Group #29505829 — subgroups

Subgroups — C₂×C₅×C₉×D₅×C₁₇ #29505829

Order 15300.

144 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 84 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×C₉×D₅×C₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₅×C₁₇	C₃	1	1	yes	maximal, characteristic
4	C₅²×C₉×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₅×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₅×C₉×C₁₇	—	5	1	no	maximal
7	C₃×C₅×D₅×C₁₇	C₂×C₃	1	2	yes	—
8	C₂×C₃×C₅²×C₁₇	C₂×C₃	1	1	yes	characteristic
9	C₂×C₅×D₅×C₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₉×C₁₇	—	2	2	no	—
11	C₂×C₅×C₉×C₁₇	—	5	2	no	—
12	C₂×C₅×C₉×C₁₇	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₅×C₉×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
14	C₉×D₅×C₁₇	C₂×C₅	1	2	yes	direct product factor
15	C₃×C₅²×C₁₇	C₂²×C₃	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₁₇	—	5	1	no	—
17	C₂×C₃×D₅×C₁₇	C₃×C₅	1	1	yes	characteristic
18	C₂×C₅×C₉×D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅²×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented
20	C₅×D₅×C₁₇	C₂×C₉	1	2	yes	direct product factor
21	C₅×C₉×C₁₇	—	2	2	no	—
22	C₅×C₉×C₁₇	C₂×D₅	1	1	yes	characteristic, direct product factor
23	C₅×C₉×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented
24	C₂²×C₉×C₁₇	—	5	1	no	Hall
25	C₂×C₃×C₅×C₁₇	—	2	2	no	—
26	C₂×C₃×C₅×C₁₇	—	5	2	no	—
27	C₂×C₃×C₅×C₁₇	C₃×D₅	1	1	yes	characteristic
28	C₂×C₃×C₅×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
29	C₃×D₅×C₁₇	C₂×C₃×C₅	1	2	yes	—
30	C₂×C₅²×C₉	C₂×C₁₇	1	1	yes	characteristic, complemented
31	C₅×C₉×D₅	C₂×C₁₇	1	2	yes	direct product factor
32	C₅²×C₁₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₅×C₁₇	—	5	1	no	—
34	C₂×D₅×C₁₇	C₅×C₉	1	1	yes	characteristic, direct product factor
35	C₂×C₉×C₁₇	—	5	2	no	—
36	C₂×C₉×C₁₇	C₅×D₅	1	1	yes	characteristic, direct product factor
37	C₂×C₃×C₅×D₅	C₃×C₁₇	1	1	yes	characteristic
38	C₃×C₅×C₁₇	—	2	2	no	—
39	C₃×C₅×C₁₇	C₂×C₃×D₅	1	1	yes	characteristic
40	C₃×C₅×C₁₇	C₂²×C₃×C₅	1	1	yes	characteristic
41	C₅²×C₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
42	C₂²×C₃×C₁₇	—	5	1	no	—
43	C₂²×C₅×C₉	—	5	1	no	—
44	C₂×C₉×D₅	C₅×C₁₇	1	1	yes	characteristic, direct product factor
45	C₂×C₅×C₁₇	—	2	2	no	—
46	C₂×C₅×C₁₇	—	5	2	no	—
47	C₂×C₅×C₁₇	C₉×D₅	1	1	yes	characteristic, direct product factor
48	C₂×C₅×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, complemented
49	D₅×C₁₇	C₂×C₅×C₉	1	2	yes	direct product factor
