Group #42124591 — subgroups

Subgroups — C₂×C₅×C₉×D₅×C₃₁ #42124591

Order 27900.

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×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅²×C₉×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₅×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₅²×C₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₅×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₅×C₉×C₃₁	—	5	1	no	maximal
7	C₃×C₅×D₅×C₃₁	C₂×C₃	1	2	yes	—
8	C₂×C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic
9	C₂×C₅×D₅×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₉×D₅×C₃₁	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₅×C₉×C₃₁	—	2	2	no	—
12	C₂×C₅×C₉×C₃₁	—	5	2	no	—
13	C₂×C₅×C₉×C₃₁	D₅	1	1	yes	characteristic, direct product factor
14	C₂×C₅×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
15	C₃×C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₃₁	—	5	1	no	—
17	C₂×C₃×D₅×C₃₁	C₃×C₅	1	1	yes	characteristic
18	C₂×C₅²×C₃₁	C₂×C₉	1	1	yes	characteristic, complemented
19	C₅×D₅×C₃₁	C₂×C₉	1	2	yes	direct product factor
20	C₅×C₉×C₃₁	—	2	2	no	—
21	C₅×C₉×C₃₁	C₂×D₅	1	1	yes	characteristic, direct product factor
22	C₅×C₉×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
23	C₂²×C₉×C₃₁	—	5	1	no	Hall
24	C₂×C₃×C₅×C₃₁	—	2	2	no	—
25	C₂×C₃×C₅×C₃₁	—	5	2	no	—
26	C₂×C₃×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic
27	C₂×C₃×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic
28	C₃×D₅×C₃₁	C₂×C₃×C₅	1	2	yes	—
29	C₂×C₅×C₉×D₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₅²×C₃₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₅×C₃₁	—	5	1	no	—
32	C₂×D₅×C₃₁	C₅×C₉	1	1	yes	characteristic, direct product factor
33	C₂×C₉×C₃₁	—	5	2	no	—
34	C₂×C₉×C₃₁	C₅×D₅	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₃₁	—	2	2	no	—
36	C₃×C₅×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic
37	C₃×C₅×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic
38	C₂×C₅²×C₉	C₂×C₃₁	1	1	yes	characteristic, complemented
39	C₅×C₉×D₅	C₂×C₃₁	1	2	yes	direct product factor
40	C₂²×C₃×C₃₁	—	5	1	no	—
41	C₂×C₅×C₃₁	—	2	2	no	—
42	C₂×C₅×C₃₁	—	5	2	no	—
43	C₂×C₅×C₃₁	C₉×D₅	1	1	yes	characteristic, direct product factor
44	C₂×C₅×C₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented
45	D₅×C₃₁	C₂×C₅×C₉	1	2	yes	direct product factor
46	C₂×C₃×C₅×D₅	C₃×C₃₁	1	1	yes	characteristic
47	C₉×C₃₁	C₂×C₅×D₅	1	1	yes	characteristic, direct product factor, Hall
48	C₅²×C₉	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
