Group #49087922 — subgroups

Subgroups — C₅²×D₃×C₇×D₁₇ #49087922

Order 35700.

320 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 160 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	C₃×C₅²×C₇×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₇×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅²×C₇×D₁₇	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₃×C₇×D₁₇	C₅	1	6	yes	maximal, direct product factor
7	C₅²×C₇×D₁₇	—	3	1	no	—
8	C₅²×C₇×D₁₇	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₅²×C₇×C₁₇	—	3	1	no	—
10	C₅²×D₃×D₁₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₇×D₅₁	C₂×C₅	1	6	yes	complemented
12	C₅×D₃×C₇×C₁₇	C₂×C₅	1	6	yes	complemented
13	C₃×C₅×C₇×D₁₇	C₂×C₅	1	6	yes	complemented
14	C₅²×C₇×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅²×D₅₁	C₂×C₇	1	1	yes	characteristic, complemented
16	C₅²×D₃×C₁₇	C₂×C₇	1	1	yes	characteristic, complemented
17	C₃×C₅²×D₁₇	C₂×C₇	1	1	yes	characteristic, complemented
18	C₂×C₅×C₇×D₁₇	—	3	6	no	—
19	C₂×C₅²×D₃×C₇	—	17	1	no	maximal, Hall
20	C₃×C₅×C₇×C₁₇	C₂²×C₅	1	6	yes	complemented
21	C₂×C₅²×D₁₇	—	3	1	no	Hall
22	D₃×C₇×D₁₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅²×C₁₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₇×C₁₇	—	3	6	no	—
25	C₅×C₇×D₁₇	—	3	6	no	—
26	C₅×C₇×D₁₇	C₅×D₃	1	6	yes	direct product factor
27	C₂×C₃×C₅²×C₇	—	17	1	no	—
28	C₅²×D₃×C₇	—	17	1	no	—
29	C₅²×D₃×C₇	D₁₇	1	1	yes	characteristic, direct product factor
30	C₅×D₃×D₁₇	C₅×C₇	1	6	yes	direct product factor
31	C₂×C₅²×C₁₇	—	3	1	no	—
32	C₅²×D₁₇	—	3	1	no	—
33	C₅²×D₁₇	D₃×C₇	1	1	yes	characteristic, direct product factor
34	C₇×D₅₁	C₂×C₅²	1	1	yes	characteristic, complemented
35	D₃×C₇×C₁₇	C₂×C₅²	1	1	yes	characteristic, complemented
36	C₃×C₇×D₁₇	C₂×C₅²	1	1	yes	characteristic, complemented
37	C₂²×C₅²×C₇	—	51	1	no	Hall
38	C₅×C₇×C₁₇	C₂×C₅×D₃	1	6	yes	complemented
39	C₃×C₅²×C₇	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
40	C₅×D₅₁	C₂×C₅×C₇	1	6	yes	complemented
41	C₅×D₃×C₁₇	C₂×C₅×C₇	1	6	yes	complemented
42	C₃×C₅×D₁₇	C₂×C₅×C₇	1	6	yes	complemented
43	C₂×C₇×D₁₇	—	3	1	no	Hall
44	C₅²×C₁₇	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×D₃×C₇	—	17	6	no	—
46	C₃×C₇×C₁₇	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
47	C₂×C₅²×C₇	—	3	1	no	—
48	C₂×C₅²×C₇	—	17	1	no	—
49	C₂×C₅²×C₇	—	51	1	no	—
50	C₂×C₅×D₁₇	—	3	6	no	—
51	C₂×C₅²×D₃	—	17	1	no	Hall
52	C₃×C₅×C₁₇	C₂²×C₅×C₇	1	6	yes	complemented
53	C₂×C₇×C₁₇	—	3	1	no	—
54	C₇×D₁₇	—	3	1	no	—
