Finite Group Databasebeta

← C29×(C3⋊D3)⋊D35 #49141627

Subgroups — C29×(C3⋊D3)⋊D35 #49141627

Order 36540.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C29×D105C212yesmaximal, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3D3×C29×D35—32nomaximal
4C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
5C29×(C3⋊D3)⋊D7—51nomaximal, Hall
6C29×D105D312yescomplemented
7C5×D3×C7×C29—32no—
8C5×D3×C7×C29—61no—
9C3×C29×D35—32no—
10C29×(C3⋊D3)⋊D5—71nomaximal, Hall
11C2×C29×D35—91noHall
12C7×C3⋊D3×C29D511yescharacteristic, complemented
13C3×C29×D21—52no—
14C3×C5×C7×C29—21no—
15C3×C5×C7×C29C2×D312yescomplemented
16C5×C3⋊D3×C29D711yescharacteristic, complemented
17C3×C29×D15—72no—
18D3×D7×C29—152no—
19C29×D35—32no—
20C2×C5×C7×C29—91no—
21C32×C7×C29C2×D511yescharacteristic, complemented, Hall
22D3×D5×C29—212no—
23C32×C5×C29C2×D711yescharacteristic, complemented, Hall
24(C3⋊D3)⋊D35C2911yesmaximal, characteristic, direct product factor, Hall
25C29×D21—52no—
26D3×C7×C29—32no—
27D3×C7×C29—61no—
28C3×D7×C29—152no—
29D32×C29—351noHall
30C5×C7×C29D3211yescharacteristic, complemented, Hall
31C29×D15—72no—
32C5×D3×C29—32no—
33C5×D3×C29—61no—
34C3×D5×C29—212no—
35C2×D7×C29—451noHall
36C5×C7×C3⋊D3C2×C2911yescharacteristic, complemented
37C3×D105C2×C2912yescomplemented
38C3×C7×C29—21no—
39C3×C7×C29D3×D512yescomplemented
40C2×D5×C29—631noHall
41C3⋊D3×C29D3511yescharacteristic, complemented
42C3×D3×C29—352no—
43C3×C5×C29—21no—
44C3×C5×C29D3×D712yescomplemented
45D3×D35—32no—
46C2×C7×C29—91no—
47D7×C29—152no—
48C2×D3×C29—1052no—
49C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
50C2×C5×C29—91no—
51D5×C29—212no—
52C32×C29C2×D3511yescharacteristic, complemented, Hall
53(C3⋊D3)⋊D7—51noHall
54D105D3×C2912yescomplemented
55C5×D3×C7—32no—
56C5×D3×C7—61no—
57C3×D35—32no—
58C7×C29(C3⋊D3)⋊D511yescharacteristic, complemented, Hall
59(C3⋊D3)⋊D5—71noHall
60C2×C3×C29—1052no—
61D3×C29—32no—
62D3×C29—61no—
63D3×C29—352no—
64C5×C29(C3⋊D3)⋊D711yescharacteristic, complemented, Hall
65C2×D35—91noHall
66C7×C3⋊D3D5×C2911yescharacteristic, complemented
67C3×D21—52no—
68C22×C29—3151noHall
69C3×C5×C7—21no—
70C3×C5×C7C2×D3×C2912yescomplemented
71C5×C3⋊D3D7×C2911yescharacteristic, complemented
72C3×D15—72no—
73C3×C29—21no—
74C3×C29D3×D3512yescomplemented
75D3×D7—152no—
76C2×C5×C7—91no—
77D35—32no—
78C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
79D3×D5—212no—
80C2×C29—91no—
81C2×C29—1052no—
82C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
83D21—52no—
84C3×D7—152no—
85D3×C7—32no—
86D3×C7—61no—
87D32—351noHall
88C5×C7D32×C2911yescharacteristic, complemented, Hall
89D15—72no—
90C3×D5—212no—
91C5×D3—32no—
92C5×D3—61no—
93C29(C3⋊D3)⋊D3511yescharacteristic, direct product factor, Sylow
94C2×D7—451noHall
95C3×C7—21no—
96C3×C7D3×D5×C2912yescomplemented
97C2×D5—631noHall
98C3⋊D3C29×D3511yescharacteristic, complemented
99C3×D3—352no—
100C3×C5—21no—
101C3×C5D3×D7×C2912yescomplemented
102C2×C7—91no—
103D7—152no—
104C2×D3—1052no—
105C2×C5—91no—
106D5—212no—
107C32C2×C29×D3511yescharacteristic, complemented, Sylow
108C7C29×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
109C2×C3—1052no—
110D3—32no—
111D3—61no—
112D3—352no—
113C5C29×(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
114C22—3151noSylow
115C3—21no—
116C3D3×C29×D3512yescomplemented
117C2—91no—
118C2—1052no—
subgroupG/H
center, hypercenterC29(C3⋊D3)⋊D35
commutator, cosocle, hypocenterC32×C5×C7C22×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7
UCSC1 ◁ C29

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C29×D105C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
4. C32×C5×C7×C29C22semidirect
6. C29×D105D3semidirect
12. C7×C3⋊D3×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D3×C29D7semidirect
21. C32×C7×C29C2×D5semidirect
23. C32×C5×C29C2×D7semidirect
24. (C3⋊D3)⋊D35C29direct (N × H)
30. C5×C7×C29D32semidirect
36. C5×C7×C3⋊D3C2×C29semidirect
37. C3×D105C2×C29semidirect
39. C3×C7×C29D3×D5semidirect
41. C3⋊D3×C29D35semidirect
44. C3×C5×C29D3×D7semidirect
49. C32×C5×C7C22×C29semidirect
52. C32×C29C2×D35semidirect
54. D105D3×C29semidirect
58. C7×C29(C3⋊D3)⋊D5semidirect
64. C5×C29(C3⋊D3)⋊D7semidirect
66. C7×C3⋊D3D5×C29semidirect
70. C3×C5×C7C2×D3×C29semidirect
71. C5×C3⋊D3D7×C29semidirect
74. C3×C29D3×D35semidirect
78. C32×C7C2×D5×C29semidirect
82. C32×C5C2×D7×C29semidirect
88. C5×C7D32×C29semidirect
93. C29(C3⋊D3)⋊D35direct (N × H)
96. C3×C7D3×D5×C29semidirect
98. C3⋊D3C29×D35semidirect
101. C3×C5D3×D7×C29semidirect
107. C32C2×C29×D35semidirect
108. C7C29×(C3⋊D3)⋊D5semidirect
113. C5C29×(C3⋊D3)⋊D7semidirect
116. C3D3×C29×D35semidirect

Maximal subgroups

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

subgroupindex
C3×C29×D1052
C5×C7×C3⋊D3×C292
D3×C29×D353
C29×(C3⋊D3)⋊D75
C29×(C3⋊D3)⋊D57
(C3⋊D3)⋊D3529