Group #37561517 — subgroups

Subgroups — C₃²×D₇×D₉₅ #37561517

Order 23940.

240 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 96 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	C₃²×C₅×D₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₇×D₉₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₆₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₇×D₉₅	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃²×D₇×D₁₉	—	5	1	no	maximal, Hall
7	C₃×D₆₆₅	C₂×C₃	1	4	yes	complemented
8	C₃×C₇×D₉₅	C₂×C₃	1	4	yes	complemented
9	C₃×C₅×D₇×C₁₉	C₂×C₃	1	4	yes	complemented
10	C₂×C₃²×D₉₅	—	7	1	no	maximal, Hall
11	D₇×D₉₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₃²×D₁₃₃	—	5	1	no	—
13	C₃²×D₇×C₁₉	D₅	1	1	yes	characteristic, complemented
14	C₃²×C₇×D₁₉	—	5	1	no	—
15	C₃×C₅×C₇×C₁₉	C₂²×C₃	1	4	yes	complemented
16	C₂×C₃²×C₅×C₁₉	—	7	1	no	—
17	C₃²×D₉₅	—	7	1	no	—
18	C₃²×D₉₅	D₇	1	1	yes	characteristic, direct product factor
19	C₃×D₇×D₁₉	—	5	4	no	—
20	D₆₆₅	C₂×C₃²	1	1	yes	characteristic, complemented
21	C₇×D₉₅	C₂×C₃²	1	1	yes	characteristic, complemented
22	C₅×D₇×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
23	C₃²×D₅×D₇	—	19	1	no	maximal, Hall
24	C₃²×C₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×D₉₅	—	7	4	no	—
26	C₃²×C₅×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
27	C₃×D₁₃₃	—	5	4	no	—
28	C₃×D₇×C₁₉	C₃×D₅	1	4	yes	complemented
29	C₃×C₇×D₁₉	—	5	4	no	—
30	C₂×C₃²×D₁₉	—	35	1	no	Hall
31	C₅×C₇×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
32	C₃²×D₃₅	—	19	1	no	—
33	C₃²×C₇×D₅	—	19	1	no	—
34	C₃²×C₅×D₇	D₁₉	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×C₁₉	—	7	4	no	—
36	C₃×D₉₅	—	7	4	no	—
37	C₃×D₉₅	C₃×D₇	1	4	yes	direct product factor
38	D₇×D₁₉	—	5	1	no	Hall
39	C₃×D₅×D₇	—	19	4	no	—
40	C₃×C₇×C₁₉	C₂×C₃×D₅	1	4	yes	complemented
41	C₂×D₉₅	—	7	1	no	Hall
42	C₂×C₃²×C₁₉	—	7	1	no	—
43	C₃²×D₁₉	—	5	1	no	—
44	C₃²×D₁₉	—	35	1	no	—
45	C₃²×C₅×C₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
46	C₃×C₅×C₁₉	C₂×C₃×D₇	1	4	yes	complemented
47	D₁₃₃	—	5	1	no	—
48	C₇×D₁₉	—	5	1	no	—
49	D₇×C₁₉	C₃²×D₅	1	1	yes	characteristic, complemented
50	C₂×C₃²×D₇	—	95	1	no	Hall
51	C₂×C₃×D₁₉	—	35	4	no	—
52	C₃×D₃₅	—	19	4	no	—
53	C₃×C₇×D₅	—	19	4	no	—
