Group #10600615 — subgroups

Subgroups — #10600615

Order 640.

308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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×#4015	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×#3948	C₂	1	4	yes	maximal
4	#65225	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₀	C₂²	1	2	yes	—
6	C₂²×C₅×C₈	C₂²	1	2	yes	—
7	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₅	—	2	2	no	—
9	C₂×C₄⋊Dic₅	C₂²	1	2	yes	—
10	#4015	—	2	2	no	—
11	#4015	C₄	1	4	yes	complemented
12	C₅×#97	—	2	2	no	—
13	#3963	—	2	2	no	—
14	#3948	—	2	8	no	—
15	#1960	—	5	1	no	maximal, Sylow
16	C₂²×C₄×C₅	D₄	1	2	yes	—
17	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₂²×Dic₅	—	2	2	no	—
19	C₂²×Dic₅	—	2	2	no	—
20	C₂×Dic₁₀	—	2	4	no	—
21	C₂×Dic₁₀	—	2	4	no	—
22	C₂×Dic₁₀	—	2	2	no	—
23	C₂×Dic₁₀	C₂×C₄	1	4	yes	—
24	C₂×C₅×C₈	—	2	2	no	—
25	C₂×C₅×C₈	—	2	2	no	—
26	C₂×C₅×C₈	D₄	1	4	yes	—
27	C₄²×C₅	C₂×C₄	1	2	yes	—
28	C₄²×C₅	D₄	1	2	yes	—
29	C₄⋊Dic₅	—	2	8	no	—
30	C₄⋊Dic₅	—	2	4	no	—
31	C₂×C₄⋊Q₈	—	5	1	no	—
32	C₂×#103	—	5	4	no	—
33	C₂×#97	D₅	1	1	yes	characteristic
34	#382	—	5	1	no	—
35	C₂³×C₅	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₅	—	2	4	no	—
37	C₂×C₄×C₅	C₂²⋊C₄	1	4	yes	—
38	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₅	#41	1	2	yes	—
42	C₂×Dic₅	—	2	4	no	—
43	C₂×Dic₅	—	4	2	no	—
44	C₂×Dic₅	—	4	2	no	—
45	C₂×Dic₅	—	4	2	no	—
46	C₂×Dic₅	—	4	4	no	—
47	Dic₁₀	—	2	8	no	—
48	Dic₁₀	—	4	4	no	—
49	C₅×C₈	—	2	4	no	—
50	C₂²×Q₈	—	5	2	no	—
51	C₂²×C₈	C₂×D₅	1	2	yes	—
52	C₄⋊Q₈	—	5	4	no	—
53	C₄⋊Q₈	—	10	2	no	—
54	C₂×C₄⋊C₄	—	5	2	no	—
55	C₂×C₄⋊C₄	—	10	2	no	—
56	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
57	#103	—	10	8	no	—
58	#97	—	2	2	no	—
59	#95	—	10	2	no	—
60	C₂²×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₅	#124	1	1	yes	characteristic
62	C₂²×C₅	#127	1	1	yes	characteristic
63	C₂²×C₅	#137	1	4	yes	—
64	C₄×C₅	—	2	4	no	—
65	C₄×C₅	C₄×D₄	1	2	yes	—
66	C₄×C₅	#121	1	2	yes	—
67	Dic₅	—	4	4	no	—
68	Dic₅	—	8	2	no	—
69	C₂×Q₈	—	5	4	no	—
70	C₂×Q₈	—	10	2	no	—
71	C₂×Q₈	—	10	4	no	—
72	C₂×Q₈	—	10	4	no	—
73	C₂²×C₄	—	10	2	no	—
74	C₂²×C₄	—	10	2	no	—
75	C₂²×C₄	D₂₀	1	2	yes	—
76	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	D₂₀	1	4	yes	—
80	C₄⋊C₄	—	10	8	no	—
81	C₄⋊C₄	—	10	4	no	—
82	C₄²	C₄×D₅	1	2	yes	—
83	C₄²	C₂²⋊D₅	1	2	yes	—
84	C₂×C₅	#390	1	1	yes	characteristic
85	C₂×C₅	#419	1	2	yes	—
86	C₂×C₅	#491	1	2	yes	—
87	C₂×C₅	#497	1	2	yes	—
88	C₂³	C₂×D₂₀	1	1	yes	characteristic
89	Q₈	—	10	8	no	—
90	Q₈	—	20	4	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	10	4	no	—
93	C₂×C₄	—	20	2	no	—
94	C₂×C₄	—	20	2	no	—
95	C₂×C₄	—	20	2	no	—
96	C₂×C₄	—	20	4	no	—
97	C₂×C₄	#685	1	4	yes	—
98	C₂×C₄	C₂×C₄×D₅	1	1	yes	characteristic
99	C₂×C₄	C₂×D₂₀	1	2	yes	—
100	C₂×C₄	#709	1	2	yes	—
101	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
102	C₈	—	2	4	no	—
103	C₅	#1960	1	1	yes	characteristic, complemented, Sylow
104	C₂²	#4020	1	1	yes	characteristic
105	C₂²	#4021	1	1	yes	characteristic
106	C₂²	#4055	1	4	yes	—
107	C₂²	C₂×#685	1	1	yes	characteristic
108	C₄	—	2	4	no	—
109	C₄	—	20	4	no	—
110	C₄	—	40	2	no	—
111	C₄	C₄×D₂₀	1	2	yes	—
112	C₄	#4076	1	2	yes	—
113	C₂	#64992	1	2	yes	—
114	C₂	#65004	1	2	yes	—
115	C₂	#65228	1	1	yes	characteristic
116	C₂	#65409	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#4015

