Group #11756071 — subgroups

Subgroups — C₅×C₃⋊#564 #11756071

Order 960.

344 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 182 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	C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic
2	C₅×#890	C₂	1	4	yes	maximal
3	C₅×#889	C₂	1	4	yes	maximal
4	C₅×#889	C₂	1	4	yes	maximal
5	C₅×#870	C₂	1	2	yes	maximal
6	C₅×#564	—	3	1	no	maximal, Hall
7	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
8	C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
9	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
11	C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₅×C₄⋊Dic₃	C₂²	1	4	yes	—
13	C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
14	C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
15	C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
16	C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
17	C₄×C₅×Dic₃	C₂²	1	4	yes	—
18	C₃⋊#564	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₅×#125	—	3	4	no	—
20	C₅×#125	—	3	4	no	—
21	C₅×#125	—	3	4	no	—
22	C₅×#125	—	3	2	no	—
23	C₅×#125	D₃	1	1	yes	characteristic
24	C₂×C₃×C₄×C₅	C₂³	1	4	yes	—
25	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
27	C₂×C₅×Dic₃	C₂³	1	4	yes	—
28	C₂×C₅×Dic₃	C₂³	1	4	yes	—
29	C₃×#125	C₂×C₅	1	1	yes	characteristic
30	#890	C₂×C₅	1	4	yes	—
31	#889	C₂×C₅	1	4	yes	—
32	#889	C₂×C₅	1	4	yes	—
33	#870	C₂×C₅	1	2	yes	—
34	C₅×C₄⋊C₄	—	3	4	no	—
35	C₅×C₄⋊C₄	—	3	4	no	—
36	C₅×C₄⋊C₄	—	3	4	no	—
37	C₅×C₄⋊C₄	—	3	4	no	—
38	C₅×C₄⋊C₄	—	3	4	no	—
39	C₅×C₄⋊C₄	—	3	2	no	—
40	C₅×C₄⋊C₄	—	3	2	no	—
41	C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
42	C₅×C₄⋊C₄	C₂×D₃	1	4	yes	—
43	C₄²×C₅	—	3	4	no	—
44	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
45	#564	—	3	1	no	Sylow
46	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
47	C₃×C₄×C₅	—	2	1	no	—
48	C₃×C₄×C₅	—	2	4	no	—
49	C₃×C₄×C₅	—	2	2	no	—
50	C₅×Dic₃	—	2	4	no	—
51	C₅×Dic₃	—	2	4	no	—
52	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
53	C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
54	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
55	C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
56	C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
57	C₄⋊Dic₃	C₂²×C₅	1	4	yes	—
58	Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
59	Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
60	Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
61	Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
62	C₄×Dic₃	C₂²×C₅	1	4	yes	—
63	C₂×C₄×C₅	—	3	4	no	—
64	C₂×C₄×C₅	—	3	4	no	—
65	C₂×C₄×C₅	C₂²×D₃	1	4	yes	—
66	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
67	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
68	#125	—	3	4	no	—
69	#125	—	3	4	no	—
70	#125	—	3	4	no	—
71	#125	—	3	2	no	—
72	#125	C₅×D₃	1	1	yes	characteristic
73	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
74	C₂×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
75	C₂×C₃×C₄	C₂³×C₅	1	4	yes	—
76	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
77	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
78	C₂×Dic₃	C₂³×C₅	1	4	yes	—
79	C₂×Dic₃	C₂³×C₅	1	4	yes	—
80	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
81	C₄×C₅	—	2	1	no	—
82	C₄×C₅	—	2	4	no	—
83	C₄×C₅	—	2	2	no	—
84	C₄×C₅	—	6	4	no	—
85	C₄×C₅	—	6	4	no	—
86	C₄⋊C₄	—	3	4	no	—
87	C₄⋊C₄	—	3	4	no	—
88	C₄⋊C₄	—	3	4	no	—
89	C₄⋊C₄	—	3	4	no	—
90	C₄⋊C₄	—	3	4	no	—
91	C₄⋊C₄	—	3	2	no	—
92	C₄⋊C₄	—	3	2	no	—
93	C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
94	C₄⋊C₄	C₂×C₅×D₃	1	4	yes	—
95	C₄²	—	3	4	no	—
96	C₄²	C₂×C₅×D₃	1	1	yes	characteristic
97	C₃×C₅	#564	1	1	yes	characteristic, complemented, Hall
98	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
99	C₃×C₄	—	2	1	no	—
100	C₃×C₄	—	2	4	no	—
101	C₃×C₄	—	2	2	no	—
102	Dic₃	—	2	4	no	—
103	Dic₃	—	2	4	no	—
104	C₂×C₅	#1007	1	1	yes	characteristic
105	C₂×C₅	#1010	1	2	yes	—
106	C₂×C₄	—	3	4	no	—
107	C₂×C₄	—	3	4	no	—
108	C₂×C₄	C₂²×C₅×D₃	1	4	yes	—
109	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
110	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
111	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
112	C₂×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
113	C₅	C₃⋊#564	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	2	4	no	—
117	C₄	—	2	2	no	—
118	C₄	—	6	4	no	—
119	C₄	—	6	4	no	—
120	C₃	C₅×#564	1	1	yes	characteristic, complemented, Sylow
121	C₂	C₅×#1007	1	1	yes	characteristic
122	C₂	C₅×#1010	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅×#125

