Group #14510764 — subgroups

Subgroups — C₅×#73040 #14510764

Order 1920.

176 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 32 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×#5407	C₂	1	2	yes	maximal, complemented
2	C₅×#504⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2221	—	3	1	no	maximal, Hall
4	C₅×#986	—	2	2	no	—
5	C₅×#131⋊C₃	C₂²	1	1	yes	characteristic
6	C₅×D₄₈	—	4	1	no	maximal
7	#73040	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×D₁₆	—	3	1	no	—
9	C₅×#504	D₃	1	1	yes	characteristic, complemented
10	C₅×#472	—	3	2	no	—
11	C₅×#368	—	3	1	no	—
12	C₅×#361	—	3	2	no	—
13	C₅×#41⋊C₃	D₄	1	1	yes	characteristic
14	C₅×GL(2,𝔽₃)	—	4	2	no	—
15	C₅×D₂₄	—	4	2	no	—
16	C₃×C₅×C₁₆	—	4	1	no	—
17	#5407	C₂×C₅	1	2	yes	complemented
18	#504⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
19	C₅×AGL(1,ℤ/8)	—	6	2	no	—
20	C₂×C₅×D₈	—	3	2	no	—
21	C₅×#131	C₂×D₃	1	1	yes	characteristic
22	C₅×D₁₆	—	6	1	no	—
23	C₅×D₁₆	—	6	1	no	—
24	C₅×M₃₂	—	3	1	no	—
25	C₂×C₅×C₁₆	—	3	1	no	—
26	C₅×#108	—	3	2	no	—
27	C₅×#100	—	6	2	no	—
28	#2221	—	3	1	no	Sylow
29	C₅×D₁₂	—	8	2	no	—
30	C₅×SL(2,𝔽₃)	D₈	1	1	yes	characteristic
31	C₃×C₅×C₈	—	4	1	no	—
32	#986	—	2	2	no	—
33	#131⋊C₃	C₂²×C₅	1	1	yes	characteristic
34	D₄₈	—	4	1	no	—
35	C₅×#41	D₁₂	1	1	yes	characteristic
36	C₂×C₅×D₄	—	6	2	no	—
37	C₅×SD₁₆	—	12	2	no	—
38	C₅×D₈	—	6	2	no	—
39	C₅×D₈	—	6	2	no	—
40	C₅×D₈	—	12	2	no	—
41	C₅×M₁₆	—	3	1	no	—
42	C₅×M₁₆	—	6	2	no	—
43	C₂×C₅×C₈	—	3	1	no	—
44	C₅×C₁₆	—	3	1	no	—
45	C₅×C₁₆	S₄	1	1	yes	characteristic
46	C₂×D₁₆	—	3	1	no	—
47	#504	C₅×D₃	1	1	yes	characteristic, complemented
48	#472	—	3	2	no	—
49	#368	—	3	1	no	—
50	#361	—	3	2	no	—
51	C₂×C₅×D₃	—	16	2	no	—
52	C₃×C₄×C₅	—	4	1	no	—
53	#41⋊C₃	C₅×D₄	1	1	yes	characteristic
54	GL(2,𝔽₃)	—	4	2	no	—
55	D₂₄	—	4	2	no	—
56	C₃×C₁₆	—	4	1	no	—
57	C₂³×C₅	—	12	2	no	—
58	C₅×Q₈	D₂₄	1	1	yes	characteristic
59	C₅×D₄	—	3	1	no	—
60	C₅×D₄	—	12	2	no	—
61	C₅×D₄	—	12	2	no	—
62	C₂×C₄×C₅	—	3	1	no	—
63	C₅×C₈	—	3	1	no	—
64	C₅×C₈	—	12	2	no	—
65	C₅×C₈	C₂×S₄	1	1	yes	characteristic
66	AGL(1,ℤ/8)	—	6	2	no	—
67	C₂×D₈	—	3	2	no	—
68	#131	C₂×C₅×D₃	1	1	yes	characteristic
69	D₁₆	—	6	1	no	—
70	D₁₆	—	6	1	no	—
71	M₃₂	—	3	1	no	—
72	C₂×C₁₆	—	3	1	no	—
73	#108	—	3	2	no	—
74	#100	—	6	2	no	—
75	C₂×C₃×C₅	—	4	1	no	—
76	C₅×D₃	—	32	2	no	—
77	D₁₂	—	8	2	no	—
78	SL(2,𝔽₃)	C₅×D₈	1	1	yes	characteristic
79	C₃×C₈	—	4	1	no	—
80	C₂²×C₅	—	3	1	no	—
81	C₂²×C₅	—	24	2	no	—
82	C₂²×C₅	—	48	2	no	—
83	C₄×C₅	—	3	1	no	—
84	C₄×C₅	C₄⋊S₄	1	1	yes	characteristic
85	#41	C₅×D₁₂	1	1	yes	characteristic
86	C₂×D₄	—	6	2	no	—
87	SD₁₆	—	12	2	no	—
88	D₈	—	6	2	no	—
89	D₈	—	6	2	no	—
90	D₈	—	12	2	no	—
91	M₁₆	—	3	1	no	—
92	M₁₆	—	6	2	no	—
93	C₂×C₈	—	3	1	no	—
94	C₁₆	—	3	1	no	—
95	C₁₆	C₅×S₄	1	1	yes	characteristic
96	C₃×C₅	—	4	1	no	Hall
97	C₂×D₃	—	16	2	no	—
98	C₃×C₄	—	4	1	no	—
99	C₂×C₅	—	6	1	no	—
100	C₂×C₅	—	48	2	no	—
101	C₂×C₅	#5402	1	1	yes	characteristic
102	C₂³	—	12	2	no	—
103	Q₈	C₅×D₂₄	1	1	yes	characteristic
104	D₄	—	3	1	no	—
105	D₄	—	12	2	no	—
106	D₄	—	12	2	no	—
107	C₂×C₄	—	3	1	no	—
108	C₈	—	3	1	no	—
109	C₈	—	12	2	no	—
110	C₈	C₂×C₅×S₄	1	1	yes	characteristic
111	C₂×C₃	—	4	1	no	—
112	D₃	—	32	2	no	—
113	C₅	#73040	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²	—	3	1	no	—
115	C₂²	—	24	2	no	—
116	C₂²	—	48	2	no	—
117	C₄	—	3	1	no	—
118	C₄	C₅×C₄⋊S₄	1	1	yes	characteristic
119	C₃	—	4	1	no	Sylow
120	C₂	—	6	1	no	—
121	C₂	—	48	2	no	—
122	C₂	C₅×#5402	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#5407

