Group #49178391 — subgroups

Subgroups — D₁₉×D₄₉₅ #49178391

Order 37620.

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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	D₉₄₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₄₉₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₉×C₁₁×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₁₆₅	—	3	1	no	maximal
5	C₅×C₉×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉×D₉₉	—	5	1	no	maximal, Hall
7	D₃₁₃₅	—	3	1	no	—
8	C₁₉×D₁₆₅	—	3	1	no	—
9	C₃×C₅×C₁₁×D₁₉	D₃	1	1	yes	characteristic
10	D₁₉×D₅₅	—	9	1	no	Hall
11	D₁₈₈₁	—	5	1	no	—
12	C₁₉×D₉₉	—	5	1	no	—
13	C₉×C₁₁×D₁₉	D₅	1	1	yes	characteristic, complemented
14	D₁₉×D₄₅	—	11	1	no	maximal, Hall
15	C₃×C₅×C₁₁×C₁₉	C₂×D₃	1	1	yes	characteristic
16	D₁₉×D₃₃	—	15	1	no	—
17	D₁₀₄₅	—	9	1	no	—
18	C₁₉×D₅₅	—	9	1	no	—
19	C₅×C₁₁×D₁₉	D₉	1	1	yes	characteristic, complemented
20	C₂×D₄₉₅	—	19	1	no	maximal, Hall
21	C₉×C₁₁×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
22	D₈₅₅	—	11	1	no	—
23	C₁₉×D₄₅	—	11	1	no	—
24	C₅×C₉×D₁₉	D₁₁	1	1	yes	characteristic, complemented
25	D₆₂₇	—	15	1	no	—
26	C₁₉×D₃₃	—	15	1	no	—
27	C₃×C₁₁×D₁₉	D₁₅	1	1	yes	characteristic
28	D₁₅×D₁₉	—	33	1	no	—
29	C₅×C₁₁×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₉×C₁₁	—	19	1	no	—
31	D₄₉₅	—	19	1	no	—
32	D₄₉₅	D₁₉	1	1	yes	characteristic, direct product factor
33	C₅×C₉×C₁₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
34	D₁₁×D₁₉	—	45	1	no	Hall
35	D₉×D₁₉	—	55	1	no	Hall
36	C₂×D₁₆₅	—	57	1	no	—
37	C₃×C₁₁×C₁₉	C₂×D₁₅	1	1	yes	characteristic
38	D₂₈₅	—	33	1	no	—
39	C₁₉×D₁₅	—	33	1	no	—
40	C₃×C₅×D₁₉	D₃₃	1	1	yes	characteristic
41	C₅×C₉×C₁₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
42	D₂₀₉	—	45	1	no	—
43	C₁₁×D₁₉	D₄₅	1	1	yes	characteristic, complemented
44	C₁₉×D₁₁	—	45	1	no	—
45	C₂×D₉₉	—	95	1	no	Hall
46	D₅×D₁₉	—	99	1	no	Hall
47	D₁₇₁	—	55	1	no	—
48	C₉×D₁₉	D₅₅	1	1	yes	characteristic, complemented
49	D₉×C₁₉	—	55	1	no	—
50	C₂×C₃×C₅×C₁₁	—	19	1	no	—
51	D₁₆₅	—	3	1	no	—
52	D₁₆₅	—	57	1	no	—
53	C₃×C₅×C₁₉	C₂×D₃₃	1	1	yes	characteristic
