Group #49141293 — subgroups

Subgroups — D₅×C₂₉×D₆₃ #49141293

Order 36540.

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

normal subgroups only

This group has 120 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	C₂₉×D₃₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₂₉×D₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₂₉×D₂₁	—	3	1	no	maximal
5	C₅×C₇×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₂₉×D₆₃	—	5	1	no	maximal, Hall
7	C₂₉×D₁₀₅	—	3	1	no	—
8	C₅×C₂₉×D₂₁	—	3	1	no	—
9	C₃×C₇×D₅×C₂₉	D₃	1	1	yes	characteristic
10	D₅×D₉×C₂₉	—	7	1	no	maximal, Hall
11	D₅×D₇×C₂₉	—	9	1	no	Hall
12	C₂₉×D₆₃	—	5	1	no	—
13	C₂₉×D₆₃	D₅	1	1	yes	characteristic, direct product factor
14	C₂×C₇×C₉×C₂₉	—	5	1	no	—
15	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic
16	C₂₉×D₄₅	—	7	1	no	—
17	C₅×D₉×C₂₉	—	7	1	no	—
18	C₉×D₅×C₂₉	D₇	1	1	yes	characteristic, complemented
19	C₂×C₂₉×D₂₁	—	15	1	no	—
20	C₂₉×D₃₅	—	9	1	no	—
21	C₇×D₅×C₂₉	D₉	1	1	yes	characteristic, complemented
22	C₅×D₇×C₂₉	—	9	1	no	—
23	C₇×C₉×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
24	D₃×D₅×C₂₉	—	21	1	no	—
25	C₅×C₉×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
26	D₅×D₆₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₃×C₇×C₂₉	—	5	1	no	—
28	C₂₉×D₂₁	—	3	1	no	—
29	C₂₉×D₂₁	—	15	1	no	—
30	C₂×D₉×C₂₉	—	35	1	no	Hall
31	C₅×C₇×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
32	C₂₉×D₁₅	—	21	1	no	—
33	C₅×D₃×C₂₉	—	21	1	no	—
34	C₃×D₅×C₂₉	D₂₁	1	1	yes	characteristic
35	C₂×D₇×C₂₉	—	45	1	no	Hall
36	D₃₁₅	C₂×C₂₉	1	1	yes	characteristic, complemented
37	C₅×D₆₃	C₂×C₂₉	1	1	yes	characteristic, complemented
38	C₇×C₉×D₅	C₂×C₂₉	1	1	yes	characteristic, complemented
39	C₃×C₇×C₂₉	D₃×D₅	1	1	yes	characteristic
40	C₂×D₅×C₂₉	—	63	1	no	Hall
41	C₂×C₉×C₂₉	—	5	1	no	—
42	D₉×C₂₉	—	7	1	no	—
43	D₉×C₂₉	—	35	1	no	—
44	C₃×C₅×C₂₉	C₂×D₂₁	1	1	yes	characteristic
45	D₅×D₂₁	—	3	1	no	—
46	C₂×C₇×C₂₉	—	5	1	no	—
47	D₇×C₂₉	—	9	1	no	—
48	D₇×C₂₉	—	45	1	no	—
49	C₂×D₃×C₂₉	—	105	1	no	—
50	C₅×C₇×C₉	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
51	C₂×C₅×C₂₉	—	63	1	no	—
52	D₅×C₂₉	—	63	1	no	—
53	D₅×C₂₉	D₆₃	1	1	yes	characteristic, direct product factor