C₂

yes

maximal, complemented

C₅×#504⋊C₃

C₂

yes

maximal, characteristic, complemented

C₅×#2221

—

maximal, Hall

C₅×#986

—

C₅×#131⋊C₃

C₂²

yes

characteristic

C₅×D₄₈

—

maximal

#73040

C₅

yes

maximal, characteristic, direct product factor, Hall

C₂×C₅×D₁₆

—

C₅×#504

D₃

yes

characteristic, complemented

C₅×#472

—

C₅×#368

—

C₅×#361

—

C₅×#41⋊C₃

D₄

yes

characteristic

C₅×GL(2,𝔽₃)

—

C₅×D₂₄

—

C₃×C₅×C₁₆

—

#5407

C₂×C₅

yes

complemented

#504⋊C₃

C₂×C₅

yes

characteristic, complemented

C₅×AGL(1,ℤ/8)

—

C₂×C₅×D₈

—

C₅×#131

C₂×D₃

yes

characteristic

C₅×D₁₆

—

C₅×D₁₆

—

C₅×M₃₂

—

C₂×C₅×C₁₆

—

—

—

—

C₅×D₁₂

—

C₅×SL(2,𝔽₃)

D₈

yes

characteristic

C₃×C₅×C₈

—

#986

—

#131⋊C₃

C₂²×C₅

yes

characteristic

D₄₈

—

C₅×#41

D₁₂

yes

characteristic

C₂×C₅×D₄

—

C₅×SD₁₆

—

C₅×D₈

—

C₅×D₈

—

C₅×D₈

—

C₅×M₁₆

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₅×C₁₆

—

C₅×C₁₆

S₄

yes

characteristic

C₂×D₁₆

—

#504

C₅×D₃

yes

characteristic, complemented

#472

—

#368

—

#361

—

C₂×C₅×D₃

—

C₃×C₄×C₅

—

#41⋊C₃

C₅×D₄

yes

characteristic

GL(2,𝔽₃)

