Group #30685897 — subgroups

Subgroups — C₅×D₁₉×C₃⋊D₁₅ #30685897

Order 17100.

288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 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×C₃⋊D₂₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₁₉×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅²×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₁₅×D₁₉	—	3	4	no	maximal
5	C₃²×C₅²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉×C₃⋊D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₅×C₃⋊D₃×D₁₉	—	5	1	no	maximal
8	C₅×D₂₈₅	—	3	4	no	—
9	C₅×C₁₉×D₁₅	—	3	4	no	—
10	C₃×C₅²×D₁₉	D₃	1	4	yes	complemented
11	C₅×D₅×D₁₉	—	9	1	no	Hall
12	C₃⋊D₂₈₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₁₉×C₃⋊D₁₅	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₃⋊D₅₇	—	5	1	no	—
15	C₅×C₃⋊D₃×C₁₉	—	5	1	no	—
16	C₃²×C₅×D₁₉	—	2	2	no	—
17	C₃²×C₅×D₁₉	D₅	1	1	yes	characteristic, complemented
18	C₃²×C₅×D₁₉	C₂×C₅	1	1	yes	characteristic, complemented
19	C₃×C₅²×C₁₉	C₂×D₃	1	4	yes	complemented
20	D₁₅×D₁₉	—	3	4	no	—
21	C₅×D₃×D₁₉	—	15	4	no	—
22	C₅×D₉₅	—	9	1	no	—
23	C₅×D₅×C₁₉	—	9	1	no	—
24	C₅²×D₁₉	C₃⋊D₃	1	1	yes	characteristic, complemented
25	C₂×C₅×C₃⋊D₁₅	—	19	1	no	maximal, Hall
26	C₃²×C₅×C₁₉	—	2	2	no	—
27	C₃²×C₅×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented
28	C₃²×C₅×C₁₉	C₂²×C₅	1	1	yes	characteristic, complemented
29	C₃⋊D₃×D₁₉	—	5	1	no	Hall
30	D₂₈₅	—	3	4	no	—
31	C₁₉×D₁₅	—	3	4	no	—
32	C₅×D₅₇	—	15	4	no	—
33	C₅×D₃×C₁₉	—	15	4	no	—
34	C₃×C₅×D₁₉	—	2	8	no	—
35	C₃×C₅×D₁₉	C₅×D₃	1	4	yes	complemented
36	C₃×C₅×D₁₉	D₁₅	1	4	yes	complemented
37	C₅²×C₁₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃²×C₅²	—	19	1	no	—
39	C₅×C₃⋊D₁₅	—	19	1	no	—
40	C₅×C₃⋊D₁₅	D₁₉	1	1	yes	characteristic, direct product factor
41	C₂×C₅×D₁₉	—	45	1	no	—
42	D₅×D₁₉	—	9	1	no	—
43	C₃⋊D₅₇	—	5	1	no	—
44	C₃⋊D₃×C₁₉	—	5	1	no	—
45	C₃²×D₁₉	C₅×D₅	1	1	yes	characteristic, complemented
46	C₂×C₅×D₁₅	—	57	4	no	—
47	C₃×C₅×C₁₉	—	2	8	no	—
48	C₃×C₅×C₁₉	C₂×C₅×D₃	1	4	yes	complemented
49	C₃×C₅×C₁₉	C₂×D₁₅	1	4	yes	complemented
50	D₃×D₁₉	—	15	4	no	—
51	C₃²×C₅²	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×C₃⋊D₃	1	1	yes	characteristic, complemented
57	C₅×D₁₉	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
