Group #39907951 — subgroups

Subgroups — C₅×D₉×D₁₄₅ #39907951

Order 26100.

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

normal subgroups only

This group has 144 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×D₁₃₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₉×D₁₄₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×D₁₄₅	—	3	1	no	maximal
5	C₅²×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×D₁₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×D₉×D₂₉	—	5	1	no	maximal
8	C₅×D₄₃₅	—	3	1	no	—
9	C₅²×D₃×C₂₉	—	3	1	no	—
10	C₃×C₅×D₁₄₅	D₃	1	1	yes	characteristic
11	C₂×C₅×D₁₄₅	—	9	1	no	Hall
12	D₁₃₀₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₂₆₁	—	5	1	no	—
14	C₅×D₉×C₂₉	—	2	2	no	—
15	C₅×D₉×C₂₉	D₅	1	1	yes	characteristic, complemented
16	C₅×D₉×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
17	C₉×D₁₄₅	C₂×C₅	1	1	yes	characteristic, complemented
18	C₅×C₉×D₂₉	—	5	1	no	—
19	C₃×C₅²×C₂₉	C₂×D₃	1	1	yes	characteristic
20	D₃×D₁₄₅	—	3	1	no	—
21	C₅×D₃×D₂₉	—	15	1	no	—
22	C₂×C₅²×C₂₉	—	9	1	no	—
23	C₅×D₁₄₅	—	9	1	no	—
24	C₅×D₁₄₅	D₉	1	1	yes	characteristic, direct product factor
25	C₅×C₉×C₂₉	—	2	2	no	—
26	C₅×C₉×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented
27	C₅×C₉×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented
28	D₉×D₂₉	—	5	1	no	Hall
29	C₅×D₅×D₉	—	29	1	no	maximal, Hall
30	D₄₃₅	—	3	1	no	—
31	C₅×D₈₇	—	15	1	no	—
32	C₅×D₃×C₂₉	—	3	1	no	—
33	C₅×D₃×C₂₉	—	3	1	no	—
34	C₅×D₃×C₂₉	—	6	2	no	—
35	C₃×D₁₄₅	C₅×D₃	1	1	yes	characteristic
36	C₃×C₅×D₂₉	—	5	1	no	—
37	C₅²×C₂₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
38	C₂×D₁₄₅	—	9	1	no	—
39	C₂×C₅×D₂₉	—	45	1	no	—
40	D₂₆₁	—	5	1	no	—
41	C₉×D₂₉	—	5	1	no	—
42	D₉×C₂₉	C₅×D₅	1	1	yes	characteristic, complemented
43	C₅×D₄₅	—	29	1	no	—
44	C₅²×D₉	D₂₉	1	1	yes	characteristic, complemented
45	C₅×C₉×D₅	—	29	1	no	—
46	C₃×C₅×C₂₉	—	2	2	no	—
47	C₃×C₅×C₂₉	D₃×D₅	1	1	yes	characteristic
48	C₃×C₅×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic
49	D₃×D₂₉	—	15	1	no	—
50	C₅×D₃×D₅	—	87	1	no	—
51	C₂×C₅×C₂₉	—	9	1	no	—
52	C₂×C₅×C₂₉	—	9	1	no	—
53	C₂×C₅×C₂₉	—	18	2	no	—
54	D₁₄₅	—	9	1	no	—
55	D₁₄₅	C₅×D₉	1	1	yes	characteristic, direct product factor
56	C₅×D₂₉	—	5	1	no	—
57	C₅×D₂₉	—	45	1	no	—
58	C₉×C₂₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
