Finite Group Databasebeta

← C5×D32×C7×C29 #49141594

Subgroups — C5×D32×C7×C29 #49141594

Order 36540.

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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×C5×D3×C7×C29C212yesmaximal, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C2×C5×D3×C7×C29—32nomaximal
4C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
5D32×C7×C29C511yesmaximal, characteristic, direct product factor, Hall
6C5×D3×C7×C29—32no—
7C5×D3×C7×C29—61no—
8C5×D3×C7×C29D312yesdirect product factor
9C2×C3×C5×C7×C29—32no—
10C5×D32×C29C711yesmaximal, characteristic, direct product factor, Hall
11C22×C5×C7×C29—91noHall
12C7×C3⋊D3×C29C2×C511yescharacteristic, complemented
13C3×D3×C7×C29C2×C512yescomplemented
14C3×C5×C7×C29—21no—
15C3×C5×C7×C29C2×D312yescomplemented
16C5×C3⋊D3×C29C2×C711yescharacteristic, complemented
17C3×C5×D3×C29C2×C712yescomplemented
18C2×D3×C7×C29—32no—
19C2×C5×C7×C29—32no—
20C2×C5×C7×C29—91no—
21C32×C7×C29C22×C511yescharacteristic, complemented, Hall
22C2×C5×D3×C29—32no—
23C32×C5×C29C22×C711yescharacteristic, complemented, Hall
24C5×D32×C7C2911yesmaximal, characteristic, direct product factor, Hall
25C2×C3×C7×C29—32no—
26D3×C7×C29—32no—
27D3×C7×C29—61no—
28D3×C7×C29C5×D312yesdirect product factor
29D32×C29C5×C711yescharacteristic, direct product factor, Hall
30C5×C7×C29D3211yescharacteristic, direct product factor, Hall
31C2×C3×C5×C29—32no—
32C5×D3×C29—32no—
33C5×D3×C29—61no—
34C5×D3×C29D3×C712yesdirect product factor
35C22×C7×C29—91noHall
36C5×C7×C3⋊D3C2×C2911yescharacteristic, complemented
37C3×C5×D3×C7C2×C2912yescomplemented
38C3×C7×C29—21no—
39C3×C7×C29C2×C5×D312yescomplemented
40C22×C5×C29—91noHall
41C3⋊D3×C29C2×C5×C711yescharacteristic, complemented
42C3×D3×C29C2×C5×C712yescomplemented
43C3×C5×C29—21no—
44C3×C5×C29C2×D3×C712yescomplemented
45C2×C5×D3×C7—32no—
46C2×C7×C29—32no—
47C2×C7×C29—91no—
48C2×D3×C29—32no—
49C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
50C2×C5×C29—32no—
51C2×C5×C29—91no—
52C32×C29C22×C5×C711yescharacteristic, complemented, Hall
53D32×C7C5×C2911yescharacteristic, direct product factor, Hall
54C2×C3×C5×C7—32no—
55C5×D3×C7—32no—
56C5×D3×C7—61no—
57C5×D3×C7D3×C2912yesdirect product factor
58C7×C29C5×D3211yescharacteristic, direct product factor, Hall
59C5×D32C7×C2911yescharacteristic, direct product factor, Hall
60C2×C3×C29—32no—
61D3×C29—32no—
62D3×C29—61no—
63D3×C29C5×D3×C712yesdirect product factor
64C5×C29D32×C711yescharacteristic, direct product factor, Hall
65C22×C5×C7—91noHall
66C7×C3⋊D3C2×C5×C2911yescharacteristic, complemented
67C3×D3×C7C2×C5×C2912yescomplemented
68C22×C29—91noHall
69C3×C5×C7—21no—
70C3×C5×C7C2×D3×C2912yescomplemented
71C5×C3⋊D3C2×C7×C2911yescharacteristic, complemented
72C3×C5×D3C2×C7×C2912yescomplemented
73C3×C29—21no—
74C3×C29C2×C5×D3×C712yescomplemented
75C2×D3×C7—32no—
76C2×C5×C7—32no—
77C2×C5×C7—91no—
78C32×C7C22×C5×C2911yescharacteristic, complemented, Hall
79C2×C5×D3—32no—
80C2×C29—32no—
81C2×C29—91no—
82C32×C5C22×C7×C2911yescharacteristic, complemented, Hall
83C2×C3×C7—32no—
84D3×C7—32no—
85D3×C7—61no—
86D3×C7C5×D3×C2912yesdirect product factor
87D32C5×C7×C2911yescharacteristic, direct product factor, Hall
88C5×C7D32×C2911yescharacteristic, direct product factor, Hall
89C2×C3×C5—32no—
90C5×D3—32no—
91C5×D3—61no—
92C5×D3D3×C7×C2912yesdirect product factor
93C29C5×D32×C711yescharacteristic, direct product factor, Sylow
94C22×C7—91noHall
95C3×C7—21no—
96C3×C7C2×C5×D3×C2912yescomplemented
97C22×C5—91noHall
98C3⋊D3C2×C5×C7×C2911yescharacteristic, complemented
99C3×D3C2×C5×C7×C2912yescomplemented
100C3×C5—21no—
101C3×C5C2×D3×C7×C2912yescomplemented
102C2×C7—32no—
103C2×C7—91no—
104C2×D3—32no—
105C2×C5—32no—
106C2×C5—91no—
107C32C22×C5×C7×C2911yescharacteristic, complemented, Sylow
108C7C5×D32×C2911yescharacteristic, direct product factor, Sylow
109C2×C3—32no—
110D3—32no—
111D3—61no—
112D3C5×D3×C7×C2912yesdirect product factor
113C5D32×C7×C2911yescharacteristic, direct product factor, Sylow
114C22—91noSylow
115C3—21no—
116C3C2×C5×D3×C7×C2912yescomplemented
117C2—32no—
118C2—91no—
subgroupG/H
center, hypercenterC5×C7×C29D32
commutator, cosocle, hypocenterC32C22×C5×C7×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32
UCSC1 ◁ C5×C7×C29