58	D₅×C₁₉	—	9	1	no	—
59	C₂×C₃⋊D₁₅	—	19	1	no	—
60	C₂×C₅×C₃⋊D₃	—	95	1	no	—
61	C₃²×C₁₉	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Hall
62	C₂×C₃×C₅²	—	19	4	no	—
63	C₅×D₁₅	—	3	4	no	—
64	C₅×D₁₅	—	57	4	no	—
65	D₅₇	—	15	4	no	—
66	C₃×D₁₉	C₅×D₁₅	1	4	yes	complemented
67	D₃×C₁₉	—	15	4	no	—
68	C₂×C₅×D₅	—	171	1	no	Hall
69	C₅×C₁₉	—	2	2	no	—
70	C₅×C₁₉	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
71	C₅×C₁₉	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented
72	C₂×C₃²×C₅	—	19	1	no	—
73	C₂×C₃²×C₅	—	19	1	no	—
74	C₂×C₃²×C₅	—	38	2	no	—
75	C₃⋊D₁₅	—	19	1	no	—
76	C₃⋊D₁₅	C₅×D₁₉	1	1	yes	characteristic, direct product factor
77	C₅×C₃⋊D₃	—	5	1	no	—
78	C₅×C₃⋊D₃	—	95	1	no	—
79	C₂×D₁₉	—	45	1	no	Hall
80	C₃×C₅²	D₃×D₁₉	1	4	yes	complemented
81	C₂×D₁₅	—	57	4	no	—
82	C₂×C₅×D₃	—	285	4	no	—
83	C₃×C₁₉	C₂×C₅×D₁₅	1	4	yes	complemented
84	C₂×C₅²	—	19	1	no	—
85	C₅×D₅	—	9	1	no	—
86	C₅×D₅	—	171	1	no	—
87	C₃²×C₅	—	2	2	no	—
88	C₃²×C₅	D₅×D₁₉	1	1	yes	characteristic, complemented
89	C₃²×C₅	C₂×C₅×D₁₉	1	1	yes	characteristic, complemented
90	C₂×C₁₉	—	45	1	no	—
91	D₁₉	—	45	1	no	—
92	D₁₉	C₅×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
93	C₂×C₃⋊D₃	—	95	1	no	Hall
94	C₂×C₃×C₅	—	19	4	no	—
95	C₂×C₃×C₅	—	19	4	no	—
96	C₂×C₃×C₅	—	38	8	no	—
97	D₁₅	—	3	4	no	—
98	D₁₅	—	57	4	no	—
99	C₅×D₃	—	15	4	no	—
100	C₅×D₃	—	285	4	no	—
101	C₅²	C₃⋊D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
102	C₂²×C₅	—	855	1	no	—
103	C₂×D₅	—	171	1	no	—
104	C₁₉	C₂×C₅×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
105	C₂×C₃²	—	19	1	no	—
106	C₃⋊D₃	—	5	1	no	—
107	C₃⋊D₃	—	95	1	no	—
108	C₃×C₅	—	2	8	no	—
109	C₃×C₅	C₅×D₃×D₁₉	1	4	yes	complemented
110	C₃×C₅	D₁₅×D₁₉	1	4	yes	complemented
111	C₂×D₃	—	285	4	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	C₃²	C₅×D₅×D₁₉	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₃	—	19	4	no	—
121	D₃	—	15	4	no	—
122	D₃	—	285	4	no	—
123	C₅	—	2	2	no	—
124	C₅	C₅×C₃⋊D₃×D₁₉	1	1	yes	characteristic, complemented
125	C₅	D₁₉×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
126	C₂²	—	855	1	no	Sylow
127	C₃	C₅×D₁₅×D₁₉	1	4	yes	complemented
128	C₂	—	19	1	no	—
129	C₂	—	45	1	no	—
130	C₂	—	855	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₃⋊D₂₈₅

