Group #10614774 — subgroups

Subgroups — #10614774

Order 640.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×#4015	C₂	1	1	yes	maximal, characteristic
3	#65275	C₂	1	8	yes	maximal
4	#65263	C₂	1	4	yes	maximal
5	#65221	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₀	C₂²	1	2	yes	—
7	C₅×#125	—	2	4	no	—
8	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₅×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₅	C₂²	1	4	yes	—
12	C₂×C₄×Dic₅	C₂²	1	2	yes	—
13	#4015	—	2	4	no	—
14	#3963	C₂²	1	4	yes	—
15	#3963	C₂²	1	16	yes	—
16	#2642	—	5	1	no	maximal, Sylow
17	C₂²×C₄×C₅	C₂³	1	4	yes	—
18	C₂²×C₄×C₅	C₂³	1	2	yes	—
19	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂²×Dic₅	C₂³	1	4	yes	—
21	C₂²×Dic₅	C₂³	1	4	yes	—
22	C₂×Dic₁₀	—	2	4	no	—
23	C₂×Dic₁₀	—	2	8	no	—
24	C₅×C₄⋊C₄	—	2	8	no	—
25	C₅×C₄⋊C₄	—	2	4	no	—
26	C₄²×C₅	D₄	1	4	yes	—
27	C₄⋊Dic₅	—	2	8	no	—
28	C₄×Dic₅	—	2	4	no	—
29	C₂×C₄⋊Q₈	—	5	1	no	—
30	C₂×#125	D₅	1	1	yes	characteristic
31	#400	—	5	8	no	—
32	#391	—	5	4	no	—
33	#376	—	5	1	no	—
34	C₂³×C₅	C₂⁴	1	1	yes	characteristic
35	C₂×C₄×C₅	—	2	4	no	—
36	C₂×C₄×C₅	—	2	4	no	—
37	C₂×C₄×C₅	—	2	8	no	—
38	C₂×C₄×C₅	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₅	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₅	#41	1	4	yes	—
41	C₂×Dic₅	—	2	4	no	—
42	C₂×Dic₅	—	2	4	no	—
43	C₂×Dic₅	—	2	8	no	—
44	C₂×Dic₅	—	2	8	no	—
45	Dic₁₀	—	4	8	no	—
46	C₂²×Q₈	—	5	2	no	—
47	C₄⋊Q₈	—	10	4	no	—
48	#125	—	2	4	no	—
49	C₂×C₄⋊C₄	—	5	4	no	—
50	C₂×C₄⋊C₄	C₂×D₅	1	2	yes	—
51	C₂×C₄⋊C₄	C₂×D₅	1	4	yes	—
52	C₂×C₄²	—	5	2	no	—
53	C₂×C₄²	C₂×D₅	1	1	yes	characteristic
54	#95	—	5	4	no	—
55	#95	—	5	16	no	—
56	C₂²×C₅	C₂²×D₄	1	1	yes	characteristic
57	C₂²×C₅	C₂×#41	1	2	yes	—
58	C₂²×C₅	2₋¹⁺⁴	1	4	yes	—
59	C₄×C₅	—	2	4	no	—
60	C₄×C₅	—	4	4	no	—
61	C₄×C₅	#124	1	4	yes	—
62	Dic₅	—	4	4	no	—
63	Dic₅	—	4	4	no	—
64	C₂×Q₈	—	10	8	no	—
65	C₂×Q₈	—	10	4	no	—
66	C₂²×C₄	—	5	4	no	—
67	C₂²×C₄	—	5	4	no	—
68	C₂²×C₄	C₂²×D₅	1	4	yes	—
69	C₂²×C₄	C₂²×D₅	1	2	yes	—
70	C₂²×C₄	C₂²×D₅	1	1	yes	characteristic
71	C₄⋊C₄	—	2	8	no	—
72	C₄⋊C₄	—	2	4	no	—
73	C₄⋊C₄	—	10	8	no	—
74	C₄²	—	10	4	no	—
75	C₄²	C₂²⋊D₅	1	4	yes	—
76	C₂×C₅	C₂×#124	1	1	yes	characteristic
77	C₂×C₅	#536	1	2	yes	—
78	C₂×C₅	#541	1	4	yes	—
79	C₂³	C₂³×D₅	1	1	yes	characteristic
80	Q₈	—	20	8	no	—
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	8	no	—
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	10	4	no	—
85	C₂×C₄	—	10	8	no	—
86	C₂×C₄	—	10	8	no	—
87	C₂×C₄	—	10	4	no	—
88	C₂×C₄	#713	1	4	yes	—
89	C₂×C₄	C₂×C₂²⋊D₅	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₅	1	2	yes	—
91	C₅	#2642	1	1	yes	characteristic, complemented, Sylow
92	C₂²	C₂×#713	1	2	yes	—
93	C₂²	#4150	1	4	yes	—
94	C₂²	C₂²×C₂²⋊D₅	1	1	yes	characteristic
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	20	4	no	—
98	C₄	—	20	4	no	—
99	C₄	#4093	1	4	yes	—
100	C₂	#66031	1	4	yes	—
101	C₂	C₂×#4093	1	1	yes	characteristic
102	C₂	#66159	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×#125

