Group #30685588 — subgroups

Subgroups — C₅×D₁₉×D₄₅ #30685588

Order 17100.

144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 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×D₈₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₉×D₄₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₉×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₁₅×D₁₉	—	3	1	no	maximal
5	C₅²×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉×D₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×D₉×D₁₉	—	5	1	no	maximal
8	C₅×D₂₈₅	—	3	1	no	—
9	C₅×C₁₉×D₁₅	—	3	1	no	—
10	C₃×C₅²×D₁₉	D₃	1	1	yes	characteristic
11	C₅×D₅×D₁₉	—	9	1	no	Hall
12	D₈₅₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₁₉×D₄₅	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×D₁₇₁	—	5	1	no	—
15	C₅×D₉×C₁₉	—	5	1	no	—
16	C₅×C₉×D₁₉	—	2	2	no	—
17	C₅×C₉×D₁₉	D₅	1	1	yes	characteristic, complemented
18	C₅×C₉×D₁₉	C₂×C₅	1	1	yes	characteristic, complemented
19	C₃×C₅²×C₁₉	C₂×D₃	1	1	yes	characteristic
20	D₁₅×D₁₉	—	3	1	no	—
21	C₅×D₃×D₁₉	—	15	1	no	—
22	C₅×D₉₅	—	9	1	no	—
23	C₅×D₅×C₁₉	—	9	1	no	—
24	C₅²×D₁₉	D₉	1	1	yes	characteristic, complemented
25	C₂×C₅×D₄₅	—	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	D₉×D₁₉	—	5	1	no	Hall
30	D₂₈₅	—	3	1	no	—
31	C₁₉×D₁₅	—	3	1	no	—
32	C₅×D₅₇	—	15	1	no	—
33	C₅×D₃×C₁₉	—	15	1	no	—
34	C₃×C₅×D₁₉	—	2	2	no	—
35	C₃×C₅×D₁₉	C₅×D₃	1	1	yes	characteristic
36	C₃×C₅×D₁₉	D₁₅	1	1	yes	characteristic
37	C₅²×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
38	C₂×C₅²×C₉	—	19	1	no	—
39	C₅×D₄₅	—	19	1	no	—
40	C₅×D₄₅	D₁₉	1	1	yes	characteristic, direct product factor
41	C₂×C₅×D₁₉	—	45	1	no	—
42	D₅×D₁₉	—	9	1	no	—
43	D₁₇₁	—	5	1	no	—
44	C₉×D₁₉	C₅×D₅	1	1	yes	characteristic, complemented
45	D₉×C₁₉	—	5	1	no	—
46	C₂×C₅×D₁₅	—	57	1	no	—
47	C₃×C₅×C₁₉	—	2	2	no	—
48	C₃×C₅×C₁₉	C₂×C₅×D₃	1	1	yes	characteristic
49	C₃×C₅×C₁₉	C₂×D₁₅	1	1	yes	characteristic
50	D₃×D₁₉	—	15	1	no	—
51	C₅²×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
52	C₂×C₅×C₁₉	—	45	1	no	—
53	D₉₅	—	9	1	no	—
54	C₅×D₁₉	—	2	2	no	—
55	C₅×D₁₉	—	45	1	no	—
56	C₅×D₁₉	C₅×D₉	1	1	yes	characteristic, complemented
57	C₅×D₁₉	D₄₅	1	1	yes	characteristic, direct product factor
58	D₅×C₁₉	—	9	1	no	—
59	C₂×D₄₅	—	19	1	no	—