C₂

yes

maximal, characteristic, complemented

C₅×C₁₉×C₃⋊D₁₅

C₂

yes

maximal, characteristic, complemented

C₃²×C₅²×D₁₉

C₂

yes

maximal, characteristic, complemented

C₅×D₁₅×D₁₉

—

maximal

C₃²×C₅²×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₁₉×C₃⋊D₁₅

C₅

yes

maximal, characteristic, direct product factor

C₅×C₃⋊D₃×D₁₉

—

maximal

C₅×D₂₈₅

—

C₅×C₁₉×D₁₅

—

C₃×C₅²×D₁₉

D₃

yes

complemented

C₅×D₅×D₁₉

—

Hall

C₃⋊D₂₈₅

C₂×C₅

yes

characteristic, complemented

C₁₉×C₃⋊D₁₅

C₂×C₅

yes

characteristic, complemented

C₅×C₃⋊D₅₇

—

C₅×C₃⋊D₃×C₁₉

—

C₃²×C₅×D₁₉

—

C₃²×C₅×D₁₉

D₅

yes

characteristic, complemented

C₃²×C₅×D₁₉

C₂×C₅

yes

characteristic, complemented

C₃×C₅²×C₁₉

C₂×D₃

yes

complemented

D₁₅×D₁₉

—

C₅×D₃×D₁₉

—

C₅×D₉₅

—

C₅×D₅×C₁₉

—

C₅²×D₁₉

C₃⋊D₃

yes

characteristic, complemented

C₂×C₅×C₃⋊D₁₅

—

maximal, Hall

C₃²×C₅×C₁₉

—

C₃²×C₅×C₁₉

C₂×D₅

yes

characteristic, complemented

C₃²×C₅×C₁₉

C₂²×C₅

yes

characteristic, complemented

C₃⋊D₃×D₁₉

—

Hall

D₂₈₅

—

C₁₉×D₁₅

—

C₅×D₅₇

—

C₅×D₃×C₁₉

—

C₃×C₅×D₁₉

—

C₃×C₅×D₁₉

C₅×D₃

yes

complemented

C₃×C₅×D₁₉

D₁₅

yes

complemented

C₅²×C₁₉

C₂×C₃⋊D₃

yes

characteristic, complemented, Hall

C₂×C₃²×C₅²

—

C₅×C₃⋊D₁₅

—

C₅×C₃⋊D₁₅

D₁₉

yes

characteristic, direct product factor

C₂×C₅×D₁₉

—

D₅×D₁₉

—

C₃⋊D₅₇

—

C₃⋊D₃×C₁₉

—

C₃²×D₁₉

C₅×D₅

yes

characteristic, complemented

C₂×C₅×D₁₅

—

C₃×C₅×C₁₉

—

C₃×C₅×C₁₉

C₂×C₅×D₃

yes

complemented

C₃×C₅×C₁₉

C₂×D₁₅

yes

complemented

D₃×D₁₉

—

C₃²×C₅²

C₂×D₁₉

yes

characteristic, complemented, Hall

C₂×C₅×C₁₉

—

D₉₅

—

C₅×D₁₉

—

C₅×D₁₉

—

C₅×D₁₉

C₅×C₃⋊D₃

yes

characteristic, complemented

C₅×D₁₉

C₃⋊D₁₅

yes

characteristic, direct product factor

D₅×C₁₉

—

C₂×C₃⋊D₁₅

—

C₂×C₅×C₃⋊D₃

—

C₃²×C₁₉

C₂×C₅×D₅

yes

characteristic, complemented, Hall

C₂×C₃×C₅²

—

C₅×D₁₅

—

C₅×D₁₅

—

D₅₇

—

C₃×D₁₉

C₅×D₁₅

yes

complemented

D₃×C₁₉

—

C₂×C₅×D₅

—

171

Hall

C₅×C₁₉

—

C₅×C₁₉

C₂×C₅×C₃⋊D₃

yes

characteristic, complemented

C₅×C₁₉

C₂×C₃⋊D₁₅

yes

characteristic, complemented

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₂×C₃²×C₅

—

C₃⋊D₁₅

—

C₃⋊D₁₅

C₅×D₁₉

yes

characteristic, direct product factor

C₅×C₃⋊D₃

—

C₅×C₃⋊D₃

—

C₂×D₁₉

—

Hall

C₃×C₅²

D₃×D₁₉

yes

complemented

C₂×D₁₅

—

C₂×C₅×D₃

—

285

—

C₃×C₁₉

C₂×C₅×D₁₅

yes

complemented

C₂×C₅²

—

C₅×D₅

—

C₅×D₅

—

171

—

C₃²×C₅

—

C₃²×C₅

D₅×D₁₉

yes

characteristic, complemented

C₃²×C₅

C₂×C₅×D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

D₁₉

—

D₁₉

C₅×C₃⋊D₁₅

yes

characteristic, direct product factor

