Finite Group Databasebeta

← C5×C7×(C3⋊D3)⋊D29 #49141596

Subgroups — C5×C7×(C3⋊D3)⋊D29 #49141596

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×C5×C7×D87C212yesmaximal, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C5×D3×C7×D29—32nomaximal
4C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
5C7×(C3⋊D3)⋊D29C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×D87D312yescomplemented
7C5×D3×C7×C29—32no—
8C5×D3×C7×C29—61no—
9C3×C5×C7×D29—32no—
10C5×(C3⋊D3)⋊D29C711yesmaximal, characteristic, direct product factor, Hall
11C2×C5×C7×D29—91noHall
12C7×C3⋊D3×C29C2×C511yescharacteristic, complemented
13C3×C7×D87C2×C512yescomplemented
14C3×C5×C7×C29—21no—
15C3×C5×C7×C29C2×D312yescomplemented
16C5×C3⋊D3×C29C2×C711yescharacteristic, complemented
17C3×C5×D87C2×C712yescomplemented
18D3×C7×D29—32no—
19C5×C7×D29—32no—
20C2×C5×C7×C29—91no—
21C32×C7×C29C22×C511yescharacteristic, complemented, Hall
22C5×D3×D29—32no—
23C32×C5×C29C22×C711yescharacteristic, complemented, Hall
24C5×D32×C7—291nomaximal, Hall
25C7×D87C5×D312yescomplemented
26D3×C7×C29—32no—
27D3×C7×C29—61no—
28C3×C7×D29—32no—
29(C3⋊D3)⋊D29C5×C711yescharacteristic, direct product factor, Hall
30C5×C7×C29D3211yescharacteristic, complemented, Hall
31C5×D87D3×C712yescomplemented
32C5×D3×C29—32no—
33C5×D3×C29—61no—
34C3×C5×D29—32no—
35C2×C7×D29—91noHall
36C5×C7×C3⋊D3D2911yescharacteristic, complemented
37C3×C5×D3×C7—292no—
38C3×C7×C29—21no—
39C3×C7×C29C2×C5×D312yescomplemented
40C2×C5×D29—91noHall
41C3⋊D3×C29C2×C5×C711yescharacteristic, complemented
42C3×D87C2×C5×C712yescomplemented
43C3×C5×C29—21no—
44C3×C5×C29C2×D3×C712yescomplemented
45C2×C5×D3×C7—872no—
46C2×C7×C29—91no—
47C7×D29—32no—
48D3×D29—32no—
49C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
50C2×C5×C29—91no—
51C5×D29—32no—
52C32×C29C22×C5×C711yescharacteristic, complemented, Hall
53D32×C7—291noHall
54C2×C3×C5×C7—872no—
55C5×D3×C7—32no—
56C5×D3×C7—61no—
57C5×D3×C7—292no—
58C7×C29C5×D3211yescharacteristic, complemented, Hall
59C5×D32—291noHall
60D87C5×D3×C712yescomplemented
61C3×D29—32no—
62D3×C29—32no—
63D3×C29—61no—
64C5×C29D32×C711yescharacteristic, complemented, Hall
65C22×C5×C7—2611noHall
66C7×C3⋊D3C5×D2911yescharacteristic, complemented
67C3×D3×C7—292no—
68C2×D29—91noHall
69C3×C5×C7—21no—
70C3×C5×C7D3×D2912yescomplemented
71C5×C3⋊D3C7×D2911yescharacteristic, complemented
72C3×C5×D3—292no—
73C3×C29—21no—
74C3×C29C2×C5×D3×C712yescomplemented
75C2×D3×C7—872no—
76C2×C5×C7—91no—
77C2×C5×C7—872no—
78C32×C7C2×C5×D2911yescharacteristic, complemented, Hall
79C2×C5×D3—872no—
80C2×C29—91no—
81D29—32no—
82C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
83C2×C3×C7—872no—
84D3×C7—32no—
85D3×C7—61no—
86D3×C7—292no—
87D32—291noHall
88C5×C7(C3⋊D3)⋊D2911yescharacteristic, direct product factor, Hall
89C2×C3×C5—872no—
90C5×D3—32no—
91C5×D3—61no—
92C5×D3—292no—
93C29C5×D32×C711yescharacteristic, complemented, Sylow
94C22×C7—2611noHall
95C3×C7—21no—
96C3×C7C5×D3×D2912yescomplemented
97C22×C5—2611noHall
98C3⋊D3C5×C7×D2911yescharacteristic, complemented
99C3×D3—292no—
100C3×C5—21no—
101C3×C5D3×C7×D2912yescomplemented
102C2×C7—91no—
103C2×C7—872no—
104C2×D3—872no—
105C2×C5—91no—
106C2×C5—872no—
107C32C2×C5×C7×D2911yescharacteristic, complemented, Sylow
108C7C5×(C3⋊D3)⋊D2911yescharacteristic, direct product factor, Sylow
109C2×C3—872no—
110D3—32no—
111D3—61no—
112D3—292no—
113C5C7×(C3⋊D3)⋊D2911yescharacteristic, direct product factor, Sylow
114C22—2611noSylow
115C3—21no—
116C3C5×D3×C7×D2912yescomplemented
117C2—91no—
118C2—872no—
subgroupG/H
center, hypercenterC5×C7(C3⋊D3)⋊D29
commutator, cosocle, hypocenterC32×C29C22×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C29
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C3×C5×C7×D87C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
4. C32×C5×C7×C29C22semidirect
5. C7×(C3⋊D3)⋊D29C5direct (N × H)
6. C5×C7×D87D3semidirect
10. C5×(C3⋊D3)⋊D29C7direct (N × H)
12. C7×C3⋊D3×C29C2×C5semidirect
13. C3×C7×D87C2×C5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D3×C29C2×C7semidirect
17. C3×C5×D87C2×C7semidirect
21. C32×C7×C29C22×C5semidirect
23. C32×C5×C29C22×C7semidirect
25. C7×D87C5×D3semidirect
29. (C3⋊D3)⋊D29C5×C7direct (N × H)
30. C5×C7×C29D32semidirect
31. C5×D87D3×C7semidirect
36. C5×C7×C3⋊D3D29semidirect
39. C3×C7×C29C2×C5×D3semidirect
41. C3⋊D3×C29C2×C5×C7semidirect
42. C3×D87C2×C5×C7semidirect
44. C3×C5×C29C2×D3×C7semidirect
49. C32×C5×C7C2×D29semidirect
52. C32×C29C22×C5×C7semidirect
58. C7×C29C5×D32semidirect
60. D87C5×D3×C7semidirect
64. C5×C29D32×C7semidirect
66. C7×C3⋊D3C5×D29semidirect
70. C3×C5×C7D3×D29semidirect
71. C5×C3⋊D3C7×D29semidirect
74. C3×C29C2×C5×D3×C7semidirect
78. C32×C7C2×C5×D29semidirect
82. C32×C5C2×C7×D29semidirect
88. C5×C7(C3⋊D3)⋊D29direct (N × H)
93. C29C5×D32×C7semidirect
96. C3×C7C5×D3×D29semidirect
98. C3⋊D3C5×C7×D29semidirect
101. C3×C5D3×C7×D29semidirect
107. C32C2×C5×C7×D29semidirect
108. C7C5×(C3⋊D3)⋊D29direct (N × H)
113. C5C7×(C3⋊D3)⋊D29direct (N × H)
116. C3C5×D3×C7×D29semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C7×D872
C5×C7×C3⋊D3×C292
C5×D3×C7×D293
C7×(C3⋊D3)⋊D295
C5×(C3⋊D3)⋊D297
C5×D32×C729