49	C₂×C₃×C₃₁	—	5	2	no	—
50	C₂×C₃×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic
51	C₂²×C₅×C₉	—	5	1	no	—
52	C₂×C₉×D₅	C₅×C₃₁	1	1	yes	characteristic, direct product factor
53	C₅×C₃₁	—	2	2	no	—
54	C₅×C₃₁	C₂×C₉×D₅	1	1	yes	characteristic, direct product factor
55	C₅×C₃₁	C₂²×C₅×C₉	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅²	C₂×C₃×C₃₁	1	1	yes	characteristic
57	C₃×C₅×D₅	C₂×C₃×C₃₁	1	2	yes	—
58	C₂²×C₃₁	—	5	1	no	Hall
59	C₂×C₅×D₅	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
60	C₃×C₃₁	C₂×C₃×C₅×D₅	1	1	yes	characteristic
61	C₂×C₅×C₉	—	2	2	no	—
62	C₂×C₅×C₉	—	5	2	no	—
63	C₂×C₅×C₉	D₅×C₃₁	1	1	yes	characteristic, direct product factor
64	C₂×C₅×C₉	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented
65	C₉×D₅	C₂×C₅×C₃₁	1	2	yes	direct product factor
66	C₃×C₅²	C₂²×C₃×C₃₁	1	1	yes	characteristic
67	C₂×C₃₁	—	5	2	no	—
68	C₂×C₃₁	C₅×C₉×D₅	1	1	yes	characteristic, direct product factor
69	C₂²×C₃×C₅	—	5	1	no	—
70	C₂×C₃×D₅	C₃×C₅×C₃₁	1	1	yes	characteristic
71	C₂×C₅²	C₂×C₉×C₃₁	1	1	yes	characteristic, complemented
72	C₅×D₅	C₂×C₉×C₃₁	1	2	yes	direct product factor
73	C₅×C₉	—	2	2	no	—
74	C₅×C₉	C₂×D₅×C₃₁	1	1	yes	characteristic, direct product factor
75	C₅×C₉	C₂²×C₅×C₃₁	1	1	yes	characteristic, complemented
76	C₂²×C₉	—	5	1	no	Hall
77	C₃₁	C₂×C₅×C₉×D₅	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₃×C₅	—	2	2	no	—
79	C₂×C₃×C₅	—	5	2	no	—
80	C₂×C₃×C₅	C₃×D₅×C₃₁	1	1	yes	characteristic
81	C₂×C₃×C₅	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic
82	C₃×D₅	C₂×C₃×C₅×C₃₁	1	2	yes	—
83	C₅²	C₂²×C₉×C₃₁	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₅	—	5	1	no	—
85	C₂×D₅	C₅×C₉×C₃₁	1	1	yes	characteristic, direct product factor
86	C₂×C₉	—	5	2	no	—
87	C₂×C₉	C₅×D₅×C₃₁	1	1	yes	characteristic, direct product factor
88	C₃×C₅	—	2	2	no	—
89	C₃×C₅	C₂×C₃×D₅×C₃₁	1	1	yes	characteristic
90	C₃×C₅	C₂²×C₃×C₅×C₃₁	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	C₂×C₅×C₉×C₃₁	1	1	yes	characteristic, complemented
95	C₂×C₅	C₉×D₅×C₃₁	1	1	yes	characteristic, direct product factor
96	D₅	C₂×C₅×C₉×C₃₁	1	2	yes	direct product factor
97	C₉	C₂×C₅×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
98	C₂×C₃	—	5	2	no	—
99	C₂×C₃	C₃×C₅×D₅×C₃₁	1	1	yes	characteristic
100	C₅	—	2	2	no	—
101	C₅	C₂²×C₅×C₉×C₃₁	1	1	yes	characteristic, complemented
102	C₅	C₂×C₉×D₅×C₃₁	1	1	yes	characteristic, direct product factor
103	C₂²	—	5	1	no	Sylow
104	C₃	C₂×C₃×C₅×D₅×C₃₁	1	1	yes	characteristic
105	C₂	—	5	2	no	—
106	C₂	C₅×C₉×D₅×C₃₁	1	1	yes	characteristic, direct product factor

