Finite Group Databasebeta

← C7×C29×(C3⋊D3)⋊D5 #49141620

Subgroups — C7×C29×(C3⋊D3)⋊D5 #49141620

Order 36540.

176 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 60 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×C7×C29×D15C212yesmaximal, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3D3×C7×D5×C29—32nomaximal
4C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
5D32×C7×C29—51nomaximal, Hall
6C7×C29×D15D312yescomplemented
7C5×D3×C7×C29—32no—
8C5×D3×C7×C29—61no—
9C3×C7×D5×C29—32no—
10C29×(C3⋊D3)⋊D5C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D5×C29—91noHall
12C7×C3⋊D3×C29D511yescharacteristic, complemented
13C3×D3×C7×C29—52no—
14C3×C5×C7×C29—21no—
15C3×C5×C7×C29C2×D312yescomplemented
16C5×C3⋊D3×C29C2×C711yescharacteristic, complemented
17C3×C29×D15C2×C712yescomplemented
18C2×D3×C7×C29—152no—
19C7×D5×C29—32no—
20C2×C5×C7×C29—91no—
21C32×C7×C29C2×D511yescharacteristic, complemented, Hall
22D3×D5×C29—32no—
23C32×C5×C29C22×C711yescharacteristic, complemented, Hall
24C7×(C3⋊D3)⋊D5C2911yesmaximal, characteristic, direct product factor, Hall
25C2×C3×C7×C29—152no—
26D3×C7×C29—32no—
27D3×C7×C29—52no—
28D3×C7×C29—61no—
29D32×C29—51noHall
30C5×C7×C29D3211yescharacteristic, complemented, Hall
31C29×D15D3×C712yescomplemented
32C5×D3×C29—32no—
33C5×D3×C29—61no—
34C3×D5×C29—32no—
35C22×C7×C29—451noHall
36C5×C7×C3⋊D3C2×C2911yescharacteristic, complemented
37C3×C7×D15C2×C2912yescomplemented
38C3×C7×C29—21no—
39C3×C7×C29D3×D512yescomplemented
40C2×D5×C29—91noHall
41C3⋊D3×C29C7×D511yescharacteristic, complemented
42C3×D3×C29—52no—
43C3×C5×C29—21no—
44C3×C5×C29C2×D3×C712yescomplemented
45D3×C7×D5—32no—
46C2×C7×C29—91no—
47C2×C7×C29—152no—
48C2×D3×C29—152no—
49C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
50C2×C5×C29—91no—
51D5×C29—32no—
52C32×C29C2×C7×D511yescharacteristic, complemented, Hall
53D32×C7—51noHall
54C7×D15D3×C2912yescomplemented
55C5×D3×C7—32no—
56C5×D3×C7—61no—
57C3×C7×D5—32no—
58C7×C29(C3⋊D3)⋊D511yescharacteristic, direct product factor, Hall
59(C3⋊D3)⋊D5C7×C2911yescharacteristic, direct product factor, Hall
60C2×C3×C29—152no—
61D3×C29—32no—
62D3×C29—52no—
63D3×C29—61no—
64C5×C29D32×C711yescharacteristic, complemented, Hall
65C2×C7×D5—91noHall
66C7×C3⋊D3D5×C2911yescharacteristic, complemented
67C3×D3×C7—52no—
68C22×C29—451noHall
69C3×C5×C7—21no—
70C3×C5×C7C2×D3×C2912yescomplemented
71C5×C3⋊D3C2×C7×C2911yescharacteristic, complemented
72C3×D15C2×C7×C2912yescomplemented
73C3×C29—21no—
74C3×C29D3×C7×D512yescomplemented
75C2×D3×C7—152no—
76C2×C5×C7—91no—
77C7×D5—32no—
78C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
79D3×D5—32no—
80C2×C29—91no—
81C2×C29—152no—
82C32×C5C22×C7×C2911yescharacteristic, complemented, Hall
83C2×C3×C7—152no—
84D3×C7—32no—
85D3×C7—52no—
86D3×C7—61no—
87D32—51noHall
88C5×C7D32×C2911yescharacteristic, complemented, Hall
89D15D3×C7×C2912yescomplemented
90C3×D5—32no—
91C5×D3—32no—
92C5×D3—61no—
93C29C7×(C3⋊D3)⋊D511yescharacteristic, direct product factor, Sylow
94C22×C7—451noHall
95C3×C7—21no—
96C3×C7D3×D5×C2912yescomplemented
97C2×D5—91noHall
98C3⋊D3C7×D5×C2911yescharacteristic, complemented
99C3×D3—52no—
100C3×C5—21no—
101C3×C5C2×D3×C7×C2912yescomplemented
102C2×C7—91no—
103C2×C7—152no—
104C2×D3—152no—
105C2×C5—91no—
106D5—32no—
107C32C2×C7×D5×C2911yescharacteristic, complemented, Sylow
108C7C29×(C3⋊D3)⋊D511yescharacteristic, direct product factor, Sylow
109C2×C3—152no—
110D3—32no—
111D3—52no—
112D3—61no—
113C5D32×C7×C2911yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3—21no—
116C3D3×C7×D5×C2912yescomplemented
117C2—91no—
118C2—152no—
subgroupG/H
center, hypercenterC7×C29(C3⋊D3)⋊D5
commutator, cosocle, hypocenterC32×C5C22×C7×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5
UCSC1 ◁ C7×C29

