Group #14511004 — subgroups

Subgroups — C₅×#3415⋊C₃ #14511004

Order 1920.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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×#576⋊C₃	C₂	1	2	yes	maximal, complemented
2	C₅×#504⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3415	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#994	—	2	2	no	—
5	C₅×#131⋊C₃	C₂²	1	1	yes	characteristic
6	C₃×C₅×Q₃₂	—	4	1	no	maximal
7	#3415⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#576	C₂×C₃	1	2	yes	—
9	C₅×#509	—	3	2	no	—
10	C₅×#508	—	3	1	no	—
11	C₂×C₅×D₁₆	—	3	1	no	—
12	C₅×#504	C₂×C₃	1	1	yes	characteristic
13	C₅×#41⋊C₃	—	4	2	no	—
14	C₅×#41⋊C₃	D₄	1	1	yes	characteristic
15	C₃×C₅×Q₁₆	—	4	2	no	—
16	C₃×C₅×C₁₆	—	4	1	no	—
17	#576⋊C₃	C₂×C₅	1	2	yes	complemented
18	#504⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
19	C₅×H(5,𝔽₂)	—	2	2	no	—
20	C₅×AGL(1,ℤ/8)	—	6	2	no	—
21	C₅×#135	—	3	2	no	—
22	C₂×C₅×D₈	—	3	2	no	—
23	C₅×#131	C₂²×C₃	1	1	yes	characteristic
24	C₅×Q₃₂	A₄	1	1	yes	characteristic
25	C₅×SD₃₂	—	3	2	no	—
26	C₅×D₁₆	—	3	2	no	—
27	C₅×D₁₆	—	3	1	no	—
28	C₅×M₃₂	—	3	1	no	—
29	C₂×C₅×C₁₆	—	3	1	no	—
30	#3415	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
31	C₃×C₅×Q₈	—	8	2	no	—
32	C₅×SL(2,𝔽₃)	D₈	1	1	yes	characteristic
33	C₃×C₅×C₈	—	4	1	no	—
34	#994	—	2	2	no	—
35	#131⋊C₃	C₂²×C₅	1	1	yes	characteristic
36	C₃×Q₃₂	—	4	1	no	—
37	C₅×#41	—	4	2	no	—
38	C₅×#41	—	6	2	no	—
39	C₅×#41	C₃×D₄	1	1	yes	characteristic
40	C₂×C₅×D₄	—	6	2	no	—
41	C₂×C₅×D₄	—	12	2	no	—
42	C₅×Q₁₆	C₂×A₄	1	2	yes	—
43	C₅×SD₁₆	—	6	2	no	—
44	C₅×D₈	—	3	2	no	—
45	C₅×D₈	—	6	2	no	—
46	C₅×M₁₆	—	3	1	no	—
47	C₂×C₅×C₈	—	3	1	no	—
48	C₅×C₁₆	—	3	1	no	—
49	C₅×C₁₆	C₂×A₄	1	1	yes	characteristic
50	#576	C₂×C₃×C₅	1	2	yes	—
51	#509	—	3	2	no	—
52	#508	—	3	1	no	—
53	C₂×D₁₆	—	3	1	no	—
54	#504	C₂×C₃×C₅	1	1	yes	characteristic
55	C₃×C₄×C₅	—	4	1	no	—
56	C₃×C₄×C₅	—	16	2	no	—
57	#41⋊C₃	—	4	2	no	—
58	#41⋊C₃	C₅×D₄	1	1	yes	characteristic
59	C₃×Q₁₆	—	4	2	no	—
60	C₃×C₁₆	—	4	1	no	—
61	C₂³×C₅	—	12	2	no	—
62	C₅×Q₈	—	2	2	no	—
63	C₅×Q₈	C₃×D₈	1	1	yes	characteristic
64	C₅×D₄	—	3	1	no	—
65	C₅×D₄	—	6	2	no	—
66	C₅×D₄	—	12	2	no	—
67	C₅×D₄	—	12	2	no	—
68	C₂×C₄×C₅	—	3	1	no	—
69	C₂×C₄×C₅	—	12	2	no	—
70	C₅×C₈	—	3	1	no	—
71	C₅×C₈	C₂²×A₄	1	1	yes	characteristic
72	H(5,𝔽₂)	—	2	2	no	—
73	AGL(1,ℤ/8)	—	6	2	no	—
74	#135	—	3	2	no	—
75	C₂×D₈	—	3	2	no	—
76	#131	C₂²×C₃×C₅	1	1	yes	characteristic
77	Q₃₂	C₅×A₄	1	1	yes	characteristic
78	SD₃₂	—	3	2	no	—
79	D₁₆	—	3	2	no	—
80	D₁₆	—	3	1	no	—
81	M₃₂	—	3	1	no	—
82	C₂×C₁₆	—	3	1	no	—
83	C₂×C₃×C₅	—	4	1	no	—
84	C₃×Q₈	—	8	2	no	—
85	SL(2,𝔽₃)	C₅×D₈	1	1	yes	characteristic
86	C₃×C₈	—	4	1	no	—
87	C₂²×C₅	—	3	1	no	—
88	C₂²×C₅	—	12	2	no	—
89	C₂²×C₅	—	48	2	no	—
90	C₄×C₅	—	3	1	no	—
91	C₄×C₅	—	4	2	no	—
92	C₄×C₅	D₄×A₄	1	1	yes	characteristic
93	#41	—	4	2	no	—
94	#41	—	6	2	no	—
95	#41	C₃×C₅×D₄	1	1	yes	characteristic
96	C₂×D₄	—	6	2	no	—
97	C₂×D₄	—	12	2	no	—
98	Q₁₆	C₂×C₅×A₄	1	2	yes	—
99	SD₁₆	—	6	2	no	—
100	D₈	—	3	2	no	—
101	D₈	—	6	2	no	—
102	M₁₆	—	3	1	no	—
103	C₂×C₈	—	3	1	no	—
104	C₁₆	—	3	1	no	—
105	C₁₆	C₂×C₅×A₄	1	1	yes	characteristic
106	C₃×C₅	—	4	1	no	Hall
107	C₃×C₄	—	4	1	no	—
108	C₃×C₄	—	16	2	no	—
109	C₂×C₅	—	6	1	no	—
110	C₂×C₅	—	24	2	no	—
111	C₂×C₅	A₄×D₈	1	1	yes	characteristic
112	C₂³	—	12	2	no	—
113	Q₈	—	2	2	no	—
114	Q₈	C₃×C₅×D₈	1	1	yes	characteristic
115	D₄	—	3	1	no	—
116	D₄	—	6	2	no	—
117	D₄	—	12	2	no	—
118	D₄	—	12	2	no	—
119	C₂×C₄	—	3	1	no	—
120	C₂×C₄	—	12	2	no	—
121	C₈	—	3	1	no	—
122	C₈	C₂²×C₅×A₄	1	1	yes	characteristic
123	C₂×C₃	—	4	1	no	—
124	C₅	#3415⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
125	C₂²	—	3	1	no	—
126	C₂²	—	12	2	no	—
127	C₂²	—	48	2	no	—
128	C₄	—	3	1	no	—
129	C₄	—	4	2	no	—
130	C₄	C₅×D₄×A₄	1	1	yes	characteristic
131	C₃	—	4	1	no	Sylow
132	C₂	—	6	1	no	—
133	C₂	—	24	2	no	—
134	C₂	C₅×A₄×D₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#576⋊C₃

