Group #37561024 — subgroups

Subgroups — D₉₅⋊D₆₃ #37561024

Order 23940.

120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 35 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	C₁₉×D₃₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₉×D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₉₅⋊D₂₁	—	3	1	no	maximal
5	C₅×C₇×C₉×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉×D₆₃	—	5	1	no	maximal, Hall
7	C₁₉×D₁₀₅	—	3	1	no	—
8	C₅×D₃₉₉	—	3	1	no	—
9	C₃×C₇×D₉₅	D₃	1	1	yes	characteristic
10	D₄₅⋊D₁₉	—	7	1	no	maximal, Hall
11	D₃₅⋊D₁₉	—	9	1	no	Hall
12	D₁₁₉₇	D₅	1	1	yes	characteristic, complemented
13	C₁₉×D₆₃	—	5	1	no	—
14	C₇×C₉×D₁₉	—	5	1	no	—
15	C₃×C₅×C₇×C₁₉	C₂×D₃	1	1	yes	characteristic
16	C₁₉×D₄₅	—	7	1	no	—
17	C₅×D₁₇₁	—	7	1	no	—
18	C₉×D₉₅	D₇	1	1	yes	characteristic, complemented
19	D₁₉×D₂₁	—	15	1	no	—
20	C₁₉×D₃₅	—	9	1	no	—
21	C₇×D₉₅	D₉	1	1	yes	characteristic, complemented
22	C₅×D₁₃₃	—	9	1	no	—
23	D₅×D₆₃	—	19	1	no	maximal, Hall
24	C₇×C₉×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
25	D₁₅⋊D₁₉	—	21	1	no	—
26	C₅×C₉×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
27	D₃₉₉	—	3	1	no	—
28	C₁₉×D₂₁	—	15	1	no	—
29	C₃×C₇×D₁₉	—	5	1	no	—
30	D₉×D₁₉	—	35	1	no	Hall
31	C₅×C₇×C₁₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
32	D₃₁₅	D₁₉	1	1	yes	characteristic, complemented
33	C₅×D₆₃	—	19	1	no	—
34	C₇×C₉×D₅	—	19	1	no	—
35	C₁₉×D₁₅	—	21	1	no	—
36	C₅×D₅₇	—	21	1	no	—
37	C₃×D₉₅	D₂₁	1	1	yes	characteristic
38	D₇×D₁₉	—	45	1	no	Hall
39	D₅×D₂₁	—	57	1	no	—
40	C₃×C₇×C₁₉	D₃×D₅	1	1	yes	characteristic
41	D₅×D₁₉	—	63	1	no	Hall
42	D₁₇₁	—	7	1	no	—
43	C₉×D₁₉	—	5	1	no	—
44	D₉×C₁₉	—	35	1	no	—
45	C₅×C₇×C₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
46	C₃×C₅×C₁₉	C₂×D₂₁	1	1	yes	characteristic
47	D₁₃₃	—	9	1	no	—
48	C₇×D₁₉	—	5	1	no	—
49	D₇×C₁₉	—	45	1	no	—
50	C₂×D₆₃	—	95	1	no	Hall
51	D₃×D₁₉	—	105	1	no	—
52	D₁₀₅	—	3	1	no	—
53	C₅×D₂₁	—	57	1	no	—
54	C₃×C₇×D₅	—	19	1	no	—
