Group #49141299 — subgroups

Subgroups — D₉×D₁₀₁₅ #49141299

Order 36540.

120 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 37 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	D₉₁₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₇×D₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₁₀₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₀₁₅	—	3	1	no	maximal
5	C₅×C₇×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×D₂₀₃	—	5	1	no	maximal, Hall
7	D₃₀₄₅	—	3	1	no	—
8	C₅×D₃×C₇×C₂₉	—	3	1	no	—
9	C₃×D₁₀₁₅	D₃	1	1	yes	characteristic
10	D₉×D₁₄₅	—	7	1	no	maximal, Hall
11	C₂×D₁₀₁₅	—	9	1	no	Hall
12	D₁₈₂₇	—	5	1	no	—
13	C₇×D₉×C₂₉	D₅	1	1	yes	characteristic, complemented
14	C₉×D₂₀₃	—	5	1	no	—
15	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic
16	D₁₃₀₅	—	7	1	no	—
17	C₅×D₉×C₂₉	D₇	1	1	yes	characteristic, complemented
18	C₉×D₁₄₅	—	7	1	no	—
19	D₃×D₂₀₃	—	15	1	no	—
20	D₁₀₁₅	—	9	1	no	—
21	D₁₀₁₅	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	—	21	1	no	—
25	C₅×C₉×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
26	D₉×D₃₅	—	29	1	no	maximal, Hall
27	D₆₀₉	—	15	1	no	—
28	D₃×C₇×C₂₉	—	3	1	no	—
29	C₃×D₂₀₃	—	5	1	no	—
30	D₉×D₂₉	—	35	1	no	Hall
31	C₅×C₇×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
32	D₄₃₅	—	21	1	no	—
33	C₅×D₃×C₂₉	—	3	1	no	—
34	C₃×D₁₄₅	—	7	1	no	—
35	C₂×D₂₀₃	—	45	1	no	Hall
36	D₃₁₅	—	29	1	no	—
37	C₅×C₇×D₉	D₂₉	1	1	yes	characteristic, complemented
38	C₉×D₃₅	—	29	1	no	—
39	C₃×C₇×C₂₉	D₃×D₅	1	1	yes	characteristic
40	C₂×D₁₄₅	—	63	1	no	Hall
41	D₂₆₁	—	35	1	no	—
42	C₉×D₂₉	—	35	1	no	—
43	D₉×C₂₉	D₃₅	1	1	yes	characteristic, complemented
44	C₃×C₅×C₂₉	D₃×D₇	1	1	yes	characteristic
45	D₃×D₃₅	—	87	1	no	—
46	C₂×C₇×C₂₉	—	9	1	no	—
47	D₂₀₃	—	5	1	no	—
48	D₂₀₃	—	45	1	no	—
49	D₃×D₂₉	—	105	1	no	—
50	C₅×C₇×C₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
51	C₂×C₅×C₂₉	—	9	1	no	—
52	D₁₄₅	—	7	1	no	—
53	D₁₄₅	—	63	1	no	—
54	C₉×C₂₉	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
55	D₇×D₉	—	145	1	no	Hall