C₂

yes

maximal, complemented

C₅×#504⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅×#3415

C₃

yes

maximal, characteristic, complemented, Hall

C₅×#994

—

C₅×#131⋊C₃

C₂²

yes

characteristic

C₃×C₅×Q₃₂

—

maximal

#3415⋊C₃

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×#576

C₂×C₃

yes

—

C₅×#509

—

C₅×#508

—

C₂×C₅×D₁₆

—

C₅×#504

C₂×C₃

yes

characteristic

C₅×#41⋊C₃

—

C₅×#41⋊C₃

D₄

yes

characteristic

C₃×C₅×Q₁₆

—

C₃×C₅×C₁₆

—

#576⋊C₃

C₂×C₅

yes

complemented

#504⋊C₃

C₂×C₅

yes

characteristic, complemented

C₅×H(5,𝔽₂)

—

C₅×AGL(1,ℤ/8)

—

C₅×#135

—

C₂×C₅×D₈

—

C₅×#131

C₂²×C₃

yes

characteristic

C₅×Q₃₂

A₄

yes

characteristic

C₅×SD₃₂

—

C₅×D₁₆

—

C₅×D₁₆

—

C₅×M₃₂

—

C₂×C₅×C₁₆

—

#3415

C₃×C₅

yes

characteristic, complemented, Sylow

C₃×C₅×Q₈

—

C₅×SL(2,𝔽₃)

