Group #30685574 — subgroups

Subgroups — C₅×C₉×D₅×D₁₉ #30685574

Order 17100.

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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×C₉×D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₉×D₅×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₉×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×D₅×D₁₉	C₃	1	1	yes	maximal, characteristic
5	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₅×C₉×D₁₉	—	5	1	no	maximal
7	C₉×D₅×D₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₃×C₅×D₉₅	C₂×C₃	1	1	yes	characteristic
9	C₃×C₅×D₅×C₁₉	C₂×C₃	1	1	yes	characteristic
10	C₃×C₅²×D₁₉	C₂×C₃	1	1	yes	characteristic
11	C₅×D₅×D₁₉	C₉	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₅×C₉×C₁₉	—	5	1	no	—
13	C₉×D₉₅	C₂×C₅	1	1	yes	characteristic, complemented
14	C₉×D₅×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
15	C₅×C₉×D₁₉	—	2	2	no	—
16	C₅×C₉×D₁₉	—	5	1	no	—
17	C₅×C₉×D₁₉	D₅	1	1	yes	characteristic, direct product factor
18	C₅×C₉×D₁₉	C₂×C₅	1	1	yes	characteristic, complemented
19	C₃×C₅²×C₁₉	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₃×C₅×D₁₉	—	5	1	no	—
21	C₃×D₅×D₁₉	C₃×C₅	1	1	yes	characteristic
22	C₅×D₉₅	C₂×C₉	1	1	yes	characteristic, complemented
23	C₅×D₅×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented
24	C₅²×D₁₉	C₂×C₉	1	1	yes	characteristic, complemented
25	C₂×C₅×C₉×D₅	—	19	1	no	maximal, Hall
26	C₅×C₉×C₁₉	—	2	2	no	—
27	C₅×C₉×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
28	C₅×C₉×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
29	C₂×C₉×D₁₉	—	5	1	no	Hall
30	C₂×C₃×C₅×C₁₉	—	5	1	no	—
31	C₃×D₉₅	C₂×C₃×C₅	1	1	yes	characteristic
32	C₃×D₅×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
33	C₃×C₅×D₁₉	—	2	2	no	—
34	C₃×C₅×D₁₉	—	5	1	no	—
35	C₃×C₅×D₁₉	C₃×D₅	1	1	yes	characteristic
36	C₃×C₅×D₁₉	C₂×C₃×C₅	1	1	yes	characteristic
37	C₅²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
38	C₂×C₅²×C₉	—	19	1	no	—
39	C₅×C₉×D₅	—	19	1	no	—
40	C₅×C₉×D₅	D₁₉	1	1	yes	characteristic, direct product factor
41	C₂×C₅×D₁₉	—	5	1	no	—
42	D₅×D₁₉	C₅×C₉	1	1	yes	characteristic, direct product factor
43	C₂×C₉×C₁₉	—	5	1	no	—
44	C₉×D₁₉	—	5	1	no	—
45	C₉×D₁₉	C₅×D₅	1	1	yes	characteristic, direct product factor
46	C₂×C₃×C₅×D₅	—	19	1	no	—
47	C₃×C₅×C₁₉	—	2	2	no	—
48	C₃×C₅×C₁₉	C₂×C₃×D₅	1	1	yes	characteristic
49	C₃×C₅×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
50	C₂×C₃×D₁₉	—	5	1	no	—
51	C₅²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
52	C₂×C₅×C₁₉	—	5	1	no	—
53	D₉₅	C₂×C₅×C₉	1	1	yes	characteristic, complemented
54	C₅×D₁₉	—	2	2	no	—
55	C₅×D₁₉	—	5	1	no	—