C₂

yes

maximal, characteristic

C₅×#890

C₂

yes

maximal

C₅×#889

C₂

yes

maximal

C₅×#889

C₂

yes

maximal

C₅×#870

C₂

yes

maximal

C₅×#564

—

maximal, Hall

C₃×C₅×C₄⋊C₄

C₂²

yes

—

C₃×C₅×C₄⋊C₄

C₂²

yes

—

C₃×C₄²×C₅

C₂²

yes

characteristic

C₅×C₄⋊Dic₃

C₂²

yes

—

C₅×C₄⋊Dic₃

C₂²

yes

—

C₅×C₄⋊Dic₃

C₂²

yes

—

C₅×Dic₃⋊C₄

C₂²

yes

—

C₅×Dic₃⋊C₄

C₂²

yes

—

C₅×Dic₃⋊C₄

C₂²

yes

—

C₅×Dic₃⋊C₄

C₂²

yes

—

C₄×C₅×Dic₃

C₂²

yes

—

C₃⋊#564

C₅

yes

maximal, characteristic, direct product factor, Hall

—

—

—

—

D₃

yes

characteristic

C₂×C₃×C₄×C₅

C₂³

yes

—

C₂×C₃×C₄×C₅

C₂³

yes

characteristic

C₂×C₃×C₄×C₅

C₂³

yes

—

C₂×C₅×Dic₃

C₂³

yes

—

C₂×C₅×Dic₃

C₂³

yes

—

C₃×#125

C₂×C₅

yes

characteristic

#890

C₂×C₅

yes

—

#889

C₂×C₅

yes

—

#889

C₂×C₅

yes

—

#870

C₂×C₅

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

C₂×D₃

yes

—

C₅×C₄⋊C₄

C₂×D₃

yes

—

C₄²×C₅

—

C₄²×C₅

C₂×D₃

yes

characteristic

#564

—

Sylow

C₂²×C₃×C₅

C₂⁴

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₃×C₄×C₅

—

C₅×Dic₃

—

C₅×Dic₃

—

C₃×C₄⋊C₄

C₂²×C₅

yes

—

C₃×C₄⋊C₄

C₂²×C₅

yes

—

C₃×C₄²

C₂²×C₅

yes

characteristic

C₄⋊Dic₃

C₂²×C₅

yes

—

C₄⋊Dic₃

C₂²×C₅

yes

—

C₄⋊Dic₃

C₂²×C₅

yes

—

Dic₃⋊C₄

C₂²×C₅

yes

—

Dic₃⋊C₄

C₂²×C₅

yes

—

Dic₃⋊C₄

C₂²×C₅

yes

—

Dic₃⋊C₄

C₂²×C₅

yes

—

C₄×Dic₃

C₂²×C₅

yes

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²×D₃

yes

—

C₂×C₄×C₅

C₂²×D₃

yes

characteristic

C₂×C₄×C₅

C₂²×D₃

yes

—

—

—

—

—

C₅×D₃

yes

characteristic

C₂×C₃×C₅

2₋¹⁺⁴

yes

characteristic

C₂×C₃×C₅

2₋¹⁺⁴

yes

—

C₂×C₃×C₄

C₂³×C₅

yes

—

C₂×C₃×C₄

C₂³×C₅

yes

characteristic

C₂×C₃×C₄

C₂³×C₅

yes

—

C₂×Dic₃

C₂³×C₅

yes

—

C₂×Dic₃

C₂³×C₅

yes

—

C₂²×C₅

C₂³×D₃

yes

characteristic

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×C₅×D₃

yes

—

C₄⋊C₄

C₂×C₅×D₃

yes

—

C₄²

—

C₄²

C₂×C₅×D₃

yes

characteristic

C₃×C₅

#564

yes

characteristic, complemented, Hall

C₂²×C₃

C₂⁴×C₅

yes

characteristic

C₃×C₄

—

100

C₃×C₄

—

101

C₃×C₄

—

102

Dic₃

—

103

Dic₃

—

104

C₂×C₅

#1007

yes

characteristic

105

C₂×C₅

#1010

yes

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₂²×C₅×D₃

yes

—

109

C₂×C₄

C₂²×C₅×D₃

yes

characteristic

110

C₂×C₄

C₂²×C₅×D₃

yes

—

111

C₂×C₃

C₅×2₋¹⁺⁴

yes

characteristic

112

C₂×C₃

C₅×2₋¹⁺⁴

yes

—

113

C₅

C₃⋊#564

yes

characteristic, direct product factor, Sylow

114

C₂²

C₂³×C₅×D₃

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₃

C₅×#564

yes

characteristic, complemented, Sylow

121

C₂

C₅×#1007

yes

characteristic

122

C₂

C₅×#1010

yes

—

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₅×#125	C₂
socle, prime radical	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#125	D₃
hypocenter	C₃	C₅×#564
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#125

subgroup

G/H

center

C₂²×C₅

C₂³×D₃

commutator, cosocle

C₂²×C₃

C₂⁴×C₅

Frattini

C₂²

C₂³×C₅×D₃

Fitting

C₃×C₅×#125

C₂

socle, prime radical

C₂²×C₃×C₅

C₂⁴

D₃

C₃

G ▷ C₂²×C₃ ▷ C₃

C₁ ◁ C₂²×C₅ ◁ C₅×#125

N	H ≅ G/N	type
18. C₃⋊#564	C₅	direct (N × H)
97. C₃×C₅	#564	semidirect
113. C₅	C₃⋊#564	direct (N × H)
120. C₃	C₅×#564	semidirect

H ≅ G/N

type

18. C₃⋊#564

C₅

direct (N × H)

97. C₃×C₅

#564

semidirect

113. C₅

C₃⋊#564

direct (N × H)

120. C₃

C₅×#564

semidirect

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

subgroup	index
C₃×C₅×#125	2
C₅×#890	2
C₅×#889	2
C₅×#870	2
C₅×#564	3
C₃⋊#564	5

subgroup

index

C₃×C₅×#125

Subgroups — C₅×C₃⋊#564 #11756071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×C3⋊#564 #11756071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#564 #11756071