60	C₂×C₅×D₉	—	95	1	no	—
61	C₉×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
62	C₂×C₃×C₅²	—	19	1	no	—
63	C₅×D₁₅	—	3	1	no	—
64	C₅×D₁₅	—	57	1	no	—
65	D₅₇	—	15	1	no	—
66	C₃×D₁₉	C₅×D₁₅	1	1	yes	characteristic
67	D₃×C₁₉	—	15	1	no	—
68	C₂×C₅×D₅	—	171	1	no	Hall
69	C₅×C₁₉	—	2	2	no	—
70	C₅×C₁₉	C₂×C₅×D₉	1	1	yes	characteristic, complemented
71	C₅×C₁₉	C₂×D₄₅	1	1	yes	characteristic, complemented
72	C₂×C₅×C₉	—	19	1	no	—
73	C₂×C₅×C₉	—	19	1	no	—
74	C₂×C₅×C₉	—	38	2	no	—
75	D₄₅	—	19	1	no	—
76	D₄₅	C₅×D₁₉	1	1	yes	characteristic, direct product factor
77	C₅×D₉	—	5	1	no	—
78	C₅×D₉	—	95	1	no	—
79	C₂×D₁₉	—	45	1	no	Hall
80	C₃×C₅²	D₃×D₁₉	1	1	yes	characteristic
81	C₂×D₁₅	—	57	1	no	—
82	C₂×C₅×D₃	—	285	1	no	—
83	C₃×C₁₉	C₂×C₅×D₁₅	1	1	yes	characteristic
84	C₂×C₅²	—	19	1	no	—
85	C₅×D₅	—	9	1	no	—
86	C₅×D₅	—	171	1	no	—
87	C₅×C₉	—	2	2	no	—
88	C₅×C₉	D₅×D₁₉	1	1	yes	characteristic, complemented
89	C₅×C₉	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented
90	C₂×C₁₉	—	45	1	no	—
91	D₁₉	—	45	1	no	—
92	D₁₉	C₅×D₄₅	1	1	yes	characteristic, direct product factor
93	C₂×D₉	—	95	1	no	Hall
94	C₂×C₃×C₅	—	19	1	no	—
95	C₂×C₃×C₅	—	19	1	no	—
96	C₂×C₃×C₅	—	38	2	no	—
97	D₁₅	—	3	1	no	—
98	D₁₅	—	57	1	no	—
99	C₅×D₃	—	15	1	no	—
100	C₅×D₃	—	285	1	no	—
101	C₅²	D₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
102	C₂²×C₅	—	855	1	no	—
103	C₂×D₅	—	171	1	no	—
104	C₁₉	C₂×C₅×D₄₅	1	1	yes	characteristic, complemented, Sylow
105	C₂×C₉	—	19	1	no	—
106	D₉	—	5	1	no	—
107	D₉	—	95	1	no	—
108	C₃×C₅	—	2	2	no	—
109	C₃×C₅	C₅×D₃×D₁₉	1	1	yes	characteristic
110	C₃×C₅	D₁₅×D₁₉	1	1	yes	characteristic
111	C₂×D₃	—	285	1	no	—
112	C₂×C₅	—	19	1	no	—
113	C₂×C₅	—	19	1	no	—
114	C₂×C₅	—	38	2	no	—
115	C₂×C₅	—	45	1	no	—
116	C₂×C₅	—	855	1	no	—
117	D₅	—	9	1	no	—
118	D₅	—	171	1	no	—
119	C₉	C₅×D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₃	—	19	1	no	—
121	D₃	—	15	1	no	—
122	D₃	—	285	1	no	—
123	C₅	—	2	2	no	—
124	C₅	C₅×D₉×D₁₉	1	1	yes	characteristic, complemented
125	C₅	D₁₉×D₄₅	1	1	yes	characteristic, direct product factor
126	C₂²	—	855	1	no	Sylow
127	C₃	C₅×D₁₅×D₁₉	1	1	yes	characteristic
128	C₂	—	19	1	no	—
129	C₂	—	45	1	no	—
130	C₂	—	855	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×D₈₅₅

