Finite Group Databasebeta

← C5×C7×C3⋊D3×D29 #49141631

Subgroups — C5×C7×C3⋊D3×D29 #49141631

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×C5×C7×D29C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C5×C7×C3⋊D87C211yesmaximal, characteristic, complemented
4C5×D3×C7×D29—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D29C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7×D87—34no—
8C5×D3×C7×C29—34no—
9C3×C5×C7×D29D314yescomplemented
10C5×C3⋊D3×D29C711yesmaximal, characteristic, direct product factor, Hall
11C2×C5×C7×D29—91noHall
12C7×C3⋊D87C2×C511yescharacteristic, complemented
13C7×C3⋊D3×C29C2×C511yescharacteristic, complemented
14C32×C7×D29C2×C511yescharacteristic, complemented
15C3×C5×C7×C29C2×D314yescomplemented
16C5×C3⋊D87C2×C711yescharacteristic, complemented
17C5×C3⋊D3×C29C2×C711yescharacteristic, complemented
18C32×C5×D29C2×C711yescharacteristic, complemented
19D3×C7×D29—34no—
20C5×C7×D29—91no—
21C5×C7×D29C3⋊D311yescharacteristic, direct product factor
22C2×C5×C7×C29—91no—
23C32×C7×C29C22×C511yescharacteristic, complemented, Hall
24C5×D3×D29—34no—
25C32×C5×C29C22×C711yescharacteristic, complemented, Hall
26C2×C5×C7×C3⋊D3—291nomaximal, Hall
27C7×D87—34no—
28D3×C7×C29—34no—
29C3×C7×D29C5×D314yescomplemented
30C3⋊D3×D29C5×C711yescharacteristic, direct product factor, Hall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32C5×D87—34no—
33C5×D3×C29—34no—
34C3×C5×D29D3×C714yescomplemented
35C2×C7×D29—91noHall
36C2×C32×C5×C7—291no—
37C5×C7×C3⋊D3—291no—
38C5×C7×C3⋊D3D2911yescharacteristic, direct product factor
39C3×C7×C29C2×C5×D314yescomplemented
40C2×C5×D29—91noHall
41C3⋊D87C2×C5×C711yescharacteristic, complemented
42C3⋊D3×C29C2×C5×C711yescharacteristic, complemented
43C32×D29C2×C5×C711yescharacteristic, complemented
44C3×C5×C29C2×D3×C714yescomplemented
45C2×C5×D3×C7—874no—
46C2×C7×C29—91no—
47C7×D29—91no—
48C7×D29C5×C3⋊D311yescharacteristic, direct product factor
49D3×D29—34no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51C2×C5×C29—91no—
52C5×D29—91no—
53C5×D29C7×C3⋊D311yescharacteristic, direct product factor
54C32×C29C22×C5×C711yescharacteristic, complemented, Hall
55C2×C7×C3⋊D3—291noHall
56C2×C3×C5×C7—294no—
57C5×D3×C7—34no—
58C5×D3×C7—874no—
59C7×C29C2×C5×C3⋊D311yescharacteristic, complemented, Hall
60C2×C5×C3⋊D3—291noHall
61D87—34no—
62C3×D29C5×D3×C714yescomplemented
63D3×C29—34no—
64C5×C29C2×C7×C3⋊D311yescharacteristic, complemented, Hall
65C22×C5×C7—2611noHall
66C2×C32×C7—291no—
67C7×C3⋊D3—291no—
68C7×C3⋊D3C5×D2911yescharacteristic, direct product factor
69C2×D29—91noHall
70C3×C5×C7D3×D2914yescomplemented
71C2×C32×C5—291no—
72C5×C3⋊D3—291no—
73C5×C3⋊D3C7×D2911yescharacteristic, direct product factor
74C3×C29C2×C5×D3×C714yescomplemented
75C2×D3×C7—874no—
76C2×C5×C7—2611no—
77C2×C5×C7—91no—
78C2×C5×C7—291no—
79C32×C7C2×C5×D2911yescharacteristic, complemented, Hall
