Group #49141291 — subgroups

Subgroups — C₇×D₉×D₁₄₅ #49141291

Order 36540.

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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	C₇×D₁₃₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇×D₁₄₅	—	3	1	no	maximal
5	C₅×C₇×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₉×D₂₉	—	5	1	no	maximal, Hall
7	C₇×D₄₃₅	—	3	1	no	—
8	C₅×D₃×C₇×C₂₉	—	3	1	no	—
9	C₃×C₇×D₁₄₅	D₃	1	1	yes	characteristic
10	D₉×D₁₄₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇×D₁₄₅	—	9	1	no	Hall
12	C₇×D₂₆₁	—	5	1	no	—
13	C₇×D₉×C₂₉	D₅	1	1	yes	characteristic, complemented
14	C₇×C₉×D₂₉	—	5	1	no	—
15	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic
16	D₁₃₀₅	C₂×C₇	1	1	yes	characteristic, complemented
17	C₅×D₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
18	C₉×D₁₄₅	C₂×C₇	1	1	yes	characteristic, complemented
19	D₃×C₇×D₂₉	—	15	1	no	—
20	C₇×D₁₄₅	—	9	1	no	—
21	C₇×D₁₄₅	D₉	1	1	yes	characteristic, direct product factor
22	C₂×C₅×C₇×C₂₉	—	9	1	no	—
23	C₇×C₉×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
24	D₃×D₁₄₅	—	3	1	no	—
25	C₅×C₉×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
26	C₇×D₅×D₉	—	29	1	no	maximal, Hall
27	C₇×D₈₇	—	15	1	no	—
28	D₃×C₇×C₂₉	—	3	1	no	—
29	C₃×C₇×D₂₉	—	5	1	no	—
30	D₉×D₂₉	—	5	1	no	Hall
31	C₅×C₇×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
32	D₄₃₅	—	3	1	no	—
33	C₅×D₃×C₂₉	—	3	1	no	—
34	C₃×D₁₄₅	D₃×C₇	1	1	yes	characteristic
35	C₂×C₇×D₂₉	—	45	1	no	Hall
36	C₇×D₄₅	—	29	1	no	—
37	C₅×C₇×D₉	D₂₉	1	1	yes	characteristic, complemented
38	C₇×C₉×D₅	—	29	1	no	—
39	C₃×C₇×C₂₉	D₃×D₅	1	1	yes	characteristic
40	C₂×D₁₄₅	—	9	1	no	Hall
41	D₂₆₁	—	5	1	no	—
42	C₉×D₂₉	—	5	1	no	—
43	D₉×C₂₉	C₇×D₅	1	1	yes	characteristic, complemented
44	C₃×C₅×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic
45	D₃×C₇×D₅	—	87	1	no	—
46	C₂×C₇×C₂₉	—	9	1	no	—
47	C₇×D₂₉	—	5	1	no	—
48	C₇×D₂₉	—	45	1	no	—
49	D₃×D₂₉	—	15	1	no	—
50	C₅×C₇×C₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
51	C₂×C₅×C₂₉	—	9	1	no	—
52	D₁₄₅	—	9	1	no	—
53	D₁₄₅	C₇×D₉	1	1	yes	characteristic, direct product factor