55	C₇×D₁₇	C₅²×D₃	1	1	yes	characteristic, direct product factor
56	C₂×C₃×C₅×C₇	—	17	6	no	—
57	C₅×D₃×C₇	—	17	6	no	—
58	C₅×D₃×C₇	C₅×D₁₇	1	6	yes	direct product factor
59	D₃×D₁₇	C₅²×C₇	1	1	yes	characteristic, direct product factor, Hall
60	C₅²×C₇	D₃×D₁₇	1	1	yes	characteristic, direct product factor, Hall
61	C₂×C₅×C₁₇	—	3	6	no	—
62	C₅×D₁₇	—	3	6	no	—
63	C₅×D₁₇	C₅×D₃×C₇	1	6	yes	direct product factor
64	C₂×C₃×C₅²	—	17	1	no	—
65	C₅²×D₃	—	17	1	no	—
66	C₅²×D₃	C₇×D₁₇	1	1	yes	characteristic, direct product factor
67	C₂²×C₅×C₇	—	51	6	no	—
68	C₇×C₁₇	C₂×C₅²×D₃	1	1	yes	characteristic, complemented, Hall
69	C₃×C₅×C₇	C₂×C₅×D₁₇	1	6	yes	complemented
70	D₅₁	C₂×C₅²×C₇	1	1	yes	characteristic, complemented
71	C₃×D₁₇	C₂×C₅²×C₇	1	1	yes	characteristic, complemented
72	D₃×C₁₇	C₂×C₅²×C₇	1	1	yes	characteristic, complemented
73	C₂²×C₅²	—	51	1	no	Hall
74	C₅×C₁₇	C₂×C₅×D₃×C₇	1	6	yes	complemented
75	C₂×D₃×C₇	—	17	1	no	Hall
76	C₃×C₅²	C₂×C₇×D₁₇	1	1	yes	characteristic, complemented, Hall
77	C₂×C₅×C₇	—	3	6	no	—
78	C₂×C₅×C₇	—	17	6	no	—
79	C₂×C₅×C₇	—	51	6	no	—
80	C₂×D₁₇	—	3	1	no	Hall
81	C₂×C₅×D₃	—	17	6	no	—
82	C₃×C₁₇	C₂²×C₅²×C₇	1	1	yes	characteristic, complemented, Hall
83	C₂×C₅²	—	3	1	no	—
84	C₂×C₅²	—	17	1	no	—
85	C₂×C₅²	—	51	1	no	—
86	C₂×C₃×C₇	—	17	1	no	—
87	D₃×C₇	—	17	1	no	—
88	D₃×C₇	C₅²×D₁₇	1	1	yes	characteristic, direct product factor
89	C₅×C₇	C₅×D₃×D₁₇	1	6	yes	direct product factor
90	C₂×C₁₇	—	3	1	no	—
91	D₁₇	—	3	1	no	—
92	D₁₇	C₅²×D₃×C₇	1	1	yes	characteristic, direct product factor
93	C₂×C₃×C₅	—	17	6	no	—
94	C₅×D₃	—	17	6	no	—
95	C₅×D₃	C₅×C₇×D₁₇	1	6	yes	direct product factor
96	C₂²×C₇	—	51	1	no	Hall
97	C₅²	D₃×C₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
98	C₃×C₇	C₂×C₅²×D₁₇	1	1	yes	characteristic, complemented, Hall
99	C₂²×C₅	—	51	6	no	—
100	C₁₇	C₂×C₅²×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
101	C₃×C₅	C₂×C₅×C₇×D₁₇	1	6	yes	complemented
102	C₂×C₇	—	3	1	no	—
103	C₂×C₇	—	17	1	no	—
104	C₂×C₇	—	51	1	no	—
105	C₂×D₃	—	17	1	no	Hall
106	C₂×C₅	—	3	6	no	—
107	C₂×C₅	—	17	6	no	—
108	C₂×C₅	—	51	6	no	—
109	C₇	C₅²×D₃×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
110	C₂×C₃	—	17	1	no	—
111	D₃	—	17	1	no	—
112	D₃	C₅²×C₇×D₁₇	1	1	yes	characteristic, direct product factor
113	C₅	C₅×D₃×C₇×D₁₇	1	6	yes	direct product factor
114	C₂²	—	51	1	no	Sylow
115	C₃	C₂×C₅²×C₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
116	C₂	—	3	1	no	—
117	C₂	—	17	1	no	—
118	C₂	—	51	1	no	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₅²×C₇×D₁₇