C₂

yes

maximal, characteristic, complemented

C₅×C₁₉×D₄₅

C₂

yes

maximal, characteristic, complemented

C₅²×C₉×D₁₉

C₂

yes

maximal, characteristic, complemented

C₅×D₁₅×D₁₉

—

maximal

C₅²×C₉×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₁₉×D₄₅

C₅

yes

maximal, characteristic, direct product factor

C₅×D₉×D₁₉

—

maximal

C₅×D₂₈₅

—

C₅×C₁₉×D₁₅

—

C₃×C₅²×D₁₉

D₃

yes

characteristic

C₅×D₅×D₁₉

—

Hall

D₈₅₅

C₂×C₅

yes

characteristic, complemented

C₁₉×D₄₅

C₂×C₅

yes

characteristic, complemented

C₅×D₁₇₁

—

C₅×D₉×C₁₉

—

C₅×C₉×D₁₉

—

C₅×C₉×D₁₉

D₅

yes

characteristic, complemented

C₅×C₉×D₁₉

C₂×C₅

yes

characteristic, complemented

C₃×C₅²×C₁₉

C₂×D₃

yes

characteristic

D₁₅×D₁₉

—

C₅×D₃×D₁₉

—

C₅×D₉₅

—

C₅×D₅×C₁₉

—

C₅²×D₁₉

D₉

yes

characteristic, complemented

C₂×C₅×D₄₅

—

maximal, Hall

C₅×C₉×C₁₉

—

C₅×C₉×C₁₉

C₂×D₅

yes

characteristic, complemented

C₅×C₉×C₁₉

C₂²×C₅

yes

characteristic, complemented

D₉×D₁₉

—

Hall

D₂₈₅

—

C₁₉×D₁₅

—

C₅×D₅₇

—

C₅×D₃×C₁₉

—

C₃×C₅×D₁₉

—

C₃×C₅×D₁₉

C₅×D₃

yes

characteristic

C₃×C₅×D₁₉

D₁₅

yes

characteristic

C₅²×C₁₉

C₂×D₉

yes

characteristic, complemented, Hall

C₂×C₅²×C₉

—

C₅×D₄₅

—

C₅×D₄₅

D₁₉

yes

characteristic, direct product factor

C₂×C₅×D₁₉

—

D₅×D₁₉

—

D₁₇₁

—

C₉×D₁₉

C₅×D₅

yes

characteristic, complemented

D₉×C₁₉

—

C₂×C₅×D₁₅

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₅×D₃

yes

characteristic

C₃×C₅×C₁₉

C₂×D₁₅

yes

characteristic

D₃×D₁₉

—

C₅²×C₉

C₂×D₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

D₉₅

—

C₅×D₁₉

—

C₅×D₁₉

—

C₅×D₁₉

C₅×D₉

yes

characteristic, complemented

C₅×D₁₉

D₄₅

yes

characteristic, direct product factor

D₅×C₁₉

—

C₂×D₄₅

—

C₂×C₅×D₉

—

C₉×C₁₉

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₅×D₁₅

—

C₅×D₁₅

—

D₅₇

—

C₃×D₁₉

C₅×D₁₅

yes

characteristic

D₃×C₁₉

—

C₂×C₅×D₅

—

171

Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₅×D₉

yes

characteristic, complemented

C₅×C₁₉

C₂×D₄₅

yes

characteristic, complemented

C₂×C₅×C₉

—

C₂×C₅×C₉

—

C₂×C₅×C₉

—

D₄₅

—

D₄₅

C₅×D₁₉

yes

characteristic, direct product factor

C₅×D₉

—

C₅×D₉

—

C₂×D₁₉

—

Hall

C₃×C₅²

D₃×D₁₉

yes

characteristic

C₂×D₁₅

—

C₂×C₅×D₃

—

285

—

C₃×C₁₉

C₂×C₅×D₁₅

yes

characteristic

C₂×C₅²

—

C₅×D₅

—

C₅×D₅

—

171

—

C₅×C₉

—

C₅×C₉

D₅×D₁₉

yes

characteristic, complemented

C₅×C₉

C₂×C₅×D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

D₁₉

—

D₁₉

C₅×D₄₅

yes

characteristic, direct product factor

C₂×D₉

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

—

D₁₅

—

D₁₅

—

C₅×D₃

—

100

C₅×D₃

—

285

—

101

C₅²

D₉×D₁₉

yes

characteristic, complemented, Sylow

102

C₂²×C₅

—

855

—

103

C₂×D₅

—

171

—

104

C₁₉

C₂×C₅×D₄₅

yes

characteristic, complemented, Sylow

105

C₂×C₉

—

106

D₉

—

107

D₉

—

108

C₃×C₅

—

109

C₃×C₅

C₅×D₃×D₁₉

yes

characteristic

110

C₃×C₅

D₁₅×D₁₉

yes

characteristic

111

C₂×D₃

—

285

—

112

C₂×C₅

—

113

C₂×C₅

—

114

C₂×C₅

—

115

C₂×C₅

—

116

C₂×C₅

—

855

—

117

D₅

—

118

D₅

—

171

—

119

C₉

C₅×D₅×D₁₉

yes

characteristic, complemented, Sylow

120

C₂×C₃

—

121

D₃

—

122

D₃

—

285

—

123

C₅

—

124

C₅

C₅×D₉×D₁₉

yes

characteristic, complemented

125

C₅

D₁₉×D₄₅

yes

characteristic, direct product factor

126

C₂²

—

855

Sylow

127

C₃

C₅×D₁₅×D₁₉

yes

characteristic

128

C₂

—

129

C₂

—

130

C₂

—

855

—

	subgroup	G/H
center, hypercenter	C₅	D₁₉×D₄₅
commutator, cosocle, hypocenter	C₅×C₉×C₁₉	C₂²×C₅
Frattini	C₃	C₅×D₁₅×D₁₉
Fitting	C₅²×C₉×C₁₉	C₂²
socle	C₃×C₅²×C₁₉	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₉
UCS	C₁ ◁ C₅