54	C₉×C₂₉	D₅×D₇	1	1	yes	characteristic, complemented, Hall
55	C₂×D₆₃	—	5	1	no	Hall
56	D₁₀₅	—	3	1	no	—
57	C₅×D₂₁	—	3	1	no	—
58	C₃×C₇×D₅	D₃×C₂₉	1	1	yes	characteristic
59	C₇×C₂₉	D₅×D₉	1	1	yes	characteristic, complemented, Hall
60	D₅×D₉	—	7	1	no	Hall
61	C₂×C₃×C₂₉	—	5	1	no	—
62	D₃×C₂₉	—	21	1	no	—
63	D₃×C₂₉	—	105	1	no	—
64	C₅×C₂₉	C₂×D₆₃	1	1	yes	characteristic, complemented, Hall
65	D₅×D₇	—	9	1	no	Hall
66	C₂×C₇×C₉	—	5	1	no	—
67	D₆₃	—	5	1	no	—
68	D₆₃	D₅×C₂₉	1	1	yes	characteristic, direct product factor
69	C₂²×C₂₉	—	315	1	no	Hall
70	C₃×C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic
71	D₄₅	—	7	1	no	—
72	C₉×D₅	D₇×C₂₉	1	1	yes	characteristic, complemented
73	C₅×D₉	—	7	1	no	—
74	C₃×C₂₉	D₅×D₂₁	1	1	yes	characteristic
75	C₂×D₂₁	—	15	1	no	—
76	D₃₅	—	9	1	no	—
77	C₅×D₇	—	9	1	no	—
78	C₇×D₅	D₉×C₂₉	1	1	yes	characteristic, complemented
79	C₇×C₉	C₂×D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
80	D₃×D₅	—	21	1	no	—
81	C₂×C₂₉	—	5	1	no	—
82	C₂×C₂₉	—	315	1	no	—
83	C₂×C₂₉	—	63	1	no	—
84	C₅×C₉	C₂×D₇×C₂₉	1	1	yes	characteristic, complemented, Hall
85	C₂×C₃×C₇	—	5	1	no	—
86	D₂₁	—	3	1	no	—
87	D₂₁	—	15	1	no	—
88	C₂×D₉	—	35	1	no	Hall
89	C₅×C₇	C₂×D₉×C₂₉	1	1	yes	characteristic, complemented, Hall
90	D₁₅	—	21	1	no	—
91	C₃×D₅	C₂₉×D₂₁	1	1	yes	characteristic
92	C₅×D₃	—	21	1	no	—
93	C₂₉	D₅×D₆₃	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×D₇	—	45	1	no	Hall
95	C₃×C₇	D₃×D₅×C₂₉	1	1	yes	characteristic
96	C₂×D₅	—	63	1	no	Hall
97	C₂×C₉	—	5	1	no	—
98	D₉	—	7	1	no	—
99	D₉	—	35	1	no	—
100	C₃×C₅	C₂×C₂₉×D₂₁	1	1	yes	characteristic
101	C₂×C₇	—	5	1	no	—
102	D₇	—	9	1	no	—
103	D₇	—	45	1	no	—
104	C₂×D₃	—	105	1	no	—
105	C₂×C₅	—	63	1	no	—
106	D₅	—	63	1	no	—
107	D₅	C₂₉×D₆₃	1	1	yes	characteristic, direct product factor
108	C₉	D₅×D₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
109	C₇	D₅×D₉×C₂₉	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	5	1	no	—
111	D₃	—	21	1	no	—
112	D₃	—	105	1	no	—
113	C₅	C₂×C₂₉×D₆₃	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	315	1	no	Sylow
115	C₃	D₅×C₂₉×D₂₁	1	1	yes	characteristic
116	C₂	—	5	1	no	—
117	C₂	—	315	1	no	—
118	C₂	—	63	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×D₃₁₅