56	C₅×D₁₉	C₉×D₅	1	1	yes	characteristic, direct product factor
57	C₅×D₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
58	D₅×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
59	C₂²×C₅×C₉	—	95	1	no	—
60	C₂×C₉×D₅	—	19	1	no	—
61	C₉×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
62	C₂×C₃×C₅²	—	19	1	no	—
63	C₃×C₅×D₅	—	19	1	no	—
64	C₃×C₅×D₅	C₃×D₁₉	1	1	yes	characteristic
65	C₂×C₃×C₁₉	—	5	1	no	—
66	C₃×D₁₉	—	5	1	no	—
67	C₃×D₁₉	C₃×C₅×D₅	1	1	yes	characteristic
68	C₂×C₅×D₅	—	19	1	no	Hall
69	C₅×C₁₉	—	2	2	no	—
70	C₅×C₁₉	C₂×C₉×D₅	1	1	yes	characteristic, complemented
71	C₅×C₁₉	C₂²×C₅×C₉	1	1	yes	characteristic, complemented
72	C₂×C₅×C₉	—	5	1	no	—
73	C₂×C₅×C₉	—	19	1	no	—
74	C₂×C₅×C₉	—	19	1	no	—
75	C₂×C₅×C₉	—	38	2	no	—
76	C₂×C₅×C₉	—	95	1	no	—
77	C₉×D₅	—	19	1	no	—
78	C₉×D₅	C₅×D₁₉	1	1	yes	characteristic, direct product factor
79	C₂×D₁₉	—	5	1	no	Hall
80	C₃×C₅²	C₂×C₃×D₁₉	1	1	yes	characteristic
81	C₂²×C₃×C₅	—	95	1	no	—
82	C₂×C₃×D₅	—	19	1	no	—
83	C₃×C₁₉	C₂×C₃×C₅×D₅	1	1	yes	characteristic
84	C₂×C₅²	—	19	1	no	—
85	C₅×D₅	—	19	1	no	—
86	C₅×D₅	C₉×D₁₉	1	1	yes	characteristic, direct product factor
87	C₅×C₉	—	2	2	no	—
88	C₅×C₉	D₅×D₁₉	1	1	yes	characteristic, direct product factor
89	C₅×C₉	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented
90	C₂×C₁₉	—	5	1	no	—
91	D₁₉	—	5	1	no	—
92	D₁₉	C₅×C₉×D₅	1	1	yes	characteristic, direct product factor
93	C₂²×C₉	—	95	1	no	Hall
94	C₂×C₃×C₅	—	5	1	no	—
95	C₂×C₃×C₅	—	19	1	no	—
96	C₂×C₃×C₅	—	19	1	no	—
97	C₂×C₃×C₅	—	38	2	no	—
98	C₂×C₃×C₅	—	95	1	no	—
99	C₃×D₅	—	19	1	no	—
100	C₃×D₅	C₃×C₅×D₁₉	1	1	yes	characteristic
101	C₅²	C₂×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
102	C₂²×C₅	—	95	1	no	—
103	C₂×D₅	—	19	1	no	—
104	C₁₉	C₂×C₅×C₉×D₅	1	1	yes	characteristic, complemented, Sylow
105	C₂×C₉	—	5	1	no	—
106	C₂×C₉	—	19	1	no	—
107	C₂×C₉	—	95	1	no	—
108	C₃×C₅	—	2	2	no	—
109	C₃×C₅	C₃×D₅×D₁₉	1	1	yes	characteristic
110	C₃×C₅	C₂×C₃×C₅×D₁₉	1	1	yes	characteristic
111	C₂²×C₃	—	95	1	no	—
112	C₂×C₅	—	5	1	no	—
113	C₂×C₅	—	19	1	no	—
114	C₂×C₅	—	19	1	no	—
115	C₂×C₅	—	38	2	no	—
116	C₂×C₅	—	95	1	no	—
117	D₅	—	19	1	no	—
118	D₅	C₅×C₉×D₁₉	1	1	yes	characteristic, direct product factor
119	C₉	C₅×D₅×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
120	C₂×C₃	—	5	1	no	—
121	C₂×C₃	—	19	1	no	—
122	C₂×C₃	—	95	1	no	—
123	C₅	—	2	2	no	—
124	C₅	C₉×D₅×D₁₉	1	1	yes	characteristic, direct product factor
125	C₅	C₂×C₅×C₉×D₁₉	1	1	yes	characteristic, complemented
126	C₂²	—	95	1	no	Sylow
127	C₃	C₃×C₅×D₅×D₁₉	1	1	yes	characteristic
128	C₂	—	5	1	no	—
129	C₂	—	19	1	no	—
130	C₂	—	95	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₉×D₉₅