C₂

yes

maximal, characteristic, complemented

C₅²×D₃×C₇×C₁₇

C₂

yes

maximal, characteristic, complemented

C₅²×C₇×D₅₁

C₂

yes

maximal, characteristic, complemented

C₂×C₅²×C₇×D₁₇

—

maximal, Hall

C₃×C₅²×C₇×C₁₇

C₂²

yes

characteristic, complemented, Hall

C₅×D₃×C₇×D₁₇

C₅

yes

maximal, direct product factor

C₅²×C₇×D₁₇

—

C₅²×C₇×D₁₇

D₃

yes

characteristic, direct product factor

C₂×C₅²×C₇×C₁₇

—

C₅²×D₃×D₁₇

C₇

yes

maximal, characteristic, direct product factor, Hall

C₅×C₇×D₅₁

C₂×C₅

yes

complemented

C₅×D₃×C₇×C₁₇

C₂×C₅

yes

complemented

C₃×C₅×C₇×D₁₇

C₂×C₅

yes

complemented

C₅²×C₇×C₁₇

C₂×D₃

yes

characteristic, complemented, Hall

C₅²×D₅₁

C₂×C₇

yes

characteristic, complemented

C₅²×D₃×C₁₇

C₂×C₇

yes

characteristic, complemented

C₃×C₅²×D₁₇

C₂×C₇

yes

characteristic, complemented

C₂×C₅×C₇×D₁₇

—

C₂×C₅²×D₃×C₇

—

maximal, Hall

C₃×C₅×C₇×C₁₇

C₂²×C₅

yes

complemented

C₂×C₅²×D₁₇

—

Hall

D₃×C₇×D₁₇

C₅²

yes

characteristic, direct product factor, Hall

C₃×C₅²×C₁₇

C₂²×C₇

yes

characteristic, complemented, Hall

C₂×C₅×C₇×C₁₇

—

C₅×C₇×D₁₇

—

C₅×C₇×D₁₇

C₅×D₃

yes

direct product factor

C₂×C₃×C₅²×C₇

—

C₅²×D₃×C₇

—

C₅²×D₃×C₇

D₁₇

yes

characteristic, direct product factor

C₅×D₃×D₁₇

C₅×C₇

yes

direct product factor

C₂×C₅²×C₁₇

—

C₅²×D₁₇

—

C₅²×D₁₇

D₃×C₇

yes

characteristic, direct product factor

C₇×D₅₁

C₂×C₅²

yes

characteristic, complemented

D₃×C₇×C₁₇

C₂×C₅²

yes

characteristic, complemented

C₃×C₇×D₁₇

C₂×C₅²

yes

characteristic, complemented

C₂²×C₅²×C₇

—

Hall

C₅×C₇×C₁₇

C₂×C₅×D₃

yes

complemented

C₃×C₅²×C₇

C₂×D₁₇

yes

characteristic, complemented, Hall

C₅×D₅₁

C₂×C₅×C₇

yes

complemented

C₅×D₃×C₁₇

C₂×C₅×C₇

yes

complemented

C₃×C₅×D₁₇

C₂×C₅×C₇

yes

complemented

C₂×C₇×D₁₇

—

Hall

C₅²×C₁₇

C₂×D₃×C₇

yes

characteristic, complemented, Hall

C₂×C₅×D₃×C₇

—

C₃×C₇×C₁₇

C₂²×C₅²

yes

characteristic, complemented, Hall

C₂×C₅²×C₇

—

C₂×C₅²×C₇

—

C₂×C₅²×C₇

—

C₂×C₅×D₁₇

—

C₂×C₅²×D₃

—

Hall

C₃×C₅×C₁₇

C₂²×C₅×C₇

yes

complemented

C₂×C₇×C₁₇

—

C₇×D₁₇

—

C₇×D₁₇

C₅²×D₃

yes

characteristic, direct product factor

C₂×C₃×C₅×C₇