54	D₃×D₁₉	—	165	1	no	—
55	C₂×D₅₅	—	171	1	no	Hall
56	C₁₁×C₁₉	C₂×D₄₅	1	1	yes	characteristic, complemented, Hall
57	C₂×C₉×C₁₁	—	19	1	no	—
58	D₉₉	—	5	1	no	—
59	D₉₉	—	95	1	no	—
60	D₉₅	—	99	1	no	—
61	C₅×D₁₉	D₉₉	1	1	yes	characteristic, complemented
62	D₅×C₁₉	—	99	1	no	—
63	C₂×D₄₅	—	209	1	no	Hall
64	C₉×C₁₉	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
65	C₃×C₅×C₁₁	D₃×D₁₉	1	1	yes	characteristic
66	C₂×D₃₃	—	285	1	no	—
67	D₅₇	—	165	1	no	—
68	C₃×D₁₉	D₁₆₅	1	1	yes	characteristic
69	D₃×C₁₉	—	165	1	no	—
70	C₂×C₅×C₁₁	—	19	1	no	—
71	D₅₅	—	9	1	no	—
72	D₅₅	—	171	1	no	—
73	C₉×C₁₁	D₅×D₁₉	1	1	yes	characteristic, complemented, Hall
74	C₅×C₁₉	C₂×D₉₉	1	1	yes	characteristic, complemented, Hall
75	C₂×C₅×C₉	—	19	1	no	—
76	D₄₅	—	11	1	no	—
77	D₄₅	—	209	1	no	—
78	C₂×D₁₉	—	495	1	no	Hall
79	C₂×C₃×C₁₁	—	19	1	no	—
80	D₃₃	—	15	1	no	—
81	D₃₃	—	285	1	no	—
82	C₂×D₁₅	—	627	1	no	—
83	C₃×C₁₉	C₂×D₁₆₅	1	1	yes	characteristic
84	C₅×C₁₁	D₉×D₁₉	1	1	yes	characteristic, complemented, Hall
85	C₅×C₉	D₁₁×D₁₉	1	1	yes	characteristic, complemented, Hall
86	C₂×D₁₁	—	855	1	no	Hall
87	C₂×C₁₉	—	495	1	no	—
88	D₁₉	—	495	1	no	—
89	D₁₉	D₄₉₅	1	1	yes	characteristic, direct product factor
90	C₂×D₉	—	1045	1	no	Hall
91	C₃×C₁₁	D₁₅×D₁₉	1	1	yes	characteristic
92	C₂×C₃×C₅	—	19	1	no	—
93	D₁₅	—	33	1	no	—
94	D₁₅	—	627	1	no	—
95	C₂×C₁₁	—	19	1	no	—
96	D₁₁	—	45	1	no	—
97	D₁₁	—	855	1	no	—
98	C₂×D₅	—	1881	1	no	Hall
99	C₁₉	C₂×D₄₉₅	1	1	yes	characteristic, complemented, Sylow
100	C₂×C₉	—	19	1	no	—
101	D₉	—	1045	1	no	—
102	D₉	—	55	1	no	—
103	C₃×C₅	D₁₉×D₃₃	1	1	yes	characteristic
104	C₂×D₃	—	3135	1	no	—
105	C₁₁	D₁₉×D₄₅	1	1	yes	characteristic, complemented, Sylow
106	C₂×C₅	—	19	1	no	—
107	D₅	—	1881	1	no	—
108	D₅	—	99	1	no	—
109	C₉	D₁₉×D₅₅	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	19	1	no	—
111	D₃	—	3135	1	no	—
112	D₃	—	165	1	no	—
113	C₅	D₁₉×D₉₉	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	9405	1	no	Sylow
115	C₃	D₁₉×D₁₆₅	1	1	yes	characteristic
116	C₂	—	19	1	no	—
117	C₂	—	9405	1	no	—
118	C₂	—	495	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