50	C₉×C₁₇	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₃×C₅²	C₂×C₃×C₁₇	1	1	yes	characteristic
52	C₃×C₅×D₅	C₂×C₃×C₁₇	1	2	yes	—
53	C₂×C₃×C₁₇	—	5	2	no	—
54	C₂×C₃×C₁₇	C₃×C₅×D₅	1	1	yes	characteristic
55	C₂×C₅×D₅	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
56	C₂×C₅×C₉	—	2	2	no	—
57	C₂×C₅×C₉	—	5	2	no	—
58	C₂×C₅×C₉	D₅×C₁₇	1	1	yes	characteristic, direct product factor
59	C₂×C₅×C₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
60	C₉×D₅	C₂×C₅×C₁₇	1	2	yes	direct product factor
61	C₅×C₁₇	—	2	2	no	—
62	C₅×C₁₇	C₂×C₉×D₅	1	1	yes	characteristic, direct product factor
63	C₅×C₁₇	C₂²×C₅×C₉	1	1	yes	characteristic, complemented
64	C₃×C₅²	C₂²×C₃×C₁₇	1	1	yes	characteristic
65	C₂²×C₁₇	—	5	1	no	Hall
66	C₂²×C₃×C₅	—	5	1	no	—
67	C₂×C₃×D₅	C₃×C₅×C₁₇	1	1	yes	characteristic
68	C₃×C₁₇	C₂×C₃×C₅×D₅	1	1	yes	characteristic
69	C₂×C₅²	C₂×C₉×C₁₇	1	1	yes	characteristic, complemented
70	C₅×D₅	C₂×C₉×C₁₇	1	2	yes	direct product factor
71	C₅×C₉	—	2	2	no	—
72	C₅×C₉	C₂×D₅×C₁₇	1	1	yes	characteristic, direct product factor
73	C₅×C₉	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented
74	C₂²×C₉	—	5	1	no	Hall
75	C₂×C₁₇	—	5	2	no	—
76	C₂×C₁₇	C₅×C₉×D₅	1	1	yes	characteristic, direct product factor
77	C₂×C₃×C₅	—	2	2	no	—
78	C₂×C₃×C₅	—	5	2	no	—
79	C₂×C₃×C₅	C₃×D₅×C₁₇	1	1	yes	characteristic
80	C₂×C₃×C₅	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic
81	C₃×D₅	C₂×C₃×C₅×C₁₇	1	2	yes	—
82	C₅²	C₂²×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₅	—	5	1	no	—
84	C₂×D₅	C₅×C₉×C₁₇	1	1	yes	characteristic, direct product factor
85	C₂×C₉	—	5	2	no	—
86	C₂×C₉	C₅×D₅×C₁₇	1	1	yes	characteristic, direct product factor
87	C₁₇	C₂×C₅×C₉×D₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₃×C₅	—	2	2	no	—
89	C₃×C₅	C₂×C₃×D₅×C₁₇	1	1	yes	characteristic
90	C₃×C₅	C₂²×C₃×C₅×C₁₇	1	1	yes	characteristic
91	C₂²×C₃	—	5	1	no	—
92	C₂×C₅	—	2	2	no	—
93	C₂×C₅	—	5	2	no	—
94	C₂×C₅	C₉×D₅×C₁₇	1	1	yes	characteristic, direct product factor
95	C₂×C₅	C₂×C₅×C₉×C₁₇	1	1	yes	characteristic, complemented
96	D₅	C₂×C₅×C₉×C₁₇	1	2	yes	direct product factor
97	C₉	C₂×C₅×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₃	—	5	2	no	—
99	C₂×C₃	C₃×C₅×D₅×C₁₇	1	1	yes	characteristic
100	C₅	—	2	2	no	—
101	C₅	C₂²×C₅×C₉×C₁₇	1	1	yes	characteristic, complemented
102	C₅	C₂×C₉×D₅×C₁₇	1	1	yes	characteristic, direct product factor
103	C₂²	—	5	1	no	Sylow
104	C₃	C₂×C₃×C₅×D₅×C₁₇	1	1	yes	characteristic
105	C₂	—	5	2	no	—
106	C₂	C₅×C₉×D₅×C₁₇	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₉×D₅×C₁₇

