Group #49141302 — subgroups

Subgroups — D₃₅⋊D₂₆₁ #49141302

Order 36540.

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

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

subgroup

G/H

class size

multiplicity

normal?

properties

C₇×D₁₃₀₅

C₂

yes

maximal, characteristic, complemented

C₅×D₁₈₂₇

C₂

yes

maximal, characteristic, complemented

C₉×C₂₉×D₃₅

C₂

yes

maximal, characteristic, complemented

D₃₅⋊D₈₇

—

maximal

C₅×C₇×C₉×C₂₉

C₂²

yes

characteristic, complemented, Hall

D₇×D₂₆₁

—

maximal, Hall

C₇×D₄₃₅

—

C₅×D₆₀₉

—

C₃×C₂₉×D₃₅

D₃

yes

characteristic

D₅×D₂₆₁

—

maximal, Hall

D₃₅⋊D₂₉

—

Hall

D₁₈₂₇

D₅

yes

characteristic, complemented

C₇×D₂₆₁

—

C₉×D₇×C₂₉

—

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic

D₁₃₀₅

D₇

yes

characteristic, complemented

C₅×D₂₆₁

—

C₉×D₅×C₂₉

—

D₇×D₈₇

—

C₂₉×D₃₅

D₉

yes

characteristic, complemented

C₇×D₁₄₅

—

C₅×D₂₀₃

—

C₇×C₉×C₂₉

C₂×D₅

yes

characteristic, complemented, Hall

D₅×D₈₇

—

C₅×C₉×C₂₉

C₂×D₇

yes

characteristic, complemented, Hall

D₃₅⋊D₉

—

maximal, Hall

D₆₀₉

—

C₇×D₈₇

—

C₃×D₇×C₂₉

—

C₂×D₂₆₁

—

Hall

C₅×C₇×C₂₉

C₂×D₉

yes

characteristic, complemented, Hall

D₄₃₅

—

C₅×D₈₇

—

C₃×D₅×C₂₉

—

D₇×D₂₉

—

Hall

C₇×D₄₅

—

C₅×D₆₃

—

C₉×D₃₅

D₂₉

yes

characteristic, complemented

C₃×C₇×C₂₉

D₃×D₅

yes

characteristic

D₅×D₂₉

—

Hall

C₂×C₉×C₂₉

—

D₂₆₁

—

D₂₆₁

—

C₃×C₅×C₂₉

D₃×D₇

yes

characteristic

D₁₅⋊D₇

—

D₂₀₃

—

C₇×D₂₉

—

D₇×C₂₉

—

C₂×D₈₇

—

105

—

C₅×C₇×C₉

C₂×D₂₉

yes

characteristic, complemented, Hall

D₁₄₅

—

C₅×D₂₉

—

D₅×C₂₉

—

C₉×C₂₉

D₅×D₇

yes

characteristic, complemented, Hall

D₇×D₉

—

145

Hall

C₇×D₁₅

—

C₅×D₂₁

—

C₃×D₃₅

D₈₇

yes

characteristic

C₇×C₂₉

D₅×D₉

yes

characteristic, complemented, Hall

D₅×D₉

—

203

Hall

C₂×C₃×C₂₉

—

D₈₇

—

D₈₇

—

C₅×C₂₉

D₇×D₉

yes

characteristic, complemented, Hall

D₅×D₇

—

261

Hall

D₆₃

—

C₉×D₇

—

C₇×D₉

—

145

—

C₂×D₂₉

—

315

Hall

C₃×C₅×C₇

C₂×D₈₇

yes

characteristic

D₄₅

—

C₉×D₅

—

C₅×D₉

—

203

—

C₃×C₂₉

D₁₅⋊D₇

yes

characteristic

D₃×D₇

—

435

—

D₃₅

D₂₆₁

yes

characteristic, complemented

C₅×D₇

—

261

—

C₇×D₅

—

261

—

C₇×C₉

D₅×D₂₉

yes

characteristic, complemented, Hall

D₃×D₅

—

609

—

C₂×C₂₉

—

D₂₉

—

D₂₉

—

C₅×C₉

D₇×D₂₉

yes

characteristic, complemented, Hall

D₂₁

—

C₃×D₇

—

D₃×C₇

—

435

—

C₂×D₉

—

1015

Hall

C₅×C₇

C₂×D₂₆₁

yes

characteristic, complemented, Hall

D₁₅

—

C₃×D₅

—

C₅×D₃

—

609

—

C₂₉

D₃₅⋊D₉

yes

characteristic, complemented, Sylow

C₂×D₇

—

1305

Hall

C₃×C₇

D₅×D₈₇