C₂

yes

maximal, characteristic, complemented

C₅×C₉×D₅×C₁₉

C₂

yes

maximal, characteristic, complemented

C₅²×C₉×D₁₉

C₂

yes

maximal, characteristic, complemented

C₃×C₅×D₅×D₁₉

C₃

yes

maximal, characteristic

C₅²×C₉×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₂×C₅×C₉×D₁₉

—

maximal

C₉×D₅×D₁₉

C₅

yes

maximal, characteristic, direct product factor

C₃×C₅×D₉₅

C₂×C₃

yes

characteristic

C₃×C₅×D₅×C₁₉

C₂×C₃

yes

characteristic

C₃×C₅²×D₁₉

C₂×C₃

yes

characteristic

C₅×D₅×D₁₉

C₉

yes

characteristic, direct product factor, Hall

C₂×C₅×C₉×C₁₉

—

C₉×D₉₅

C₂×C₅

yes

characteristic, complemented

C₉×D₅×C₁₉

C₂×C₅

yes

characteristic, complemented

C₅×C₉×D₁₉

—

C₅×C₉×D₁₉

—

C₅×C₉×D₁₉

D₅

yes

characteristic, direct product factor

C₅×C₉×D₁₉

C₂×C₅

yes

characteristic, complemented

C₃×C₅²×C₁₉

C₂²×C₃

yes

characteristic

C₂×C₃×C₅×D₁₉

—

C₃×D₅×D₁₉

C₃×C₅

yes

characteristic

C₅×D₉₅

C₂×C₉

yes

characteristic, complemented

C₅×D₅×C₁₉

C₂×C₉

yes

characteristic, complemented

C₅²×D₁₉

C₂×C₉

yes

characteristic, complemented

C₂×C₅×C₉×D₅

—

maximal, Hall

C₅×C₉×C₁₉

—

C₅×C₉×C₁₉

C₂×D₅

yes

characteristic, complemented

C₅×C₉×C₁₉

C₂²×C₅

yes

characteristic, complemented

C₂×C₉×D₁₉

—

Hall

C₂×C₃×C₅×C₁₉

—

C₃×D₉₅

C₂×C₃×C₅

yes

characteristic

C₃×D₅×C₁₉

C₂×C₃×C₅

yes

characteristic

C₃×C₅×D₁₉

—

C₃×C₅×D₁₉

—

C₃×C₅×D₁₉

C₃×D₅

yes

characteristic

C₃×C₅×D₁₉

C₂×C₃×C₅

yes

characteristic

C₅²×C₁₉

C₂²×C₉

yes

characteristic, complemented, Hall

C₂×C₅²×C₉

—

C₅×C₉×D₅

—

C₅×C₉×D₅

D₁₉

yes

characteristic, direct product factor

C₂×C₅×D₁₉

—

D₅×D₁₉

C₅×C₉

yes

characteristic, direct product factor

C₂×C₉×C₁₉

—

C₉×D₁₉

—

C₉×D₁₉

C₅×D₅

yes

characteristic, direct product factor

C₂×C₃×C₅×D₅

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₃×D₅

yes

characteristic

C₃×C₅×C₁₉

C₂²×C₃×C₅

yes

characteristic

C₂×C₃×D₁₉

—

C₅²×C₉

C₂×D₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

D₉₅

C₂×C₅×C₉

yes

characteristic, complemented

C₅×D₁₉

—

C₅×D₁₉

—

C₅×D₁₉

C₉×D₅

yes

characteristic, direct product factor

C₅×D₁₉

C₂×C₅×C₉

yes

characteristic, complemented

D₅×C₁₉

C₂×C₅×C₉

yes

characteristic, complemented

C₂²×C₅×C₉

—

C₂×C₉×D₅

—

C₉×C₁₉

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₃×C₅×D₅

—

C₃×C₅×D₅

C₃×D₁₉

yes

characteristic

C₂×C₃×C₁₉

—

C₃×D₁₉

—

C₃×D₁₉

C₃×C₅×D₅

yes

characteristic

C₂×C₅×D₅

—

Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₉×D₅

yes

characteristic, complemented

C₅×C₁₉

C₂²×C₅×C₉

yes

characteristic, complemented

C₂×C₅×C₉

—

C₂×C₅×C₉

—

C₂×C₅×C₉

—

C₂×C₅×C₉

—

C₂×C₅×C₉

—

C₉×D₅

—

C₉×D₅

C₅×D₁₉

yes

characteristic, direct product factor

C₂×D₁₉

—

Hall

C₃×C₅²

C₂×C₃×D₁₉

yes

characteristic

C₂²×C₃×C₅

—

C₂×C₃×D₅

—

C₃×C₁₉

C₂×C₃×C₅×D₅

yes

characteristic

C₂×C₅²

—

C₅×D₅

—

C₅×D₅

C₉×D₁₉

yes

characteristic, direct product factor