56	D₁₀₅	—	87	1	no	—
57	C₅×D₃×C₇	—	3	1	no	—
58	C₃×D₃₅	—	29	1	no	—
59	C₇×C₂₉	D₅×D₉	1	1	yes	characteristic, complemented, Hall
60	D₅×D₉	—	203	1	no	Hall
61	D₈₇	—	105	1	no	—
62	C₃×D₂₉	—	35	1	no	—
63	D₃×C₂₉	—	3	1	no	—
64	C₅×C₂₉	D₇×D₉	1	1	yes	characteristic, complemented, Hall
65	C₂×D₃₅	—	261	1	no	Hall
66	D₆₃	—	145	1	no	—
67	C₉×D₇	—	145	1	no	—
68	C₇×D₉	D₁₄₅	1	1	yes	characteristic, complemented
69	C₂×D₂₉	—	315	1	no	Hall
70	C₃×C₅×C₇	D₃×D₂₉	1	1	yes	characteristic
71	D₄₅	—	203	1	no	—
72	C₉×D₅	—	203	1	no	—
73	C₅×D₉	D₂₀₃	1	1	yes	characteristic, complemented
74	C₃×C₂₉	D₃×D₃₅	1	1	yes	characteristic
75	D₃×D₇	—	435	1	no	—
76	C₂×C₅×C₇	—	9	1	no	—
77	D₃₅	—	261	1	no	—
78	D₃₅	—	29	1	no	—
79	C₇×C₉	C₂×D₁₄₅	1	1	yes	characteristic, complemented, Hall
80	D₃×D₅	—	609	1	no	—
81	C₂×C₂₉	—	9	1	no	—
82	D₂₉	—	35	1	no	—
83	D₂₉	—	315	1	no	—
84	C₅×C₉	C₂×D₂₀₃	1	1	yes	characteristic, complemented, Hall
85	D₂₁	—	435	1	no	—
86	C₃×D₇	—	145	1	no	—
87	D₃×C₇	—	3	1	no	—
88	C₂×D₉	—	1015	1	no	Hall
89	C₅×C₇	D₉×D₂₉	1	1	yes	characteristic, complemented, Hall
90	D₁₅	—	609	1	no	—
91	C₃×D₅	—	203	1	no	—
92	C₅×D₃	—	3	1	no	—
93	C₂₉	D₉×D₃₅	1	1	yes	characteristic, complemented, Sylow
94	C₂×D₇	—	1305	1	no	Hall
95	C₃×C₇	D₃×D₁₄₅	1	1	yes	characteristic
96	C₂×D₅	—	1827	1	no	Hall
97	C₂×C₉	—	1015	1	no	—
98	D₉	—	1015	1	no	—
99	D₉	D₁₀₁₅	1	1	yes	characteristic, direct product factor
100	C₃×C₅	D₃×D₂₀₃	1	1	yes	characteristic
101	C₂×C₇	—	9	1	no	—
102	D₇	—	1305	1	no	—
103	D₇	—	145	1	no	—
104	C₂×D₃	—	3045	1	no	—
105	C₂×C₅	—	9	1	no	—
106	D₅	—	1827	1	no	—
107	D₅	—	203	1	no	—
108	C₉	C₂×D₁₀₁₅	1	1	yes	characteristic, complemented, Sylow
109	C₇	D₉×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	1015	1	no	—
111	D₃	—	3	1	no	—
112	D₃	—	3045	1	no	—
113	C₅	D₉×D₂₀₃	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	9135	1	no	Sylow
115	C₃	D₃×D₁₀₁₅	1	1	yes	characteristic
116	C₂	—	9	1	no	—
117	C₂	—	9135	1	no	—
118	C₂	—	1015	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