Complements

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

NH ≅ G/Ntype
1. C3×C5×D3×C7×C29C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
4. C32×C5×C7×C29C22semidirect
5. D32×C7×C29C5direct (N × H)
8. C5×D3×C7×C29D3direct (N × H)
10. C5×D32×C29C7direct (N × H)
12. C7×C3⋊D3×C29C2×C5semidirect
13. C3×D3×C7×C29C2×C5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D3×C29C2×C7semidirect
17. C3×C5×D3×C29C2×C7semidirect
21. C32×C7×C29C22×C5semidirect
23. C32×C5×C29C22×C7semidirect
24. C5×D32×C7C29direct (N × H)
28. D3×C7×C29C5×D3direct (N × H)
29. D32×C29C5×C7direct (N × H)
30. C5×C7×C29D32direct (N × H)
34. C5×D3×C29D3×C7direct (N × H)
36. C5×C7×C3⋊D3C2×C29semidirect
37. C3×C5×D3×C7C2×C29semidirect
39. C3×C7×C29C2×C5×D3semidirect
41. C3⋊D3×C29C2×C5×C7semidirect
42. C3×D3×C29C2×C5×C7semidirect
44. C3×C5×C29C2×D3×C7semidirect
49. C32×C5×C7C22×C29semidirect
52. C32×C29C22×C5×C7semidirect
53. D32×C7C5×C29direct (N × H)
57. C5×D3×C7D3×C29direct (N × H)
58. C7×C29C5×D32direct (N × H)
59. C5×D32C7×C29direct (N × H)
63. D3×C29C5×D3×C7direct (N × H)
64. C5×C29D32×C7direct (N × H)
66. C7×C3⋊D3C2×C5×C29semidirect
67. C3×D3×C7C2×C5×C29semidirect
70. C3×C5×C7C2×D3×C29semidirect
71. C5×C3⋊D3C2×C7×C29semidirect
72. C3×C5×D3C2×C7×C29semidirect
74. C3×C29C2×C5×D3×C7semidirect
78. C32×C7C22×C5×C29semidirect
82. C32×C5C22×C7×C29semidirect
86. D3×C7C5×D3×C29direct (N × H)
87. D32C5×C7×C29direct (N × H)
88. C5×C7D32×C29direct (N × H)
92. C5×D3D3×C7×C29direct (N × H)
93. C29C5×D32×C7direct (N × H)
96. C3×C7C2×C5×D3×C29semidirect
98. C3⋊D3C2×C5×C7×C29semidirect
99. C3×D3C2×C5×C7×C29semidirect
101. C3×C5C2×D3×C7×C29semidirect
107. C32C22×C5×C7×C29semidirect
108. C7C5×D32×C29direct (N × H)
112. D3C5×D3×C7×C29direct (N × H)
113. C5D32×C7×C29direct (N × H)
116. C3C2×C5×D3×C7×C29semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C7×C292
C5×C7×C3⋊D3×C292
C2×C5×D3×C7×C293
D32×C7×C295
C5×D32×C297
C5×D32×C729