Complements

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

NH ≅ G/Ntype
1. C3×C7×C29×D15C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
4. C32×C5×C7×C29C22semidirect
6. C7×C29×D15D3semidirect
10. C29×(C3⋊D3)⋊D5C7direct (N × H)
12. C7×C3⋊D3×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D3×C29C2×C7semidirect
17. C3×C29×D15C2×C7semidirect
21. C32×C7×C29C2×D5semidirect
23. C32×C5×C29C22×C7semidirect
24. C7×(C3⋊D3)⋊D5C29direct (N × H)
30. C5×C7×C29D32semidirect
31. C29×D15D3×C7semidirect
36. C5×C7×C3⋊D3C2×C29semidirect
37. C3×C7×D15C2×C29semidirect
39. C3×C7×C29D3×D5semidirect
41. C3⋊D3×C29C7×D5semidirect
44. C3×C5×C29C2×D3×C7semidirect
49. C32×C5×C7C22×C29semidirect
52. C32×C29C2×C7×D5semidirect
54. C7×D15D3×C29semidirect
58. C7×C29(C3⋊D3)⋊D5direct (N × H)
59. (C3⋊D3)⋊D5C7×C29direct (N × H)
64. C5×C29D32×C7semidirect
66. C7×C3⋊D3D5×C29semidirect
70. C3×C5×C7C2×D3×C29semidirect
71. C5×C3⋊D3C2×C7×C29semidirect
72. C3×D15C2×C7×C29semidirect
74. C3×C29D3×C7×D5semidirect
78. C32×C7C2×D5×C29semidirect
82. C32×C5C22×C7×C29semidirect
88. C5×C7D32×C29semidirect
89. D15D3×C7×C29semidirect
93. C29C7×(C3⋊D3)⋊D5direct (N × H)
96. C3×C7D3×D5×C29semidirect
98. C3⋊D3C7×D5×C29semidirect
101. C3×C5C2×D3×C7×C29semidirect
107. C32C2×C7×D5×C29semidirect
108. C7C29×(C3⋊D3)⋊D5direct (N × H)
113. C5D32×C7×C29semidirect
116. C3D3×C7×D5×C29semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C29×D152
C5×C7×C3⋊D3×C292
D3×C7×D5×C293
D32×C7×C295
C29×(C3⋊D3)⋊D57
C7×(C3⋊D3)⋊D529