Group #10601239 — subgroups

Subgroups — #10601239

Order 640.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#3946	C₂	1	4	yes	maximal
3	#65221	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅×C₈	C₂²	1	2	yes	—
6	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₅	C₂²	1	2	yes	—
8	C₂²×#168	C₂²	1	2	yes	—
9	C₅×C₄⋊C₈	—	2	2	no	—
10	#3963	C₄	1	2	yes	—
11	#3963	C₄	1	2	yes	—
12	#3946	—	2	8	no	—
13	C₄⋊#168	—	2	2	no	—
14	#1843	—	5	1	no	maximal, Sylow
15	C₂²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
18	C₂²×Dic₅	C₂×C₄	1	4	yes	—
19	C₂×C₅×C₈	—	2	4	no	—
20	C₂×C₅×C₈	—	2	2	no	—
21	C₄²×C₅	D₄	1	2	yes	—
22	C₄²×C₅	Q₈	1	2	yes	—
23	C₄×Dic₅	D₄	1	4	yes	—
24	C₄×Dic₅	Q₈	1	4	yes	—
25	C₂×#168	—	2	2	no	—
26	C₂×#168	—	2	4	no	—
27	C₂×C₄⋊C₈	—	5	4	no	—
28	C₂×C₄⋊C₈	—	5	1	no	—
29	C₂×C₄⋊C₈	D₅	1	1	yes	characteristic
30	#376	—	5	1	no	—
31	C₂³×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄×C₅	—	2	2	no	—
33	C₂×C₄×C₅	—	2	2	no	—
34	C₂×C₄×C₅	C₄⋊C₄	1	2	yes	—
35	C₂×C₄×C₅	C₄⋊C₄	1	2	yes	—
36	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₅	C₂×Q₈	1	2	yes	—
40	C₂×Dic₅	—	2	4	no	—
41	C₂×Dic₅	—	2	4	no	—
42	C₂×Dic₅	C₄⋊C₄	1	8	yes	—
43	C₅×C₈	—	4	2	no	—
44	#168	—	4	2	no	—
45	C₂²×C₈	—	5	2	no	—
46	C₂²×C₈	C₂×D₅	1	2	yes	—
47	C₂×C₄²	—	5	2	no	—
48	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
49	C₄⋊C₈	—	2	2	no	—
50	C₄⋊C₈	—	10	8	no	—
51	C₄⋊C₈	—	10	2	no	—
52	#95	—	5	2	no	—
53	#95	—	5	2	no	—
54	C₂²×C₅	C₂×C₄⋊C₄	1	2	yes	—
55	C₂²×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₅	#131	1	2	yes	—
57	C₂²×C₅	#131	1	2	yes	—
58	C₄×C₅	—	2	2	no	—
59	C₄×C₅	—	2	2	no	—
60	C₄×C₅	#127	1	1	yes	characteristic
61	C₄×C₅	C₄⋊Q₈	1	2	yes	—
62	C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
63	Dic₅	—	2	8	no	—
64	C₂²×C₄	—	5	4	no	—
65	C₂²×C₄	C₄×D₅	1	1	yes	characteristic
66	C₂²×C₄	C₄×D₅	1	1	yes	characteristic
67	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
68	C₂×C₈	—	2	4	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	10	4	no	—
71	C₂×C₈	—	10	2	no	—
72	C₄²	—	5	4	no	—
73	C₄²	—	5	4	no	—
74	C₄²	Dic₁₀	1	2	yes	—
75	C₄²	C₂²⋊D₅	1	2	yes	—
76	C₂×C₅	#384	1	1	yes	characteristic
77	C₂×C₅	#424	1	4	yes	—
78	C₂×C₅	#424	1	1	yes	characteristic
79	C₂×C₅	#424	1	1	yes	characteristic
80	C₂³	C₂×C₄×D₅	1	1	yes	characteristic
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	5	8	no	—
84	C₂×C₄	—	10	4	no	—
85	C₂×C₄	—	10	4	no	—
86	C₂×C₄	#683	1	2	yes	—
87	C₂×C₄	#683	1	2	yes	—
88	C₂×C₄	C₂×Dic₁₀	1	1	yes	characteristic
89	C₂×C₄	D₄×D₅	1	2	yes	—
90	C₂×C₄	Q₈×D₅	1	2	yes	—
91	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
92	C₈	—	4	2	no	—
93	C₈	—	20	2	no	—
94	C₅	#1843	1	1	yes	characteristic, complemented, Sylow
95	C₂²	D₅×C₄⋊C₄	1	2	yes	—
96	C₂²	#4047	1	2	yes	—
97	C₂²	#4053	1	2	yes	—
98	C₂²	C₂×#683	1	1	yes	characteristic
99	C₄	—	2	2	no	—
100	C₄	—	2	2	no	—
101	C₄	—	10	8	no	—
102	C₄	#4034	1	2	yes	—
103	C₄	#4086	1	1	yes	characteristic
104	C₄	#4090	1	1	yes	characteristic
105	C₂	#65128	1	4	yes	—
106	C₂	#65265	1	1	yes	characteristic
107	C₂	#65391	1	1	yes	characteristic
108	C₂	#65408	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂×#3946