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×C₉×D₅×C₃₁

C₂

yes

maximal, direct product factor

C₂×C₅²×C₉×C₃₁

C₂

yes

maximal, characteristic, complemented

C₂×C₃×C₅×D₅×C₃₁

C₃

yes

maximal, characteristic

C₅²×C₉×C₃₁

C₂²

yes

characteristic, complemented, Hall

C₂×C₉×D₅×C₃₁

C₅

yes

maximal, characteristic, direct product factor

C₂²×C₅×C₉×C₃₁

—

maximal

C₃×C₅×D₅×C₃₁

C₂×C₃

yes

—

C₂×C₃×C₅²×C₃₁

C₂×C₃

yes

characteristic

C₂×C₅×D₅×C₃₁

C₉

yes

characteristic, direct product factor, Hall

C₉×D₅×C₃₁

C₂×C₅

yes

direct product factor

C₂×C₅×C₉×C₃₁

—

C₂×C₅×C₉×C₃₁

—

C₂×C₅×C₉×C₃₁

D₅

yes

characteristic, direct product factor

C₂×C₅×C₉×C₃₁

C₂×C₅

yes

characteristic, complemented

C₃×C₅²×C₃₁

C₂²×C₃

yes

characteristic

C₂²×C₃×C₅×C₃₁

—

C₂×C₃×D₅×C₃₁

C₃×C₅

yes

characteristic

C₂×C₅²×C₃₁

C₂×C₉

yes

characteristic, complemented

C₅×D₅×C₃₁

C₂×C₉

yes

direct product factor

C₅×C₉×C₃₁

—

C₅×C₉×C₃₁

C₂×D₅

yes

characteristic, direct product factor

C₅×C₉×C₃₁

C₂²×C₅

yes

characteristic, complemented

C₂²×C₉×C₃₁

—

Hall

C₂×C₃×C₅×C₃₁

—

C₂×C₃×C₅×C₃₁

—

C₂×C₃×C₅×C₃₁

C₃×D₅

yes

characteristic

C₂×C₃×C₅×C₃₁

C₂×C₃×C₅

yes

characteristic

C₃×D₅×C₃₁

C₂×C₃×C₅

yes

—

C₂×C₅×C₉×D₅

C₃₁

yes

maximal, characteristic, direct product factor, Hall

C₅²×C₃₁

C₂²×C₉

yes

characteristic, complemented, Hall

C₂²×C₅×C₃₁

—

C₂×D₅×C₃₁

C₅×C₉

yes

characteristic, direct product factor

C₂×C₉×C₃₁

—

C₂×C₉×C₃₁

C₅×D₅

yes

characteristic, direct product factor

C₃×C₅×C₃₁

—

C₃×C₅×C₃₁

C₂×C₃×D₅

yes

characteristic

C₃×C₅×C₃₁

C₂²×C₃×C₅

yes

characteristic

C₂×C₅²×C₉

C₂×C₃₁

yes

characteristic, complemented

C₅×C₉×D₅

C₂×C₃₁

yes

direct product factor

C₂²×C₃×C₃₁

—

C₂×C₅×C₃₁

—

C₂×C₅×C₃₁

—

C₂×C₅×C₃₁

C₉×D₅

yes

characteristic, direct product factor

C₂×C₅×C₃₁

C₂×C₅×C₉

yes

characteristic, complemented

D₅×C₃₁

C₂×C₅×C₉

yes

direct product factor

C₂×C₃×C₅×D₅

C₃×C₃₁

yes

characteristic

C₉×C₃₁

C₂×C₅×D₅

yes

characteristic, direct product factor, Hall

C₅²×C₉

C₂²×C₃₁

yes

characteristic, complemented, Hall

C₂×C₃×C₃₁

—

C₂×C₃×C₃₁

C₃×C₅×D₅

yes

characteristic

C₂²×C₅×C₉

—

C₂×C₉×D₅

C₅×C₃₁

yes

characteristic, direct product factor

C₅×C₃₁

—

C₅×C₃₁

C₂×C₉×D₅

yes

characteristic, direct product factor