54	C₉×C₂₉	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Hall
55	C₂×C₇×D₉	—	145	1	no	Hall
56	C₇×D₁₅	—	87	1	no	—
57	C₅×D₃×C₇	—	3	1	no	—
58	C₃×C₇×D₅	—	29	1	no	—
59	C₇×C₂₉	D₅×D₉	1	1	yes	characteristic, complemented, Hall
60	D₅×D₉	—	29	1	no	Hall
61	D₈₇	—	15	1	no	—
62	C₃×D₂₉	—	5	1	no	—
63	D₃×C₂₉	—	3	1	no	—
64	C₅×C₂₉	C₂×C₇×D₉	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇×D₅	—	261	1	no	Hall
66	C₂×C₇×C₉	—	145	1	no	—
67	C₇×D₉	—	145	1	no	—
68	C₇×D₉	D₁₄₅	1	1	yes	characteristic, direct product factor
69	C₂×D₂₉	—	45	1	no	Hall
70	C₃×C₅×C₇	D₃×D₂₉	1	1	yes	characteristic
71	D₄₅	—	29	1	no	—
72	C₉×D₅	—	29	1	no	—
73	C₅×D₉	C₇×D₂₉	1	1	yes	characteristic, complemented
74	C₃×C₂₉	D₃×C₇×D₅	1	1	yes	characteristic
75	C₂×D₃×C₇	—	435	1	no	—
76	C₂×C₅×C₇	—	9	1	no	—
77	C₇×D₅	—	261	1	no	—
78	C₇×D₅	—	29	1	no	—
79	C₇×C₉	C₂×D₁₄₅	1	1	yes	characteristic, complemented, Hall
80	D₃×D₅	—	87	1	no	—
81	C₂×C₂₉	—	9	1	no	—
82	D₂₉	—	5	1	no	—
83	D₂₉	—	45	1	no	—
84	C₅×C₉	C₂×C₇×D₂₉	1	1	yes	characteristic, complemented, Hall
85	C₂×C₃×C₇	—	145	1	no	—
86	D₃×C₇	—	3	1	no	—
87	D₃×C₇	—	435	1	no	—
88	C₂×D₉	—	145	1	no	Hall
89	C₅×C₇	D₉×D₂₉	1	1	yes	characteristic, complemented, Hall
90	D₁₅	—	87	1	no	—
91	C₃×D₅	—	29	1	no	—
92	C₅×D₃	—	3	1	no	—
93	C₂₉	C₇×D₅×D₉	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₇	—	1305	1	no	Hall
95	C₃×C₇	D₃×D₁₄₅	1	1	yes	characteristic
96	C₂×D₅	—	261	1	no	Hall
97	C₂×C₉	—	145	1	no	—
98	D₉	—	145	1	no	—
99	D₉	C₇×D₁₄₅	1	1	yes	characteristic, direct product factor
100	C₃×C₅	D₃×C₇×D₂₉	1	1	yes	characteristic
101	C₂×C₇	—	9	1	no	—
102	C₂×C₇	—	1305	1	no	—
103	C₂×C₇	—	145	1	no	—
104	C₂×D₃	—	435	1	no	—
105	C₂×C₅	—	9	1	no	—
106	D₅	—	261	1	no	—
107	D₅	—	29	1	no	—
108	C₉	C₂×C₇×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
109	C₇	D₉×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
110	C₂×C₃	—	145	1	no	—
111	D₃	—	3	1	no	—
112	D₃	—	435	1	no	—
113	C₅	C₇×D₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	1305	1	no	Sylow
115	C₃	D₃×C₇×D₁₄₅	1	1	yes	characteristic
116	C₂	—	9	1	no	—
117	C₂	—	1305	1	no	—
118	C₂	—	145	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₇×D₁₃₀₅