—

C₅×D₃×C₇

—

C₅×D₃×C₇

C₅×D₁₇

yes

direct product factor

D₃×D₁₇

C₅²×C₇

yes

characteristic, direct product factor, Hall

C₅²×C₇

D₃×D₁₇

yes

characteristic, direct product factor, Hall

C₂×C₅×C₁₇

—

C₅×D₁₇

—

C₅×D₁₇

C₅×D₃×C₇

yes

direct product factor

C₂×C₃×C₅²

—

C₅²×D₃

—

C₅²×D₃

C₇×D₁₇

yes

characteristic, direct product factor

C₂²×C₅×C₇

—

C₇×C₁₇

C₂×C₅²×D₃

yes

characteristic, complemented, Hall

C₃×C₅×C₇

C₂×C₅×D₁₇

yes

complemented

D₅₁

C₂×C₅²×C₇

yes

characteristic, complemented

C₃×D₁₇

C₂×C₅²×C₇

yes

characteristic, complemented

D₃×C₁₇

C₂×C₅²×C₇

yes

characteristic, complemented

C₂²×C₅²

—

Hall

C₅×C₁₇

C₂×C₅×D₃×C₇

yes

complemented

C₂×D₃×C₇

—

Hall

C₃×C₅²

C₂×C₇×D₁₇

yes

characteristic, complemented, Hall

C₂×C₅×C₇

—

C₂×C₅×C₇

—

C₂×C₅×C₇

—

C₂×D₁₇

—

Hall

C₂×C₅×D₃

—

C₃×C₁₇

C₂²×C₅²×C₇

yes

characteristic, complemented, Hall

C₂×C₅²

—

C₂×C₅²

—

C₂×C₅²

—

C₂×C₃×C₇

—

D₃×C₇

—

D₃×C₇

C₅²×D₁₇

yes

characteristic, direct product factor

C₅×C₇

C₅×D₃×D₁₇

yes

direct product factor

C₂×C₁₇

—

D₁₇

—

D₁₇

C₅²×D₃×C₇

yes

characteristic, direct product factor

C₂×C₃×C₅

—

C₅×D₃

—

C₅×D₃

C₅×C₇×D₁₇

yes

direct product factor

C₂²×C₇

—

Hall

C₅²

D₃×C₇×D₁₇

yes

characteristic, direct product factor, Sylow

C₃×C₇

C₂×C₅²×D₁₇

yes

characteristic, complemented, Hall

C₂²×C₅

—

100

C₁₇

C₂×C₅²×D₃×C₇

yes

characteristic, complemented, Sylow

101

C₃×C₅

C₂×C₅×C₇×D₁₇

yes

complemented

102

C₂×C₇

—

103

C₂×C₇

—

104

C₂×C₇

—

105

C₂×D₃

—

Hall

106

C₂×C₅

—

107

C₂×C₅

—

108

C₂×C₅

—

109

C₇

C₅²×D₃×D₁₇

yes

characteristic, direct product factor, Sylow

110

C₂×C₃

—

111

D₃

—

112

D₃

C₅²×C₇×D₁₇

yes

characteristic, direct product factor

113

C₅

C₅×D₃×C₇×D₁₇

yes

direct product factor

114

C₂²

—

Sylow

115

C₃

C₂×C₅²×C₇×D₁₇

yes

characteristic, complemented, Sylow

116

C₂

—

117

C₂

—

118

C₂

—

	subgroup	G/H
center, hypercenter	C₅²×C₇	D₃×D₁₇
commutator, cosocle, hypocenter	C₃×C₁₇	C₂²×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₁₇	C₂²
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₅²×C₇