D₉₄₀₅

C₂

yes

maximal, characteristic, complemented

C₁₉×D₄₉₅

C₂

yes

maximal, characteristic, complemented

C₅×C₉×C₁₁×D₁₉

C₂

yes

maximal, characteristic, complemented

D₁₉×D₁₆₅

—

maximal

C₅×C₉×C₁₁×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₁₉×D₉₉

—

maximal, Hall

D₃₁₃₅

—

C₁₉×D₁₆₅

—

C₃×C₅×C₁₁×D₁₉

D₃

yes

characteristic

D₁₉×D₅₅

—

Hall

D₁₈₈₁

—

C₁₉×D₉₉

—

C₉×C₁₁×D₁₉

D₅

yes

characteristic, complemented

D₁₉×D₄₅

—

maximal, Hall

C₃×C₅×C₁₁×C₁₉

C₂×D₃

yes

characteristic

D₁₉×D₃₃

—

D₁₀₄₅

—

C₁₉×D₅₅

—

C₅×C₁₁×D₁₉

D₉

yes

characteristic, complemented

C₂×D₄₉₅

—

maximal, Hall

C₉×C₁₁×C₁₉

C₂×D₅

yes

characteristic, complemented, Hall

D₈₅₅

—

C₁₉×D₄₅

—

C₅×C₉×D₁₉

D₁₁

yes

characteristic, complemented

D₆₂₇

—

C₁₉×D₃₃

—

C₃×C₁₁×D₁₉

D₁₅

yes

characteristic

D₁₅×D₁₉

—

C₅×C₁₁×C₁₉

C₂×D₉

yes

characteristic, complemented, Hall

C₂×C₅×C₉×C₁₁

—

D₄₉₅

—

D₄₉₅

D₁₉

yes

characteristic, direct product factor

C₅×C₉×C₁₉

C₂×D₁₁

yes

characteristic, complemented, Hall

D₁₁×D₁₉

—

Hall

D₉×D₁₉

—

Hall

C₂×D₁₆₅

—

C₃×C₁₁×C₁₉

C₂×D₁₅

yes

characteristic

D₂₈₅

—

C₁₉×D₁₅

—

C₃×C₅×D₁₉

D₃₃

yes

characteristic

C₅×C₉×C₁₁

C₂×D₁₉

yes

characteristic, complemented, Hall

D₂₀₉

—

C₁₁×D₁₉

D₄₅

yes

characteristic, complemented

C₁₉×D₁₁

—

C₂×D₉₉

—

Hall

D₅×D₁₉

—

Hall

D₁₇₁

—

C₉×D₁₉

D₅₅

yes

characteristic, complemented

D₉×C₁₉

—

C₂×C₃×C₅×C₁₁

—

D₁₆₅

—

D₁₆₅

—

C₃×C₅×C₁₉

C₂×D₃₃

yes

characteristic

D₃×D₁₉

—

165

—

C₂×D₅₅

—

171

Hall

C₁₁×C₁₉

C₂×D₄₅

yes

characteristic, complemented, Hall

C₂×C₉×C₁₁

—

D₉₉

—

D₉₉

—

D₉₅

—

C₅×D₁₉

D₉₉

yes

characteristic, complemented

D₅×C₁₉

—

C₂×D₄₅

—

209

Hall

C₉×C₁₉

C₂×D₅₅

yes

characteristic, complemented, Hall

C₃×C₅×C₁₁

D₃×D₁₉

yes

characteristic

C₂×D₃₃

—

285

—

D₅₇

—

165

—

C₃×D₁₉

D₁₆₅

yes

characteristic

D₃×C₁₉

—

165

—

C₂×C₅×C₁₁

—

D₅₅

—

D₅₅

—

171

—

C₉×C₁₁

D₅×D₁₉

yes

characteristic, complemented, Hall

C₅×C₁₉

C₂×D₉₉

yes

characteristic, complemented, Hall

C₂×C₅×C₉

—

D₄₅

—

D₄₅

—

209

—

C₂×D₁₉

—

495

Hall

C₂×C₃×C₁₁

—

D₃₃

—

D₃₃

—

285

—

C₂×D₁₅

—

627

—

C₃×C₁₉

C₂×D₁₆₅

yes

characteristic

C₅×C₁₁

D₉×D₁₉

yes

characteristic, complemented, Hall

C₅×C₉

D₁₁×D₁₉

yes

characteristic, complemented, Hall

C₂×D₁₁

—

855

Hall

C₂×C₁₉

—

495

—

D₁₉

—

495

—

D₁₉

D₄₉₅

yes

characteristic, direct product factor

C₂×D₉

—

1045

Hall

C₃×C₁₁

D₁₅×D₁₉

yes

characteristic

C₂×C₃×C₅

—

D₁₅

—

D₁₅

—

627

—

C₂×C₁₁

—

D₁₁

—

D₁₁

—

855

—

C₂×D₅

—

1881

Hall

C₁₉

C₂×D₄₉₅

yes

characteristic, complemented, Sylow

100

C₂×C₉

—

101

D₉

—

1045

—

102

D₉

—

103

C₃×C₅

D₁₉×D₃₃

yes

characteristic

104

C₂×D₃

—

3135

—

105

C₁₁

D₁₉×D₄₅

yes

characteristic, complemented, Sylow

106

C₂×C₅

—

107

D₅

—

1881

—

108

D₅

—

109

C₉

D₁₉×D₅₅

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

3135

—

112

D₃

—

165

—

113

C₅

D₁₉×D₉₉

yes

characteristic, complemented, Sylow

114

C₂²

—

9405

Sylow

115

C₃

D₁₉×D₁₆₅

yes

characteristic

116

C₂

—

117

C₂

—

9405

—

118

C₂

—

495

—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₁×C₁₉	C₂²
Frattini	C₃	D₁₉×D₁₆₅
socle	C₃×C₅×C₁₁×C₁₉	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₁×C₁₉
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, Fitting, cosocle, hypocenter

