Group #10602081 — subgroups

Subgroups — #10602081

Order 640.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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×#493	C₂	1	1	yes	maximal, characteristic
2	#64971	C₂	1	1	yes	maximal, characteristic, complemented
3	#64782	C₂	1	4	yes	maximal, complemented
4	C₄×#672	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×D₈	—	2	1	no	—
6	C₂×C₅×D₈	C₂²	1	2	yes	—
7	C₅×#127	—	2	1	no	—
8	#4015	—	2	1	no	—
9	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
10	#3950	—	2	1	no	—
11	#3950	C₂²	1	2	yes	—
12	C₂×#672	C₂²	1	2	yes	—
13	#2240	—	5	1	no	maximal, Sylow
14	C₂×C₅×D₄	—	2	2	no	—
15	C₂×C₅×D₄	—	4	1	no	—
16	C₂×C₅×D₄	—	4	1	no	—
17	C₂×Dic₁₀	—	4	1	no	—
18	C₅×D₈	—	2	4	no	—
19	C₅×D₈	—	4	2	no	—
20	C₂×C₅×C₈	D₄	1	1	yes	characteristic
21	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
22	C₄²×C₅	D₄	1	1	yes	characteristic
23	C₄⋊Dic₅	—	2	2	no	—
24	C₄⋊Dic₅	—	4	1	no	—
25	#672	—	2	2	no	—
26	#500	—	5	1	no	—
27	#493	D₅	1	1	yes	characteristic
28	#357	—	5	4	no	—
29	C₄×C₁₆	—	5	1	no	—
30	C₂³×C₅	—	4	2	no	—
31	C₅×D₄	—	4	2	no	—
32	C₅×D₄	—	4	2	no	—
33	C₅×D₄	—	8	2	no	—
34	C₅×D₄	—	8	2	no	—
35	C₂×C₄×C₅	D₈	1	1	yes	characteristic
36	C₂×C₄×C₅	D₈	1	1	yes	characteristic
37	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₅	—	4	2	no	—
39	Dic₁₀	—	8	2	no	—
40	C₅×C₈	SD₁₆	1	2	yes	—
41	C₅×C₈	#41	1	2	yes	—
42	C₂×D₈	—	2	1	no	—
43	C₂×D₈	C₂×D₅	1	2	yes	—
44	C₄⋊Q₈	—	10	1	no	—
45	#127	—	2	1	no	—
46	C₂×C₁₆	—	5	2	no	—
47	#107	—	5	2	no	—
48	#107	—	10	1	no	—
49	C₄×C₈	C₂×D₅	1	1	yes	characteristic
50	C₂²×C₅	—	8	2	no	—
51	C₂²×C₅	—	8	2	no	—
52	C₂²×C₅	—	8	2	no	—
53	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
54	C₄×C₅	D₁₆	1	2	yes	—
55	C₄×C₅	SD₃₂	1	2	yes	—
56	C₄×C₅	#124	1	1	yes	characteristic
57	C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
58	Dic₅	—	8	2	no	—
59	C₂×Q₈	—	20	1	no	—
60	C₂×D₄	—	2	2	no	—
61	C₂×D₄	—	4	1	no	—
62	C₂×D₄	—	4	1	no	—
63	D₈	—	2	4	no	—
64	D₈	—	4	2	no	—
65	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
66	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
67	C₄⋊C₄	—	10	2	no	—
68	C₄⋊C₄	—	20	1	no	—
69	C₄²	C₂²⋊D₅	1	1	yes	characteristic
70	C₁₆	—	10	2	no	—
71	C₂×C₅	—	16	2	no	—
72	C₂×C₅	#486	1	1	yes	characteristic
73	C₂×C₅	C₂×D₁₆	1	1	yes	characteristic
74	C₂×C₅	C₂×SD₃₂	1	1	yes	characteristic
75	C₂³	—	4	2	no	—
76	Q₈	—	40	2	no	—
77	D₄	—	4	2	no	—
78	D₄	—	4	2	no	—
79	D₄	—	8	2	no	—
80	D₄	—	8	2	no	—
81	C₂×C₄	—	20	2	no	—
82	C₂×C₄	#686	1	1	yes	characteristic
83	C₂×C₄	#686	1	1	yes	characteristic
84	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
85	C₈	#687	1	2	yes	—
86	C₈	#711	1	2	yes	—
87	C₅	#2240	1	1	yes	characteristic, complemented, Sylow
88	C₂²	—	8	2	no	—
89	C₂²	—	8	2	no	—
90	C₂²	—	8	2	no	—
91	C₂²	C₂×#686	1	1	yes	characteristic
92	C₄	—	40	2	no	—
93	C₄	#3958	1	2	yes	—
94	C₄	#3959	1	2	yes	—
95	C₄	C₂×#687	1	1	yes	characteristic
96	C₄	#4082	1	1	yes	characteristic
97	C₂	—	16	2	no	—
98	C₂	#65359	1	1	yes	characteristic
99	C₂	C₂×#3958	1	1	yes	characteristic
100	C₂	C₂×#3959	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#493