C₂

yes

maximal, direct product factor

C₂×C₅²×C₉×C₁₇

C₂

yes

maximal, characteristic, complemented

C₂×C₃×C₅×D₅×C₁₇

C₃

yes

maximal, characteristic

C₅²×C₉×C₁₇

C₂²

yes

characteristic, complemented, Hall

C₂×C₉×D₅×C₁₇

C₅

yes

maximal, characteristic, direct product factor

C₂²×C₅×C₉×C₁₇

—

maximal

C₃×C₅×D₅×C₁₇

C₂×C₃

yes

—

C₂×C₃×C₅²×C₁₇

C₂×C₃

yes

characteristic

C₂×C₅×D₅×C₁₇

C₉

yes

characteristic, direct product factor, Hall

C₂×C₅×C₉×C₁₇

—

C₂×C₅×C₉×C₁₇

—

C₂×C₅×C₉×C₁₇

D₅

yes

characteristic, direct product factor

C₂×C₅×C₉×C₁₇

C₂×C₅

yes

characteristic, complemented

C₉×D₅×C₁₇

C₂×C₅

yes

direct product factor

C₃×C₅²×C₁₇

C₂²×C₃

yes

characteristic

C₂²×C₃×C₅×C₁₇

—

C₂×C₃×D₅×C₁₇

C₃×C₅

yes

characteristic

C₂×C₅×C₉×D₅

C₁₇

yes

maximal, characteristic, direct product factor, Hall

C₂×C₅²×C₁₇

C₂×C₉

yes

characteristic, complemented

C₅×D₅×C₁₇

C₂×C₉

yes

direct product factor

C₅×C₉×C₁₇

—

C₅×C₉×C₁₇

C₂×D₅

yes

characteristic, direct product factor

C₅×C₉×C₁₇

C₂²×C₅

yes

characteristic, complemented

C₂²×C₉×C₁₇

—

Hall

C₂×C₃×C₅×C₁₇

—

C₂×C₃×C₅×C₁₇

—

C₂×C₃×C₅×C₁₇

C₃×D₅

yes

characteristic

C₂×C₃×C₅×C₁₇

C₂×C₃×C₅

yes

characteristic

C₃×D₅×C₁₇

C₂×C₃×C₅

yes

—

C₂×C₅²×C₉

C₂×C₁₇

yes

characteristic, complemented

C₅×C₉×D₅

C₂×C₁₇

yes

direct product factor

C₅²×C₁₇

C₂²×C₉

yes

characteristic, complemented, Hall

C₂²×C₅×C₁₇

—

C₂×D₅×C₁₇

C₅×C₉

yes

characteristic, direct product factor

C₂×C₉×C₁₇

—

C₂×C₉×C₁₇

C₅×D₅

yes

characteristic, direct product factor

C₂×C₃×C₅×D₅

C₃×C₁₇

yes

characteristic

C₃×C₅×C₁₇

—

C₃×C₅×C₁₇

C₂×C₃×D₅

yes

characteristic

C₃×C₅×C₁₇

C₂²×C₃×C₅

yes

characteristic

C₅²×C₉

C₂²×C₁₇

yes

characteristic, complemented, Hall

C₂²×C₃×C₁₇

—

C₂²×C₅×C₉

—

C₂×C₉×D₅

C₅×C₁₇

yes

characteristic, direct product factor

C₂×C₅×C₁₇

—

C₂×C₅×C₁₇

—

C₂×C₅×C₁₇

C₉×D₅

yes

characteristic, direct product factor

C₂×C₅×C₁₇

C₂×C₅×C₉

yes

characteristic, complemented

D₅×C₁₇

C₂×C₅×C₉

yes

direct product factor

C₉×C₁₇

C₂×C₅×D₅

yes

characteristic, direct product factor, Hall

C₂×C₃×C₅²

C₂×C₃×C₁₇

yes

characteristic

C₃×C₅×D₅

C₂×C₃×C₁₇

yes

—

C₂×C₃×C₁₇

—

C₂×C₃×C₁₇

C₃×C₅×D₅

yes

characteristic

C₂×C₅×D₅

C₉×C₁₇

yes