C₅×C₉

—

C₅×C₉

D₅×D₁₉

yes

characteristic, direct product factor

C₅×C₉

C₂×C₅×D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

D₁₉

—

D₁₉

C₅×C₉×D₅

yes

characteristic, direct product factor

C₂²×C₉

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₃×D₅

—

100

C₃×D₅

C₃×C₅×D₁₉

yes

characteristic

101

C₅²

C₂×C₉×D₁₉

yes

characteristic, complemented, Sylow

102

C₂²×C₅

—

103

C₂×D₅

—

104

C₁₉

C₂×C₅×C₉×D₅

yes

characteristic, complemented, Sylow

105

C₂×C₉

—

106

C₂×C₉

—

107

C₂×C₉

—

108

C₃×C₅

—

109

C₃×C₅

C₃×D₅×D₁₉

yes

characteristic

110

C₃×C₅

C₂×C₃×C₅×D₁₉

yes

characteristic

111

C₂²×C₃

—

112

C₂×C₅

—

113

C₂×C₅

—

114

C₂×C₅

—

115

C₂×C₅

—

116

C₂×C₅

—

117

D₅

—

118

D₅

C₅×C₉×D₁₉

yes

characteristic, direct product factor

119

C₉

C₅×D₅×D₁₉

yes

characteristic, direct product factor, Sylow

120

C₂×C₃

—

121

C₂×C₃

—

122

C₂×C₃

—

123

C₅

—

124

C₅

C₉×D₅×D₁₉

yes

characteristic, direct product factor

125

C₅

C₂×C₅×C₉×D₁₉

yes

characteristic, complemented

126

C₂²

—

Sylow

127

C₃

C₃×C₅×D₅×D₁₉

yes

characteristic

128

C₂

—

129

C₂

—

130

C₂

—

	subgroup	G/H
center, hypercenter	C₅×C₉	D₅×D₁₉
commutator, hypocenter	C₅×C₁₉	C₂²×C₅×C₉
Frattini	C₃	C₃×C₅×D₅×D₁₉
Fitting	C₅²×C₉×C₁₉	C₂²
socle	C₃×C₅²×C₁₉	C₂²×C₃
prime radical	C₃×C₅×D₅×D₁₉	C₃
cosocle	C₃×C₅×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₅×C₉

subgroup

G/H

center, hypercenter

C₅×C₉

D₅×D₁₉

commutator, hypocenter

C₅×C₁₉

C₂²×C₅×C₉

Frattini

C₃

C₃×C₅×D₅×D₁₉

Fitting

C₅²×C₉×C₁₉

C₂²

socle

C₃×C₅²×C₁₉

C₂²×C₃

prime radical

C₃×C₅×D₅×D₁₉

C₃

cosocle

C₃×C₅×C₁₉

C₂²×C₃×C₅

LCS

G ▷ C₅×C₁₉

UCS

C₁ ◁ C₅×C₉

N	H ≅ G/N	type
1. C₅×C₉×D₉₅	C₂	semidirect
2. C₅×C₉×D₅×C₁₉	C₂	semidirect
3. C₅²×C₉×D₁₉	C₂	semidirect
5. C₅²×C₉×C₁₉	C₂²	semidirect
7. C₉×D₅×D₁₉	C₅	direct (N × H)
11. C₅×D₅×D₁₉	C₉	direct (N × H)
13. C₉×D₉₅	C₂×C₅	semidirect
14. C₉×D₅×C₁₉	C₂×C₅	semidirect
17. C₅×C₉×D₁₉	D₅	direct (N × H)
18. C₅×C₉×D₁₉	C₂×C₅	semidirect
22. C₅×D₉₅	C₂×C₉	semidirect
23. C₅×D₅×C₁₉	C₂×C₉	semidirect
24. C₅²×D₁₉	C₂×C₉	semidirect
27. C₅×C₉×C₁₉	C₂×D₅	semidirect
28. C₅×C₉×C₁₉	C₂²×C₅	semidirect
37. C₅²×C₁₉	C₂²×C₉	semidirect
40. C₅×C₉×D₅	D₁₉	direct (N × H)
42. D₅×D₁₉	C₅×C₉	direct (N × H)
45. C₉×D₁₉	C₅×D₅	direct (N × H)
51. C₅²×C₉	C₂×D₁₉	semidirect
53. D₉₅	C₂×C₅×C₉	semidirect
56. C₅×D₁₉	C₉×D₅	direct (N × H)
57. C₅×D₁₉	C₂×C₅×C₉	semidirect
58. D₅×C₁₉	C₂×C₅×C₉	semidirect
61. C₉×C₁₉	C₂×C₅×D₅	semidirect
70. C₅×C₁₉	C₂×C₉×D₅	semidirect
71. C₅×C₁₉	C₂²×C₅×C₉	semidirect
78. C₉×D₅	C₅×D₁₉	direct (N × H)
86. C₅×D₅	C₉×D₁₉	direct (N × H)
88. C₅×C₉	D₅×D₁₉	direct (N × H)
89. C₅×C₉	C₂×C₅×D₁₉	semidirect
92. D₁₉	C₅×C₉×D₅	direct (N × H)
101. C₅²	C₂×C₉×D₁₉	semidirect
104. C₁₉	C₂×C₅×C₉×D₅	semidirect
118. D₅	C₅×C₉×D₁₉	direct (N × H)
119. C₉	C₅×D₅×D₁₉	direct (N × H)
124. C₅	C₉×D₅×D₁₉	direct (N × H)
125. C₅	C₂×C₅×C₉×D₁₉	semidirect

