Finite Group Databasebeta

← C7×D29×C3⋊D15 #49141647

Subgroups — C7×D29×C3⋊D15 #49141647

Order 36540.

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

normal subgroups only

This group has 240 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
1C32×C5×C7×D29C211yesmaximal, characteristic, complemented
2C7×C29×C3⋊D15C211yesmaximal, characteristic, complemented
3C7×C3⋊D435C211yesmaximal, characteristic, complemented
4C7×D15×D29—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D29—51nomaximal, Hall
7C7×D435—34no—
8C7×C29×D15—34no—
9C3×C5×C7×D29D314yescomplemented
10D29×C3⋊D15C711yesmaximal, characteristic, direct product factor, Hall
11C7×D5×D29—91noHall
12C7×C3⋊D87—51no—
13C7×C3⋊D3×C29—51no—
14C32×C7×D29D511yescharacteristic, complemented
15C3×C5×C7×C29C2×D314yescomplemented
16C3⋊D435C2×C711yescharacteristic, complemented
17C29×C3⋊D15C2×C711yescharacteristic, complemented
18C32×C5×D29C2×C711yescharacteristic, complemented
19D3×C7×D29—154no—
20C7×D145—91no—
21C7×D5×C29—91no—
22C5×C7×D29C3⋊D311yescharacteristic, complemented
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D15×D29—34no—
25C32×C5×C29C22×C711yescharacteristic, complemented, Hall
26C2×C7×C3⋊D15—291nomaximal, Hall
27C7×D87—154no—
28D3×C7×C29—154no—
29C3×C7×D29D1514yescomplemented
30C3⋊D3×D29—51noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32D435—34no—
33C29×D15—34no—
34C3×C5×D29D3×C714yescomplemented
35C2×C7×D29—451noHall
36C2×C32×C5×C7—291no—
37C7×C3⋊D15—291no—
38C7×C3⋊D15D2911yescharacteristic, direct product factor
39C3×C7×C29C2×D1514yescomplemented
40D5×D29—91noHall
41C3⋊D87—51no—
42C3⋊D3×C29—51no—
43C32×D29C7×D511yescharacteristic, complemented
44C3×C5×C29C2×D3×C714yescomplemented
45C2×C7×D15—874no—
46C2×C7×C29—451no—
47C7×D29—451no—
48C7×D29C3⋊D1511yescharacteristic, direct product factor
49D3×D29—154no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51D145—91no—
52C5×D29C7×C3⋊D311yescharacteristic, complemented
53D5×C29—91no—
54C32×C29C2×C7×D511yescharacteristic, complemented, Hall
55C2×C7×C3⋊D3—1451noHall
56C2×C3×C5×C7—294no—
57C7×D15—34no—
58C7×D15—874no—
59C7×C29C2×C3⋊D1511yescharacteristic, complemented, Hall
60C2×C3⋊D15—291noHall
61D87—154no—
62C3×D29C7×D1514yescomplemented
63D3×C29—154no—
64C5×C29C2×C7×C3⋊D311yescharacteristic, complemented, Hall
65C2×C7×D5—2611noHall
66C2×C32×C7—291no—
67C7×C3⋊D3—51no—
68C7×C3⋊D3—1451no—
69C2×D29—451noHall
70C3×C5×C7D3×D2914yescomplemented
71C2×C32×C5—291no—
72C3⋊D15—291no—
73C3⋊D15C7×D2911yescharacteristic, direct product factor
74C3×C29C2×C7×D1514yescomplemented
75C2×D3×C7—4354no—
76C2×C5×C7—291no—
77C7×D5—2611no—
78C7×D5—91no—
79C32×C7D5×D2911yescharacteristic, complemented, Hall
80C2×D15—874no—
81C2×C29—451no—
82D29—451no—
83D29C7×C3⋊D1511yescharacteristic, direct product factor
84C32×C5C2×C7×D2911yescharacteristic, complemented, Hall
85C2×C3×C7—294no—
86D3×C7—154no—
87D3×C7—4354no—
88C2×C3⋊D3—1451noHall
89C5×C7C3⋊D3×D2911yescharacteristic, complemented, Hall
90C2×C3×C5—294no—
91D15—34no—
92D15—874no—
93C29C2×C7×C3⋊D1511yescharacteristic, complemented, Sylow
94C22×C7—13051noHall
95C3×C7D15×D2914yescomplemented
96C2×D5—2611noHall
97C2×C32—291no—
98C3⋊D3—51no—
99C3⋊D3—1451no—
100C3×C5D3×C7×D2914yescomplemented
101C2×C7—13051no—
102C2×C7—291no—
103C2×C7—451no—
104C2×D3—4354no—
105C2×C5—291no—
106D5—2611no—
107D5—91no—
108C32C7×D5×D2911yescharacteristic, complemented, Sylow
109C7D29×C3⋊D1511yescharacteristic, direct product factor, Sylow
110C2×C3—294no—
111D3—154no—
112D3—4354no—
113C5C7×C3⋊D3×D2911yescharacteristic, complemented, Sylow
114C22—13051noSylow
115C3C7×D15×D2914yescomplemented
116C2—13051no—
117C2—291no—
118C2—451no—
subgroupG/H
center, hypercenterC7D29×C3⋊D15
commutator, cosocle, hypocenterC32×C5×C29C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5×C29
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C32×C5×C7×D29C2semidirect
2. C7×C29×C3⋊D15C2semidirect
3. C7×C3⋊D435C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C5×C7×D29D3semidirect
10. D29×C3⋊D15C7direct (N × H)
14. C32×C7×D29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C3⋊D435C2×C7semidirect
17. C29×C3⋊D15C2×C7semidirect
18. C32×C5×D29C2×C7semidirect
22. C5×C7×D29C3⋊D3semidirect
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C22×C7semidirect
29. C3×C7×D29D15semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
34. C3×C5×D29D3×C7semidirect
38. C7×C3⋊D15D29direct (N × H)
39. C3×C7×C29C2×D15semidirect
43. C32×D29C7×D5semidirect
44. C3×C5×C29C2×D3×C7semidirect
48. C7×D29C3⋊D15direct (N × H)
50. C32×C5×C7C2×D29semidirect
52. C5×D29C7×C3⋊D3semidirect
54. C32×C29C2×C7×D5semidirect
59. C7×C29C2×C3⋊D15semidirect
62. C3×D29C7×D15semidirect
64. C5×C29C2×C7×C3⋊D3semidirect
70. C3×C5×C7D3×D29semidirect
73. C3⋊D15C7×D29direct (N × H)
74. C3×C29C2×C7×D15semidirect
79. C32×C7D5×D29semidirect
83. D29C7×C3⋊D15direct (N × H)
84. C32×C5C2×C7×D29semidirect
89. C5×C7C3⋊D3×D29semidirect
93. C29C2×C7×C3⋊D15semidirect
95. C3×C7D15×D29semidirect
100. C3×C5D3×C7×D29semidirect
108. C32C7×D5×D29semidirect
109. C7D29×C3⋊D15direct (N × H)
113. C5C7×C3⋊D3×D29semidirect
115. C3C7×D15×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
C7×C29×C3⋊D152
C7×C3⋊D4352
C7×D15×D293
C7×C3⋊D3×D295
D29×C3⋊D157
C2×C7×C3⋊D1529