55	D₉₅	D₆₃	1	1	yes	characteristic, complemented
56	C₅×D₁₉	—	63	1	no	—
57	D₅×C₁₉	—	63	1	no	—
58	D₅×D₉	—	133	1	no	Hall
59	C₉×C₁₉	D₅×D₇	1	1	yes	characteristic, complemented, Hall
60	D₅×D₇	—	171	1	no	Hall
61	C₇×C₁₉	D₅×D₉	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇×C₉	—	95	1	no	—
63	D₆₃	—	5	1	no	—
64	D₆₃	—	19	1	no	—
65	D₅₇	—	21	1	no	—
66	C₃×D₁₉	—	5	1	no	—
67	D₃×C₁₉	—	105	1	no	—
68	C₃×C₅×C₇	D₃×D₁₉	1	1	yes	characteristic
69	C₅×C₁₉	C₂×D₆₃	1	1	yes	characteristic, complemented, Hall
70	D₄₅	—	7	1	no	—
71	C₉×D₅	—	19	1	no	—
72	C₅×D₉	—	133	1	no	—
73	C₂×D₂₁	—	285	1	no	—
74	C₂×D₁₉	—	315	1	no	Hall
75	D₃₅	—	9	1	no	—
76	C₅×D₇	—	171	1	no	—
77	C₇×D₅	—	19	1	no	—
78	C₇×C₉	D₅×D₁₉	1	1	yes	characteristic, complemented, Hall
79	D₃×D₅	—	399	1	no	—
80	C₃×C₁₉	D₅×D₂₁	1	1	yes	characteristic
81	C₅×C₉	D₇×D₁₉	1	1	yes	characteristic, complemented, Hall
82	C₂×C₃×C₇	—	95	1	no	—
83	D₂₁	—	15	1	no	—
84	D₂₁	—	57	1	no	—
85	C₂×C₁₉	—	315	1	no	—
86	D₁₉	—	5	1	no	—
87	D₁₉	—	63	1	no	—
88	C₂×D₉	—	665	1	no	Hall
89	C₅×C₇	D₉×D₁₉	1	1	yes	characteristic, complemented, Hall
90	D₁₅	—	21	1	no	—
91	C₃×D₅	—	19	1	no	—
92	C₅×D₃	—	399	1	no	—
93	C₂×D₇	—	855	1	no	Hall
94	C₃×C₇	D₁₅⋊D₁₉	1	1	yes	characteristic
95	C₂×D₅	—	1197	1	no	Hall
96	C₁₉	D₅×D₆₃	1	1	yes	characteristic, complemented, Sylow
97	C₂×C₉	—	95	1	no	—
98	D₉	—	35	1	no	—
99	D₉	—	133	1	no	—
100	C₃×C₅	D₁₉×D₂₁	1	1	yes	characteristic
101	C₂×C₇	—	95	1	no	—
102	D₇	—	45	1	no	—
103	D₇	—	171	1	no	—
104	C₂×D₃	—	1995	1	no	—
105	C₂×C₅	—	1197	1	no	—
106	D₅	—	19	1	no	—
107	D₅	—	63	1	no	—
108	C₉	D₃₅⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
109	C₇	D₄₅⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	95	1	no	—
111	D₃	—	105	1	no	—
112	D₃	—	399	1	no	—
113	C₅	D₁₉×D₆₃	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	5985	1	no	Sylow
115	C₃	D₉₅⋊D₂₁	1	1	yes	characteristic
116	C₂	—	315	1	no	—
117	C₂	—	95	1	no	—
118	C₂	—	1197	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×D₃₁₅