C₅×C₃₁

C₂²×C₅×C₉

yes

characteristic, complemented

C₂×C₃×C₅²

C₂×C₃×C₃₁

yes

characteristic

C₃×C₅×D₅

C₂×C₃×C₃₁

yes

—

C₂²×C₃₁

—

Hall

C₂×C₅×D₅

C₉×C₃₁

yes

characteristic, direct product factor, Hall

C₃×C₃₁

C₂×C₃×C₅×D₅

yes

characteristic

C₂×C₅×C₉

—

C₂×C₅×C₉

—

C₂×C₅×C₉

D₅×C₃₁

yes

characteristic, direct product factor

C₂×C₅×C₉

C₂×C₅×C₃₁

yes

characteristic, complemented

C₉×D₅

C₂×C₅×C₃₁

yes

direct product factor

C₃×C₅²

C₂²×C₃×C₃₁

yes

characteristic

C₂×C₃₁

—

C₂×C₃₁

C₅×C₉×D₅

yes

characteristic, direct product factor

C₂²×C₃×C₅

—

C₂×C₃×D₅

C₃×C₅×C₃₁

yes

characteristic

C₂×C₅²

C₂×C₉×C₃₁

yes

characteristic, complemented

C₅×D₅

C₂×C₉×C₃₁

yes

direct product factor

C₅×C₉

—

C₅×C₉

C₂×D₅×C₃₁

yes

characteristic, direct product factor

C₅×C₉

C₂²×C₅×C₃₁

yes

characteristic, complemented

C₂²×C₉

—

Hall

C₃₁

C₂×C₅×C₉×D₅

yes

characteristic, direct product factor, Sylow

C₂×C₃×C₅

—

C₂×C₃×C₅

—

C₂×C₃×C₅

C₃×D₅×C₃₁

yes

characteristic

C₂×C₃×C₅

C₂×C₃×C₅×C₃₁

yes

characteristic

C₃×D₅

C₂×C₃×C₅×C₃₁

yes

—

C₅²

C₂²×C₉×C₃₁

yes

characteristic, complemented, Sylow

C₂²×C₅

—

C₂×D₅

C₅×C₉×C₃₁

yes

characteristic, direct product factor

C₂×C₉

—

C₂×C₉

C₅×D₅×C₃₁

yes

characteristic, direct product factor

C₃×C₅

—

C₃×C₅

C₂×C₃×D₅×C₃₁

yes

characteristic

C₃×C₅

C₂²×C₃×C₅×C₃₁

yes

characteristic

C₂²×C₃

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

C₂×C₅×C₉×C₃₁

yes

characteristic, complemented

C₂×C₅

C₉×D₅×C₃₁

yes

characteristic, direct product factor

D₅

C₂×C₅×C₉×C₃₁

yes

direct product factor

C₉

C₂×C₅×D₅×C₃₁

yes

characteristic, direct product factor, Sylow

C₂×C₃

—

C₂×C₃

C₃×C₅×D₅×C₃₁

yes

characteristic

100

C₅

—

101

C₅

C₂²×C₅×C₉×C₃₁

yes

characteristic, complemented

102

C₅

C₂×C₉×D₅×C₃₁

yes

characteristic, direct product factor

103

C₂²

—

Sylow

104

C₃

C₂×C₃×C₅×D₅×C₃₁

yes

characteristic

105

C₂

—

106

C₂

C₅×C₉×D₅×C₃₁

yes

characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉×C₃₁	D₅
commutator, hypocenter	C₅	C₂²×C₅×C₉×C₃₁
Frattini	C₃	C₂×C₃×C₅×D₅×C₃₁
Fitting	C₂×C₅²×C₉×C₃₁	C₂
socle	C₂×C₃×C₅²×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₅×D₅×C₃₁	C₃
cosocle	C₃×C₅	C₂²×C₃×C₅×C₃₁
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₅×C₉×C₃₁