C₂

yes

maximal, characteristic, complemented

C₅×C₇×D₉×C₂₉

C₂

yes

maximal, characteristic, complemented

C₇×C₉×D₁₄₅

C₂

yes

maximal, characteristic, complemented

D₃×C₇×D₁₄₅

—

maximal

C₅×C₇×C₉×C₂₉

C₂²

yes

characteristic, complemented, Hall

C₇×D₉×D₂₉

—

maximal, Hall

C₇×D₄₃₅

—

C₅×D₃×C₇×C₂₉

—

C₃×C₇×D₁₄₅

D₃

yes

characteristic

D₉×D₁₄₅

C₇

yes

maximal, characteristic, direct product factor, Hall

C₂×C₇×D₁₄₅

—

Hall

C₇×D₂₆₁

—

C₇×D₉×C₂₉

D₅

yes

characteristic, complemented

C₇×C₉×D₂₉

—

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic

D₁₃₀₅

C₂×C₇

yes

characteristic, complemented

C₅×D₉×C₂₉

C₂×C₇

yes

characteristic, complemented

C₉×D₁₄₅

C₂×C₇

yes

characteristic, complemented

D₃×C₇×D₂₉

—

C₇×D₁₄₅

—

C₇×D₁₄₅

D₉

yes

characteristic, direct product factor

C₂×C₅×C₇×C₂₉

—

C₇×C₉×C₂₉

C₂×D₅

yes

characteristic, complemented, Hall

D₃×D₁₄₅

—

C₅×C₉×C₂₉

C₂²×C₇

yes

characteristic, complemented, Hall

C₇×D₅×D₉

—

maximal, Hall

C₇×D₈₇

—

D₃×C₇×C₂₉

—

C₃×C₇×D₂₉

—

D₉×D₂₉

—

Hall

C₅×C₇×C₂₉

C₂×D₉

yes

characteristic, complemented, Hall

D₄₃₅

—

C₅×D₃×C₂₉

—

C₃×D₁₄₅

D₃×C₇

yes

characteristic

C₂×C₇×D₂₉

—

Hall

C₇×D₄₅

—

C₅×C₇×D₉

D₂₉

yes

characteristic, complemented

C₇×C₉×D₅

—

C₃×C₇×C₂₉

D₃×D₅

yes

characteristic

C₂×D₁₄₅

—

Hall

D₂₆₁

—

C₉×D₂₉

—

D₉×C₂₉

C₇×D₅

yes

characteristic, complemented

C₃×C₅×C₂₉

C₂×D₃×C₇

yes

characteristic

D₃×C₇×D₅

—

C₂×C₇×C₂₉

—

C₇×D₂₉

—

C₇×D₂₉

—

D₃×D₂₉

—

C₅×C₇×C₉

C₂×D₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

D₁₄₅

—

D₁₄₅

C₇×D₉

yes

characteristic, direct product factor

C₉×C₂₉

C₂×C₇×D₅

yes

characteristic, complemented, Hall

C₂×C₇×D₉

—

145

Hall

C₇×D₁₅

—

C₅×D₃×C₇

—

C₃×C₇×D₅

—

C₇×C₂₉

D₅×D₉

yes

characteristic, complemented, Hall

D₅×D₉

—

Hall

D₈₇

—

C₃×D₂₉

—

D₃×C₂₉

—

C₅×C₂₉

C₂×C₇×D₉

yes

characteristic, complemented, Hall

C₂×C₇×D₅

—

261

Hall

C₂×C₇×C₉

—

145

—

C₇×D₉

—

145

—

C₇×D₉

D₁₄₅

yes

characteristic, direct product factor

C₂×D₂₉

—

Hall

C₃×C₅×C₇

D₃×D₂₉

yes

characteristic

D₄₅

—

C₉×D₅

—

C₅×D₉

C₇×D₂₉

yes

characteristic, complemented

C₃×C₂₉

D₃×C₇×D₅

yes

characteristic

C₂×D₃×C₇

—

435

—

C₂×C₅×C₇

—

C₇×D₅

—

261

—

C₇×D₅

—

C₇×C₉

C₂×D₁₄₅

yes

characteristic, complemented, Hall

D₃×D₅

—

C₂×C₂₉

—

D₂₉

—

D₂₉

—

C₅×C₉

C₂×C₇×D₂₉

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

145

—

D₃×C₇

—

D₃×C₇

—

435

—

C₂×D₉

—

145

Hall

C₅×C₇

D₉×D₂₉

yes

characteristic, complemented, Hall

D₁₅

—

C₃×D₅

—

C₅×D₃

—

C₂₉

C₇×D₅×D₉

yes

characteristic, complemented, Sylow

C₂²×C₇

—

1305

Hall

C₃×C₇

D₃×D₁₄₅

yes

characteristic

C₂×D₅

—

261

Hall

C₂×C₉

—

145

—

D₉

—

145

—

D₉

C₇×D₁₄₅

yes

characteristic, direct product factor

100

C₃×C₅

D₃×C₇×D₂₉

yes

characteristic

101

C₂×C₇

—

102

C₂×C₇

—

1305

—

103

C₂×C₇

—

145

—

104

C₂×D₃

—

435

—

105

C₂×C₅

—

106

D₅

—

261

—

107

D₅

—

108

C₉

C₂×C₇×D₁₄₅

yes

characteristic, complemented, Sylow

109

C₇

D₉×D₁₄₅

yes

characteristic, direct product factor, Sylow

110

C₂×C₃

—

145

—

111

D₃

—

112

D₃

—

435

—

113

C₅

C₇×D₉×D₂₉

yes

characteristic, complemented, Sylow

114

C₂²

—

1305

Sylow

115

C₃

D₃×C₇×D₁₄₅

yes

characteristic

116

C₂

—

117

C₂

—

1305

—

118

C₂

—

145

—

	subgroup	G/H
center, hypercenter	C₇	D₉×D₁₄₅
commutator, cosocle, hypocenter	C₅×C₉×C₂₉	C₂²×C₇
Frattini	C₃	D₃×C₇×D₁₄₅
Fitting	C₅×C₇×C₉×C₂₉	C₂²
socle	C₃×C₅×C₇×C₂₉	C₂×D₃
LCS	G ▷ C₅×C₉×C₂₉
UCS	C₁ ◁ C₇