C₂

yes

maximal, characteristic, complemented

C₅×D₁₁₉₇

C₂

yes

maximal, characteristic, complemented

C₇×C₉×D₉₅

C₂

yes

maximal, characteristic, complemented

D₉₅⋊D₂₁

—

maximal

C₅×C₇×C₉×C₁₉

C₂²

yes

characteristic, complemented, Hall

D₁₉×D₆₃

—

maximal, Hall

C₁₉×D₁₀₅

—

C₅×D₃₉₉

—

C₃×C₇×D₉₅

D₃

yes

characteristic

D₄₅⋊D₁₉

—

maximal, Hall

D₃₅⋊D₁₉

—

Hall

D₁₁₉₇

D₅

yes

characteristic, complemented

C₁₉×D₆₃

—

C₇×C₉×D₁₉

—

C₃×C₅×C₇×C₁₉

C₂×D₃

yes

characteristic

C₁₉×D₄₅

—

C₅×D₁₇₁

—

C₉×D₉₅

D₇

yes

characteristic, complemented

D₁₉×D₂₁

—

C₁₉×D₃₅

—

C₇×D₉₅

D₉

yes

characteristic, complemented

C₅×D₁₃₃

—

D₅×D₆₃

—

maximal, Hall

C₇×C₉×C₁₉

C₂×D₅

yes

characteristic, complemented, Hall

D₁₅⋊D₁₉

—

C₅×C₉×C₁₉

C₂×D₇

yes

characteristic, complemented, Hall

D₃₉₉

—

C₁₉×D₂₁

—

C₃×C₇×D₁₉

—

D₉×D₁₉

—

Hall

C₅×C₇×C₁₉

C₂×D₉

yes

characteristic, complemented, Hall

D₃₁₅

D₁₉

yes

characteristic, complemented

C₅×D₆₃

—

C₇×C₉×D₅

—

C₁₉×D₁₅

—

C₅×D₅₇

—

C₃×D₉₅

D₂₁

yes

characteristic

D₇×D₁₉

—

Hall

D₅×D₂₁

—

C₃×C₇×C₁₉

D₃×D₅

yes

characteristic

D₅×D₁₉

—

Hall

D₁₇₁

—

C₉×D₁₉

—

D₉×C₁₉

—

C₅×C₇×C₉

C₂×D₁₉

yes

characteristic, complemented, Hall

C₃×C₅×C₁₉

C₂×D₂₁

yes

characteristic

D₁₃₃

—

C₇×D₁₉

—

D₇×C₁₉

—

C₂×D₆₃

—

Hall

D₃×D₁₉

—

105

—

D₁₀₅

—

C₅×D₂₁

—

C₃×C₇×D₅

—

D₉₅

D₆₃

yes

characteristic, complemented

C₅×D₁₉

—

D₅×C₁₉

—

D₅×D₉

—

133

Hall

C₉×C₁₉

D₅×D₇

yes

characteristic, complemented, Hall

D₅×D₇

—

171

Hall

C₇×C₁₉

D₅×D₉

yes

characteristic, complemented, Hall

C₂×C₇×C₉

—

D₆₃

—

D₆₃

—

D₅₇

—

C₃×D₁₉

—

D₃×C₁₉

—

105

—

C₃×C₅×C₇

D₃×D₁₉

yes

characteristic

C₅×C₁₉

C₂×D₆₃

yes

characteristic, complemented, Hall

D₄₅

—

C₉×D₅

—

C₅×D₉

—

133

—

C₂×D₂₁

—

285

—

C₂×D₁₉

—

315

Hall

D₃₅

—

C₅×D₇

—

171

—

C₇×D₅

—

C₇×C₉

D₅×D₁₉

yes

characteristic, complemented, Hall

D₃×D₅

—

399

—

C₃×C₁₉

D₅×D₂₁

yes

characteristic

C₅×C₉

D₇×D₁₉

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

D₂₁

—

D₂₁

—

C₂×C₁₉

—

315

—

D₁₉

—

D₁₉

—

C₂×D₉

—

665

Hall

C₅×C₇

D₉×D₁₉

yes

characteristic, complemented, Hall

D₁₅

—

C₃×D₅

—

C₅×D₃

—

399

—

C₂×D₇

—

855

Hall

C₃×C₇

D₁₅⋊D₁₉

yes

characteristic

C₂×D₅

—

1197

Hall

C₁₉

D₅×D₆₃

yes

characteristic, complemented, Sylow

C₂×C₉

—

D₉

—

D₉

—

133

—

100

C₃×C₅

D₁₉×D₂₁

yes

characteristic

101

C₂×C₇

—

102

D₇

—

103

D₇

—

171

—

104

C₂×D₃

—

1995

—

105

C₂×C₅

—

1197

—

106

D₅

—

107

D₅

—

108

C₉

D₃₅⋊D₁₉

yes

characteristic, complemented, Sylow

109

C₇

D₄₅⋊D₁₉

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

D₃

—

105

—

112

D₃

—

399

—

113

C₅

D₁₉×D₆₃

yes

characteristic, complemented, Sylow

114

C₂²

—

5985

Sylow

115

C₃

D₉₅⋊D₂₁

yes

characteristic

116

C₂

—

315

—

117

C₂

—

118

C₂

—

1197

—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₇×C₉×C₁₉	C₂²
Frattini	C₃	D₉₅⋊D₂₁
socle	C₃×C₅×C₇×C₁₉	C₂×D₃
LCS	G ▷ C₅×C₇×C₉×C₁₉
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, Fitting, cosocle, hypocenter