D₉₁₃₅

C₂

yes

maximal, characteristic, complemented

C₅×C₇×D₉×C₂₉

C₂

yes

maximal, characteristic, complemented

C₉×D₁₀₁₅

C₂

yes

maximal, characteristic, complemented

D₃×D₁₀₁₅

—

maximal

C₅×C₇×C₉×C₂₉

C₂²

yes

characteristic, complemented, Hall

D₉×D₂₀₃

—

maximal, Hall

D₃₀₄₅

—

C₅×D₃×C₇×C₂₉

—

C₃×D₁₀₁₅

D₃

yes

characteristic

D₉×D₁₄₅

—

maximal, Hall

C₂×D₁₀₁₅

—

Hall

D₁₈₂₇

—

C₇×D₉×C₂₉

D₅

yes

characteristic, complemented

C₉×D₂₀₃

—

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic

D₁₃₀₅

—

C₅×D₉×C₂₉

D₇

yes

characteristic, complemented

C₉×D₁₄₅

—

D₃×D₂₀₃

—

D₁₀₁₅

—

D₁₀₁₅

D₉

yes

characteristic, direct product factor

C₂×C₅×C₇×C₂₉

—

C₇×C₉×C₂₉

C₂×D₅

yes

characteristic, complemented, Hall

D₃×D₁₄₅

—

C₅×C₉×C₂₉

C₂×D₇

yes

characteristic, complemented, Hall

D₉×D₃₅

—

maximal, Hall

D₆₀₉

—

D₃×C₇×C₂₉

—

C₃×D₂₀₃

—

D₉×D₂₉

—

Hall

C₅×C₇×C₂₉

C₂×D₉

yes

characteristic, complemented, Hall

D₄₃₅

—

C₅×D₃×C₂₉

—

C₃×D₁₄₅

—

C₂×D₂₀₃

—

Hall

D₃₁₅

—

C₅×C₇×D₉

D₂₉

yes

characteristic, complemented

C₉×D₃₅

—

C₃×C₇×C₂₉

D₃×D₅

yes

characteristic

C₂×D₁₄₅

—

Hall

D₂₆₁

—

C₉×D₂₉

—

D₉×C₂₉

D₃₅

yes

characteristic, complemented

C₃×C₅×C₂₉

D₃×D₇

yes

characteristic

D₃×D₃₅

—

C₂×C₇×C₂₉

—

D₂₀₃

—

D₂₀₃

—

D₃×D₂₉

—

105

—

C₅×C₇×C₉

C₂×D₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

D₁₄₅

—

D₁₄₅

—

C₉×C₂₉

C₂×D₃₅

yes

characteristic, complemented, Hall

D₇×D₉

—

145

Hall

D₁₀₅

—

C₅×D₃×C₇

—

C₃×D₃₅

—

C₇×C₂₉

D₅×D₉

yes

characteristic, complemented, Hall

D₅×D₉

—

203

Hall

D₈₇

—

105

—

C₃×D₂₉

—

D₃×C₂₉

—

C₅×C₂₉

D₇×D₉

yes

characteristic, complemented, Hall

C₂×D₃₅

—

261

Hall

D₆₃

—

145

—

C₉×D₇

—

145

—

C₇×D₉

D₁₄₅

yes

characteristic, complemented

C₂×D₂₉

—

315

Hall

C₃×C₅×C₇

D₃×D₂₉

yes

characteristic

D₄₅

—

203

—

C₉×D₅

—

203

—

C₅×D₉

D₂₀₃

yes

characteristic, complemented

C₃×C₂₉

D₃×D₃₅

yes

characteristic

D₃×D₇

—

435

—

C₂×C₅×C₇

—

D₃₅

—

261

—

D₃₅

—

C₇×C₉

C₂×D₁₄₅

yes

characteristic, complemented, Hall

D₃×D₅

—

609

—

C₂×C₂₉

—

D₂₉

—

D₂₉

—

315

—

C₅×C₉

C₂×D₂₀₃

yes

characteristic, complemented, Hall

D₂₁

—

435

—

C₃×D₇

—

145

—

D₃×C₇

—

C₂×D₉

—

1015

Hall

C₅×C₇

D₉×D₂₉

yes

characteristic, complemented, Hall

D₁₅

—

609

—

C₃×D₅

—

203

—

C₅×D₃

—

C₂₉

D₉×D₃₅

yes

characteristic, complemented, Sylow

C₂×D₇

—

1305

Hall

C₃×C₇

D₃×D₁₄₅

yes

characteristic

C₂×D₅

—

1827

Hall

C₂×C₉

—

1015

—

D₉

—

1015

—

D₉

D₁₀₁₅

yes

characteristic, direct product factor

100

C₃×C₅

D₃×D₂₀₃

yes

characteristic

101

C₂×C₇

—

102

D₇

—

1305

—

103

D₇

—

145

—

104

C₂×D₃

—

3045

—

105

C₂×C₅

—

106

D₅

—

1827

—

107

D₅

—

203

—

108

C₉

C₂×D₁₀₁₅

yes

characteristic, complemented, Sylow

109

C₇

D₉×D₁₄₅

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

1015

—

111

D₃

—

112

D₃

—

3045

—

113

C₅

D₉×D₂₀₃

yes

characteristic, complemented, Sylow

114

C₂²

—

9135

Sylow

115

C₃

D₃×D₁₀₁₅

yes

characteristic

116

C₂

—

117

C₂

—

9135

—

118

C₂

—

1015

—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₇×C₉×C₂₉	C₂²
Frattini	C₃	D₃×D₁₀₁₅
socle	C₃×C₅×C₇×C₂₉	C₂×D₃
LCS	G ▷ C₅×C₇×C₉×C₂₉
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, Fitting, cosocle, hypocenter

