Finite Group Databasebeta

← C7×D5×C3⋊D3×C29 #49141654

Subgroups — C7×D5×C3⋊D3×C29 #49141654

Order 36540.

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C32×C7×D5×C29C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C7×C29×C3⋊D15C211yesmaximal, characteristic, complemented
4D3×C7×D5×C29—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C2×C7×C3⋊D3×C29—51nomaximal, Hall
7C7×C29×D15—34no—
8C5×D3×C7×C29—34no—
9C3×C7×D5×C29D314yescomplemented
10D5×C3⋊D3×C29C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D5×C29—91noHall
12C7×C3⋊D3×C29—51no—
13C7×C3⋊D3×C29D511yescharacteristic, direct product factor
14C2×C32×C7×C29—51no—
15C3×C5×C7×C29C2×D314yescomplemented
16C29×C3⋊D15C2×C711yescharacteristic, complemented
17C5×C3⋊D3×C29C2×C711yescharacteristic, complemented
18C32×D5×C29C2×C711yescharacteristic, complemented
19C2×D3×C7×C29—154no—
20C7×D5×C29—91no—
21C7×D5×C29C3⋊D311yescharacteristic, direct product factor
22C2×C5×C7×C29—91no—
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D3×D5×C29—34no—
25C32×C5×C29C22×C711yescharacteristic, complemented, Hall
26C7×D5×C3⋊D3C2911yesmaximal, characteristic, direct product factor, Hall
27C2×C3×C7×C29—54no—
28D3×C7×C29—34no—
29D3×C7×C29—154no—
30C2×C3⋊D3×C29—51noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32C29×D15—34no—
33C5×D3×C29—34no—
34C3×D5×C29D3×C714yescomplemented
35C22×C7×C29—451noHall
36C7×C3⋊D15C2×C2911yescharacteristic, complemented
37C5×C7×C3⋊D3C2×C2911yescharacteristic, complemented
38C32×C7×D5C2×C2911yescharacteristic, complemented
39C3×C7×C29D3×D514yescomplemented
40C2×D5×C29—91noHall
41C2×C32×C29—51no—
42C3⋊D3×C29—51no—
43C3⋊D3×C29C7×D511yescharacteristic, direct product factor
44C3×C5×C29C2×D3×C714yescomplemented
45D3×C7×D5—34no—
46C2×C7×C29—51no—
47C2×C7×C29—91no—
48C2×C7×C29—451no—
49C2×D3×C29—154no—
50C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
51C2×C5×C29—91no—
52D5×C29—91no—
53D5×C29C7×C3⋊D311yescharacteristic, direct product factor
54C32×C29C2×C7×D511yescharacteristic, complemented, Hall
55C2×C7×C3⋊D3—51noHall
56C7×D15—34no—
57C5×D3×C7—34no—
58C3×C7×D5D3×C2914yescomplemented
59C7×C29D5×C3⋊D311yescharacteristic, direct product factor, Hall
60D5×C3⋊D3C7×C2911yescharacteristic, direct product factor, Hall
61C2×C3×C29—54no—
62D3×C29—34no—
63D3×C29—154no—
64C5×C29C2×C7×C3⋊D311yescharacteristic, complemented, Hall
65C2×C7×D5—91noHall
66C2×C32×C7—51no—
67C7×C3⋊D3—51no—
68C7×C3⋊D3D5×C2911yescharacteristic, direct product factor
69C22×C29—451noHall
70C3×C5×C7C2×D3×C2914yescomplemented
71C3⋊D15C2×C7×C2911yescharacteristic, complemented
72C5×C3⋊D3C2×C7×C2911yescharacteristic, complemented
73C32×D5C2×C7×C2911yescharacteristic, complemented
74C3×C29D3×C7×D514yescomplemented
75C2×D3×C7—154no—
76C2×C5×C7—91no—
77C7×D5—91no—
78C7×D5C3⋊D3×C2911yescharacteristic, direct product factor
79C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
