Group #10602102 — subgroups

Subgroups — #10602102

Order 640.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	C₅×#494	C₂	1	1	yes	maximal, characteristic
2	#65383	C₂	1	2	yes	maximal
3	#64968	C₂	1	1	yes	maximal, characteristic
4	#64767	C₂	1	2	yes	maximal
5	#64677	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×Q₁₆	—	2	1	no	—
7	C₂×C₅×Q₁₆	—	2	1	no	—
8	C₅×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₄×Dic₁₀	C₂²	1	1	yes	characteristic
10	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	#3947	—	2	1	no	—
12	#3946	—	2	1	no	—
13	#3942	—	2	2	no	—
14	#3940	—	2	2	no	—
15	C₄⋊#168	C₂²	1	2	yes	—
16	C₄⋊#168	C₂²	1	1	yes	characteristic
17	#1690	—	5	1	no	maximal, Sylow
18	C₂×C₅×Q₈	—	2	2	no	—
19	C₂×Dic₁₀	D₄	1	1	yes	characteristic
20	C₅×Q₁₆	—	4	2	no	—
21	C₅×Q₁₆	—	4	2	no	—
22	C₂×C₅×C₈	D₄	1	1	yes	characteristic
23	C₂×C₅×C₈	D₄	1	1	yes	characteristic
24	C₅×C₄⋊C₄	—	2	2	no	—
25	C₅×C₄⋊C₄	—	2	2	no	—
26	C₄²×C₅	C₂³	1	1	yes	characteristic
27	C₄⋊Dic₅	D₄	1	1	yes	characteristic
28	#683	—	2	1	no	—
29	C₄×Dic₅	—	2	1	no	—
30	C₂×#168	—	2	2	no	—
31	C₂×#168	—	2	1	no	—
32	#494	D₅	1	1	yes	characteristic
33	#475	—	5	2	no	—
34	#446	—	5	1	no	—
35	#334	—	5	1	no	—
36	#332	—	5	2	no	—
37	C₅×Q₈	—	4	2	no	—
38	C₅×Q₈	—	4	2	no	—
39	C₂×C₄×C₅	—	4	2	no	—
40	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₅	#41	1	1	yes	characteristic
43	C₂×Dic₅	—	2	1	no	—
44	C₂×Dic₅	—	2	1	no	—
45	Dic₁₀	—	2	2	no	—
46	C₅×C₈	—	2	1	no	—
47	C₅×C₈	SD₁₆	1	2	yes	—
48	#168	—	4	1	no	—
49	#168	—	4	2	no	—
50	C₂×Q₁₆	—	2	1	no	—
51	C₂×Q₁₆	—	2	1	no	—
52	C₄⋊Q₈	C₂×D₅	1	2	yes	—
53	C₄×Q₈	—	5	1	no	—
54	#106	—	10	2	no	—
55	C₄⋊C₈	—	5	1	no	—
56	C₄⋊C₈	—	5	2	no	—
57	C₄⋊C₈	—	10	1	no	—
58	#103	—	10	2	no	—
59	#97	—	10	1	no	—
60	C₄×C₈	C₂×D₅	1	1	yes	characteristic
61	C₂²×C₅	#121	1	1	yes	characteristic
62	C₄×C₅	—	2	1	no	—
63	C₄×C₅	—	8	2	no	—
64	C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
65	C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₄×C₅	#137	1	2	yes	—
67	Dic₅	—	4	1	no	—
68	Dic₅	—	4	1	no	—
69	C₂×Q₈	—	2	2	no	—
70	C₂×Q₈	—	5	1	no	—
71	Q₁₆	—	4	2	no	—
72	Q₁₆	—	4	2	no	—
73	C₂×C₈	—	10	2	no	—
74	C₂×C₈	—	10	1	no	—
75	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
76	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	—	2	2	no	—
79	C₄⋊C₄	—	5	1	no	—
80	C₄⋊C₄	—	10	1	no	—
81	C₄²	—	10	1	no	—
82	C₄²	C₂²×D₅	1	1	yes	characteristic
83	C₂×C₅	#460	1	1	yes	characteristic
84	C₂×C₅	#470	1	1	yes	characteristic
85	C₂×C₅	#473	1	1	yes	characteristic
86	Q₈	—	4	2	no	—
87	Q₈	—	4	2	no	—
88	Q₈	—	10	2	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	10	1	no	—
91	C₂×C₄	—	10	1	no	—
92	C₂×C₄	D₄×D₅	1	1	yes	characteristic
93	C₂×C₄	#711	1	1	yes	characteristic
94	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	20	2	no	—
97	C₈	—	20	1	no	—
98	C₈	#687	1	2	yes	—
99	C₅	#1690	1	1	yes	characteristic, complemented, Sylow
100	C₂²	#4084	1	1	yes	characteristic
101	C₄	—	2	1	no	—
102	C₄	—	8	2	no	—
103	C₄	—	20	1	no	—
104	C₄	—	20	1	no	—
105	C₄	#4064	1	2	yes	—
106	C₄	#4078	1	1	yes	characteristic
107	C₄	C₂×#687	1	1	yes	characteristic
108	C₂	#65364	1	1	yes	characteristic
109	C₂	#65478	1	1	yes	characteristic
110	C₂	#65481	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#494