54	C₃×C₅×D₇	C₃×D₁₉	1	4	yes	complemented
55	C₂×C₅×C₁₉	—	7	1	no	—
56	D₉₅	—	7	1	no	—
57	D₉₅	C₃²×D₇	1	1	yes	characteristic, direct product factor
58	C₂×C₃²×D₅	—	133	1	no	Hall
59	C₃²×C₁₉	D₅×D₇	1	1	yes	characteristic, complemented, Hall
60	D₅×D₇	—	19	1	no	Hall
61	C₇×C₁₉	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Hall
62	C₂×C₃²×C₇	—	95	1	no	—
63	C₃²×D₇	—	95	1	no	—
64	C₃²×D₇	D₉₅	1	1	yes	characteristic, direct product factor
65	C₂×C₃×C₁₉	—	7	4	no	—
66	C₃×D₁₉	—	5	4	no	—
67	C₃×D₁₉	—	35	4	no	—
68	C₃×C₅×C₇	C₂×C₃×D₁₉	1	4	yes	complemented
69	C₅×C₁₉	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Hall
70	C₂×C₃²×C₅	—	7	1	no	—
71	C₃²×D₅	—	19	1	no	—
72	C₃²×D₅	—	133	1	no	—
73	C₂×C₃×D₇	—	95	4	no	—
74	C₂×D₁₉	—	35	1	no	Hall
75	D₃₅	—	19	1	no	—
76	C₅×D₇	C₃²×D₁₉	1	1	yes	characteristic, complemented
77	C₇×D₅	—	19	1	no	—
78	C₃²×C₇	C₂×D₉₅	1	1	yes	characteristic, complemented, Hall
79	C₂×C₃×D₅	—	133	4	no	—
80	C₃×C₁₉	C₃×D₅×D₇	1	4	yes	complemented
81	C₃²×C₅	D₇×D₁₉	1	1	yes	characteristic, complemented, Hall
82	C₂×C₃×C₇	—	95	4	no	—
83	C₃×D₇	—	95	4	no	—
84	C₃×D₇	C₃×D₉₅	1	4	yes	direct product factor
85	C₂×C₁₉	—	7	1	no	—
86	D₁₉	—	5	1	no	—
87	D₁₉	—	35	1	no	—
88	C₂²×C₃²	—	665	1	no	Hall
89	C₅×C₇	C₂×C₃²×D₁₉	1	1	yes	characteristic, complemented, Hall
90	C₂×C₃×C₅	—	7	4	no	—
91	C₃×D₅	—	19	4	no	—
92	C₃×D₅	—	133	4	no	—
93	C₂×D₇	—	95	1	no	Hall
94	C₃×C₇	C₂×C₃×D₉₅	1	4	yes	complemented
95	C₂×D₅	—	133	1	no	Hall
96	C₁₉	C₃²×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
97	C₂×C₃²	—	7	1	no	—
98	C₂×C₃²	—	95	1	no	—
99	C₂×C₃²	—	665	1	no	—
100	C₃×C₅	C₃×D₇×D₁₉	1	4	yes	complemented
101	C₂×C₇	—	95	1	no	—
102	D₇	—	95	1	no	—
103	D₇	C₃²×D₉₅	1	1	yes	characteristic, direct product factor
104	C₂²×C₃	—	665	4	no	—
105	C₂×C₅	—	7	1	no	—
106	D₅	—	19	1	no	—
107	D₅	—	133	1	no	—
108	C₃²	D₇×D₉₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₇	C₂×C₃²×D₉₅	1	1	yes	characteristic, complemented, Sylow
110	C₂×C₃	—	7	4	no	—
111	C₂×C₃	—	95	4	no	—
112	C₂×C₃	—	665	4	no	—
113	C₅	C₃²×D₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
114	C₂²	—	665	1	no	Sylow
115	C₃	C₃×D₇×D₉₅	1	4	yes	direct product factor
116	C₂	—	7	1	no	—
117	C₂	—	95	1	no	—
118	C₂	—	665	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×C₅×D₇×C₁₉

