	1	1	yes	characteristic
37	#389	—	5	8	no	—
38	#384	—	5	2	no	—
39	#382	—	5	2	no	—
40	C₄³	—	5	1	no	—
41	C₂³×C₅	C₂⁴	1	1	yes	characteristic
42	C₂×C₄×C₅	—	2	4	no	—
43	C₂×C₄×C₅	—	2	4	no	—
44	C₂×C₄×C₅	—	2	8	no	—
45	C₂×C₄×C₅	C₂×D₄	1	4	yes	—
46	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₅	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₅	C₂×Q₈	1	2	yes	—
49	C₂×Dic₅	—	2	4	no	—
50	C₂×Dic₅	—	2	4	no	—
51	C₂×Dic₅	—	2	8	no	—
52	C₂×Dic₅	C₂×Q₈	1	4	yes	—
53	C₂×Dic₅	C₂×Q₈	1	4	yes	—
54	C₂×Dic₅	#41	1	8	yes	—
55	#125	—	2	4	no	—
56	#125	—	10	4	no	—
57	C₂×C₄⋊C₄	—	5	2	no	—
58	C₂×C₄⋊C₄	—	5	4	no	—
59	C₂×C₄⋊C₄	—	5	8	no	—
60	C₂×C₄⋊C₄	C₂×D₅	1	2	yes	—
61	C₂×C₄⋊C₄	C₂×D₅	1	4	yes	—
62	C₂×C₄²	—	5	1	no	—
63	C₂×C₄²	—	5	1	no	—
64	C₂×C₄²	—	5	4	no	—
65	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
66	#95	—	5	8	no	—
67	C₂²×C₅	C₂²×D₄	1	1	yes	characteristic
68	C₂²×C₅	C₂²×Q₈	1	1	yes	characteristic
69	C₂²×C₅	C₂²×Q₈	1	1	yes	characteristic
70	C₂²×C₅	C₂×#41	1	4	yes	—
71	C₄×C₅	—	2	4	no	—
72	C₄×C₅	—	4	4	no	—
73	C₄×C₅	C₄⋊Q₈	1	4	yes	—
74	Dic₅	—	2	4	no	—
75	Dic₅	—	4	4	no	—
76	Dic₅	#125	1	8	yes	complemented
77	C₂²×C₄	—	5	2	no	—
78	C₂²×C₄	—	5	2	no	—
79	C₂²×C₄	—	5	4	no	—
80	C₂²×C₄	C₂²×D₅	1	4	yes	—
81	C₂²×C₄	C₂²×D₅	1	2	yes	—
82	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
83	C₄⋊C₄	—	2	8	no	—
84	C₄⋊C₄	—	2	4	no	—
85	C₄⋊C₄	—	10	16	no	—
86	C₄⋊C₄	—	10	8	no	—
87	C₄⋊C₄	—	10	4	no	—
88	C₄²	—	5	4	no	—
89	C₄²	—	5	4	no	—
90	C₄²	—	10	8	no	—
91	C₄²	C₂²⋊D₅	1	4	yes	—
92	C₂×C₅	C₂×#125	1	2	yes	—
93	C₂×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
94	C₂×C₅	#532	1	2	yes	—
95	C₂×C₅	#533	1	2	yes	—
96	C₂³	C₂³×D₅	1	1	yes	characteristic
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	2	8	no	—
99	C₂×C₄	—	2	4	no	—
100	C₂×C₄	—	5	4	no	—
101	C₂×C₄	—	5	8	no	—
102	C₂×C₄	—	5	4	no	—
103	C₂×C₄	—	10	4	no	—
104	C₂×C₄	—	10	8	no	—
105	C₂×C₄	—	10	4	no	—
106	C₂×C₄	Q₈×D₅	1	2	yes	—
107	C₂×C₄	Q₈×D₅	1	2	yes	—
108	C₂×C₄	C₂×C₂²⋊D₅	1	4	yes	—
109	C₂×C₄	C₂×C₂²⋊D₅	1	2	yes	—
110	C₅	#2859	1	1	yes	characteristic, complemented, Sylow
111	C₂²	C₂×Q₈×D₅	1	1	yes	characteristic
112	C₂²	C₂×Q₈×D₅	1	1	yes	characteristic
113	C₂²	D₅×#41	1	4	yes	—
114	C₂²	C₂²×C₂²⋊D₅	1	1	yes	characteristic
115	C₄	—	2	4	no	—
116	C₄	—	4	4	no	—
117	C₄	—	5	8	no	—
118	C₄	—	10	4	no	—
119	C₄	—	20	4	no	—
120	C₄	#4090	1	4	yes	—
121	C₂	D₅×#125	1	2	yes	—
122	C₂	#66022	1	2	yes	—
123	C₂	C₂×#4090	1	1	yes	characteristic
124	C₂	#66166	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×#125