characteristic, direct product factor, Hall

C₂×C₅×C₉

—

C₂×C₅×C₉

—

C₂×C₅×C₉

D₅×C₁₇

yes

characteristic, direct product factor

C₂×C₅×C₉

C₂×C₅×C₁₇

yes

characteristic, complemented

C₉×D₅

C₂×C₅×C₁₇

yes

direct product factor

C₅×C₁₇

—

C₅×C₁₇

C₂×C₉×D₅

yes

characteristic, direct product factor

C₅×C₁₇

C₂²×C₅×C₉

yes

characteristic, complemented

C₃×C₅²

C₂²×C₃×C₁₇

yes

characteristic

C₂²×C₁₇

—

Hall

C₂²×C₃×C₅

—

C₂×C₃×D₅

C₃×C₅×C₁₇

yes

characteristic

C₃×C₁₇

C₂×C₃×C₅×D₅

yes

characteristic

C₂×C₅²

C₂×C₉×C₁₇

yes

characteristic, complemented

C₅×D₅

C₂×C₉×C₁₇

yes

direct product factor

C₅×C₉

—

C₅×C₉

C₂×D₅×C₁₇

yes

characteristic, direct product factor

C₅×C₉

C₂²×C₅×C₁₇

yes

characteristic, complemented

C₂²×C₉

—

Hall

C₂×C₁₇

—

C₂×C₁₇

C₅×C₉×D₅

yes

characteristic, direct product factor

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₃×D₅×C₁₇

yes

characteristic

C₂×C₃×C₅

C₂×C₃×C₅×C₁₇

yes

characteristic

C₃×D₅

C₂×C₃×C₅×C₁₇

yes

—

C₅²

C₂²×C₉×C₁₇

yes

characteristic, complemented, Sylow

C₂²×C₅

—

C₂×D₅

C₅×C₉×C₁₇

yes

characteristic, direct product factor

C₂×C₉

—

C₂×C₉

C₅×D₅×C₁₇

yes

characteristic, direct product factor

C₁₇

C₂×C₅×C₉×D₅

yes

characteristic, direct product factor, Sylow

C₃×C₅

—

C₃×C₅

C₂×C₃×D₅×C₁₇

yes

characteristic

C₃×C₅

C₂²×C₃×C₅×C₁₇

yes

characteristic

C₂²×C₃

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

C₉×D₅×C₁₇

yes

characteristic, direct product factor

C₂×C₅

C₂×C₅×C₉×C₁₇

yes

characteristic, complemented

D₅

C₂×C₅×C₉×C₁₇

yes

direct product factor

C₉

C₂×C₅×D₅×C₁₇

yes

characteristic, direct product factor, Sylow

C₂×C₃

—

C₂×C₃

C₃×C₅×D₅×C₁₇

yes

characteristic

100

C₅

—

101

C₅

C₂²×C₅×C₉×C₁₇

yes

characteristic, complemented

102

C₅

C₂×C₉×D₅×C₁₇

yes

characteristic, direct product factor

103

C₂²

—

Sylow

104

C₃

C₂×C₃×C₅×D₅×C₁₇

yes

characteristic

105

C₂

—

106

C₂

C₅×C₉×D₅×C₁₇

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉×C₁₇	D₅
commutator, hypocenter	C₅	C₂²×C₅×C₉×C₁₇
Frattini	C₃	C₂×C₃×C₅×D₅×C₁₇
Fitting	C₂×C₅²×C₉×C₁₇	C₂
socle	C₂×C₃×C₅²×C₁₇	C₂×C₃
prime radical	C₂×C₃×C₅×D₅×C₁₇	C₃
cosocle	C₃×C₅	C₂²×C₃×C₅×C₁₇
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₅×C₉×C₁₇