80C2×C5×D3—874no—
81C2×C29—91no—
82D29—91no—
83D29C5×C7×C3⋊D311yescharacteristic, direct product factor
84C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
85C2×C3×C7—294no—
86D3×C7—34no—
87D3×C7—874no—
88C2×C3⋊D3—291noHall
89C5×C7C3⋊D3×D2911yescharacteristic, direct product factor, Hall
90C2×C3×C5—294no—
91C5×D3—34no—
92C5×D3—874no—
93C29C2×C5×C7×C3⋊D311yescharacteristic, complemented, Sylow
94C22×C7—2611noHall
95C3×C7C5×D3×D2914yescomplemented
96C22×C5—2611noHall
97C2×C32—291no—
98C3⋊D3—291no—
99C3⋊D3C5×C7×D2911yescharacteristic, direct product factor
100C3×C5D3×C7×D2914yescomplemented
101C2×C7—2611no—
102C2×C7—91no—
103C2×C7—291no—
104C2×D3—874no—
105C2×C5—2611no—
106C2×C5—91no—
107C2×C5—291no—
108C32C2×C5×C7×D2911yescharacteristic, complemented, Sylow
109C7C5×C3⋊D3×D2911yescharacteristic, direct product factor, Sylow
110C2×C3—294no—
111D3—34no—
112D3—874no—
113C5C7×C3⋊D3×D2911yescharacteristic, direct product factor, Sylow
114C22—2611noSylow
115C3C5×D3×C7×D2914yescomplemented
116C2—2611no—
117C2—91no—
118C2—291no—
subgroupG/H
center, hypercenterC5×C7C3⋊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. C32×C5×C7×D29C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
3. C5×C7×C3⋊D87C2semidirect
5. C32×C5×C7×C29C22semidirect
6. C7×C3⋊D3×D29C5direct (N × H)
9. C3×C5×C7×D29D3semidirect
10. C5×C3⋊D3×D29C7direct (N × H)
12. C7×C3⋊D87C2×C5semidirect
13. C7×C3⋊D3×C29C2×C5semidirect
14. C32×C7×D29C2×C5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C5×C3⋊D87C2×C7semidirect
17. C5×C3⋊D3×C29C2×C7semidirect
18. C32×C5×D29C2×C7semidirect
21. C5×C7×D29C3⋊D3direct (N × H)
23. C32×C7×C29C22×C5semidirect
25. C32×C5×C29C22×C7semidirect
29. C3×C7×D29C5×D3semidirect
30. C3⋊D3×D29C5×C7direct (N × H)
31. C5×C7×C29C2×C3⋊D3semidirect
34. C3×C5×D29D3×C7semidirect
38. C5×C7×C3⋊D3D29direct (N × H)
39. C3×C7×C29C2×C5×D3semidirect
41. C3⋊D87C2×C5×C7semidirect
42. C3⋊D3×C29C2×C5×C7semidirect
43. C32×D29C2×C5×C7semidirect
44. C3×C5×C29C2×D3×C7semidirect
48. C7×D29C5×C3⋊D3direct (N × H)
50. C32×C5×C7C2×D29semidirect
53. C5×D29C7×C3⋊D3direct (N × H)
54. C32×C29C22×C5×C7semidirect
59. C7×C29C2×C5×C3⋊D3semidirect
62. C3×D29C5×D3×C7semidirect
64. C5×C29C2×C7×C3⋊D3semidirect
68. C7×C3⋊D3C5×D29direct (N × H)
70. C3×C5×C7D3×D29semidirect
73. C5×C3⋊D3C7×D29direct (N × H)
74. C3×C29C2×C5×D3×C7semidirect
79. C32×C7C2×C5×D29semidirect
83. D29C5×C7×C3⋊D3direct (N × H)
84. C32×C5C2×C7×D29semidirect
89. C5×C7C3⋊D3×D29direct (N × H)
93. C29C2×C5×C7×C3⋊D3semidirect
95. C3×C7C5×D3×D29semidirect
99. C3⋊D3C5×C7×D29direct (N × H)
100. C3×C5D3×C7×D29semidirect
108. C32C2×C5×C7×D29semidirect
109. C7C5×C3⋊D3×D29direct (N × H)
113. C5C7×C3⋊D3×D29direct (N × H)
115. C3C5×D3×C7×D29semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C7×D292
C5×C7×C3⋊D3×C292
C5×C7×C3⋊D872
C5×D3×C7×D293
C7×C3⋊D3×D295
C5×C3⋊D3×D297
C2×C5×C7×C3⋊D329