Group #49141271 — subgroups

Subgroups — C₅×D₉×D₂₀₃ #49141271

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

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×D₁₈₂₇

C₂

yes

maximal, characteristic, complemented

C₅×C₇×D₉×C₂₉

C₂

yes

maximal, characteristic, complemented

C₅×C₉×D₂₀₃

C₂

yes

maximal, characteristic, complemented

C₅×D₃×D₂₀₃

—

maximal

C₅×C₇×C₉×C₂₉

C₂²

yes

characteristic, complemented, Hall

D₉×D₂₀₃

C₅

yes

maximal, characteristic, direct product factor, Hall

C₅×D₆₀₉

—

C₅×D₃×C₇×C₂₉

—

C₃×C₅×D₂₀₃

D₃

yes

characteristic

C₅×D₉×D₂₉

—

maximal, Hall

C₂×C₅×D₂₀₃

—

Hall

D₁₈₂₇

C₂×C₅

yes

characteristic, complemented

C₇×D₉×C₂₉

C₂×C₅

yes

characteristic, complemented

C₉×D₂₀₃

C₂×C₅

yes

characteristic, complemented

C₃×C₅×C₇×C₂₉

C₂×D₃

yes

characteristic

C₅×D₂₆₁

—

C₅×D₉×C₂₉

D₇

yes

characteristic, complemented

C₅×C₉×D₂₉

—

D₃×D₂₀₃

—

C₅×D₂₀₃

—

C₅×D₂₀₃

D₉

yes

characteristic, direct product factor

C₂×C₅×C₇×C₂₉

—

C₇×C₉×C₂₉

C₂²×C₅

yes

characteristic, complemented, Hall

C₅×D₃×D₂₉

—

C₅×C₉×C₂₉

C₂×D₇

yes

characteristic, complemented, Hall

C₅×D₇×D₉

—

maximal, Hall

D₆₀₉

—

D₃×C₇×C₂₉

—

C₃×D₂₀₃

C₅×D₃

yes

characteristic

D₉×D₂₉

—

Hall

C₅×C₇×C₂₉

C₂×D₉

yes

characteristic, complemented, Hall

C₅×D₈₇

—

C₅×D₃×C₂₉

—

C₃×C₅×D₂₉

—

C₂×D₂₀₃

—

Hall

C₅×D₆₃

—

C₅×C₇×D₉

D₂₉

yes

characteristic, complemented

C₅×C₉×D₇

—

C₃×C₇×C₂₉

C₂×C₅×D₃

yes

characteristic

C₂×C₅×D₂₉

—

Hall

D₂₆₁

—

C₉×D₂₉

—

D₉×C₂₉

C₅×D₇

yes

characteristic, complemented

C₃×C₅×C₂₉

D₃×D₇

yes

characteristic

C₅×D₃×D₇

—

C₂×C₇×C₂₉

—

D₂₀₃

—

D₂₀₃

C₅×D₉

yes

characteristic, direct product factor

D₃×D₂₉

—

C₅×C₇×C₉

C₂×D₂₉

yes

characteristic, complemented, Hall

C₂×C₅×C₂₉

—

C₅×D₂₉

—

C₅×D₂₉

—

C₉×C₂₉

C₂×C₅×D₇

yes

characteristic, complemented, Hall

