Group #10600673 — subgroups

Subgroups — #10600673

Order 640.

228 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 93 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×#4016	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#65213	C₂	1	1	yes	maximal, characteristic
4	#64774	C₂	1	4	yes	maximal
5	C₂×C₅×M₁₆	C₂²	1	2	yes	—
6	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₅	C₂²	1	2	yes	—
8	C₂×#683	C₄	1	4	yes	—
9	C₂×#681	C₂²	1	2	yes	—
10	#4016	—	2	2	no	—
11	#4016	—	2	1	no	—
12	#4016	—	2	1	no	—
13	C₅×#97	—	2	1	no	—
14	C₄×C₅×C₈	—	2	1	no	—
15	C₄⋊#168	—	2	2	no	—
16	#1998	—	5	1	no	maximal, Sylow
17	C₂²×C₄×C₅	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂²×Dic₅	C₂×C₄	1	4	yes	—
20	C₅×M₁₆	—	2	2	no	—
21	C₅×M₁₆	Q₈	1	4	yes	—
22	C₂×C₅×C₈	—	2	2	no	—
23	C₄²×C₅	D₄	1	2	yes	—
24	C₄²×C₅	D₄	1	1	yes	characteristic
25	C₄²×C₅	D₄	1	1	yes	characteristic
26	C₄⋊Dic₅	—	2	2	no	—
27	C₄⋊Dic₅	—	2	2	no	—
28	#683	—	2	4	no	—
29	#683	—	2	4	no	—
30	#681	—	2	4	no	—
31	C₂×#168	—	2	2	no	—
32	C₂×#125	—	5	1	no	—
33	#423	—	5	1	no	—
34	C₄×M₁₆	D₅	1	1	yes	characteristic
35	#343	—	5	4	no	—
36	C₂³×C₅	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅	—	4	2	no	—
38	C₂×C₄×C₅	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₅	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₅	C₂×Q₈	1	2	yes	—
43	C₂×C₄×C₅	#41	1	2	yes	—
44	C₂×Dic₅	—	2	4	no	—
45	C₂×Dic₅	—	4	4	no	—
46	C₅×C₈	—	2	4	no	—
47	#168	—	4	2	no	—
48	C₂×M₁₆	—	5	2	no	—
49	C₂×M₁₆	C₂×D₅	1	2	yes	—
50	#125	—	10	2	no	—
51	#125	—	10	1	no	—
52	#125	—	10	1	no	—
53	C₂×C₄⋊C₄	—	5	4	no	—
54	C₂×C₄⋊C₄	—	5	2	no	—
55	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
56	C₄⋊C₈	—	10	2	no	—
57	#97	—	2	1	no	—
58	C₄×C₈	—	2	1	no	—
59	C₂²×C₅	—	2	2	no	—
60	C₂²×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₅	C₄×Q₈	1	2	yes	—
62	C₄×C₅	—	2	2	no	—
63	C₄×C₅	—	2	2	no	—
64	C₄×C₅	C₂²⋊Q₈	1	2	yes	—
65	C₄×C₅	#124	1	1	yes	characteristic
66	C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
67	Dic₅	—	4	4	no	—
68	C₂²×C₄	—	5	4	no	—
69	C₂²×C₄	C₄×D₅	1	2	yes	—
70	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
71	M₁₆	—	2	2	no	—
72	M₁₆	—	10	4	no	—
73	M₁₆	Dic₁₀	1	4	yes	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	10	2	no	—
76	C₄⋊C₄	—	10	4	no	—
77	C₄⋊C₄	—	10	4	no	—
78	C₄⋊C₄	—	10	2	no	—
79	C₄⋊C₄	—	10	2	no	—
80	C₄²	D₂₀	1	2	yes	—
81	C₄²	C₂²⋊D₅	1	1	yes	characteristic
82	C₄²	C₂²⋊D₅	1	1	yes	characteristic
83	C₂×C₅	—	2	2	no	—
84	C₂×C₅	#391	1	1	yes	characteristic
85	C₂×C₅	#413	1	2	yes	—
86	C₂³	C₂×C₄×D₅	1	1	yes	characteristic
87	C₂×C₄	—	4	2	no	—
88	C₂×C₄	—	10	4	no	—
89	C₂×C₄	—	20	4	no	—
90	C₂×C₄	#685	1	2	yes	—
91	C₂×C₄	#685	1	2	yes	—
92	C₂×C₄	C₂×Dic₁₀	1	2	yes	—
93	C₂×C₄	C₂×D₂₀	1	1	yes	characteristic
94	C₂×C₄	#709	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
96	C₈	—	2	4	no	—
97	C₈	—	20	2	no	—
98	C₅	#1998	1	1	yes	characteristic, complemented, Sylow
99	C₂²	—	2	2	no	—
100	C₂²	C₄×Dic₁₀	1	2	yes	—
101	C₂²	C₂×#685	1	1	yes	characteristic
102	C₄	—	2	2	no	—
103	C₄	—	2	2	no	—
104	C₄	—	20	4	no	—
105	C₄	#4015	1	1	yes	characteristic
106	C₄	#4021	1	1	yes	characteristic
107	C₄	#4070	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	#65218	1	1	yes	characteristic
110	C₂	#65421	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#4016