C₂

yes

maximal, characteristic

C₂×#4015

C₂

yes

maximal, characteristic

#65275

C₂

yes

maximal

#65263

C₂

yes

maximal

#65221

C₂

yes

maximal, characteristic

C₂²×Dic₁₀

C₂²

yes

—

C₅×#125

—

C₂×C₅×C₄⋊C₄

C₂²

yes

—

C₂×C₅×C₄⋊C₄

C₂²

yes

—

C₂×C₄²×C₅

C₂²

yes

characteristic

C₂×C₄⋊Dic₅

C₂²

yes

—

C₂×C₄×Dic₅

C₂²

yes

—

#4015

—

#3963

C₂²

yes

—

#3963

C₂²

yes

—

#2642

—

maximal, Sylow

C₂²×C₄×C₅

C₂³

yes

—

C₂²×C₄×C₅

C₂³

yes

—

C₂²×C₄×C₅

C₂³

yes

characteristic

C₂²×Dic₅

C₂³

yes

—

C₂²×Dic₅

C₂³

yes

—

C₂×Dic₁₀

—

C₂×Dic₁₀

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

D₄

yes

—

C₄⋊Dic₅

—

C₄×Dic₅

—

C₂×C₄⋊Q₈

—

C₂×#125

D₅

yes

—

—

—

C₂³×C₅

C₂⁴

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

C₂×D₄

yes

—

C₂×C₄×C₅

#41

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

C₂×Dic₅

—

Dic₁₀

—

C₂²×Q₈

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₅

yes

—

C₂×C₄⋊C₄

C₂×D₅

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₅

yes

characteristic

#95

—

#95

—

C₂²×C₅

C₂²×D₄

yes

characteristic

C₂²×C₅

C₂×#41

yes

—

C₂²×C₅

2₋¹⁺⁴

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

#124

yes

—

Dic₅

—

Dic₅

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₅

yes

—

C₂²×C₄

C₂²×D₅

yes

—

C₂²×C₄

C₂²×D₅

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₅

yes

—

C₂×C₅

C₂×#124

yes

characteristic

C₂×C₅

#536

yes

—

C₂×C₅

#541

yes

—

C₂³

C₂³×D₅

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#713

yes

—

C₂×C₄

C₂×C₂²⋊D₅

yes

—

C₂×C₄

C₂×C₂²⋊D₅

yes

—

C₅

#2642

yes

characteristic, complemented, Sylow

C₂²

C₂×#713

yes

—

C₂²

#4150

yes

—

C₂²

C₂²×C₂²⋊D₅

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#4093

yes

—

100

C₂

#66031

yes

—

101

C₂

C₂×#4093

yes

characteristic

102

C₂

#66159

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅
commutator, socle, prime radical, cosocle	C₂³×C₅	C₂⁴
Fitting	C₂×C₅×#125	C₂
hypercenter	C₂×#125	D₅
hypocenter	C₅	#2642
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#125

subgroup

G/H

center, Frattini

C₂³

C₂³×D₅

commutator, socle, prime radical, cosocle

C₂³×C₅

C₂⁴

Fitting

C₂×C₅×#125

C₂

D₅

C₅

G ▷ C₂³×C₅ ▷ C₅

C₁ ◁ C₂³ ◁ C₂×#125

N	H ≅ G/N	type
91. C₅	#2642	semidirect

H ≅ G/N

type

91. C₅

#2642

semidirect

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

subgroup	index
C₂×C₅×#125	2
C₂×#4015	2
#65275	2
#65263	2
#65221	2
#2642	5

subgroup

index

C₂×C₅×#125

Subgroups — #10614774

Conjugacy classes of subgroups

Complements

Maximal subgroups