59	C₅²×C₉	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
60	C₂×C₅×D₉	—	145	1	no	—
61	D₅×D₉	—	29	1	no	—
62	D₈₇	—	15	1	no	—
63	C₃×D₂₉	—	5	1	no	—
64	D₃×C₂₉	—	3	1	no	—
65	C₅×D₁₅	—	87	1	no	—
66	C₅²×D₃	—	3	1	no	—
67	C₃×C₅×D₅	—	29	1	no	—
68	C₅×C₂₉	—	2	2	no	—
69	C₅×C₂₉	D₅×D₉	1	1	yes	characteristic, complemented
70	C₅×C₂₉	C₂×C₅×D₉	1	1	yes	characteristic, complemented
71	C₂×D₂₉	—	45	1	no	Hall
72	C₂×C₅×D₅	—	261	1	no	Hall
73	C₂×C₅×C₉	—	145	1	no	—
74	D₄₅	—	29	1	no	—
75	C₉×D₅	—	29	1	no	—
76	C₅×D₉	—	2	2	no	—
77	C₅×D₉	—	145	1	no	—
78	C₅×D₉	C₅×D₂₉	1	1	yes	characteristic, complemented
79	C₅×D₉	D₁₄₅	1	1	yes	characteristic, direct product factor
80	C₃×C₂₉	C₅×D₃×D₅	1	1	yes	characteristic
81	C₃×C₅²	D₃×D₂₉	1	1	yes	characteristic
82	C₂×C₅×D₃	—	435	1	no	—
83	D₃×D₅	—	87	1	no	—
84	C₂×C₂₉	—	9	1	no	—
85	D₂₉	—	5	1	no	—
86	D₂₉	—	45	1	no	—
87	C₂×C₅²	—	9	1	no	—
88	C₅×D₅	—	261	1	no	—
89	C₅×D₅	—	29	1	no	—
90	C₅×C₉	—	2	2	no	—
91	C₅×C₉	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented
92	C₅×C₉	C₂×D₁₄₅	1	1	yes	characteristic, complemented
93	C₂×D₉	—	145	1	no	Hall
94	C₂×C₃×C₅	—	145	1	no	—
95	D₁₅	—	87	1	no	—
96	C₃×D₅	—	29	1	no	—
97	C₅×D₃	—	3	1	no	—
98	C₅×D₃	—	3	1	no	—
99	C₅×D₃	—	6	2	no	—
100	C₅×D₃	—	435	1	no	—
101	C₂₉	C₅×D₅×D₉	1	1	yes	characteristic, complemented, Sylow
102	C₅²	D₉×D₂₉	1	1	yes	characteristic, complemented, Sylow
103	C₂²×C₅	—	1305	1	no	—
104	C₂×D₅	—	261	1	no	—
105	C₂×C₉	—	145	1	no	—
106	D₉	—	145	1	no	—
107	D₉	C₅×D₁₄₅	1	1	yes	characteristic, direct product factor
108	C₃×C₅	—	2	2	no	—
109	C₃×C₅	C₅×D₃×D₂₉	1	1	yes	characteristic
110	C₃×C₅	D₃×D₁₄₅	1	1	yes	characteristic
111	C₂×D₃	—	435	1	no	—
112	C₂×C₅	—	9	1	no	—
113	C₂×C₅	—	9	1	no	—
114	C₂×C₅	—	18	2	no	—
115	C₂×C₅	—	1305	1	no	—
116	C₂×C₅	—	145	1	no	—
117	D₅	—	261	1	no	—
118	D₅	—	29	1	no	—
119	C₉	C₂×C₅×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₃	—	145	1	no	—
121	D₃	—	3	1	no	—
122	D₃	—	435	1	no	—
123	C₅	—	2	2	no	—
124	C₅	C₅×D₉×D₂₉	1	1	yes	characteristic, complemented
125	C₅	D₉×D₁₄₅	1	1	yes	characteristic, direct product factor
126	C₂²	—	1305	1	no	Sylow
127	C₃	C₅×D₃×D₁₄₅	1	1	yes	characteristic
128	C₂	—	9	1	no	—
129	C₂	—	1305	1	no	—
130	C₂	—	145	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×D₁₃₀₅