C₅×C₉×C₁₁×C₁₉

C₂²

Frattini

C₃

D₁₉×D₁₆₅

socle

C₃×C₅×C₁₁×C₁₉

C₂×D₃

LCS

G ▷ C₅×C₉×C₁₁×C₁₉

UCS

C₁

N	H ≅ G/N	type
1. D₉₄₀₅	C₂	semidirect
2. C₁₉×D₄₉₅	C₂	semidirect
3. C₅×C₉×C₁₁×D₁₉	C₂	semidirect
5. C₅×C₉×C₁₁×C₁₉	C₂²	semidirect
13. C₉×C₁₁×D₁₉	D₅	semidirect
19. C₅×C₁₁×D₁₉	D₉	semidirect
21. C₉×C₁₁×C₁₉	C₂×D₅	semidirect
24. C₅×C₉×D₁₉	D₁₁	semidirect
29. C₅×C₁₁×C₁₉	C₂×D₉	semidirect
32. D₄₉₅	D₁₉	direct (N × H)
33. C₅×C₉×C₁₉	C₂×D₁₁	semidirect
41. C₅×C₉×C₁₁	C₂×D₁₉	semidirect
43. C₁₁×D₁₉	D₄₅	semidirect
48. C₉×D₁₉	D₅₅	semidirect
56. C₁₁×C₁₉	C₂×D₄₅	semidirect
61. C₅×D₁₉	D₉₉	semidirect
64. C₉×C₁₉	C₂×D₅₅	semidirect
73. C₉×C₁₁	D₅×D₁₉	semidirect
74. C₅×C₁₉	C₂×D₉₉	semidirect
84. C₅×C₁₁	D₉×D₁₉	semidirect
85. C₅×C₉	D₁₁×D₁₉	semidirect
89. D₁₉	D₄₉₅	direct (N × H)
99. C₁₉	C₂×D₄₉₅	semidirect
105. C₁₁	D₁₉×D₄₅	semidirect
109. C₉	D₁₉×D₅₅	semidirect
113. C₅	D₁₉×D₉₉	semidirect

H ≅ G/N

type

1. D₉₄₀₅

C₂

semidirect

2. C₁₉×D₄₉₅

C₂

semidirect

3. C₅×C₉×C₁₁×D₁₉

C₂

semidirect

5. C₅×C₉×C₁₁×C₁₉

C₂²

semidirect

13. C₉×C₁₁×D₁₉

D₅

semidirect

19. C₅×C₁₁×D₁₉

D₉

semidirect

21. C₉×C₁₁×C₁₉

C₂×D₅

semidirect

24. C₅×C₉×D₁₉

D₁₁

semidirect

29. C₅×C₁₁×C₁₉

C₂×D₉

semidirect

32. D₄₉₅

D₁₉

direct (N × H)

33. C₅×C₉×C₁₉

C₂×D₁₁

semidirect

41. C₅×C₉×C₁₁

C₂×D₁₉

semidirect

43. C₁₁×D₁₉

D₄₅

semidirect

48. C₉×D₁₉

D₅₅

semidirect

56. C₁₁×C₁₉

C₂×D₄₅

semidirect

61. C₅×D₁₉

D₉₉

semidirect

64. C₉×C₁₉

C₂×D₅₅

semidirect

73. C₉×C₁₁

D₅×D₁₉

semidirect

74. C₅×C₁₉

C₂×D₉₉

semidirect

84. C₅×C₁₁

D₉×D₁₉

semidirect

85. C₅×C₉

D₁₁×D₁₉

semidirect

89. D₁₉

D₄₉₅

direct (N × H)

99. C₁₉

C₂×D₄₉₅

semidirect

105. C₁₁

D₁₉×D₄₅

semidirect

109. C₉

D₁₉×D₅₅

semidirect

113. C₅

D₁₉×D₉₉

semidirect

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

subgroup	index
D₉₄₀₅	2
C₁₉×D₄₉₅	2
C₅×C₉×C₁₁×D₁₉	2
D₁₉×D₁₆₅	3
D₁₉×D₉₉	5
D₁₉×D₄₅	11
C₂×D₄₉₅	19

subgroup

index

D₉₄₀₅

C₁₉×D₄₉₅

C₅×C₉×C₁₁×D₁₉

D₁₉×D₁₆₅

D₁₉×D₉₉

D₁₉×D₄₅

C₂×D₄₉₅

Subgroups — D₁₉×D₄₉₅ #49178391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D19×D495 #49178391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₉×D₄₉₅ #49178391