subgroup

G/H

center, hypercenter

C₅²×C₇

D₃×D₁₇

commutator, cosocle, hypocenter

C₃×C₁₇

C₂²×C₅²×C₇

Frattini

C₁

Fitting, socle

C₃×C₅²×C₇×C₁₇

C₂²

LCS

G ▷ C₃×C₁₇

UCS

C₁ ◁ C₅²×C₇

N	H ≅ G/N	type
1. C₃×C₅²×C₇×D₁₇	C₂	semidirect
2. C₅²×D₃×C₇×C₁₇	C₂	semidirect
3. C₅²×C₇×D₅₁	C₂	semidirect
5. C₃×C₅²×C₇×C₁₇	C₂²	semidirect
6. C₅×D₃×C₇×D₁₇	C₅	direct (N × H)
8. C₅²×C₇×D₁₇	D₃	direct (N × H)
10. C₅²×D₃×D₁₇	C₇	direct (N × H)
11. C₅×C₇×D₅₁	C₂×C₅	semidirect
12. C₅×D₃×C₇×C₁₇	C₂×C₅	semidirect
13. C₃×C₅×C₇×D₁₇	C₂×C₅	semidirect
14. C₅²×C₇×C₁₇	C₂×D₃	semidirect
15. C₅²×D₅₁	C₂×C₇	semidirect
16. C₅²×D₃×C₁₇	C₂×C₇	semidirect
17. C₃×C₅²×D₁₇	C₂×C₇	semidirect
20. C₃×C₅×C₇×C₁₇	C₂²×C₅	semidirect
22. D₃×C₇×D₁₇	C₅²	direct (N × H)
23. C₃×C₅²×C₁₇	C₂²×C₇	semidirect
26. C₅×C₇×D₁₇	C₅×D₃	direct (N × H)
29. C₅²×D₃×C₇	D₁₇	direct (N × H)
30. C₅×D₃×D₁₇	C₅×C₇	direct (N × H)
33. C₅²×D₁₇	D₃×C₇	direct (N × H)
34. C₇×D₅₁	C₂×C₅²	semidirect
35. D₃×C₇×C₁₇	C₂×C₅²	semidirect
36. C₃×C₇×D₁₇	C₂×C₅²	semidirect
38. C₅×C₇×C₁₇	C₂×C₅×D₃	semidirect
39. C₃×C₅²×C₇	C₂×D₁₇	semidirect
40. C₅×D₅₁	C₂×C₅×C₇	semidirect
41. C₅×D₃×C₁₇	C₂×C₅×C₇	semidirect
42. C₃×C₅×D₁₇	C₂×C₅×C₇	semidirect
44. C₅²×C₁₇	C₂×D₃×C₇	semidirect
46. C₃×C₇×C₁₇	C₂²×C₅²	semidirect
52. C₃×C₅×C₁₇	C₂²×C₅×C₇	semidirect
55. C₇×D₁₇	C₅²×D₃	direct (N × H)
58. C₅×D₃×C₇	C₅×D₁₇	direct (N × H)
59. D₃×D₁₇	C₅²×C₇	direct (N × H)
60. C₅²×C₇	D₃×D₁₇	direct (N × H)
63. C₅×D₁₇	C₅×D₃×C₇	direct (N × H)
66. C₅²×D₃	C₇×D₁₇	direct (N × H)
68. C₇×C₁₇	C₂×C₅²×D₃	semidirect
69. C₃×C₅×C₇	C₂×C₅×D₁₇	semidirect
70. D₅₁	C₂×C₅²×C₇	semidirect
71. C₃×D₁₇	C₂×C₅²×C₇	semidirect
72. D₃×C₁₇	C₂×C₅²×C₇	semidirect
74. C₅×C₁₇	C₂×C₅×D₃×C₇	semidirect
76. C₃×C₅²	C₂×C₇×D₁₇	semidirect
82. C₃×C₁₇	C₂²×C₅²×C₇	semidirect
88. D₃×C₇	C₅²×D₁₇	direct (N × H)
89. C₅×C₇	C₅×D₃×D₁₇	direct (N × H)
92. D₁₇	C₅²×D₃×C₇	direct (N × H)
95. C₅×D₃	C₅×C₇×D₁₇	direct (N × H)
97. C₅²	D₃×C₇×D₁₇	direct (N × H)
98. C₃×C₇	C₂×C₅²×D₁₇	semidirect
100. C₁₇	C₂×C₅²×D₃×C₇	semidirect
101. C₃×C₅	C₂×C₅×C₇×D₁₇	semidirect
109. C₇	C₅²×D₃×D₁₇	direct (N × H)
112. D₃	C₅²×C₇×D₁₇	direct (N × H)
113. C₅	C₅×D₃×C₇×D₁₇	direct (N × H)
115. C₃	C₂×C₅²×C₇×D₁₇	semidirect

H ≅ G/N

type

1. C₃×C₅²×C₇×D₁₇

C₂

semidirect

2. C₅²×D₃×C₇×C₁₇

C₂

semidirect

3. C₅²×C₇×D₅₁

C₂

semidirect

5. C₃×C₅²×C₇×C₁₇

C₂²

semidirect

6. C₅×D₃×C₇×D₁₇

C₅

direct (N × H)

8. C₅²×C₇×D₁₇

D₃

direct (N × H)

10. C₅²×D₃×D₁₇

C₇

direct (N × H)

11. C₅×C₇×D₅₁

C₂×C₅

semidirect

12. C₅×D₃×C₇×C₁₇

C₂×C₅

semidirect

13. C₃×C₅×C₇×D₁₇

C₂×C₅

semidirect

14. C₅²×C₇×C₁₇

C₂×D₃

semidirect

15. C₅²×D₅₁

C₂×C₇

semidirect

16. C₅²×D₃×C₁₇

C₂×C₇

semidirect

17. C₃×C₅²×D₁₇

C₂×C₇

semidirect

20. C₃×C₅×C₇×C₁₇

C₂²×C₅

semidirect

22. D₃×C₇×D₁₇

C₅²

direct (N × H)