C₂

yes

maximal, characteristic

C₄×C₅×M₁₆

C₂

yes

maximal, characteristic

#65213

C₂

yes

maximal, characteristic

#64774

C₂

yes

maximal

C₂×C₅×M₁₆

C₂²

yes

—

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄⋊Dic₅

C₂²

yes

—

C₂×#683

C₄

yes

—

C₂×#681

C₂²

yes

—

#4016

—

#4016

—

#4016

—

C₅×#97

—

C₄×C₅×C₈

—

C₄⋊#168

—

#1998

—

maximal, Sylow

C₂²×C₄×C₅

C₂×C₄

yes

—

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

C₂×C₄

yes

—

C₅×M₁₆

—

C₅×M₁₆

Q₈

yes

—

C₂×C₅×C₈

—

C₄²×C₅

D₄

yes

—

C₄²×C₅

D₄

yes

characteristic

C₄²×C₅

D₄

yes

characteristic

C₄⋊Dic₅

—

C₄⋊Dic₅

—

—

—

—

—

—

—

C₄×M₁₆

D₅

yes

characteristic

#343

—

C₂³×C₅

C₂²×C₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊C₄

yes

—

C₂×C₄×C₅

C₂²⋊C₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×Q₈

yes

—

C₂×C₄×C₅

#41

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₅×C₈

—

#168

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₅

yes

—

#125

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₅

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

C₂²×C₅

—

C₂²×C₅

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₅

C₄×Q₈

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₂²⋊Q₈

yes

—

C₄×C₅

#124

yes

characteristic

C₄×C₅

C₄⋊Q₈

yes

characteristic

Dic₅

—

C₂²×C₄

—

C₂²×C₄

C₄×D₅

yes

—

C₂²×C₄

C₂²×D₅

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Dic₁₀

yes

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₂₀

yes

—

C₄²

C₂²⋊D₅

yes

characteristic

C₄²

C₂²⋊D₅

yes

characteristic

C₂×C₅

—

C₂×C₅

#391

yes

characteristic

C₂×C₅

#413

yes

—

C₂³

C₂×C₄×D₅

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#685

yes

—

C₂×C₄

#685

yes

—

C₂×C₄

C₂×Dic₁₀

yes

—

C₂×C₄

C₂×D₂₀

yes

characteristic

C₂×C₄

#709

yes

—

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

C₈

—

C₈

—

C₅

#1998

yes

characteristic, complemented, Sylow

C₂²

—

100

C₂²

C₄×Dic₁₀

yes

—

101

C₂²

C₂×#685

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#4015

yes

characteristic

106

C₄

#4021

yes

characteristic

107

C₄

#4070

yes

—

108

C₂

—

109

C₂

#65218

yes

characteristic

110

C₂

#65421

yes

—

	subgroup	G/H
center	C₂²	C₂×#685
commutator, prime radical	C₂³×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅
Fitting	C₄×C₅×M₁₆	C₂
socle	C₂²×C₅	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₅	C₂³
hypercenter	C₄×M₁₆	D₅
hypocenter	C₅	#1998
LCS	G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂×#685

commutator, prime radical

C₂³×C₅

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅

Fitting

C₄×C₅×M₁₆

C₂

socle

C₂²×C₅

C₂×C₂²⋊C₄

cosocle

C₂²×C₄×C₅

C₂³

hypercenter

C₄×M₁₆

D₅

hypocenter

C₅

#1998

LCS

G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
98. C₅	#1998	semidirect

H ≅ G/N

type

98. C₅

#1998

semidirect

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

subgroup	index
C₂×#4016	2
C₄×C₅×M₁₆	2
#65213	2
#64774	2
#1998	5

subgroup

index

C₄×C₅×M₁₆

Subgroups — #10600673

Conjugacy classes of subgroups

Complements

Maximal subgroups