C₂

yes

maximal, characteristic

C₂×C₅×#97

C₂

yes

maximal, characteristic

C₂×#3948

C₂

yes

maximal

#65225

C₂

yes

maximal, characteristic

C₂²×Dic₁₀

C₂²

yes

—

C₂²×C₅×C₈

C₂²

yes

—

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄⋊Dic₅

—

C₂×C₄⋊Dic₅

C₂²

yes

—

#4015

—

#4015

C₄

yes

complemented

C₅×#97

—

—

—

—

C₂²×C₄×C₅

D₄

yes

—

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

—

C₂²×Dic₅

—

C₂×Dic₁₀

—

C₂×Dic₁₀

—

C₂×Dic₁₀

—

C₂×Dic₁₀

C₂×C₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

D₄

yes

—

C₄²×C₅

C₂×C₄

yes

—

C₄²×C₅

D₄

yes

—

C₄⋊Dic₅

—

C₄⋊Dic₅

—

C₂×C₄⋊Q₈

—

C₂×#103

—

C₂×#97

D₅

yes

characteristic

#382

—

C₂³×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊C₄

yes

—

C₂×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

#41

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

Dic₁₀

—

Dic₁₀

—

C₅×C₈

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₅

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₅

yes

—

—

—

C₂²×C₅

C₂×C₂²⋊C₄

yes

C₂²×C₅

yes

C₂²×C₅

yes

C₂²×C₅

yes

—

C₄×C₅

—

C₄×C₅

C₄×D₄

yes

—

C₄×C₅

#121

yes

—

Dic₅

—

Dic₅

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₂₀

yes

—

C₂²×C₄

C₂²×D₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₂₀

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₄×D₅

yes

—

C₄²

C₂²⋊D₅

yes

—

C₂×C₅

#390

yes

characteristic

C₂×C₅

#419

yes

—

C₂×C₅

#491

yes

—

C₂×C₅

#497

yes

—

C₂³

C₂×D₂₀

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#685

yes

—

C₂×C₄

C₂×C₄×D₅

yes

characteristic

C₂×C₄

C₂×D₂₀

yes

—

100

C₂×C₄

#709

yes

—

101

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

102

C₈

—

103

C₅

#1960

yes

characteristic, complemented, Sylow

104

C₂²

#4020

yes

characteristic

105

C₂²

#4021

yes

characteristic

106

C₂²

#4055

yes

—

107

C₂²

C₂×#685

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

C₄×D₂₀

yes

—

112

C₄

#4076

yes

—

113

C₂

#64992

yes

—

114

C₂

#65004

yes

—

115

C₂

#65228

yes

characteristic

116

C₂

#65409

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₀
commutator	C₂×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅
Fitting	C₂×C₅×#97	C₂
socle, prime radical	C₂³×C₅	C₂×D₄
cosocle	C₂²×C₄×C₅	C₂³
hypercenter	C₂×#97	D₅
hypocenter	C₅	#1960
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₂₀

commutator

C₂×C₄×C₅

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅

Fitting

C₂×C₅×#97

C₂

socle, prime radical

C₂³×C₅

C₂×D₄

cosocle

C₂²×C₄×C₅

C₂³

hypercenter

C₂×#97

D₅

hypocenter

C₅

#1960

LCS

G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
11. #4015	C₄	semidirect
103. C₅	#1960	semidirect

H ≅ G/N

type

11. #4015

C₄

semidirect

103. C₅

#1960

semidirect

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

subgroup	index
C₂×#4015	2
C₂×C₅×#97	2
C₂×#3948	2
#65225	2
#1960	5

subgroup

index

C₂×C₅×#97

Subgroups — #10600615

Conjugacy classes of subgroups

Complements

Maximal subgroups