C₂

yes

maximal, characteristic

#64971

C₂

yes

maximal, characteristic, complemented

#64782

C₂

yes

maximal, complemented

C₄×#672

C₂

yes

maximal, characteristic, complemented

C₂×C₅×D₈

—

C₂×C₅×D₈

C₂²

yes

—

C₅×#127

—

#4015

—

C₄×C₅×C₈

C₂²

yes

characteristic

#3950

—

#3950

C₂²

yes

—

C₂×#672

C₂²

yes

—

#2240

—

maximal, Sylow

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂×Dic₁₀

—

C₅×D₈

—

C₅×D₈

—

C₂×C₅×C₈

D₄

yes

characteristic

C₂×C₅×C₈

C₂³

yes

characteristic

C₄²×C₅

D₄

yes

characteristic

C₄⋊Dic₅

—

C₄⋊Dic₅

—

#672

—

#500

—

#493

D₅

yes

characteristic

#357

—

C₄×C₁₆

—

C₂³×C₅

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

D₈

yes

characteristic

C₂×C₄×C₅

D₈

yes

characteristic

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×Dic₅

—

Dic₁₀

—

C₅×C₈

SD₁₆

yes

—

C₅×C₈

#41

yes

—

C₂×D₈

—

C₂×D₈

C₂×D₅

yes

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

#107

—

#107

—

C₄×C₈

C₂×D₅

yes

characteristic

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

C₂×D₈

yes

characteristic

C₄×C₅

D₁₆

yes

—

C₄×C₅

SD₃₂

yes

—

C₄×C₅

#124

yes

characteristic

C₄×C₅

C₂×SD₁₆

yes

characteristic

Dic₅

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

C₂×C₈

C₂²⋊D₅

yes

characteristic

C₂×C₈

C₂²×D₅

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₅

yes

characteristic

C₁₆

—

C₂×C₅

—

C₂×C₅

#486

yes

characteristic

C₂×C₅

C₂×D₁₆

yes

characteristic

C₂×C₅

C₂×SD₃₂

yes

characteristic

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

C₈

#687

yes

—

C₈

#711

yes

—

C₅

#2240

yes

characteristic, complemented, Sylow

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×#686

yes

characteristic

C₄

—

C₄

#3958

yes

—

C₄

#3959

yes

—

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

100

C₂

C₂×#3959

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#686
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting, prime radical	C₅×#493	C₂
socle	C₂²×C₅	C₂×D₈
hypercenter	#493	D₅
hypocenter	C₅	#2240
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#686

commutator, cosocle

C₂×C₅×C₈

C₂³

Frattini

C₂×C₈

C₂²×D₅

Fitting, prime radical

C₅×#493

C₂

socle

C₂²×C₅

C₂×D₈

D₅

C₅

G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
2. #64971	C₂	semidirect
3. #64782	C₂	semidirect
4. C₄×#672	C₂	semidirect
87. C₅	#2240	semidirect

H ≅ G/N

type

2. #64971

C₂

semidirect

3. #64782

C₂

semidirect

4. C₄×#672

C₂

semidirect

87. C₅

#2240

semidirect

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

subgroup	index
C₅×#493	2
#64971	2
#64782	2
C₄×#672	2
#2240	5

subgroup

index

Subgroups — #10602081

Conjugacy classes of subgroups

Complements

Maximal subgroups