subgroup

G/H

center, hypercenter

C₇

D₉×D₁₄₅

commutator, cosocle, hypocenter

C₅×C₉×C₂₉

C₂²×C₇

Frattini

C₃

D₃×C₇×D₁₄₅

Fitting

C₅×C₇×C₉×C₂₉

C₂²

socle

C₃×C₅×C₇×C₂₉

C₂×D₃

LCS

G ▷ C₅×C₉×C₂₉

UCS

C₁ ◁ C₇

N	H ≅ G/N	type
1. C₇×D₁₃₀₅	C₂	semidirect
2. C₅×C₇×D₉×C₂₉	C₂	semidirect
3. C₇×C₉×D₁₄₅	C₂	semidirect
5. C₅×C₇×C₉×C₂₉	C₂²	semidirect
10. D₉×D₁₄₅	C₇	direct (N × H)
13. C₇×D₉×C₂₉	D₅	semidirect
16. D₁₃₀₅	C₂×C₇	semidirect
17. C₅×D₉×C₂₉	C₂×C₇	semidirect
18. C₉×D₁₄₅	C₂×C₇	semidirect
21. C₇×D₁₄₅	D₉	direct (N × H)
23. C₇×C₉×C₂₉	C₂×D₅	semidirect
25. C₅×C₉×C₂₉	C₂²×C₇	semidirect
31. C₅×C₇×C₂₉	C₂×D₉	semidirect
37. C₅×C₇×D₉	D₂₉	semidirect
43. D₉×C₂₉	C₇×D₅	semidirect
50. C₅×C₇×C₉	C₂×D₂₉	semidirect
53. D₁₄₅	C₇×D₉	direct (N × H)
54. C₉×C₂₉	C₂×C₇×D₅	semidirect
59. C₇×C₂₉	D₅×D₉	semidirect
64. C₅×C₂₉	C₂×C₇×D₉	semidirect
68. C₇×D₉	D₁₄₅	direct (N × H)
73. C₅×D₉	C₇×D₂₉	semidirect
79. C₇×C₉	C₂×D₁₄₅	semidirect
84. C₅×C₉	C₂×C₇×D₂₉	semidirect
89. C₅×C₇	D₉×D₂₉	semidirect
93. C₂₉	C₇×D₅×D₉	semidirect
99. D₉	C₇×D₁₄₅	direct (N × H)
108. C₉	C₂×C₇×D₁₄₅	semidirect
109. C₇	D₉×D₁₄₅	direct (N × H)
113. C₅	C₇×D₉×D₂₉	semidirect

H ≅ G/N

type

1. C₇×D₁₃₀₅

C₂

semidirect

2. C₅×C₇×D₉×C₂₉

C₂

semidirect

3. C₇×C₉×D₁₄₅

C₂

semidirect

5. C₅×C₇×C₉×C₂₉

C₂²

semidirect

10. D₉×D₁₄₅

C₇

direct (N × H)

13. C₇×D₉×C₂₉

D₅

semidirect

16. D₁₃₀₅

C₂×C₇

semidirect

17. C₅×D₉×C₂₉

C₂×C₇

semidirect

18. C₉×D₁₄₅

C₂×C₇

semidirect

21. C₇×D₁₄₅

D₉

direct (N × H)

23. C₇×C₉×C₂₉

C₂×D₅

semidirect

25. C₅×C₉×C₂₉

C₂²×C₇

semidirect

31. C₅×C₇×C₂₉

C₂×D₉

semidirect

37. C₅×C₇×D₉

D₂₉

semidirect

43. D₉×C₂₉

C₇×D₅

semidirect

50. C₅×C₇×C₉

C₂×D₂₉

semidirect

53. D₁₄₅

C₇×D₉

direct (N × H)

54. C₉×C₂₉

C₂×C₇×D₅

semidirect

59. C₇×C₂₉

D₅×D₉

semidirect

64. C₅×C₂₉

C₂×C₇×D₉

semidirect

68. C₇×D₉

D₁₄₅

direct (N × H)

73. C₅×D₉

C₇×D₂₉

semidirect

79. C₇×C₉

C₂×D₁₄₅

semidirect

84. C₅×C₉

C₂×C₇×D₂₉

semidirect

89. C₅×C₇

D₉×D₂₉

semidirect

93. C₂₉

C₇×D₅×D₉

semidirect

99. D₉

C₇×D₁₄₅

direct (N × H)

108. C₉

C₂×C₇×D₁₄₅

semidirect

109. C₇

D₉×D₁₄₅

direct (N × H)

113. C₅

C₇×D₉×D₂₉

semidirect

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

subgroup	index
C₇×D₁₃₀₅	2
C₅×C₇×D₉×C₂₉	2
C₇×C₉×D₁₄₅	2
D₃×C₇×D₁₄₅	3
C₇×D₉×D₂₉	5
D₉×D₁₄₅	7
C₇×D₅×D₉	29

subgroup

index

C₇×D₁₃₀₅

C₅×C₇×D₉×C₂₉

C₇×C₉×D₁₄₅

D₃×C₇×D₁₄₅

C₇×D₉×D₂₉

D₉×D₁₄₅

C₇×D₅×D₉

Subgroups — C₇×D₉×D₁₄₅ #49141291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C7×D9×D145 #49141291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₉×D₁₄₅ #49141291