C₂

yes

maximal, characteristic

#65383

C₂

yes

maximal

#64968

C₂

yes

maximal, characteristic

#64767

C₂

yes

maximal

#64677

C₂

yes

maximal, characteristic

C₂×C₅×Q₁₆

—

C₂×C₅×Q₁₆

—

C₅×C₄⋊Q₈

C₂²

yes

—

C₄×Dic₁₀

C₂²

yes

characteristic

C₄×C₅×C₈

C₂²

yes

—

—

—

—

C₂²

yes

—

C₄⋊#168

C₂²

yes

characteristic

#1690

—

maximal, Sylow

C₂×C₅×Q₈

—

C₂×Dic₁₀

D₄

yes

characteristic

C₅×Q₁₆

—

C₅×Q₁₆

—

C₂×C₅×C₈

D₄

yes

characteristic

C₂×C₅×C₈

D₄

yes

characteristic

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂³

yes

characteristic

C₄⋊Dic₅

D₄

yes

characteristic

#683

—

C₄×Dic₅

—

C₂×#168

—

C₂×#168

—

#494

D₅

yes

—

—

—

—

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

#41

yes

characteristic

C₂×Dic₅

—

C₂×Dic₅

—

Dic₁₀

—

C₅×C₈

—

C₅×C₈

SD₁₆

yes

—

#168

—

#168

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

C₂×D₅

yes

—

C₄×Q₈

—

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

C₄×C₈

C₂×D₅

yes

characteristic

C₂²×C₅

#121

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₂×SD₁₆

yes

C₄×C₅

yes

C₄×C₅

yes

—

Dic₅

—

Dic₅

—

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₅

yes

characteristic

C₂×C₈

C₂²⋊D₅

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₅

yes

C₂×C₅

yes

C₂×C₅

yes

C₂×C₅

yes

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₅

yes

characteristic

C₂×C₄

#711

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

#687

yes

—

C₅

#1690

yes

characteristic, complemented, Sylow

100

C₂²

#4084

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

#4064

yes

—

106

C₄

#4078

yes

characteristic

107

C₄

C₂×#687

yes

characteristic

108

C₂

#65364

yes

characteristic

109

C₂

#65478

yes

characteristic

110

C₂

#65481

yes

characteristic

	subgroup	G/H
center	C₂²	#4084
commutator, cosocle	C₄²×C₅	C₂³
Frattini	C₄²	C₂²×D₅
Fitting	C₅×#494	C₂
socle, prime radical	C₂²×C₅	#121
hypercenter	#494	D₅
hypocenter	C₅	#1690
LCS	G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#4084

commutator, cosocle

C₄²×C₅

C₂³

Frattini

C₄²

C₂²×D₅

C₂

C₂²×C₅

D₅

C₅

G ▷ C₄²×C₅ ▷ C₂²×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
99. C₅	#1690	semidirect

H ≅ G/N

type

99. C₅

#1690

semidirect

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

subgroup	index
C₅×#494	2
#65383	2
#64968	2
#64767	2
#64677	2
#1690	5

subgroup

index

Subgroups — #10602102

Conjugacy classes of subgroups

Complements

Maximal subgroups