C₂

yes

maximal, characteristic

C₂×#4016

C₂

yes

maximal, characteristic

#65266

C₂

yes

maximal

#65265

C₂

yes

maximal

#65261

C₂

yes

maximal

C₄²×Dic₅

C₂

yes

maximal, characteristic

C₅×#125

—

C₂×C₅×C₄⋊C₄

C₂²

yes

—

C₂×C₅×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄⋊Dic₅

C₂²

yes

—

C₂×#683

C₂²

yes

—

C₂×#683

C₂²

yes

—

C₂×C₄×Dic₅

C₂²

yes

—

C₂×C₄×Dic₅

C₂²

yes

characteristic

C₂×C₄×Dic₅

C₂²

yes

characteristic

#4016

—

#3963

C₂²

yes

—

#2859

—

maximal, Sylow

C₂²×C₄×C₅

C₂³

yes

—

C₂²×C₄×C₅

C₂³

yes

—

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

C₂³

yes

—

C₂²×Dic₅

C₂³

yes

—

C₂²×Dic₅

C₂³

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

D₄

yes

—

C₄⋊Dic₅

—

#683

—

#683

—

C₄×Dic₅

—

C₄×Dic₅

Q₈

yes

—

C₄×Dic₅

Q₈

yes

—

C₂×#125

—

C₂×#125

D₅

yes

—

—

—

C₄³

—

C₂³×C₅

C₂⁴

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

C₂×Q₈

yes

—

C₂×C₄×C₅

C₂×Q₈

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

C₂×Q₈

yes

—

C₂×Dic₅

C₂×Q₈

yes

—

C₂×Dic₅

#41

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅

yes

—

C₂×C₄⋊C₄

C₂×D₅

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅

yes

characteristic

#95

—

C₂²×C₅

C₂²×D₄

yes

characteristic

C₂²×C₅

C₂²×Q₈

yes

characteristic

C₂²×C₅

C₂²×Q₈

yes

characteristic

C₂²×C₅

C₂×#41

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₄⋊Q₈

yes

—

Dic₅

—

Dic₅

—

Dic₅

#125

yes

complemented

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅

yes

—

C₂²×C₄

C₂²×D₅

yes

—

C₂²×C₄

C₂²×D₅

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²⋊D₅

yes

—

C₂×C₅

C₂×#125

yes

—

C₂×C₅

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₅

#532

yes

—

C₂×C₅

#533

yes

—

C₂³

C₂³×D₅

yes

characteristic

C₂×C₄

—

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

Q₈×D₅

yes

—

107

C₂×C₄

Q₈×D₅

yes

—

108

C₂×C₄

C₂×C₂²⋊D₅

yes

—

109

C₂×C₄

C₂×C₂²⋊D₅

yes

—

110

C₅

#2859

yes

characteristic, complemented, Sylow

111

C₂²

C₂×Q₈×D₅

yes

characteristic

112

C₂²

C₂×Q₈×D₅

yes

characteristic

113

C₂²

D₅×#41

yes

—

114

C₂²

C₂²×C₂²⋊D₅

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

#4090

yes

—

121

C₂

D₅×#125

yes

—

122

C₂

#66022

yes

—

123

C₂

C₂×#4090

yes

characteristic

124

C₂

#66166

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅
commutator, socle, prime radical, cosocle	C₂³×C₅	C₂⁴
Fitting	C₂×C₅×#125	C₂
hypercenter	C₂×#125	D₅
hypocenter	C₅	#2859
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅

commutator, socle, prime radical, cosocle

C₂³×C₅

C₂⁴

Fitting

C₂×C₅×#125

C₂

D₅

C₅

G ▷ C₂³×C₅ ▷ C₅

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
76. Dic₅	#125	semidirect
110. C₅	#2859	semidirect

H ≅ G/N

type

76. Dic₅

#125

semidirect

110. C₅

#2859

semidirect

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

subgroup	index
C₂×C₅×#125	2
C₂×#4016	2
#65266	2
#65265	2
#65261	2
C₄²×Dic₅	2
#2859	5

subgroup

index

C₂×C₅×#125

C₄²×Dic₅

Subgroups — #10614787

Conjugacy classes of subgroups

Complements

Maximal subgroups