D₈

yes

characteristic

C₃×C₅×C₈

—

#994

—

#131⋊C₃

C₂²×C₅

yes

characteristic

C₃×Q₃₂

—

C₅×#41

—

C₅×#41

—

C₅×#41

C₃×D₄

yes

characteristic

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₅×Q₁₆

C₂×A₄

yes

—

C₅×SD₁₆

—

C₅×D₈

—

C₅×D₈

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₅×C₁₆

—

C₅×C₁₆

C₂×A₄

yes

characteristic

#576

C₂×C₃×C₅

yes

—

#509

—

#508

—

C₂×D₁₆

—

#504

C₂×C₃×C₅

yes

characteristic

C₃×C₄×C₅

—

C₃×C₄×C₅

—

#41⋊C₃

—

#41⋊C₃

C₅×D₄

yes

characteristic

C₃×Q₁₆

—

C₃×C₁₆

—

C₂³×C₅

—

C₅×Q₈

—

C₅×Q₈

C₃×D₈

yes

characteristic

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₅×C₈

—

C₅×C₈

C₂²×A₄

yes

—

—

—

C₂×D₈

—

#131

C₂²×C₃×C₅

yes

characteristic

Q₃₂

C₅×A₄

yes

characteristic

SD₃₂

—

D₁₆

—

D₁₆

—

M₃₂

—

C₂×C₁₆

—

C₂×C₃×C₅

—

C₃×Q₈

—

SL(2,𝔽₃)

C₅×D₈

yes

characteristic

C₃×C₈

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

D₄×A₄

yes

—

—

C₃×C₅×D₄

yes

characteristic

C₂×D₄

—

C₂×D₄

—

Q₁₆

C₂×C₅×A₄

yes

—

SD₁₆

—

100

D₈

—

101

D₈

—

102

M₁₆

—

103

C₂×C₈

—

104

C₁₆

—

105

C₁₆

C₂×C₅×A₄

yes

characteristic

106

C₃×C₅

—

Hall

107

C₃×C₄

—

108

C₃×C₄

—

109

C₂×C₅

—

110

C₂×C₅

—

111

C₂×C₅

A₄×D₈

yes

characteristic

112

C₂³

—

113

Q₈

—

114

Q₈

C₃×C₅×D₈

yes

characteristic

115

D₄

—

116

D₄

—

117

D₄

—

118

D₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₈

—

122

C₈

C₂²×C₅×A₄

yes

characteristic

123

C₂×C₃

—

124

C₅

#3415⋊C₃

yes

characteristic, direct product factor, Sylow

125

C₂²

—

126

C₂²

—

127

C₂²

—

128

C₄

—

129

C₄

—

130

C₄

C₅×D₄×A₄

yes

characteristic

131

C₃

—

Sylow

132

C₂

—

133

C₂

—

134

C₂

C₅×A₄×D₈

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₅	A₄×D₈
commutator, cosocle	#131	C₂²×C₃×C₅
Frattini	C₈	C₂²×C₅×A₄
Fitting	C₅×#3415	C₃
hypercenter	C₅×Q₃₂	A₄
hypocenter	Q₈	C₃×C₅×D₈
LCS	G ▷ #131 ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×Q₃₂

subgroup

G/H

center, socle

C₂×C₅

A₄×D₈

commutator, cosocle

#131

C₂²×C₃×C₅

Frattini

C₈

C₂²×C₅×A₄

Fitting

C₅×#3415

C₃

hypercenter

C₅×Q₃₂

A₄

hypocenter

Q₈

C₃×C₅×D₈

LCS

G ▷ #131 ▷ #41 ▷ Q₈

UCS

C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×Q₃₂

N	H ≅ G/N	type
1. C₅×#576⋊C₃	C₂	semidirect
2. C₅×#504⋊C₃	C₂	semidirect
3. C₅×#3415	C₃	semidirect
7. #3415⋊C₃	C₅	direct (N × H)
17. #576⋊C₃	C₂×C₅	semidirect
18. #504⋊C₃	C₂×C₅	semidirect
30. #3415	C₃×C₅	semidirect
124. C₅	#3415⋊C₃	direct (N × H)

H ≅ G/N

type

1. C₅×#576⋊C₃

C₂

semidirect

2. C₅×#504⋊C₃

C₂

semidirect

3. C₅×#3415

C₃

semidirect

7. #3415⋊C₃

C₅

direct (N × H)

17. #576⋊C₃

C₂×C₅

semidirect

18. #504⋊C₃

C₂×C₅

semidirect

30. #3415

C₃×C₅

semidirect

124. C₅

#3415⋊C₃

direct (N × H)

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

subgroup	index
C₅×#576⋊C₃	2
C₅×#504⋊C₃	2
C₅×#3415	3
C₃×C₅×Q₃₂	4
#3415⋊C₃	5

subgroup

index

C₅×#576⋊C₃

C₅×#504⋊C₃

C₅×#3415

C₃×C₅×Q₃₂

#3415⋊C₃

Subgroups — C₅×#3415⋊C₃ #14511004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#3415⋊C3 #14511004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3415⋊C₃ #14511004