C₂×C₃⋊D₃

—

Hall

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

—

D₁₅

—

D₁₅

—

C₅×D₃

—

100

C₅×D₃

—

285

—

101

C₅²

C₃⋊D₃×D₁₉

yes

characteristic, complemented, Sylow

102

C₂²×C₅

—

855

—

103

C₂×D₅

—

171

—

104

C₁₉

C₂×C₅×C₃⋊D₁₅

yes

characteristic, complemented, Sylow

105

C₂×C₃²

—

106

C₃⋊D₃

—

107

C₃⋊D₃

—

108

C₃×C₅

—

109

C₃×C₅

C₅×D₃×D₁₉

yes

complemented

110

C₃×C₅

D₁₅×D₁₉

yes

complemented

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

C₃²

C₅×D₅×D₁₉

yes

characteristic, complemented, Sylow

120

C₂×C₃

—

121

D₃

—

122

D₃

—

285

—

123

C₅

—

124

C₅

C₅×C₃⋊D₃×D₁₉

yes

characteristic, complemented

125

C₅

D₁₉×C₃⋊D₁₅

yes

characteristic, direct product factor

126

C₂²

—

855

Sylow

127

C₃

C₅×D₁₅×D₁₉

yes

complemented

128

C₂

—

129

C₂

—

130

C₂

—

855

—

	subgroup	G/H
center, hypercenter	C₅	D₁₉×C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅×C₁₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₁₉	C₂²
LCS	G ▷ C₃²×C₅×C₁₉
UCS	C₁ ◁ C₅

subgroup

G/H

center, hypercenter

C₅

D₁₉×C₃⋊D₁₅

commutator, cosocle, hypocenter

C₃²×C₅×C₁₉

C₂²×C₅

Frattini

C₁

Fitting, socle

C₃²×C₅²×C₁₉

C₂²

LCS

G ▷ C₃²×C₅×C₁₉

UCS

C₁ ◁ C₅

N	H ≅ G/N	type
1. C₅×C₃⋊D₂₈₅	C₂	semidirect
2. C₅×C₁₉×C₃⋊D₁₅	C₂	semidirect
3. C₃²×C₅²×D₁₉	C₂	semidirect
5. C₃²×C₅²×C₁₉	C₂²	semidirect
6. D₁₉×C₃⋊D₁₅	C₅	direct (N × H)
10. C₃×C₅²×D₁₉	D₃	semidirect
12. C₃⋊D₂₈₅	C₂×C₅	semidirect
13. C₁₉×C₃⋊D₁₅	C₂×C₅	semidirect
17. C₃²×C₅×D₁₉	D₅	semidirect
18. C₃²×C₅×D₁₉	C₂×C₅	semidirect
19. C₃×C₅²×C₁₉	C₂×D₃	semidirect
24. C₅²×D₁₉	C₃⋊D₃	semidirect
27. C₃²×C₅×C₁₉	C₂×D₅	semidirect
28. C₃²×C₅×C₁₉	C₂²×C₅	semidirect
35. C₃×C₅×D₁₉	C₅×D₃	semidirect
36. C₃×C₅×D₁₉	D₁₅	semidirect
37. C₅²×C₁₉	C₂×C₃⋊D₃	semidirect
40. C₅×C₃⋊D₁₅	D₁₉	direct (N × H)
45. C₃²×D₁₉	C₅×D₅	semidirect
48. C₃×C₅×C₁₉	C₂×C₅×D₃	semidirect
49. C₃×C₅×C₁₉	C₂×D₁₅	semidirect
51. C₃²×C₅²	C₂×D₁₉	semidirect
56. C₅×D₁₉	C₅×C₃⋊D₃	semidirect
57. C₅×D₁₉	C₃⋊D₁₅	direct (N × H)
61. C₃²×C₁₉	C₂×C₅×D₅	semidirect
66. C₃×D₁₉	C₅×D₁₅	semidirect
70. C₅×C₁₉	C₂×C₅×C₃⋊D₃	semidirect
71. C₅×C₁₉	C₂×C₃⋊D₁₅	semidirect
76. C₃⋊D₁₅	C₅×D₁₉	direct (N × H)
80. C₃×C₅²	D₃×D₁₉	semidirect
83. C₃×C₁₉	C₂×C₅×D₁₅	semidirect
88. C₃²×C₅	D₅×D₁₉	semidirect
89. C₃²×C₅	C₂×C₅×D₁₉	semidirect
92. D₁₉	C₅×C₃⋊D₁₅	direct (N × H)
101. C₅²	C₃⋊D₃×D₁₉	semidirect
104. C₁₉	C₂×C₅×C₃⋊D₁₅	semidirect
109. C₃×C₅	C₅×D₃×D₁₉	semidirect
110. C₃×C₅	D₁₅×D₁₉	semidirect
119. C₃²	C₅×D₅×D₁₉	semidirect
124. C₅	C₅×C₃⋊D₃×D₁₉	semidirect
125. C₅	D₁₉×C₃⋊D₁₅	direct (N × H)
127. C₃	C₅×D₁₅×D₁₉	semidirect