C₂

yes

maximal

#65221

C₂

yes

maximal, characteristic

C₂×C₄⋊#168

C₂

yes

maximal, characteristic

C₂²×C₅×C₈

C₂²

yes

—

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄×Dic₅

C₂²

yes

—

C₂²×#168

C₂²

yes

—

C₅×C₄⋊C₈

—

#3963

C₄

yes

—

#3963

C₄

yes

—

—

—

—

C₂²×C₄×C₅

C₂×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×C₄

yes

characteristic

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

C₂×C₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₄²×C₅

D₄

yes

—

C₄²×C₅

Q₈

yes

—

C₄×Dic₅

D₄

yes

—

C₄×Dic₅

Q₈

yes

—

C₂×#168

—

C₂×#168

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₅

yes

characteristic

#376

—

C₂³×C₅

C₂²×C₄

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄⋊C₄

yes

—

C₂×C₄×C₅

C₄⋊C₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₄×C₅

C₂×Q₈

yes

characteristic

C₂×C₄×C₅

C₂×Q₈

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

C₄⋊C₄

yes

—

C₅×C₈

—

#168

—

C₂²×C₈

—

C₂²×C₈

C₂×D₅

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

—

C₂²×C₅

C₂×C₄⋊C₄

yes

—

C₂²×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₅

#131

yes

—

C₂²×C₅

#131

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#127

yes

characteristic

C₄×C₅

C₄⋊Q₈

yes

—

C₄×C₅

C₄⋊Q₈

yes

characteristic

Dic₅

—

C₂²×C₄

—

C₂²×C₄

C₄×D₅

yes

characteristic

C₂²×C₄

C₄×D₅

yes

characteristic

C₂²×C₄

C₂²×D₅

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

Dic₁₀

yes

—

C₄²

C₂²⋊D₅

yes

—

C₂×C₅

#384

yes

characteristic

C₂×C₅

#424

yes

—

C₂×C₅

yes

C₂×C₅

yes

C₂³

C₂×C₄×D₅

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#683

yes

—

C₂×C₄

#683

yes

—

C₂×C₄

C₂×Dic₁₀

yes

characteristic

C₂×C₄

D₄×D₅

yes

—

C₂×C₄

Q₈×D₅

yes

—

C₂×C₄

C₂×C₂²⋊D₅

yes

characteristic

C₈

—

C₈

—

C₅

#1843

yes

characteristic, complemented, Sylow

C₂²

D₅×C₄⋊C₄

yes

—

C₂²

#4047

yes

—

C₂²

#4053

yes

—

C₂²

C₂×#683

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

#4034

yes

—

103

C₄

#4086

yes

characteristic

104

C₄

#4090

yes

characteristic

105

C₂

#65128

yes

—

106

C₂

#65265

yes

characteristic

107

C₂

#65391

yes

characteristic

108

C₂

#65408

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅
commutator, socle, prime radical	C₂³×C₅	C₂²×C₄
Fitting	C₂×C₅×C₄⋊C₈	C₂
cosocle	C₂²×C₄×C₅	C₂³
hypercenter	C₂×C₄⋊C₈	D₅
hypocenter	C₅	#1843
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₅

commutator, socle, prime radical

C₂³×C₅

C₂²×C₄

Fitting

C₂×C₅×C₄⋊C₈

C₂

cosocle

C₂²×C₄×C₅

C₂³

hypercenter

C₂×C₄⋊C₈

D₅

C₅

G ▷ C₂³×C₅ ▷ C₅

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
94. C₅	#1843	semidirect

H ≅ G/N

type

94. C₅

#1843

semidirect

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

subgroup	index
C₂×C₅×C₄⋊C₈	2
C₂×#3946	2
#65221	2
C₂×C₄⋊#168	2
#1843	5

subgroup

index

C₂×C₅×C₄⋊C₈

C₂×#3946

#65221

C₂×C₄⋊#168

#1843

Subgroups — #10601239

Conjugacy classes of subgroups

Complements

Maximal subgroups