C₅×C₇×C₉×C₂₉

C₂²

Frattini

C₃

D₃×D₁₀₁₅

socle

C₃×C₅×C₇×C₂₉

C₂×D₃

LCS

G ▷ C₅×C₇×C₉×C₂₉

UCS

C₁

N	H ≅ G/N	type
1. D₉₁₃₅	C₂	semidirect
2. C₅×C₇×D₉×C₂₉	C₂	semidirect
3. C₉×D₁₀₁₅	C₂	semidirect
5. C₅×C₇×C₉×C₂₉	C₂²	semidirect
13. C₇×D₉×C₂₉	D₅	semidirect
17. C₅×D₉×C₂₉	D₇	semidirect
21. D₁₀₁₅	D₉	direct (N × H)
23. C₇×C₉×C₂₉	C₂×D₅	semidirect
25. C₅×C₉×C₂₉	C₂×D₇	semidirect
31. C₅×C₇×C₂₉	C₂×D₉	semidirect
37. C₅×C₇×D₉	D₂₉	semidirect
43. D₉×C₂₉	D₃₅	semidirect
50. C₅×C₇×C₉	C₂×D₂₉	semidirect
54. C₉×C₂₉	C₂×D₃₅	semidirect
59. C₇×C₂₉	D₅×D₉	semidirect
64. C₅×C₂₉	D₇×D₉	semidirect
68. C₇×D₉	D₁₄₅	semidirect
73. C₅×D₉	D₂₀₃	semidirect
79. C₇×C₉	C₂×D₁₄₅	semidirect
84. C₅×C₉	C₂×D₂₀₃	semidirect
89. C₅×C₇	D₉×D₂₉	semidirect
93. C₂₉	D₉×D₃₅	semidirect
99. D₉	D₁₀₁₅	direct (N × H)
108. C₉	C₂×D₁₀₁₅	semidirect
109. C₇	D₉×D₁₄₅	semidirect
113. C₅	D₉×D₂₀₃	semidirect

H ≅ G/N

type

1. D₉₁₃₅

C₂

semidirect

2. C₅×C₇×D₉×C₂₉

C₂

semidirect

3. C₉×D₁₀₁₅

C₂

semidirect

5. C₅×C₇×C₉×C₂₉

C₂²

semidirect

13. C₇×D₉×C₂₉

D₅

semidirect

17. C₅×D₉×C₂₉

D₇

semidirect

21. D₁₀₁₅

D₉

direct (N × H)

23. C₇×C₉×C₂₉

C₂×D₅

semidirect

25. C₅×C₉×C₂₉

C₂×D₇

semidirect

31. C₅×C₇×C₂₉

C₂×D₉

semidirect

37. C₅×C₇×D₉

D₂₉

semidirect

43. D₉×C₂₉

D₃₅

semidirect

50. C₅×C₇×C₉

C₂×D₂₉

semidirect

54. C₉×C₂₉

C₂×D₃₅

semidirect

59. C₇×C₂₉

D₅×D₉

semidirect

64. C₅×C₂₉

D₇×D₉

semidirect

68. C₇×D₉

D₁₄₅

semidirect

73. C₅×D₉

D₂₀₃

semidirect

79. C₇×C₉

C₂×D₁₄₅

semidirect

84. C₅×C₉

C₂×D₂₀₃

semidirect

89. C₅×C₇

D₉×D₂₉

semidirect

93. C₂₉

D₉×D₃₅

semidirect

99. D₉

D₁₀₁₅

direct (N × H)

108. C₉

C₂×D₁₀₁₅

semidirect

109. C₇

D₉×D₁₄₅

semidirect

113. C₅

D₉×D₂₀₃

semidirect

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

subgroup	index
D₉₁₃₅	2
C₅×C₇×D₉×C₂₉	2
C₉×D₁₀₁₅	2
D₃×D₁₀₁₅	3
D₉×D₂₀₃	5
D₉×D₁₄₅	7
D₉×D₃₅	29

subgroup

index

D₉₁₃₅

C₅×C₇×D₉×C₂₉

C₉×D₁₀₁₅

D₃×D₁₀₁₅

D₉×D₂₀₃

D₉×D₁₄₅

D₉×D₃₅

Subgroups — D₉×D₁₀₁₅ #49141299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D9×D1015 #49141299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₁₀₁₅ #49141299