subgroup

G/H

center, hypercenter

C₅

D₁₉×D₄₅

commutator, cosocle, hypocenter

C₅×C₉×C₁₉

C₂²×C₅

Frattini

C₃

C₅×D₁₅×D₁₉

Fitting

C₅²×C₉×C₁₉

C₂²

socle

C₃×C₅²×C₁₉

C₂×D₃

LCS

G ▷ C₅×C₉×C₁₉

UCS

C₁ ◁ C₅

N	H ≅ G/N	type
1. C₅×D₈₅₅	C₂	semidirect
2. C₅×C₁₉×D₄₅	C₂	semidirect
3. C₅²×C₉×D₁₉	C₂	semidirect
5. C₅²×C₉×C₁₉	C₂²	semidirect
6. D₁₉×D₄₅	C₅	direct (N × H)
12. D₈₅₅	C₂×C₅	semidirect
13. C₁₉×D₄₅	C₂×C₅	semidirect
17. C₅×C₉×D₁₉	D₅	semidirect
18. C₅×C₉×D₁₉	C₂×C₅	semidirect
24. C₅²×D₁₉	D₉	semidirect
27. C₅×C₉×C₁₉	C₂×D₅	semidirect
28. C₅×C₉×C₁₉	C₂²×C₅	semidirect
37. C₅²×C₁₉	C₂×D₉	semidirect
40. C₅×D₄₅	D₁₉	direct (N × H)
44. C₉×D₁₉	C₅×D₅	semidirect
51. C₅²×C₉	C₂×D₁₉	semidirect
56. C₅×D₁₉	C₅×D₉	semidirect
57. C₅×D₁₉	D₄₅	direct (N × H)
61. C₉×C₁₉	C₂×C₅×D₅	semidirect
70. C₅×C₁₉	C₂×C₅×D₉	semidirect
71. C₅×C₁₉	C₂×D₄₅	semidirect
76. D₄₅	C₅×D₁₉	direct (N × H)
88. C₅×C₉	D₅×D₁₉	semidirect
89. C₅×C₉	C₂×C₅×D₁₉	semidirect
92. D₁₉	C₅×D₄₅	direct (N × H)
101. C₅²	D₉×D₁₉	semidirect
104. C₁₉	C₂×C₅×D₄₅	semidirect
119. C₉	C₅×D₅×D₁₉	semidirect
124. C₅	C₅×D₉×D₁₉	semidirect
125. C₅	D₁₉×D₄₅	direct (N × H)

H ≅ G/N

type

1. C₅×D₈₅₅

C₂

semidirect

2. C₅×C₁₉×D₄₅

C₂

semidirect

3. C₅²×C₉×D₁₉

C₂

semidirect

5. C₅²×C₉×C₁₉

C₂²

semidirect

6. D₁₉×D₄₅

C₅

direct (N × H)

12. D₈₅₅

C₂×C₅

semidirect

13. C₁₉×D₄₅

C₂×C₅

semidirect

17. C₅×C₉×D₁₉

D₅

semidirect

18. C₅×C₉×D₁₉

C₂×C₅

semidirect

24. C₅²×D₁₉

D₉

semidirect

27. C₅×C₉×C₁₉

C₂×D₅

semidirect

28. C₅×C₉×C₁₉

C₂²×C₅

semidirect

37. C₅²×C₁₉

C₂×D₉

semidirect

40. C₅×D₄₅

D₁₉

direct (N × H)

44. C₉×D₁₉

C₅×D₅

semidirect

51. C₅²×C₉

C₂×D₁₉

semidirect

56. C₅×D₁₉

C₅×D₉

semidirect

57. C₅×D₁₉

D₄₅

direct (N × H)

61. C₉×C₁₉

C₂×C₅×D₅

semidirect

70. C₅×C₁₉

C₂×C₅×D₉

semidirect

71. C₅×C₁₉

C₂×D₄₅

semidirect

76. D₄₅

C₅×D₁₉

direct (N × H)

88. C₅×C₉

D₅×D₁₉

semidirect

89. C₅×C₉

C₂×C₅×D₁₉

semidirect

92. D₁₉

C₅×D₄₅

direct (N × H)

101. C₅²

D₉×D₁₉

semidirect

104. C₁₉

C₂×C₅×D₄₅

semidirect

119. C₉

C₅×D₅×D₁₉

semidirect

124. C₅

C₅×D₉×D₁₉

semidirect

125. C₅

D₁₉×D₄₅

direct (N × H)

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

subgroup	index
C₅×D₈₅₅	2
C₅×C₁₉×D₄₅	2
C₅²×C₉×D₁₉	2
C₅×D₁₅×D₁₉	3
D₁₉×D₄₅	5
C₅×D₉×D₁₉	5
C₂×C₅×D₄₅	19

subgroup

index

C₅×D₈₅₅

C₅×C₁₉×D₄₅

C₅²×C₉×D₁₉

C₅×D₁₅×D₁₉

D₁₉×D₄₅

C₅×D₉×D₁₉

C₂×C₅×D₄₅

Subgroups — C₅×D₁₉×D₄₅ #30685588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D19×D45 #30685588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₉×D₄₅ #30685588