C₂

yes

maximal, characteristic, complemented

C₃²×C₇×D₉₅

C₂

yes

maximal, characteristic, complemented

C₃²×D₆₆₅

C₂

yes

maximal, characteristic, complemented

C₃×D₇×D₉₅

C₃

yes

maximal, direct product factor

C₃²×C₅×C₇×C₁₉

C₂²

yes

characteristic, complemented, Hall

C₃²×D₇×D₁₉

—

maximal, Hall

C₃×D₆₆₅

C₂×C₃

yes

complemented

C₃×C₇×D₉₅

C₂×C₃

yes

complemented

C₃×C₅×D₇×C₁₉

C₂×C₃

yes

complemented

C₂×C₃²×D₉₅

—

maximal, Hall

D₇×D₉₅

C₃²

yes

characteristic, direct product factor, Hall

C₃²×D₁₃₃

—

C₃²×D₇×C₁₉

D₅

yes

characteristic, complemented

C₃²×C₇×D₁₉

—

C₃×C₅×C₇×C₁₉

C₂²×C₃

yes

complemented

C₂×C₃²×C₅×C₁₉

—

C₃²×D₉₅

—

C₃²×D₉₅

D₇

yes

characteristic, direct product factor

C₃×D₇×D₁₉

—

D₆₆₅

C₂×C₃²

yes

characteristic, complemented

C₇×D₉₅

C₂×C₃²

yes

characteristic, complemented

C₅×D₇×C₁₉

C₂×C₃²

yes

characteristic, complemented

C₃²×D₅×D₇

—

maximal, Hall

C₃²×C₇×C₁₉

C₂×D₅

yes

characteristic, complemented, Hall

C₂×C₃×D₉₅

—

C₃²×C₅×C₁₉

C₂×D₇

yes

characteristic, complemented, Hall

C₃×D₁₃₃

—

C₃×D₇×C₁₉

C₃×D₅

yes

complemented

C₃×C₇×D₁₉

—

C₂×C₃²×D₁₉

—

Hall

C₅×C₇×C₁₉

C₂²×C₃²

yes

characteristic, complemented, Hall

C₃²×D₃₅

—

C₃²×C₇×D₅

—

C₃²×C₅×D₇

D₁₉

yes

characteristic, complemented

C₂×C₃×C₅×C₁₉

—

C₃×D₉₅

—

C₃×D₉₅

C₃×D₇

yes

direct product factor

D₇×D₁₉

—

Hall

C₃×D₅×D₇

—

C₃×C₇×C₁₉

C₂×C₃×D₅

yes

complemented

C₂×D₉₅

—

Hall

C₂×C₃²×C₁₉

—

C₃²×D₁₉

—

C₃²×D₁₉

—

C₃²×C₅×C₇

C₂×D₁₉

yes

characteristic, complemented, Hall

C₃×C₅×C₁₉

C₂×C₃×D₇

yes

complemented

D₁₃₃

—

C₇×D₁₉

—

D₇×C₁₉

C₃²×D₅

yes

characteristic, complemented

C₂×C₃²×D₇

—

Hall

C₂×C₃×D₁₉

—

C₃×D₃₅

—

C₃×C₇×D₅

—

C₃×C₅×D₇

C₃×D₁₉

yes

complemented

C₂×C₅×C₁₉

—

D₉₅

—

D₉₅

C₃²×D₇

yes

characteristic, direct product factor

C₂×C₃²×D₅

—

133

Hall

C₃²×C₁₉

D₅×D₇

yes

characteristic, complemented, Hall

D₅×D₇

—

Hall

C₇×C₁₉

C₂×C₃²×D₅

yes

characteristic, complemented, Hall

C₂×C₃²×C₇

—

C₃²×D₇

—

C₃²×D₇

D₉₅

yes

characteristic, direct product factor

C₂×C₃×C₁₉

—

C₃×D₁₉

—

C₃×D₁₉

—

C₃×C₅×C₇

C₂×C₃×D₁₉

yes

complemented

C₅×C₁₉

C₂×C₃²×D₇

yes

characteristic, complemented, Hall

C₂×C₃²×C₅

—

C₃²×D₅

—

C₃²×D₅

—

133

—

C₂×C₃×D₇

—

C₂×D₁₉

—

Hall

D₃₅

—

C₅×D₇

C₃²×D₁₉

yes

characteristic, complemented

C₇×D₅

—

C₃²×C₇

C₂×D₉₅

yes

characteristic, complemented, Hall

C₂×C₃×D₅

—

133

—

C₃×C₁₉

C₃×D₅×D₇

yes

complemented

C₃²×C₅

D₇×D₁₉

yes

characteristic, complemented, Hall

C₂×C₃×C₇

—

C₃×D₇

—

C₃×D₇

C₃×D₉₅

yes

direct product factor

C₂×C₁₉

—

D₁₉

—

D₁₉

—

C₂²×C₃²

—