subgroup

G/H

center, hypercenter

C₂×C₅×C₉×C₃₁

D₅

commutator, hypocenter

C₅

C₂²×C₅×C₉×C₃₁

Frattini

C₃

C₂×C₃×C₅×D₅×C₃₁

Fitting

C₂×C₅²×C₉×C₃₁

C₂

socle

C₂×C₃×C₅²×C₃₁

C₂×C₃

prime radical

C₂×C₃×C₅×D₅×C₃₁

C₃

cosocle

C₃×C₅

C₂²×C₃×C₅×C₃₁

LCS

G ▷ C₅

UCS

C₁ ◁ C₂×C₅×C₉×C₃₁

N	H ≅ G/N	type
1. C₅×C₉×D₅×C₃₁	C₂	direct (N × H)
2. C₂×C₅²×C₉×C₃₁	C₂	semidirect
4. C₅²×C₉×C₃₁	C₂²	semidirect
5. C₂×C₉×D₅×C₃₁	C₅	direct (N × H)
9. C₂×C₅×D₅×C₃₁	C₉	direct (N × H)
10. C₉×D₅×C₃₁	C₂×C₅	direct (N × H)
13. C₂×C₅×C₉×C₃₁	D₅	direct (N × H)
14. C₂×C₅×C₉×C₃₁	C₂×C₅	semidirect
18. C₂×C₅²×C₃₁	C₂×C₉	semidirect
19. C₅×D₅×C₃₁	C₂×C₉	direct (N × H)
21. C₅×C₉×C₃₁	C₂×D₅	direct (N × H)
22. C₅×C₉×C₃₁	C₂²×C₅	semidirect
29. C₂×C₅×C₉×D₅	C₃₁	direct (N × H)
30. C₅²×C₃₁	C₂²×C₉	semidirect
32. C₂×D₅×C₃₁	C₅×C₉	direct (N × H)
34. C₂×C₉×C₃₁	C₅×D₅	direct (N × H)
38. C₂×C₅²×C₉	C₂×C₃₁	semidirect
39. C₅×C₉×D₅	C₂×C₃₁	direct (N × H)
43. C₂×C₅×C₃₁	C₉×D₅	direct (N × H)
44. C₂×C₅×C₃₁	C₂×C₅×C₉	semidirect
45. D₅×C₃₁	C₂×C₅×C₉	direct (N × H)
47. C₉×C₃₁	C₂×C₅×D₅	direct (N × H)
48. C₅²×C₉	C₂²×C₃₁	semidirect
52. C₂×C₉×D₅	C₅×C₃₁	direct (N × H)
54. C₅×C₃₁	C₂×C₉×D₅	direct (N × H)
55. C₅×C₃₁	C₂²×C₅×C₉	semidirect
59. C₂×C₅×D₅	C₉×C₃₁	direct (N × H)
63. C₂×C₅×C₉	D₅×C₃₁	direct (N × H)
64. C₂×C₅×C₉	C₂×C₅×C₃₁	semidirect
65. C₉×D₅	C₂×C₅×C₃₁	direct (N × H)
68. C₂×C₃₁	C₅×C₉×D₅	direct (N × H)
71. C₂×C₅²	C₂×C₉×C₃₁	semidirect
72. C₅×D₅	C₂×C₉×C₃₁	direct (N × H)
74. C₅×C₉	C₂×D₅×C₃₁	direct (N × H)
75. C₅×C₉	C₂²×C₅×C₃₁	semidirect
77. C₃₁	C₂×C₅×C₉×D₅	direct (N × H)
83. C₅²	C₂²×C₉×C₃₁	semidirect
85. C₂×D₅	C₅×C₉×C₃₁	direct (N × H)
87. C₂×C₉	C₅×D₅×C₃₁	direct (N × H)
94. C₂×C₅	C₂×C₅×C₉×C₃₁	semidirect
95. C₂×C₅	C₉×D₅×C₃₁	direct (N × H)
96. D₅	C₂×C₅×C₉×C₃₁	direct (N × H)
97. C₉	C₂×C₅×D₅×C₃₁	direct (N × H)
101. C₅	C₂²×C₅×C₉×C₃₁	semidirect
102. C₅	C₂×C₉×D₅×C₃₁	direct (N × H)
106. C₂	C₅×C₉×D₅×C₃₁	direct (N × H)

H ≅ G/N

type

1. C₅×C₉×D₅×C₃₁

C₂

direct (N × H)

2. C₂×C₅²×C₉×C₃₁

C₂

semidirect

4. C₅²×C₉×C₃₁

C₂²

semidirect

5. C₂×C₉×D₅×C₃₁

C₅

direct (N × H)

9. C₂×C₅×D₅×C₃₁

C₉

direct (N × H)

