Finite Group Databasebeta

← C7×C3⋊D3×D65 #30655700

Subgroups — C7×C3⋊D3×D65 #30655700

Order 16380.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C7×C3⋊D195C211yesmaximal, characteristic, complemented
2C5×C7×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C7×D65C211yesmaximal, characteristic, complemented
4D3×C7×D65—34nomaximal
5C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
6C7×C3⋊D3×D13—51nomaximal, Hall
7C7×D195—34no—
8C5×D3×C7×C13—34no—
9C3×C7×D65D314yescomplemented
10C3⋊D3×D65C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D65—91noHall
12C7×C3⋊D39—51no—
13C7×C13×C3⋊D3D511yescharacteristic, complemented
14C32×C7×D13—51no—
15C3×C5×C7×C13C2×D314yescomplemented
16C7×D5×C3⋊D3—131nomaximal, Hall
17C3⋊D195C2×C711yescharacteristic, complemented
18C5×C13×C3⋊D3C2×C711yescharacteristic, complemented
19C32×D65C2×C711yescharacteristic, complemented
20D3×C7×D13—154no—
21C2×C5×C7×C13—91no—
22C7×D65—91no—
23C7×D65C3⋊D311yescharacteristic, direct product factor
24C32×C7×C13C2×D511yescharacteristic, complemented, Hall
25D3×D65—34no—
26C7×C3⋊D15—131no—
27C5×C7×C3⋊D3D1311yescharacteristic, complemented
28C32×C7×D5—131no—
29C32×C5×C13C22×C711yescharacteristic, complemented, Hall
30C7×D39—154no—
31D3×C7×C13—34no—
32C3×C7×D13—54no—
33C3⋊D3×D13—51noHall
34C5×C7×C13C2×C3⋊D311yescharacteristic, complemented, Hall
35D3×C7×D5—394no—
36D195—34no—
37C5×D3×C13—34no—
38C3×D65D3×C714yescomplemented
39C2×C7×D13—451noHall
40C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
41C3×C7×C13D3×D514yescomplemented
42C2×D65—91noHall
43C2×C7×C3⋊D3—651noHall
44C3⋊D39—51no—
45C13×C3⋊D3C7×D511yescharacteristic, complemented
46C32×D13—51no—
47C7×D15—394no—
48C5×D3×C7—34no—
49C3×C7×D5—134no—
50C3×C5×C13C2×D3×C714yescomplemented
51C2×C7×C13—91no—
52C7×D13—51no—
53C7×D13—451no—
54D5×C3⋊D3—131noHall
55D3×D13—154no—
56C2×C7×D5—1171noHall
57C2×C5×C13—91no—
58D65—91no—
59D65C7×C3⋊D311yescharacteristic, direct product factor
60C2×C32×C7—651no—
61C7×C3⋊D3—651no—
62C7×C3⋊D3D6511yescharacteristic, direct product factor
63C32×C13C2×C7×D511yescharacteristic, complemented, Hall
64C3×C5×C7D3×D1314yescomplemented
65C7×C13D5×C3⋊D311yescharacteristic, complemented, Hall
66C3⋊D15—131no—
67C5×C3⋊D3C7×D1311yescharacteristic, complemented
68C32×D5—131no—
69C2×D3×C7—1954no—
70D39—154no—
71C3×D13—54no—
72D3×C13—34no—
73C2×C5×C7—91no—
74C7×D5—131no—
75C7×D5—1171no—
76C5×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
77C32×C7C2×D6511yescharacteristic, complemented, Hall
78D3×D5—394no—
79C2×D13—451noHall
80C32×C5C2×C7×D1311yescharacteristic, complemented, Hall
81C2×C3×C7—654no—
82D3×C7—34no—
83D3×C7—1954no—
84C3×C13D3×C7×D514yescomplemented
85C2×C3⋊D3—651noHall
86C5×C7C3⋊D3×D1311yescharacteristic, complemented, Hall
87D15—394no—
88C3×D5—134no—
89C5×D3—34no—
90C22×C7—5851noHall
91C2×C13—91no—
92D13—51no—
93D13—451no—
94C3×C7D3×D6514yescomplemented
95C2×D5—1171noHall
96C2×C32—651no—
97C3⋊D3—651no—
98C3⋊D3C7×D6511yescharacteristic, direct product factor
99C3×C5D3×C7×D1314yescomplemented
100C2×C7—91no—
101C2×C7—651no—
102C2×C7—5851no—
103C13C7×D5×C3⋊D311yescharacteristic, complemented, Sylow
104C2×D3—1954no—
105C2×C5—91no—
106D5—131no—
107D5—1171no—
108C32C2×C7×D6511yescharacteristic, complemented, Sylow
109C7C3⋊D3×D6511yescharacteristic, direct product factor, Sylow
110C2×C3—654no—
111D3—34no—
112D3—1954no—
113C5C7×C3⋊D3×D1311yescharacteristic, complemented, Sylow
114C22—5851noSylow
115C3D3×C7×D6514yescomplemented
116C2—91no—
117C2—651no—
118C2—5851no—
subgroupG/H
center, hypercenterC7C3⋊D3×D65
commutator, cosocle, hypocenterC32×C5×C13C22×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C32×C5×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×C3⋊D195C2semidirect
2. C5×C7×C13×C3⋊D3C2semidirect
3. C32×C7×D65C2semidirect
5. C32×C5×C7×C13C22semidirect
9. C3×C7×D65D3semidirect
10. C3⋊D3×D65C7direct (N × H)
13. C7×C13×C3⋊D3D5semidirect
15. C3×C5×C7×C13C2×D3semidirect
17. C3⋊D195C2×C7semidirect
18. C5×C13×C3⋊D3C2×C7semidirect
19. C32×D65C2×C7semidirect
23. C7×D65C3⋊D3direct (N × H)
24. C32×C7×C13C2×D5semidirect
27. C5×C7×C3⋊D3D13semidirect
29. C32×C5×C13C22×C7semidirect
34. C5×C7×C13C2×C3⋊D3semidirect
38. C3×D65D3×C7semidirect
40. C32×C5×C7C2×D13semidirect
41. C3×C7×C13D3×D5semidirect
45. C13×C3⋊D3C7×D5semidirect
50. C3×C5×C13C2×D3×C7semidirect
59. D65C7×C3⋊D3direct (N × H)
62. C7×C3⋊D3D65direct (N × H)
63. C32×C13C2×C7×D5semidirect
64. C3×C5×C7D3×D13semidirect
65. C7×C13D5×C3⋊D3semidirect
67. C5×C3⋊D3C7×D13semidirect
76. C5×C13C2×C7×C3⋊D3semidirect
77. C32×C7C2×D65semidirect
80. C32×C5C2×C7×D13semidirect
84. C3×C13D3×C7×D5semidirect
86. C5×C7C3⋊D3×D13semidirect
94. C3×C7D3×D65semidirect
98. C3⋊D3C7×D65direct (N × H)
99. C3×C5D3×C7×D13semidirect
103. C13C7×D5×C3⋊D3semidirect
108. C32C2×C7×D65semidirect
109. C7C3⋊D3×D65direct (N × H)
113. C5C7×C3⋊D3×D13semidirect
115. C3D3×C7×D65semidirect

Maximal subgroups

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

subgroupindex
C7×C3⋊D1952
C5×C7×C13×C3⋊D32
C32×C7×D652
D3×C7×D653
C7×C3⋊D3×D135
C3⋊D3×D657
C7×D5×C3⋊D313