subgroup

G/H

center, hypercenter

C₂×C₅×C₉×C₁₇

D₅

commutator, hypocenter

C₅

C₂²×C₅×C₉×C₁₇

Frattini

C₃

C₂×C₃×C₅×D₅×C₁₇

Fitting

C₂×C₅²×C₉×C₁₇

C₂

socle

C₂×C₃×C₅²×C₁₇

C₂×C₃

prime radical

C₂×C₃×C₅×D₅×C₁₇

C₃

cosocle

C₃×C₅

C₂²×C₃×C₅×C₁₇

LCS

G ▷ C₅

UCS

C₁ ◁ C₂×C₅×C₉×C₁₇

N	H ≅ G/N	type
1. C₅×C₉×D₅×C₁₇	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₁₇	C₂	semidirect
4. C₅²×C₉×C₁₇	C₂²	semidirect
5. C₂×C₉×D₅×C₁₇	C₅	direct (N × H)
9. C₂×C₅×D₅×C₁₇	C₉	direct (N × H)
12. C₂×C₅×C₉×C₁₇	D₅	direct (N × H)
13. C₂×C₅×C₉×C₁₇	C₂×C₅	semidirect
14. C₉×D₅×C₁₇	C₂×C₅	direct (N × H)
18. C₂×C₅×C₉×D₅	C₁₇	direct (N × H)
19. C₂×C₅²×C₁₇	C₂×C₉	semidirect
20. C₅×D₅×C₁₇	C₂×C₉	direct (N × H)
22. C₅×C₉×C₁₇	C₂×D₅	direct (N × H)
23. C₅×C₉×C₁₇	C₂²×C₅	semidirect
30. C₂×C₅²×C₉	C₂×C₁₇	semidirect
31. C₅×C₉×D₅	C₂×C₁₇	direct (N × H)
32. C₅²×C₁₇	C₂²×C₉	semidirect
34. C₂×D₅×C₁₇	C₅×C₉	direct (N × H)
36. C₂×C₉×C₁₇	C₅×D₅	direct (N × H)
41. C₅²×C₉	C₂²×C₁₇	semidirect
44. C₂×C₉×D₅	C₅×C₁₇	direct (N × H)
47. C₂×C₅×C₁₇	C₉×D₅	direct (N × H)
48. C₂×C₅×C₁₇	C₂×C₅×C₉	semidirect
49. D₅×C₁₇	C₂×C₅×C₉	direct (N × H)
50. C₉×C₁₇	C₂×C₅×D₅	direct (N × H)
55. C₂×C₅×D₅	C₉×C₁₇	direct (N × H)
58. C₂×C₅×C₉	D₅×C₁₇	direct (N × H)
59. C₂×C₅×C₉	C₂×C₅×C₁₇	semidirect
60. C₉×D₅	C₂×C₅×C₁₇	direct (N × H)
62. C₅×C₁₇	C₂×C₉×D₅	direct (N × H)
63. C₅×C₁₇	C₂²×C₅×C₉	semidirect
69. C₂×C₅²	C₂×C₉×C₁₇	semidirect
70. C₅×D₅	C₂×C₉×C₁₇	direct (N × H)
72. C₅×C₉	C₂×D₅×C₁₇	direct (N × H)
73. C₅×C₉	C₂²×C₅×C₁₇	semidirect
76. C₂×C₁₇	C₅×C₉×D₅	direct (N × H)
82. C₅²	C₂²×C₉×C₁₇	semidirect
84. C₂×D₅	C₅×C₉×C₁₇	direct (N × H)
86. C₂×C₉	C₅×D₅×C₁₇	direct (N × H)
87. C₁₇	C₂×C₅×C₉×D₅	direct (N × H)
94. C₂×C₅	C₉×D₅×C₁₇	direct (N × H)
95. C₂×C₅	C₂×C₅×C₉×C₁₇	semidirect
96. D₅	C₂×C₅×C₉×C₁₇	direct (N × H)
97. C₉	C₂×C₅×D₅×C₁₇	direct (N × H)
101. C₅	C₂²×C₅×C₉×C₁₇	semidirect
102. C₅	C₂×C₉×D₅×C₁₇	direct (N × H)
106. C₂	C₅×C₉×D₅×C₁₇	direct (N × H)

H ≅ G/N

type

1. C₅×C₉×D₅×C₁₇

C₂

direct (N × H)

2. C₂×C₅²×C₉×C₁₇

C₂

semidirect

4. C₅²×C₉×C₁₇

C₂²

semidirect

5. C₂×C₉×D₅×C₁₇

C₅

direct (N × H)

9. C₂×C₅×D₅×C₁₇

C₉

direct (N × H)