H ≅ G/N

type

1. C₅×C₉×D₉₅

C₂

semidirect

2. C₅×C₉×D₅×C₁₉

C₂

semidirect

3. C₅²×C₉×D₁₉

C₂

semidirect

5. C₅²×C₉×C₁₉

C₂²

semidirect

7. C₉×D₅×D₁₉

C₅

direct (N × H)

11. C₅×D₅×D₁₉

C₉

direct (N × H)

13. C₉×D₉₅

C₂×C₅

semidirect

14. C₉×D₅×C₁₉

C₂×C₅

semidirect

17. C₅×C₉×D₁₉

D₅

direct (N × H)

18. C₅×C₉×D₁₉

C₂×C₅

semidirect

22. C₅×D₉₅

C₂×C₉

semidirect

23. C₅×D₅×C₁₉

C₂×C₉

semidirect

24. C₅²×D₁₉

C₂×C₉

semidirect

27. C₅×C₉×C₁₉

C₂×D₅

semidirect

28. C₅×C₉×C₁₉

C₂²×C₅

semidirect

37. C₅²×C₁₉

C₂²×C₉

semidirect

40. C₅×C₉×D₅

D₁₉

direct (N × H)

42. D₅×D₁₉

C₅×C₉

direct (N × H)

45. C₉×D₁₉

C₅×D₅

direct (N × H)

51. C₅²×C₉

C₂×D₁₉

semidirect

53. D₉₅

C₂×C₅×C₉

semidirect

56. C₅×D₁₉

C₉×D₅

direct (N × H)

57. C₅×D₁₉

C₂×C₅×C₉

semidirect

58. D₅×C₁₉

C₂×C₅×C₉

semidirect

61. C₉×C₁₉

C₂×C₅×D₅

semidirect

70. C₅×C₁₉

C₂×C₉×D₅

semidirect

71. C₅×C₁₉

C₂²×C₅×C₉

semidirect

78. C₉×D₅

C₅×D₁₉

direct (N × H)

86. C₅×D₅

C₉×D₁₉

direct (N × H)

88. C₅×C₉

D₅×D₁₉

direct (N × H)

89. C₅×C₉

C₂×C₅×D₁₉

semidirect

92. D₁₉

C₅×C₉×D₅

direct (N × H)

101. C₅²

C₂×C₉×D₁₉

semidirect

104. C₁₉

C₂×C₅×C₉×D₅

semidirect

118. D₅

C₅×C₉×D₁₉

direct (N × H)

119. C₉

C₅×D₅×D₁₉

direct (N × H)

124. C₅

C₉×D₅×D₁₉

direct (N × H)

125. C₅

C₂×C₅×C₉×D₁₉

semidirect

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

subgroup	index
C₅×C₉×D₉₅	2
C₅×C₉×D₅×C₁₉	2
C₅²×C₉×D₁₉	2
C₃×C₅×D₅×D₁₉	3
C₂×C₅×C₉×D₁₉	5
C₉×D₅×D₁₉	5
C₂×C₅×C₉×D₅	19

subgroup

index

C₅×C₉×D₉₅

C₅×C₉×D₅×C₁₉

C₅²×C₉×D₁₉

C₃×C₅×D₅×D₁₉

C₂×C₅×C₉×D₁₉

C₉×D₅×D₁₉

C₂×C₅×C₉×D₅

Subgroups — C₅×C₉×D₅×D₁₉ #30685574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×C9×D5×D19 #30685574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×D₅×D₁₉ #30685574