80D3×D5—34no—
81C2×C29—51no—
82C2×C29—91no—
83C2×C29—451no—
84C32×C5C22×C7×C2911yescharacteristic, complemented, Hall
85C2×C3×C7—54no—
86D3×C7—34no—
87D3×C7—154no—
88C2×C3⋊D3—51noHall
89C5×C7C2×C3⋊D3×C2911yescharacteristic, complemented, Hall
90D15—34no—
91C3×D5D3×C7×C2914yescomplemented
92C5×D3—34no—
93C29C7×D5×C3⋊D311yescharacteristic, direct product factor, Sylow
94C22×C7—451noHall
95C3×C7D3×D5×C2914yescomplemented
96C2×D5—91noHall
97C2×C32—51no—
98C3⋊D3—51no—
99C3⋊D3C7×D5×C2911yescharacteristic, direct product factor
100C3×C5C2×D3×C7×C2914yescomplemented
101C2×C7—51no—
102C2×C7—91no—
103C2×C7—451no—
104C2×D3—154no—
105C2×C5—91no—
106D5—91no—
107D5C7×C3⋊D3×C2911yescharacteristic, direct product factor
108C32C2×C7×D5×C2911yescharacteristic, complemented, Sylow
109C7D5×C3⋊D3×C2911yescharacteristic, direct product factor, Sylow
110C2×C3—54no—
111D3—34no—
112D3—154no—
113C5C2×C7×C3⋊D3×C2911yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×C7×D5×C2914yescomplemented
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC7×C29D5×C3⋊D3
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. C32×C7×D5×C29C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
3. C7×C29×C3⋊D15C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C7×D5×C29D3semidirect
10. D5×C3⋊D3×C29C7direct (N × H)
13. C7×C3⋊D3×C29D5direct (N × H)
15. C3×C5×C7×C29C2×D3semidirect
16. C29×C3⋊D15C2×C7semidirect
17. C5×C3⋊D3×C29C2×C7semidirect
18. C32×D5×C29C2×C7semidirect
21. C7×D5×C29C3⋊D3direct (N × H)
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C22×C7semidirect
26. C7×D5×C3⋊D3C29direct (N × H)
31. C5×C7×C29C2×C3⋊D3semidirect
34. C3×D5×C29D3×C7semidirect
36. C7×C3⋊D15C2×C29semidirect
37. C5×C7×C3⋊D3C2×C29semidirect
38. C32×C7×D5C2×C29semidirect
39. C3×C7×C29D3×D5semidirect
43. C3⋊D3×C29C7×D5direct (N × H)
44. C3×C5×C29C2×D3×C7semidirect
50. C32×C5×C7C22×C29semidirect
53. D5×C29C7×C3⋊D3direct (N × H)
54. C32×C29C2×C7×D5semidirect
58. C3×C7×D5D3×C29semidirect
59. C7×C29D5×C3⋊D3direct (N × H)
60. D5×C3⋊D3C7×C29direct (N × H)
64. C5×C29C2×C7×C3⋊D3semidirect
68. C7×C3⋊D3D5×C29direct (N × H)
70. C3×C5×C7C2×D3×C29semidirect
71. C3⋊D15C2×C7×C29semidirect
72. C5×C3⋊D3C2×C7×C29semidirect
73. C32×D5C2×C7×C29semidirect
74. C3×C29D3×C7×D5semidirect
78. C7×D5C3⋊D3×C29direct (N × H)
79. C32×C7C2×D5×C29semidirect
84. C32×C5C22×C7×C29semidirect
89. C5×C7C2×C3⋊D3×C29semidirect
91. C3×D5D3×C7×C29semidirect
93. C29C7×D5×C3⋊D3direct (N × H)
95. C3×C7D3×D5×C29semidirect
99. C3⋊D3C7×D5×C29direct (N × H)
100. C3×C5C2×D3×C7×C29semidirect
107. D5C7×C3⋊D3×C29direct (N × H)
108. C32C2×C7×D5×C29semidirect
109. C7D5×C3⋊D3×C29direct (N × H)
113. C5C2×C7×C3⋊D3×C29semidirect
115. C3D3×C7×D5×C29semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D5×C292
C5×C7×C3⋊D3×C292
C7×C29×C3⋊D152
D3×C7×D5×C293
C2×C7×C3⋊D3×C295
D5×C3⋊D3×C297
C7×D5×C3⋊D329