C₂

yes

maximal, characteristic, complemented

C₅²×D₉×C₂₉

C₂

yes

maximal, characteristic, complemented

C₅×C₉×D₁₄₅

C₂

yes

maximal, characteristic, complemented

C₅×D₃×D₁₄₅

—

maximal

C₅²×C₉×C₂₉

C₂²

yes

characteristic, complemented, Hall

D₉×D₁₄₅

C₅

yes

maximal, characteristic, direct product factor

C₅×D₉×D₂₉

—

maximal

C₅×D₄₃₅

—

C₅²×D₃×C₂₉

—

C₃×C₅×D₁₄₅

D₃

yes

characteristic

C₂×C₅×D₁₄₅

—

Hall

D₁₃₀₅

C₂×C₅

yes

characteristic, complemented

C₅×D₂₆₁

—

C₅×D₉×C₂₉

—

C₅×D₉×C₂₉

D₅

yes

characteristic, complemented

C₅×D₉×C₂₉

C₂×C₅

yes

characteristic, complemented

C₉×D₁₄₅

C₂×C₅

yes

characteristic, complemented

C₅×C₉×D₂₉

—

C₃×C₅²×C₂₉

C₂×D₃

yes

characteristic

D₃×D₁₄₅

—

C₅×D₃×D₂₉

—

C₂×C₅²×C₂₉

—

C₅×D₁₄₅

—

C₅×D₁₄₅

D₉

yes

characteristic, direct product factor

C₅×C₉×C₂₉

—

C₅×C₉×C₂₉

C₂×D₅

yes

characteristic, complemented

C₅×C₉×C₂₉

C₂²×C₅

yes

characteristic, complemented

D₉×D₂₉

—

Hall

C₅×D₅×D₉

—

maximal, Hall

D₄₃₅

—

C₅×D₈₇

—

C₅×D₃×C₂₉

—

C₅×D₃×C₂₉

—

C₅×D₃×C₂₉

—

C₃×D₁₄₅

C₅×D₃

yes

characteristic

C₃×C₅×D₂₉

—

C₅²×C₂₉

C₂×D₉

yes

characteristic, complemented, Hall

C₂×D₁₄₅

—

C₂×C₅×D₂₉

—

D₂₆₁

—

C₉×D₂₉

—

D₉×C₂₉

C₅×D₅

yes

characteristic, complemented

C₅×D₄₅

—

C₅²×D₉

D₂₉

yes

characteristic, complemented

C₅×C₉×D₅

—

C₃×C₅×C₂₉

—

C₃×C₅×C₂₉

D₃×D₅

yes

characteristic

C₃×C₅×C₂₉

C₂×C₅×D₃

yes

characteristic

D₃×D₂₉

—

C₅×D₃×D₅

—

C₂×C₅×C₂₉

—

C₂×C₅×C₂₉

—

C₂×C₅×C₂₉

—

D₁₄₅

—

D₁₄₅

C₅×D₉

yes

characteristic, direct product factor

C₅×D₂₉

—

C₅×D₂₉

—

C₉×C₂₉

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₅²×C₉

C₂×D₂₉

yes

characteristic, complemented, Hall

C₂×C₅×D₉

—

145

—

D₅×D₉

—

D₈₇

—

C₃×D₂₉

—

D₃×C₂₉

—

C₅×D₁₅

—

C₅²×D₃

—

C₃×C₅×D₅

—

C₅×C₂₉

—

C₅×C₂₉