10. C₉×D₅×C₃₁

C₂×C₅

direct (N × H)

13. C₂×C₅×C₉×C₃₁

D₅

direct (N × H)

14. C₂×C₅×C₉×C₃₁

C₂×C₅

semidirect

18. C₂×C₅²×C₃₁

C₂×C₉

semidirect

19. C₅×D₅×C₃₁

C₂×C₉

direct (N × H)

21. C₅×C₉×C₃₁

C₂×D₅

direct (N × H)

22. C₅×C₉×C₃₁

C₂²×C₅

semidirect

29. C₂×C₅×C₉×D₅

C₃₁

direct (N × H)

30. C₅²×C₃₁

C₂²×C₉

semidirect

32. C₂×D₅×C₃₁

C₅×C₉

direct (N × H)

34. C₂×C₉×C₃₁

C₅×D₅

direct (N × H)

38. C₂×C₅²×C₉

C₂×C₃₁

semidirect

39. C₅×C₉×D₅

C₂×C₃₁

direct (N × H)

43. C₂×C₅×C₃₁

C₉×D₅

direct (N × H)

44. C₂×C₅×C₃₁

C₂×C₅×C₉

semidirect

45. D₅×C₃₁

C₂×C₅×C₉

direct (N × H)

47. C₉×C₃₁

C₂×C₅×D₅

direct (N × H)

48. C₅²×C₉

C₂²×C₃₁

semidirect

52. C₂×C₉×D₅

C₅×C₃₁

direct (N × H)

54. C₅×C₃₁

C₂×C₉×D₅

direct (N × H)

55. C₅×C₃₁

C₂²×C₅×C₉

semidirect

59. C₂×C₅×D₅

C₉×C₃₁

direct (N × H)

63. C₂×C₅×C₉

D₅×C₃₁

direct (N × H)

64. C₂×C₅×C₉

C₂×C₅×C₃₁

semidirect

65. C₉×D₅

C₂×C₅×C₃₁

direct (N × H)

68. C₂×C₃₁

C₅×C₉×D₅

direct (N × H)

71. C₂×C₅²

C₂×C₉×C₃₁

semidirect

72. C₅×D₅

C₂×C₉×C₃₁

direct (N × H)

74. C₅×C₉

C₂×D₅×C₃₁

direct (N × H)

75. C₅×C₉

C₂²×C₅×C₃₁

semidirect

77. C₃₁

C₂×C₅×C₉×D₅

direct (N × H)

83. C₅²

C₂²×C₉×C₃₁

semidirect

85. C₂×D₅

C₅×C₉×C₃₁

direct (N × H)

87. C₂×C₉

C₅×D₅×C₃₁

direct (N × H)

94. C₂×C₅

C₂×C₅×C₉×C₃₁

semidirect

95. C₂×C₅

C₉×D₅×C₃₁

direct (N × H)

96. D₅

C₂×C₅×C₉×C₃₁

direct (N × H)

97. C₉

C₂×C₅×D₅×C₃₁

direct (N × H)

101. C₅

C₂²×C₅×C₉×C₃₁

semidirect

102. C₅

C₂×C₉×D₅×C₃₁

direct (N × H)

106. C₂

C₅×C₉×D₅×C₃₁

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×C₃₁	2
C₂×C₅²×C₉×C₃₁	2
C₂×C₃×C₅×D₅×C₃₁	3
C₂×C₉×D₅×C₃₁	5
C₂²×C₅×C₉×C₃₁	5
C₂×C₅×C₉×D₅	31

subgroup

index

C₅×C₉×D₅×C₃₁

C₂×C₅²×C₉×C₃₁

C₂×C₃×C₅×D₅×C₃₁

C₂×C₉×D₅×C₃₁

C₂²×C₅×C₉×C₃₁

C₂×C₅×C₉×D₅

Subgroups — C₂×C₅×C₉×D₅×C₃₁ #42124591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C5×C9×D5×C31 #42124591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉×D₅×C₃₁ #42124591