665

Hall

C₅×C₇

C₂×C₃²×D₁₉

yes

characteristic, complemented, Hall

C₂×C₃×C₅

—

C₃×D₅

—

C₃×D₅

—

133

—

C₂×D₇

—

Hall

C₃×C₇

C₂×C₃×D₉₅

yes

complemented

C₂×D₅

—

133

Hall

C₁₉

C₃²×D₅×D₇

yes

characteristic, complemented, Sylow

C₂×C₃²

—

C₂×C₃²

—

C₂×C₃²

—

665

—

100

C₃×C₅

C₃×D₇×D₁₉

yes

complemented

101

C₂×C₇

—

102

D₇

—

103

D₇

C₃²×D₉₅

yes

characteristic, direct product factor

104

C₂²×C₃

—

665

—

105

C₂×C₅

—

106

D₅

—

107

D₅

—

133

—

108

C₃²

D₇×D₉₅

yes

characteristic, direct product factor, Sylow

109

C₇

C₂×C₃²×D₉₅

yes

characteristic, complemented, Sylow

110

C₂×C₃

—

111

C₂×C₃

—

112

C₂×C₃

—

665

—

113

C₅

C₃²×D₇×D₁₉

yes

characteristic, complemented, Sylow

114

C₂²

—

665

Sylow

115

C₃

C₃×D₇×D₉₅

yes

direct product factor

116

C₂

—

117

C₂

—

118

C₂

—

665

—

	subgroup	G/H
center, hypercenter	C₃²	D₇×D₉₅
commutator, cosocle, hypocenter	C₅×C₇×C₁₉	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₃²

subgroup

G/H

center, hypercenter

C₃²

D₇×D₉₅

commutator, cosocle, hypocenter

C₅×C₇×C₁₉

C₂²×C₃²

Frattini

C₁

Fitting, socle

C₃²×C₅×C₇×C₁₉

C₂²

LCS

G ▷ C₅×C₇×C₁₉

UCS

C₁ ◁ C₃²

N	H ≅ G/N	type
1. C₃²×C₅×D₇×C₁₉	C₂	semidirect
2. C₃²×C₇×D₉₅	C₂	semidirect
3. C₃²×D₆₆₅	C₂	semidirect
4. C₃×D₇×D₉₅	C₃	direct (N × H)
5. C₃²×C₅×C₇×C₁₉	C₂²	semidirect
7. C₃×D₆₆₅	C₂×C₃	semidirect
8. C₃×C₇×D₉₅	C₂×C₃	semidirect
9. C₃×C₅×D₇×C₁₉	C₂×C₃	semidirect
11. D₇×D₉₅	C₃²	direct (N × H)
13. C₃²×D₇×C₁₉	D₅	semidirect
15. C₃×C₅×C₇×C₁₉	C₂²×C₃	semidirect
18. C₃²×D₉₅	D₇	direct (N × H)
20. D₆₆₅	C₂×C₃²	semidirect
21. C₇×D₉₅	C₂×C₃²	semidirect
22. C₅×D₇×C₁₉	C₂×C₃²	semidirect
24. C₃²×C₇×C₁₉	C₂×D₅	semidirect
26. C₃²×C₅×C₁₉	C₂×D₇	semidirect
28. C₃×D₇×C₁₉	C₃×D₅	semidirect
31. C₅×C₇×C₁₉	C₂²×C₃²	semidirect
34. C₃²×C₅×D₇	D₁₉	semidirect
37. C₃×D₉₅	C₃×D₇	direct (N × H)
40. C₃×C₇×C₁₉	C₂×C₃×D₅	semidirect
45. C₃²×C₅×C₇	C₂×D₁₉	semidirect
46. C₃×C₅×C₁₉	C₂×C₃×D₇	semidirect
49. D₇×C₁₉	C₃²×D₅	semidirect
54. C₃×C₅×D₇	C₃×D₁₉	semidirect
57. D₉₅	C₃²×D₇	direct (N × H)
59. C₃²×C₁₉	D₅×D₇	semidirect
61. C₇×C₁₉	C₂×C₃²×D₅	semidirect
64. C₃²×D₇	D₉₅	direct (N × H)
68. C₃×C₅×C₇	C₂×C₃×D₁₉	semidirect
69. C₅×C₁₉	C₂×C₃²×D₇	semidirect
76. C₅×D₇	C₃²×D₁₉	semidirect
78. C₃²×C₇	C₂×D₉₅	semidirect
80. C₃×C₁₉	C₃×D₅×D₇	semidirect
81. C₃²×C₅	D₇×D₁₉	semidirect
84. C₃×D₇	C₃×D₉₅	direct (N × H)
89. C₅×C₇	C₂×C₃²×D₁₉	semidirect
94. C₃×C₇	C₂×C₃×D₉₅	semidirect
96. C₁₉	C₃²×D₅×D₇	semidirect
100. C₃×C₅	C₃×D₇×D₁₉	semidirect
103. D₇	C₃²×D₉₅	direct (N × H)
108. C₃²	D₇×D₉₅	direct (N × H)
109. C₇	C₂×C₃²×D₉₅	semidirect
113. C₅	C₃²×D₇×D₁₉	semidirect
115. C₃	C₃×D₇×D₉₅	direct (N × H)