12. C₂×C₅×C₉×C₁₇

D₅

direct (N × H)

13. C₂×C₅×C₉×C₁₇

C₂×C₅

semidirect

14. C₉×D₅×C₁₇

C₂×C₅

direct (N × H)

18. C₂×C₅×C₉×D₅

C₁₇

direct (N × H)

19. C₂×C₅²×C₁₇

C₂×C₉

semidirect

20. C₅×D₅×C₁₇

C₂×C₉

direct (N × H)

22. C₅×C₉×C₁₇

C₂×D₅

direct (N × H)

23. C₅×C₉×C₁₇

C₂²×C₅

semidirect

30. C₂×C₅²×C₉

C₂×C₁₇

semidirect

31. C₅×C₉×D₅

C₂×C₁₇

direct (N × H)

32. C₅²×C₁₇

C₂²×C₉

semidirect

34. C₂×D₅×C₁₇

C₅×C₉

direct (N × H)

36. C₂×C₉×C₁₇

C₅×D₅

direct (N × H)

41. C₅²×C₉

C₂²×C₁₇

semidirect

44. C₂×C₉×D₅

C₅×C₁₇

direct (N × H)

47. C₂×C₅×C₁₇

C₉×D₅

direct (N × H)

48. C₂×C₅×C₁₇

C₂×C₅×C₉

semidirect

49. D₅×C₁₇

C₂×C₅×C₉

direct (N × H)

50. C₉×C₁₇

C₂×C₅×D₅

direct (N × H)

55. C₂×C₅×D₅

C₉×C₁₇

direct (N × H)

58. C₂×C₅×C₉

D₅×C₁₇

direct (N × H)

59. C₂×C₅×C₉

C₂×C₅×C₁₇

semidirect

60. C₉×D₅

C₂×C₅×C₁₇

direct (N × H)

62. C₅×C₁₇

C₂×C₉×D₅

direct (N × H)

63. C₅×C₁₇

C₂²×C₅×C₉

semidirect

69. C₂×C₅²

C₂×C₉×C₁₇

semidirect

70. C₅×D₅

C₂×C₉×C₁₇

direct (N × H)

72. C₅×C₉

C₂×D₅×C₁₇

direct (N × H)

73. C₅×C₉

C₂²×C₅×C₁₇

semidirect

76. C₂×C₁₇

C₅×C₉×D₅

direct (N × H)

82. C₅²

C₂²×C₉×C₁₇

semidirect

84. C₂×D₅

C₅×C₉×C₁₇

direct (N × H)

86. C₂×C₉

C₅×D₅×C₁₇

direct (N × H)

87. C₁₇

C₂×C₅×C₉×D₅

direct (N × H)

94. C₂×C₅

C₉×D₅×C₁₇

direct (N × H)

95. C₂×C₅

C₂×C₅×C₉×C₁₇

semidirect

96. D₅

C₂×C₅×C₉×C₁₇

direct (N × H)

97. C₉

C₂×C₅×D₅×C₁₇

direct (N × H)

101. C₅

C₂²×C₅×C₉×C₁₇

semidirect

102. C₅

C₂×C₉×D₅×C₁₇

direct (N × H)

106. C₂

C₅×C₉×D₅×C₁₇

direct (N × H)

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

subgroup	index
C₅×C₉×D₅×C₁₇	2
C₂×C₅²×C₉×C₁₇	2
C₂×C₃×C₅×D₅×C₁₇	3
C₂×C₉×D₅×C₁₇	5
C₂²×C₅×C₉×C₁₇	5
C₂×C₅×C₉×D₅	17

subgroup

index

C₅×C₉×D₅×C₁₇

C₂×C₅²×C₉×C₁₇

C₂×C₃×C₅×D₅×C₁₇

C₂×C₉×D₅×C₁₇

C₂²×C₅×C₉×C₁₇

C₂×C₅×C₉×D₅

Subgroups — C₂×C₅×C₉×D₅×C₁₇ #29505829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C5×C9×D5×C17 #29505829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉×D₅×C₁₇ #29505829