H ≅ G/N

type

1. C₅×C₃⋊D₂₈₅

C₂

semidirect

2. C₅×C₁₉×C₃⋊D₁₅

C₂

semidirect

3. C₃²×C₅²×D₁₉

C₂

semidirect

5. C₃²×C₅²×C₁₉

C₂²

semidirect

6. D₁₉×C₃⋊D₁₅

C₅

direct (N × H)

10. C₃×C₅²×D₁₉

D₃

semidirect

12. C₃⋊D₂₈₅

C₂×C₅

semidirect

13. C₁₉×C₃⋊D₁₅

C₂×C₅

semidirect

17. C₃²×C₅×D₁₉

D₅

semidirect

18. C₃²×C₅×D₁₉

C₂×C₅

semidirect

19. C₃×C₅²×C₁₉

C₂×D₃

semidirect

24. C₅²×D₁₉

C₃⋊D₃

semidirect

27. C₃²×C₅×C₁₉

C₂×D₅

semidirect

28. C₃²×C₅×C₁₉

C₂²×C₅

semidirect

35. C₃×C₅×D₁₉

C₅×D₃

semidirect

36. C₃×C₅×D₁₉

D₁₅

semidirect

37. C₅²×C₁₉

C₂×C₃⋊D₃

semidirect

40. C₅×C₃⋊D₁₅

D₁₉

direct (N × H)

45. C₃²×D₁₉

C₅×D₅

semidirect

48. C₃×C₅×C₁₉

C₂×C₅×D₃

semidirect

49. C₃×C₅×C₁₉

C₂×D₁₅

semidirect

51. C₃²×C₅²

C₂×D₁₉

semidirect

56. C₅×D₁₉

C₅×C₃⋊D₃

semidirect

57. C₅×D₁₉

C₃⋊D₁₅

direct (N × H)

61. C₃²×C₁₉

C₂×C₅×D₅

semidirect

66. C₃×D₁₉

C₅×D₁₅

semidirect

70. C₅×C₁₉

C₂×C₅×C₃⋊D₃

semidirect

71. C₅×C₁₉

C₂×C₃⋊D₁₅

semidirect

76. C₃⋊D₁₅

C₅×D₁₉

direct (N × H)

80. C₃×C₅²

D₃×D₁₉

semidirect

83. C₃×C₁₉

C₂×C₅×D₁₅

semidirect

88. C₃²×C₅

D₅×D₁₉

semidirect

89. C₃²×C₅

C₂×C₅×D₁₉

semidirect

92. D₁₉

C₅×C₃⋊D₁₅

direct (N × H)

101. C₅²

C₃⋊D₃×D₁₉

semidirect

104. C₁₉

C₂×C₅×C₃⋊D₁₅

semidirect

109. C₃×C₅

C₅×D₃×D₁₉

semidirect

110. C₃×C₅

D₁₅×D₁₉

semidirect

119. C₃²

C₅×D₅×D₁₉

semidirect

124. C₅

C₅×C₃⋊D₃×D₁₉

semidirect

125. C₅

D₁₉×C₃⋊D₁₅

direct (N × H)

127. C₃

C₅×D₁₅×D₁₉

semidirect

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

subgroup	index
C₅×C₃⋊D₂₈₅	2
C₅×C₁₉×C₃⋊D₁₅	2
C₃²×C₅²×D₁₉	2
C₅×D₁₅×D₁₉	3
D₁₉×C₃⋊D₁₅	5
C₅×C₃⋊D₃×D₁₉	5
C₂×C₅×C₃⋊D₁₅	19

subgroup

index

C₅×C₃⋊D₂₈₅

C₅×C₁₉×C₃⋊D₁₅

C₃²×C₅²×D₁₉

C₅×D₁₅×D₁₉

D₁₉×C₃⋊D₁₅

C₅×C₃⋊D₃×D₁₉

C₂×C₅×C₃⋊D₁₅

Subgroups — C₅×D₁₉×C₃⋊D₁₅ #30685897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×D19×C3⋊D15 #30685897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₉×C₃⋊D₁₅ #30685897