H ≅ G/N

type

1. C₃²×C₅×D₇×C₁₉

C₂

semidirect

2. C₃²×C₇×D₉₅

C₂

semidirect

3. C₃²×D₆₆₅

C₂

semidirect

4. C₃×D₇×D₉₅

C₃

direct (N × H)

5. C₃²×C₅×C₇×C₁₉

C₂²

semidirect

7. C₃×D₆₆₅

C₂×C₃

semidirect

8. C₃×C₇×D₉₅

C₂×C₃

semidirect

9. C₃×C₅×D₇×C₁₉

C₂×C₃

semidirect

11. D₇×D₉₅

C₃²

direct (N × H)

13. C₃²×D₇×C₁₉

D₅

semidirect

15. C₃×C₅×C₇×C₁₉

C₂²×C₃

semidirect

18. C₃²×D₉₅

D₇

direct (N × H)

20. D₆₆₅

C₂×C₃²

semidirect

21. C₇×D₉₅

C₂×C₃²

semidirect

22. C₅×D₇×C₁₉

C₂×C₃²

semidirect

24. C₃²×C₇×C₁₉

C₂×D₅

semidirect

26. C₃²×C₅×C₁₉

C₂×D₇

semidirect

28. C₃×D₇×C₁₉

C₃×D₅

semidirect

31. C₅×C₇×C₁₉

C₂²×C₃²

semidirect

34. C₃²×C₅×D₇

D₁₉

semidirect

37. C₃×D₉₅

C₃×D₇

direct (N × H)

40. C₃×C₇×C₁₉

C₂×C₃×D₅

semidirect

45. C₃²×C₅×C₇

C₂×D₁₉

semidirect

46. C₃×C₅×C₁₉

C₂×C₃×D₇

semidirect

49. D₇×C₁₉

C₃²×D₅

semidirect

54. C₃×C₅×D₇

C₃×D₁₉

semidirect

57. D₉₅

C₃²×D₇

direct (N × H)

59. C₃²×C₁₉

D₅×D₇

semidirect

61. C₇×C₁₉

C₂×C₃²×D₅

semidirect

64. C₃²×D₇

D₉₅

direct (N × H)

68. C₃×C₅×C₇

C₂×C₃×D₁₉

semidirect

69. C₅×C₁₉

C₂×C₃²×D₇

semidirect

76. C₅×D₇

C₃²×D₁₉

semidirect

78. C₃²×C₇

C₂×D₉₅

semidirect

80. C₃×C₁₉

C₃×D₅×D₇

semidirect

81. C₃²×C₅

D₇×D₁₉

semidirect

84. C₃×D₇

C₃×D₉₅

direct (N × H)

89. C₅×C₇

C₂×C₃²×D₁₉

semidirect

94. C₃×C₇

C₂×C₃×D₉₅

semidirect

96. C₁₉

C₃²×D₅×D₇

semidirect

100. C₃×C₅

C₃×D₇×D₁₉

semidirect

103. D₇

C₃²×D₉₅

direct (N × H)

108. C₃²

D₇×D₉₅

direct (N × H)

109. C₇

C₂×C₃²×D₉₅

semidirect

113. C₅

C₃²×D₇×D₁₉

semidirect

115. C₃

C₃×D₇×D₉₅

direct (N × H)

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

subgroup	index
C₃²×C₅×D₇×C₁₉	2
C₃²×C₇×D₉₅	2
C₃²×D₆₆₅	2
C₃×D₇×D₉₅	3
C₃²×D₇×D₁₉	5
C₂×C₃²×D₉₅	7
C₃²×D₅×D₇	19

subgroup

index

C₃²×C₅×D₇×C₁₉

C₃²×C₇×D₉₅

C₃²×D₆₆₅

C₃×D₇×D₉₅

C₃²×D₇×D₁₉

C₂×C₃²×D₉₅

C₃²×D₅×D₇

Subgroups — C₃²×D₇×D₉₅ #37561517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C32×D7×D95 #37561517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×D₇×D₉₅ #37561517