23. C₃×C₅²×C₁₇

C₂²×C₇

semidirect

26. C₅×C₇×D₁₇

C₅×D₃

direct (N × H)

29. C₅²×D₃×C₇

D₁₇

direct (N × H)

30. C₅×D₃×D₁₇

C₅×C₇

direct (N × H)

33. C₅²×D₁₇

D₃×C₇

direct (N × H)

34. C₇×D₅₁

C₂×C₅²

semidirect

35. D₃×C₇×C₁₇

C₂×C₅²

semidirect

36. C₃×C₇×D₁₇

C₂×C₅²

semidirect

38. C₅×C₇×C₁₇

C₂×C₅×D₃

semidirect

39. C₃×C₅²×C₇

C₂×D₁₇

semidirect

40. C₅×D₅₁

C₂×C₅×C₇

semidirect

41. C₅×D₃×C₁₇

C₂×C₅×C₇

semidirect

42. C₃×C₅×D₁₇

C₂×C₅×C₇

semidirect

44. C₅²×C₁₇

C₂×D₃×C₇

semidirect

46. C₃×C₇×C₁₇

C₂²×C₅²

semidirect

52. C₃×C₅×C₁₇

C₂²×C₅×C₇

semidirect

55. C₇×D₁₇

C₅²×D₃

direct (N × H)

58. C₅×D₃×C₇

C₅×D₁₇

direct (N × H)

59. D₃×D₁₇

C₅²×C₇

direct (N × H)

60. C₅²×C₇

D₃×D₁₇

direct (N × H)

63. C₅×D₁₇

C₅×D₃×C₇

direct (N × H)

66. C₅²×D₃

C₇×D₁₇

direct (N × H)

68. C₇×C₁₇

C₂×C₅²×D₃

semidirect

69. C₃×C₅×C₇

C₂×C₅×D₁₇

semidirect

70. D₅₁

C₂×C₅²×C₇

semidirect

71. C₃×D₁₇

C₂×C₅²×C₇

semidirect

72. D₃×C₁₇

C₂×C₅²×C₇

semidirect

74. C₅×C₁₇

C₂×C₅×D₃×C₇

semidirect

76. C₃×C₅²

C₂×C₇×D₁₇

semidirect

82. C₃×C₁₇

C₂²×C₅²×C₇

semidirect

88. D₃×C₇

C₅²×D₁₇

direct (N × H)

89. C₅×C₇

C₅×D₃×D₁₇

direct (N × H)

92. D₁₇

C₅²×D₃×C₇

direct (N × H)

95. C₅×D₃

C₅×C₇×D₁₇

direct (N × H)

97. C₅²

D₃×C₇×D₁₇

direct (N × H)

98. C₃×C₇

C₂×C₅²×D₁₇

semidirect

100. C₁₇

C₂×C₅²×D₃×C₇

semidirect

101. C₃×C₅

C₂×C₅×C₇×D₁₇

semidirect

109. C₇

C₅²×D₃×D₁₇

direct (N × H)

112. D₃

C₅²×C₇×D₁₇

direct (N × H)

113. C₅

C₅×D₃×C₇×D₁₇

direct (N × H)

115. C₃

C₂×C₅²×C₇×D₁₇

semidirect

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

subgroup	index
C₃×C₅²×C₇×D₁₇	2
C₅²×D₃×C₇×C₁₇	2
C₅²×C₇×D₅₁	2
C₂×C₅²×C₇×D₁₇	3
C₅×D₃×C₇×D₁₇	5
C₅²×D₃×D₁₇	7
C₂×C₅²×D₃×C₇	17

subgroup

index

C₃×C₅²×C₇×D₁₇

C₅²×D₃×C₇×C₁₇

C₅²×C₇×D₅₁

C₂×C₅²×C₇×D₁₇

C₅×D₃×C₇×D₁₇

C₅²×D₃×D₁₇

C₂×C₅²×D₃×C₇

Subgroups — C₅²×D₃×C₇×D₁₇ #49087922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C52×D3×C7×D17 #49087922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃×C₇×D₁₇ #49087922