—

D₂₄

—

C₃×C₁₆

—

C₂³×C₅

—

C₅×Q₈

D₂₄

yes

characteristic

C₅×D₄

—

C₅×D₄

—

C₅×D₄

—

C₂×C₄×C₅

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

C₂×S₄

yes

characteristic

AGL(1,ℤ/8)

—

C₂×D₈

—

#131

C₂×C₅×D₃

yes

characteristic

D₁₆

—

D₁₆

—

M₃₂

—

C₂×C₁₆

—

#108

—

#100

—

C₂×C₃×C₅

—

C₅×D₃

—

D₁₂

—

SL(2,𝔽₃)

C₅×D₈

yes

characteristic

C₃×C₈

—

C₂²×C₅

—

C₂²×C₅

—

C₂²×C₅

—

C₄×C₅

—

C₄×C₅

C₄⋊S₄

yes

characteristic

#41

C₅×D₁₂

yes

characteristic

C₂×D₄

—

SD₁₆

—

D₈

—

D₈

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₁₆

—

C₁₆

C₅×S₄

yes

characteristic

C₃×C₅

—

Hall

C₂×D₃

—

C₃×C₄

—

C₂×C₅

—

100

C₂×C₅

—

101

C₂×C₅

#5402

yes

characteristic

102

C₂³

—

103

Q₈

C₅×D₂₄

yes

characteristic

104

D₄

—

105

D₄

—

106

D₄

—

107

C₂×C₄

—

108

C₈

—

109

C₈

—

110

C₈

C₂×C₅×S₄

yes

characteristic

111

C₂×C₃

—

112

D₃

—

113

C₅

#73040

yes

characteristic, direct product factor, Sylow

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₄

—

118

C₄

C₅×C₄⋊S₄

yes

characteristic

119

C₃

—

Sylow

120

C₂

—

121

C₂

—

122

C₂

C₅×#5402

yes

characteristic

	subgroup	G/H
center, socle	C₂×C₅	#5402
commutator, cosocle	#131⋊C₃	C₂²×C₅
Frattini	C₈	C₂×C₅×S₄
Fitting	C₅×#504	D₃
hypercenter	C₅×C₁₆	S₄
hypocenter	SL(2,𝔽₃)	C₅×D₈
LCS	G ▷ #131⋊C₃ ▷ #41⋊C₃ ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

subgroup

G/H

C₂×C₅

C₂²×C₅

C₈

C₂×C₅×S₄

Fitting

C₅×#504

D₃

hypercenter

C₅×C₁₆

S₄

hypocenter

SL(2,𝔽₃)

C₅×D₈

LCS

G ▷ #131⋊C₃ ▷ #41⋊C₃ ▷ SL(2,𝔽₃)

UCS

C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

N	H ≅ G/N	type
1. C₅×#5407	C₂	semidirect
2. C₅×#504⋊C₃	C₂	semidirect
7. #73040	C₅	direct (N × H)
9. C₅×#504	D₃	semidirect
17. #5407	C₂×C₅	semidirect
18. #504⋊C₃	C₂×C₅	semidirect
47. #504	C₅×D₃	semidirect
113. C₅	#73040	direct (N × H)

H ≅ G/N

type

1. C₅×#5407

C₂

semidirect

2. C₅×#504⋊C₃

C₂

semidirect

7. #73040

C₅

direct (N × H)

9. C₅×#504

D₃

semidirect

17. #5407

C₂×C₅

semidirect

18. #504⋊C₃

C₂×C₅

semidirect

47. #504

C₅×D₃

semidirect

113. C₅

#73040

direct (N × H)

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

subgroup	index
C₅×#5407	2
C₅×#504⋊C₃	2
C₅×#2221	3
C₅×D₄₈	4
#73040	5

subgroup

index

C₅×#5407

C₅×#504⋊C₃

C₅×#2221

C₅×D₄₈

#73040

Subgroups — C₅×#73040 #14510764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#73040 #14510764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73040 #14510764