C₂

yes

maximal, characteristic, complemented

C₅×C₂₉×D₆₃

C₂

yes

maximal, characteristic, complemented

C₇×C₉×D₅×C₂₉

C₂

yes

maximal, characteristic, complemented

D₅×C₂₉×D₂₁

—

maximal

C₅×C₇×C₉×C₂₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₂₉×D₆₃

—

maximal, Hall

C₂₉×D₁₀₅

—

C₅×C₂₉×D₂₁

—

C₃×C₇×D₅×C₂₉

D₃

yes

characteristic

D₅×D₉×C₂₉

—

maximal, Hall

D₅×D₇×C₂₉

—

Hall

C₂₉×D₆₃

—

C₂₉×D₆₃

D₅

yes

characteristic, direct product factor

C₂×C₇×C₉×C₂₉

—

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic

C₂₉×D₄₅

—

C₅×D₉×C₂₉

—

C₉×D₅×C₂₉

D₇

yes

characteristic, complemented

C₂×C₂₉×D₂₁

—

C₂₉×D₃₅

—

C₇×D₅×C₂₉

D₉

yes

characteristic, complemented

C₅×D₇×C₂₉

—

C₇×C₉×C₂₉

C₂×D₅

yes

characteristic, complemented, Hall

D₃×D₅×C₂₉

—

C₅×C₉×C₂₉

C₂×D₇

yes

characteristic, complemented, Hall

D₅×D₆₃

C₂₉

yes

maximal, characteristic, direct product factor, Hall

C₂×C₃×C₇×C₂₉

—

C₂₉×D₂₁

—

C₂₉×D₂₁

—

C₂×D₉×C₂₉

—

Hall

C₅×C₇×C₂₉

C₂×D₉

yes

characteristic, complemented, Hall

C₂₉×D₁₅

—

C₅×D₃×C₂₉

—

C₃×D₅×C₂₉

D₂₁

yes

characteristic

C₂×D₇×C₂₉

—

Hall

D₃₁₅

C₂×C₂₉

yes

characteristic, complemented

C₅×D₆₃

C₂×C₂₉

yes

characteristic, complemented

C₇×C₉×D₅

C₂×C₂₉

yes

characteristic, complemented

C₃×C₇×C₂₉

D₃×D₅

yes

characteristic

C₂×D₅×C₂₉

—

Hall

C₂×C₉×C₂₉

—

D₉×C₂₉

—

D₉×C₂₉

—

C₃×C₅×C₂₉

C₂×D₂₁

yes

characteristic

D₅×D₂₁

—

C₂×C₇×C₂₉

—

D₇×C₂₉

—

D₇×C₂₉

—

C₂×D₃×C₂₉

—

105

—

C₅×C₇×C₉

C₂²×C₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

D₅×C₂₉

—

D₅×C₂₉

D₆₃

yes

characteristic, direct product factor

C₉×C₂₉

D₅×D₇

yes

characteristic, complemented, Hall

C₂×D₆₃

—

Hall

D₁₀₅

—

C₅×D₂₁

—

C₃×C₇×D₅

D₃×C₂₉

yes

characteristic

C₇×C₂₉

D₅×D₉

yes

characteristic, complemented, Hall

D₅×D₉

—

Hall

C₂×C₃×C₂₉

—

D₃×C₂₉

—

D₃×C₂₉

—

105

—

C₅×C₂₉

C₂×D₆₃

yes

characteristic, complemented, Hall

D₅×D₇

—

Hall

C₂×C₇×C₉

—

D₆₃

—

D₆₃

D₅×C₂₉

yes

characteristic, direct product factor

C₂²×C₂₉

—

315

Hall

C₃×C₅×C₇

C₂×D₃×C₂₉

yes

characteristic

D₄₅

—

C₉×D₅

D₇×C₂₉

yes

characteristic, complemented

C₅×D₉

—

C₃×C₂₉

D₅×D₂₁

yes

characteristic

C₂×D₂₁

—

D₃₅

—

C₅×D₇

—

C₇×D₅

D₉×C₂₉

yes

characteristic, complemented

C₇×C₉

C₂×D₅×C₂₉

yes

characteristic, complemented, Hall

D₃×D₅

—

C₂×C₂₉

—

C₂×C₂₉

—

315

—

C₂×C₂₉

—

C₅×C₉

C₂×D₇×C₂₉

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

D₂₁

—

D₂₁

—

C₂×D₉

—

Hall

C₅×C₇

C₂×D₉×C₂₉

yes

characteristic, complemented, Hall

D₁₅

—

C₃×D₅

C₂₉×D₂₁

yes

characteristic

C₅×D₃

—

C₂₉

D₅×D₆₃

yes

characteristic, direct product factor, Sylow

C₂×D₇

—

Hall

C₃×C₇

D₃×D₅×C₂₉

yes

characteristic

C₂×D₅

—

Hall

C₂×C₉

—

D₉

—

D₉

—

100

C₃×C₅

C₂×C₂₉×D₂₁

yes

characteristic

101

C₂×C₇

—

102

D₇

—

103

D₇

—

104

C₂×D₃

—

105

—

105

C₂×C₅

—

106

D₅

—

107

D₅

C₂₉×D₆₃

yes

characteristic, direct product factor

108

C₉

D₅×D₇×C₂₉

yes

characteristic, complemented, Sylow

109

C₇

D₅×D₉×C₂₉

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

112

D₃

—

105

—

113

C₅

C₂×C₂₉×D₆₃

yes

characteristic, complemented, Sylow

114

C₂²

—

315

Sylow

115

C₃

D₅×C₂₉×D₂₁

yes

characteristic

116

C₂

—

117

C₂

—

315

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₂₉	D₅×D₆₃
commutator, cosocle, hypocenter	C₅×C₇×C₉	C₂²×C₂₉
Frattini	C₃	D₅×C₂₉×D₂₁
Fitting	C₅×C₇×C₉×C₂₉	C₂²
socle	C₃×C₅×C₇×C₂₉	C₂×D₃
LCS	G ▷ C₅×C₇×C₉
UCS	C₁ ◁ C₂₉