yes

characteristic

C₂×D₅

—

1827

Hall

C₂×C₉

—

D₉

—

145

—

D₉

—

203

—

100

C₃×C₅

D₇×D₈₇

yes

characteristic

101

C₂×C₇

—

1305

—

102

D₇

—

103

D₇

—

261

—

104

C₂×D₃

—

3045

—

105

C₂×C₅

—

1827

—

106

D₅

—

261

—

107

D₅

—

108

C₉

D₃₅⋊D₂₉

yes

characteristic, complemented, Sylow

109

C₇

D₅×D₂₆₁

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

609

—

112

D₃

—

435

—

113

C₅

D₇×D₂₆₁

yes

characteristic, complemented, Sylow

114

C₂²

—

9135

Sylow

115

C₃

D₃₅⋊D₈₇

yes

characteristic

116

C₂

—

1305

—

117

C₂

—

118

C₂

—

1827

—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₇×C₉×C₂₉	C₂²
Frattini	C₃	D₃₅⋊D₈₇
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

D₃₅⋊D₈₇

socle

C₃×C₅×C₇×C₂₉

C₂×D₃

LCS

G ▷ C₅×C₇×C₉×C₂₉

UCS

C₁

N	H ≅ G/N	type
1. C₇×D₁₃₀₅	C₂	semidirect
2. C₅×D₁₈₂₇	C₂	semidirect
3. C₉×C₂₉×D₃₅	C₂	semidirect
5. C₅×C₇×C₉×C₂₉	C₂²	semidirect
12. D₁₈₂₇	D₅	semidirect
16. D₁₃₀₅	D₇	semidirect
20. C₂₉×D₃₅	D₉	semidirect
23. C₇×C₉×C₂₉	C₂×D₅	semidirect
25. C₅×C₉×C₂₉	C₂×D₇	semidirect
31. C₅×C₇×C₂₉	C₂×D₉	semidirect
38. C₉×D₃₅	D₂₉	semidirect
50. C₅×C₇×C₉	C₂×D₂₉	semidirect
54. C₉×C₂₉	D₅×D₇	semidirect
59. C₇×C₂₉	D₅×D₉	semidirect
64. C₅×C₂₉	D₇×D₉	semidirect
76. D₃₅	D₂₆₁	semidirect
79. C₇×C₉	D₅×D₂₉	semidirect
84. C₅×C₉	D₇×D₂₉	semidirect
89. C₅×C₇	C₂×D₂₆₁	semidirect
93. C₂₉	D₃₅⋊D₉	semidirect
108. C₉	D₃₅⋊D₂₉	semidirect
109. C₇	D₅×D₂₆₁	semidirect
113. C₅	D₇×D₂₆₁	semidirect

H ≅ G/N

type

1. C₇×D₁₃₀₅

C₂

semidirect

2. C₅×D₁₈₂₇

C₂

semidirect

3. C₉×C₂₉×D₃₅

C₂

semidirect

5. C₅×C₇×C₉×C₂₉

C₂²

semidirect

12. D₁₈₂₇

D₅

semidirect

16. D₁₃₀₅

D₇

semidirect

20. C₂₉×D₃₅

D₉

semidirect

23. C₇×C₉×C₂₉

C₂×D₅

semidirect

25. C₅×C₉×C₂₉

C₂×D₇

semidirect

31. C₅×C₇×C₂₉

C₂×D₉

semidirect

38. C₉×D₃₅

D₂₉

semidirect

50. C₅×C₇×C₉

C₂×D₂₉

semidirect

54. C₉×C₂₉

D₅×D₇

semidirect

59. C₇×C₂₉

D₅×D₉

semidirect

64. C₅×C₂₉

D₇×D₉

semidirect

76. D₃₅

D₂₆₁

semidirect

79. C₇×C₉

D₅×D₂₉

semidirect

84. C₅×C₉

D₇×D₂₉

semidirect

89. C₅×C₇

C₂×D₂₆₁

semidirect

93. C₂₉

D₃₅⋊D₉

semidirect

108. C₉

D₃₅⋊D₂₉

semidirect

109. C₇

D₅×D₂₆₁

semidirect

113. C₅

D₇×D₂₆₁

semidirect

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

subgroup	index
C₇×D₁₃₀₅	2
C₅×D₁₈₂₇	2
C₉×C₂₉×D₃₅	2
D₃₅⋊D₈₇	3
D₇×D₂₆₁	5
D₅×D₂₆₁	7
D₃₅⋊D₉	29

subgroup

index

C₇×D₁₃₀₅

C₅×D₁₈₂₇

C₉×C₂₉×D₃₅

D₃₅⋊D₈₇

D₇×D₂₆₁

D₅×D₂₆₁

D₃₅⋊D₉

Subgroups — D₃₅⋊D₂₆₁ #49141302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D35⋊D261 #49141302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₅⋊D₂₆₁ #49141302