D₅×D₉

yes

characteristic, complemented

C₅×C₂₉

C₂×C₅×D₉

yes

characteristic, complemented

C₂×D₂₉

—

Hall

C₂×C₅×D₅

—

261

Hall

C₂×C₅×C₉

—

145

—

D₄₅

—

C₉×D₅

—

C₅×D₉

—

C₅×D₉

—

145

—

C₅×D₉

C₅×D₂₉

yes

characteristic, complemented

C₅×D₉

D₁₄₅

yes

characteristic, direct product factor

C₃×C₂₉

C₅×D₃×D₅

yes

characteristic

C₃×C₅²

D₃×D₂₉

yes

characteristic

C₂×C₅×D₃

—

435

—

D₃×D₅

—

C₂×C₂₉

—

D₂₉

—

D₂₉

—

C₂×C₅²

—

C₅×D₅

—

261

—

C₅×D₅

—

C₅×C₉

—

C₅×C₉

C₂×C₅×D₂₉

yes

characteristic, complemented

C₅×C₉

C₂×D₁₄₅

yes

characteristic, complemented

C₂×D₉

—

145

Hall

C₂×C₃×C₅

—

145

—

D₁₅

—

C₃×D₅

—

C₅×D₃

—

C₅×D₃

—

C₅×D₃

—

100

C₅×D₃

—

435

—

101

C₂₉

C₅×D₅×D₉

yes

characteristic, complemented, Sylow

102

C₅²

D₉×D₂₉

yes

characteristic, complemented, Sylow

103

C₂²×C₅

—

1305

—

104

C₂×D₅

—

261

—

105

C₂×C₉

—

145

—

106

D₉

—

145

—

107

D₉

C₅×D₁₄₅

yes

characteristic, direct product factor

108

C₃×C₅

—

109

C₃×C₅

C₅×D₃×D₂₉

yes

characteristic

110

C₃×C₅

D₃×D₁₄₅

yes

characteristic

111

C₂×D₃

—

435

—

112

C₂×C₅

—

113

C₂×C₅

—

114

C₂×C₅

—

115

C₂×C₅

—

1305

—

116

C₂×C₅

—

145

—

117

D₅

—

261

—

118

D₅

—

119

C₉

C₂×C₅×D₁₄₅

yes

characteristic, complemented, Sylow

120

C₂×C₃

—

145

—

121

D₃

—

122

D₃

—

435

—

123

C₅

—

124

C₅

C₅×D₉×D₂₉

yes

characteristic, complemented

125

C₅

D₉×D₁₄₅

yes

characteristic, direct product factor

126

C₂²

—

1305

Sylow

127

C₃

C₅×D₃×D₁₄₅

yes

characteristic

128

C₂

—

129

C₂

—

1305

—

130

C₂

—

145

—

	subgroup	G/H
center, hypercenter	C₅	D₉×D₁₄₅
commutator, cosocle, hypocenter	C₅×C₉×C₂₉	C₂²×C₅
Frattini	C₃	C₅×D₃×D₁₄₅
Fitting	C₅²×C₉×C₂₉	C₂²
socle	C₃×C₅²×C₂₉	C₂×D₃
LCS	G ▷ C₅×C₉×C₂₉
UCS	C₁ ◁ C₅