C₅×C₇×C₉×C₁₉

C₂²

Frattini

C₃

D₉₅⋊D₂₁

socle

C₃×C₅×C₇×C₁₉

C₂×D₃

LCS

G ▷ C₅×C₇×C₉×C₁₉

UCS

C₁

N	H ≅ G/N	type
1. C₁₉×D₃₁₅	C₂	semidirect
2. C₅×D₁₁₉₇	C₂	semidirect
3. C₇×C₉×D₉₅	C₂	semidirect
5. C₅×C₇×C₉×C₁₉	C₂²	semidirect
12. D₁₁₉₇	D₅	semidirect
18. C₉×D₉₅	D₇	semidirect
21. C₇×D₉₅	D₉	semidirect
24. C₇×C₉×C₁₉	C₂×D₅	semidirect
26. C₅×C₉×C₁₉	C₂×D₇	semidirect
31. C₅×C₇×C₁₉	C₂×D₉	semidirect
32. D₃₁₅	D₁₉	semidirect
45. C₅×C₇×C₉	C₂×D₁₉	semidirect
55. D₉₅	D₆₃	semidirect
59. C₉×C₁₉	D₅×D₇	semidirect
61. C₇×C₁₉	D₅×D₉	semidirect
69. C₅×C₁₉	C₂×D₆₃	semidirect
78. C₇×C₉	D₅×D₁₉	semidirect
81. C₅×C₉	D₇×D₁₉	semidirect
89. C₅×C₇	D₉×D₁₉	semidirect
96. C₁₉	D₅×D₆₃	semidirect
108. C₉	D₃₅⋊D₁₉	semidirect
109. C₇	D₄₅⋊D₁₉	semidirect
113. C₅	D₁₉×D₆₃	semidirect

H ≅ G/N

type

1. C₁₉×D₃₁₅

C₂

semidirect

2. C₅×D₁₁₉₇

C₂

semidirect

3. C₇×C₉×D₉₅

C₂

semidirect

5. C₅×C₇×C₉×C₁₉

C₂²

semidirect

12. D₁₁₉₇

D₅

semidirect

18. C₉×D₉₅

D₇

semidirect

21. C₇×D₉₅

D₉

semidirect

24. C₇×C₉×C₁₉

C₂×D₅

semidirect

26. C₅×C₉×C₁₉

C₂×D₇

semidirect

31. C₅×C₇×C₁₉

C₂×D₉

semidirect

32. D₃₁₅

D₁₉

semidirect

45. C₅×C₇×C₉

C₂×D₁₉

semidirect

55. D₉₅

D₆₃

semidirect

59. C₉×C₁₉

D₅×D₇

semidirect

61. C₇×C₁₉

D₅×D₉

semidirect

69. C₅×C₁₉

C₂×D₆₃

semidirect

78. C₇×C₉

D₅×D₁₉

semidirect

81. C₅×C₉

D₇×D₁₉

semidirect

89. C₅×C₇

D₉×D₁₉

semidirect

96. C₁₉

D₅×D₆₃

semidirect

108. C₉

D₃₅⋊D₁₉

semidirect

109. C₇

D₄₅⋊D₁₉

semidirect

113. C₅

D₁₉×D₆₃

semidirect

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

subgroup	index
C₁₉×D₃₁₅	2
C₅×D₁₁₉₇	2
C₇×C₉×D₉₅	2
D₉₅⋊D₂₁	3
D₁₉×D₆₃	5
D₄₅⋊D₁₉	7
D₅×D₆₃	19

subgroup

index

C₁₉×D₃₁₅

C₅×D₁₁₉₇

C₇×C₉×D₉₅

D₉₅⋊D₂₁

D₁₉×D₆₃

D₄₅⋊D₁₉

D₅×D₆₃

Subgroups — D₉₅⋊D₆₃ #37561024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D95⋊D63 #37561024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉₅⋊D₆₃ #37561024