D₇×D₉

—

Hall

C₅×D₂₁

—

C₅×D₃×C₇

—

C₃×C₅×D₇

—

C₇×C₂₉

C₂×C₅×D₉

yes

characteristic, complemented, Hall

C₂×C₅×D₉

—

203

Hall

D₈₇

—

C₃×D₂₉

—

D₃×C₂₉

—

C₅×C₂₉

D₇×D₉

yes

characteristic, complemented, Hall

C₂×C₅×D₇

—

261

Hall

D₆₃

—

C₉×D₇

—

C₇×D₉

C₅×D₂₉

yes

characteristic, complemented

C₂×D₂₉

—

Hall

C₃×C₅×C₇

D₃×D₂₉

yes

characteristic

C₂×C₅×C₉

—

203

—

C₅×D₉

—

203

—

C₅×D₉

D₂₀₃

yes

characteristic, direct product factor

C₃×C₂₉

C₅×D₃×D₇

yes

characteristic

D₃×D₇

—

C₂×C₅×C₇

—

C₅×D₇

—

261

—

C₅×D₇

—

C₇×C₉

C₂×C₅×D₂₉

yes

characteristic, complemented, Hall

C₂×C₅×D₃

—

609

—

C₂×C₂₉

—

D₂₉

—

D₂₉

—

C₅×C₉

C₂×D₂₀₃

yes

characteristic, complemented, Hall

D₂₁

—

C₃×D₇

—

D₃×C₇

—

C₂×D₉

—

203

Hall

C₅×C₇

D₉×D₂₉

yes

characteristic, complemented, Hall

C₂×C₃×C₅

—

203

—

C₅×D₃

—

C₅×D₃

—

609

—

C₂₉

C₅×D₇×D₉

yes

characteristic, complemented, Sylow

C₂×D₇

—

261

Hall

C₃×C₇

C₅×D₃×D₂₉

yes

characteristic

C₂²×C₅

—

1827

Hall

C₂×C₉

—

203

—

D₉

—

203

—

D₉

C₅×D₂₀₃

yes

characteristic, direct product factor

100

C₃×C₅

D₃×D₂₀₃

yes

characteristic

101

C₂×C₇

—

102

D₇

—

261

—

103

D₇

—

104

C₂×D₃

—

609

—

105

C₂×C₅

—

106

C₂×C₅

—

1827

—

107

C₂×C₅

—

203

—

108

C₉

C₂×C₅×D₂₀₃

yes

characteristic, complemented, Sylow

109

C₇

C₅×D₉×D₂₉

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

203

—

111

D₃

—

112

D₃

—

609

—

113

C₅

D₉×D₂₀₃

yes

characteristic, direct product factor, Sylow

114

C₂²

—

1827

Sylow

115

C₃

C₅×D₃×D₂₀₃

yes

characteristic

116

C₂

—

117

C₂

—

1827

—

118

C₂

—

203

—

	subgroup	G/H
center, hypercenter	C₅	D₉×D₂₀₃
commutator, cosocle, hypocenter	C₇×C₉×C₂₉	C₂²×C₅
Frattini	C₃	C₅×D₃×D₂₀₃
Fitting	C₅×C₇×C₉×C₂₉	C₂²
socle	C₃×C₅×C₇×C₂₉	C₂×D₃
LCS	G ▷ C₇×C₉×C₂₉
UCS	C₁ ◁ C₅