subgroup

G/H

center, hypercenter

C₅

D₉×D₁₄₅

commutator, cosocle, hypocenter

C₅×C₉×C₂₉

C₂²×C₅

Frattini

C₃

C₅×D₃×D₁₄₅

Fitting

C₅²×C₉×C₂₉

C₂²

socle

C₃×C₅²×C₂₉

C₂×D₃

LCS

G ▷ C₅×C₉×C₂₉

UCS

C₁ ◁ C₅

N	H ≅ G/N	type
1. C₅×D₁₃₀₅	C₂	semidirect
2. C₅²×D₉×C₂₉	C₂	semidirect
3. C₅×C₉×D₁₄₅	C₂	semidirect
5. C₅²×C₉×C₂₉	C₂²	semidirect
6. D₉×D₁₄₅	C₅	direct (N × H)
12. D₁₃₀₅	C₂×C₅	semidirect
15. C₅×D₉×C₂₉	D₅	semidirect
16. C₅×D₉×C₂₉	C₂×C₅	semidirect
17. C₉×D₁₄₅	C₂×C₅	semidirect
24. C₅×D₁₄₅	D₉	direct (N × H)
26. C₅×C₉×C₂₉	C₂×D₅	semidirect
27. C₅×C₉×C₂₉	C₂²×C₅	semidirect
37. C₅²×C₂₉	C₂×D₉	semidirect
42. D₉×C₂₉	C₅×D₅	semidirect
44. C₅²×D₉	D₂₉	semidirect
55. D₁₄₅	C₅×D₉	direct (N × H)
58. C₉×C₂₉	C₂×C₅×D₅	semidirect
59. C₅²×C₉	C₂×D₂₉	semidirect
69. C₅×C₂₉	D₅×D₉	semidirect
70. C₅×C₂₉	C₂×C₅×D₉	semidirect
78. C₅×D₉	C₅×D₂₉	semidirect
79. C₅×D₉	D₁₄₅	direct (N × H)
91. C₅×C₉	C₂×C₅×D₂₉	semidirect
92. C₅×C₉	C₂×D₁₄₅	semidirect
101. C₂₉	C₅×D₅×D₉	semidirect
102. C₅²	D₉×D₂₉	semidirect
107. D₉	C₅×D₁₄₅	direct (N × H)
119. C₉	C₂×C₅×D₁₄₅	semidirect
124. C₅	C₅×D₉×D₂₉	semidirect
125. C₅	D₉×D₁₄₅	direct (N × H)

H ≅ G/N

type

1. C₅×D₁₃₀₅

C₂

semidirect

2. C₅²×D₉×C₂₉

C₂

semidirect

3. C₅×C₉×D₁₄₅

C₂

semidirect

5. C₅²×C₉×C₂₉

C₂²

semidirect

6. D₉×D₁₄₅

C₅

direct (N × H)

12. D₁₃₀₅

C₂×C₅

semidirect

15. C₅×D₉×C₂₉

D₅

semidirect

16. C₅×D₉×C₂₉

C₂×C₅

semidirect

17. C₉×D₁₄₅

C₂×C₅

semidirect

24. C₅×D₁₄₅

D₉

direct (N × H)

26. C₅×C₉×C₂₉

C₂×D₅

semidirect

27. C₅×C₉×C₂₉

C₂²×C₅

semidirect

37. C₅²×C₂₉

C₂×D₉

semidirect

42. D₉×C₂₉

C₅×D₅

semidirect

44. C₅²×D₉

D₂₉

semidirect

55. D₁₄₅

C₅×D₉

direct (N × H)

58. C₉×C₂₉

C₂×C₅×D₅

semidirect

59. C₅²×C₉

C₂×D₂₉

semidirect

69. C₅×C₂₉

D₅×D₉

semidirect

70. C₅×C₂₉

C₂×C₅×D₉

semidirect

78. C₅×D₉

C₅×D₂₉

semidirect

79. C₅×D₉

D₁₄₅

direct (N × H)

91. C₅×C₉

C₂×C₅×D₂₉

semidirect

92. C₅×C₉

C₂×D₁₄₅

semidirect

101. C₂₉

C₅×D₅×D₉

semidirect

102. C₅²

D₉×D₂₉

semidirect

107. D₉

C₅×D₁₄₅

direct (N × H)

119. C₉

C₂×C₅×D₁₄₅

semidirect

124. C₅

C₅×D₉×D₂₉

semidirect

125. C₅

D₉×D₁₄₅

direct (N × H)

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

subgroup	index
C₅×D₁₃₀₅	2
C₅²×D₉×C₂₉	2
C₅×C₉×D₁₄₅	2
C₅×D₃×D₁₄₅	3
D₉×D₁₄₅	5
C₅×D₉×D₂₉	5
C₅×D₅×D₉	29

subgroup

index

C₅×D₁₃₀₅

C₅²×D₉×C₂₉

C₅×C₉×D₁₄₅

C₅×D₃×D₁₄₅

D₉×D₁₄₅

C₅×D₉×D₂₉

C₅×D₅×D₉

Subgroups — C₅×D₉×D₁₄₅ #39907951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D9×D145 #39907951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₉×D₁₄₅ #39907951