subgroup

G/H

center, hypercenter

C₂₉

D₅×D₆₃

commutator, cosocle, hypocenter

C₅×C₇×C₉

C₂²×C₂₉

Frattini

C₃

D₅×C₂₉×D₂₁

Fitting

C₅×C₇×C₉×C₂₉

C₂²

socle

C₃×C₅×C₇×C₂₉

C₂×D₃

LCS

G ▷ C₅×C₇×C₉

UCS

C₁ ◁ C₂₉

N	H ≅ G/N	type
1. C₂₉×D₃₁₅	C₂	semidirect
2. C₅×C₂₉×D₆₃	C₂	semidirect
3. C₇×C₉×D₅×C₂₉	C₂	semidirect
5. C₅×C₇×C₉×C₂₉	C₂²	semidirect
13. C₂₉×D₆₃	D₅	direct (N × H)
18. C₉×D₅×C₂₉	D₇	semidirect
21. C₇×D₅×C₂₉	D₉	semidirect
23. C₇×C₉×C₂₉	C₂×D₅	semidirect
25. C₅×C₉×C₂₉	C₂×D₇	semidirect
26. D₅×D₆₃	C₂₉	direct (N × H)
31. C₅×C₇×C₂₉	C₂×D₉	semidirect
36. D₃₁₅	C₂×C₂₉	semidirect
37. C₅×D₆₃	C₂×C₂₉	semidirect
38. C₇×C₉×D₅	C₂×C₂₉	semidirect
50. C₅×C₇×C₉	C₂²×C₂₉	semidirect
53. D₅×C₂₉	D₆₃	direct (N × H)
54. C₉×C₂₉	D₅×D₇	semidirect
59. C₇×C₂₉	D₅×D₉	semidirect
64. C₅×C₂₉	C₂×D₆₃	semidirect
68. D₆₃	D₅×C₂₉	direct (N × H)
72. C₉×D₅	D₇×C₂₉	semidirect
78. C₇×D₅	D₉×C₂₉	semidirect
79. C₇×C₉	C₂×D₅×C₂₉	semidirect
84. C₅×C₉	C₂×D₇×C₂₉	semidirect
89. C₅×C₇	C₂×D₉×C₂₉	semidirect
93. C₂₉	D₅×D₆₃	direct (N × H)
107. D₅	C₂₉×D₆₃	direct (N × H)
108. C₉	D₅×D₇×C₂₉	semidirect
109. C₇	D₅×D₉×C₂₉	semidirect
113. C₅	C₂×C₂₉×D₆₃	semidirect

H ≅ G/N

type

1. C₂₉×D₃₁₅

C₂

semidirect

2. C₅×C₂₉×D₆₃

C₂

semidirect

3. C₇×C₉×D₅×C₂₉

C₂

semidirect

5. C₅×C₇×C₉×C₂₉

C₂²

semidirect

13. C₂₉×D₆₃

D₅

direct (N × H)

18. C₉×D₅×C₂₉

D₇

semidirect

21. C₇×D₅×C₂₉

D₉

semidirect

23. C₇×C₉×C₂₉

C₂×D₅

semidirect

25. C₅×C₉×C₂₉

C₂×D₇

semidirect

26. D₅×D₆₃

C₂₉

direct (N × H)

31. C₅×C₇×C₂₉

C₂×D₉

semidirect

36. D₃₁₅

C₂×C₂₉

semidirect

37. C₅×D₆₃

C₂×C₂₉

semidirect

38. C₇×C₉×D₅

C₂×C₂₉

semidirect

50. C₅×C₇×C₉

C₂²×C₂₉

semidirect

53. D₅×C₂₉

D₆₃

direct (N × H)

54. C₉×C₂₉

D₅×D₇

semidirect

59. C₇×C₂₉

D₅×D₉

semidirect

64. C₅×C₂₉

C₂×D₆₃

semidirect

68. D₆₃

D₅×C₂₉

direct (N × H)

72. C₉×D₅

D₇×C₂₉

semidirect

78. C₇×D₅

D₉×C₂₉

semidirect

79. C₇×C₉

C₂×D₅×C₂₉

semidirect

84. C₅×C₉

C₂×D₇×C₂₉

semidirect

89. C₅×C₇

C₂×D₉×C₂₉

semidirect

93. C₂₉

D₅×D₆₃

direct (N × H)

107. D₅

C₂₉×D₆₃

direct (N × H)

108. C₉

D₅×D₇×C₂₉

semidirect

109. C₇

D₅×D₉×C₂₉

semidirect

113. C₅

C₂×C₂₉×D₆₃

semidirect

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

subgroup	index
C₂₉×D₃₁₅	2
C₅×C₂₉×D₆₃	2
C₇×C₉×D₅×C₂₉	2
D₅×C₂₉×D₂₁	3
C₂×C₂₉×D₆₃	5
D₅×D₉×C₂₉	7
D₅×D₆₃	29

subgroup

index

C₂₉×D₃₁₅

C₅×C₂₉×D₆₃

C₇×C₉×D₅×C₂₉

D₅×C₂₉×D₂₁

C₂×C₂₉×D₆₃

D₅×D₉×C₂₉

D₅×D₆₃

Subgroups — D₅×C₂₉×D₆₃ #49141293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D5×C29×D63 #49141293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₂₉×D₆₃ #49141293