subgroup

G/H

center, hypercenter

C₅

D₉×D₂₀₃

commutator, cosocle, hypocenter

C₇×C₉×C₂₉

C₂²×C₅

Frattini

C₃

C₅×D₃×D₂₀₃

Fitting

C₅×C₇×C₉×C₂₉

C₂²

socle

C₃×C₅×C₇×C₂₉

C₂×D₃

LCS

G ▷ C₇×C₉×C₂₉

UCS

C₁ ◁ C₅

N	H ≅ G/N	type
1. C₅×D₁₈₂₇	C₂	semidirect
2. C₅×C₇×D₉×C₂₉	C₂	semidirect
3. C₅×C₉×D₂₀₃	C₂	semidirect
5. C₅×C₇×C₉×C₂₉	C₂²	semidirect
6. D₉×D₂₀₃	C₅	direct (N × H)
12. D₁₈₂₇	C₂×C₅	semidirect
13. C₇×D₉×C₂₉	C₂×C₅	semidirect
14. C₉×D₂₀₃	C₂×C₅	semidirect
17. C₅×D₉×C₂₉	D₇	semidirect
21. C₅×D₂₀₃	D₉	direct (N × H)
23. C₇×C₉×C₂₉	C₂²×C₅	semidirect
25. C₅×C₉×C₂₉	C₂×D₇	semidirect
31. C₅×C₇×C₂₉	C₂×D₉	semidirect
37. C₅×C₇×D₉	D₂₉	semidirect
43. D₉×C₂₉	C₅×D₇	semidirect
48. D₂₀₃	C₅×D₉	direct (N × H)
50. C₅×C₇×C₉	C₂×D₂₉	semidirect
54. C₉×C₂₉	C₂×C₅×D₇	semidirect
59. C₇×C₂₉	C₂×C₅×D₉	semidirect
64. C₅×C₂₉	D₇×D₉	semidirect
68. C₇×D₉	C₅×D₂₉	semidirect
73. C₅×D₉	D₂₀₃	direct (N × H)
79. C₇×C₉	C₂×C₅×D₂₉	semidirect
84. C₅×C₉	C₂×D₂₀₃	semidirect
89. C₅×C₇	D₉×D₂₉	semidirect
93. C₂₉	C₅×D₇×D₉	semidirect
99. D₉	C₅×D₂₀₃	direct (N × H)
108. C₉	C₂×C₅×D₂₀₃	semidirect
109. C₇	C₅×D₉×D₂₉	semidirect
113. C₅	D₉×D₂₀₃	direct (N × H)

H ≅ G/N

type

1. C₅×D₁₈₂₇

C₂

semidirect

2. C₅×C₇×D₉×C₂₉

C₂

semidirect

3. C₅×C₉×D₂₀₃

C₂

semidirect

5. C₅×C₇×C₉×C₂₉

C₂²

semidirect

6. D₉×D₂₀₃

C₅

direct (N × H)

12. D₁₈₂₇

C₂×C₅

semidirect

13. C₇×D₉×C₂₉

C₂×C₅

semidirect

14. C₉×D₂₀₃

C₂×C₅

semidirect

17. C₅×D₉×C₂₉

D₇

semidirect

21. C₅×D₂₀₃

D₉

direct (N × H)

23. C₇×C₉×C₂₉

C₂²×C₅

semidirect

25. C₅×C₉×C₂₉

C₂×D₇

semidirect

31. C₅×C₇×C₂₉

C₂×D₉

semidirect

37. C₅×C₇×D₉

D₂₉

semidirect

43. D₉×C₂₉

C₅×D₇

semidirect

48. D₂₀₃

C₅×D₉

direct (N × H)

50. C₅×C₇×C₉

C₂×D₂₉

semidirect

54. C₉×C₂₉

C₂×C₅×D₇

semidirect

59. C₇×C₂₉

C₂×C₅×D₉

semidirect

64. C₅×C₂₉

D₇×D₉

semidirect

68. C₇×D₉

C₅×D₂₉

semidirect

73. C₅×D₉

D₂₀₃

direct (N × H)

79. C₇×C₉

C₂×C₅×D₂₉

semidirect

84. C₅×C₉

C₂×D₂₀₃

semidirect

89. C₅×C₇

D₉×D₂₉

semidirect

93. C₂₉

C₅×D₇×D₉

semidirect

99. D₉

C₅×D₂₀₃

direct (N × H)

108. C₉

C₂×C₅×D₂₀₃

semidirect

109. C₇

C₅×D₉×D₂₉

semidirect

113. C₅

D₉×D₂₀₃

direct (N × H)

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

subgroup	index
C₅×D₁₈₂₇	2
C₅×C₇×D₉×C₂₉	2
C₅×C₉×D₂₀₃	2
C₅×D₃×D₂₀₃	3
D₉×D₂₀₃	5
C₅×D₉×D₂₉	7
C₅×D₇×D₉	29

subgroup

index

C₅×D₁₈₂₇

C₅×C₇×D₉×C₂₉

C₅×C₉×D₂₀₃

C₅×D₃×D₂₀₃

D₉×D₂₀₃

C₅×D₉×D₂₉

C₅×D₇×D₉

Subgroups — C₅×D₉×D₂₀₃ #49141271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D9×D203 #49141271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₉×D₂₀₃ #49141271