Finite Group Databasebeta

← C7×D5×C13×C3⋊D3 #30655698

Subgroups — C7×D5×C13×C3⋊D3 #30655698

Order 16380.

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
1C7×C13×C3⋊D15C211yesmaximal, characteristic, complemented
2C5×C7×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C7×D5×C13C211yesmaximal, characteristic, complemented
4D3×C7×D5×C13—34nomaximal
5C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
6C2×C7×C13×C3⋊D3—51nomaximal, Hall
7C7×C13×D15—34no—
8C5×D3×C7×C13—34no—
9C3×C7×D5×C13D314yescomplemented
10D5×C13×C3⋊D3C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D5×C13—91noHall
12C2×C32×C7×C13—51no—
13C7×C13×C3⋊D3—51no—
14C7×C13×C3⋊D3D511yescharacteristic, direct product factor
15C3×C5×C7×C13C2×D314yescomplemented
16C7×D5×C3⋊D3C1311yesmaximal, characteristic, direct product factor, Hall
17C13×C3⋊D15C2×C711yescharacteristic, complemented
18C5×C13×C3⋊D3C2×C711yescharacteristic, complemented
19C32×D5×C13C2×C711yescharacteristic, complemented
20C2×D3×C7×C13—154no—
21C2×C5×C7×C13—91no—
22C7×D5×C13—91no—
23C7×D5×C13C3⋊D311yescharacteristic, direct product factor
24C32×C7×C13C2×D511yescharacteristic, complemented, Hall
25D3×D5×C13—34no—
26C7×C3⋊D15C2×C1311yescharacteristic, complemented
27C5×C7×C3⋊D3C2×C1311yescharacteristic, complemented
28C32×C7×D5C2×C1311yescharacteristic, complemented
29C32×C5×C13C22×C711yescharacteristic, complemented, Hall
30C2×C3×C7×C13—54no—
31D3×C7×C13—34no—
32D3×C7×C13—154no—
33C2×C13×C3⋊D3—51noHall
34C5×C7×C13C2×C3⋊D311yescharacteristic, complemented, Hall
35D3×C7×D5—34no—
36C13×D15—34no—
37C5×D3×C13—34no—
38C3×D5×C13D3×C714yescomplemented
39C22×C7×C13—451noHall
40C32×C5×C7C22×C1311yescharacteristic, complemented, Hall
41C3×C7×C13D3×D514yescomplemented
42C2×D5×C13—91noHall
43C2×C7×C3⋊D3—51noHall
44C2×C32×C13—51no—
45C13×C3⋊D3—51no—
46C13×C3⋊D3C7×D511yescharacteristic, direct product factor
47C7×D15—34no—
48C5×D3×C7—34no—
49C3×C7×D5D3×C1314yescomplemented
50C3×C5×C13C2×D3×C714yescomplemented
51C2×C7×C13—51no—
52C2×C7×C13—91no—
53C2×C7×C13—451no—
54D5×C3⋊D3C7×C1311yescharacteristic, direct product factor, Hall
55C2×D3×C13—154no—
56C2×C7×D5—91noHall
57C2×C5×C13—91no—
58D5×C13—91no—
59D5×C13C7×C3⋊D311yescharacteristic, direct product factor
60C2×C32×C7—51no—
61C7×C3⋊D3—51no—
62C7×C3⋊D3D5×C1311yescharacteristic, direct product factor
63C32×C13C2×C7×D511yescharacteristic, complemented, Hall
64C3×C5×C7C2×D3×C1314yescomplemented
65C7×C13D5×C3⋊D311yescharacteristic, direct product factor, Hall
66C3⋊D15C2×C7×C1311yescharacteristic, complemented
67C5×C3⋊D3C2×C7×C1311yescharacteristic, complemented
68C32×D5C2×C7×C1311yescharacteristic, complemented
69C2×D3×C7—154no—
70C2×C3×C13—54no—
71D3×C13—34no—
72D3×C13—154no—
73C2×C5×C7—91no—
74C7×D5—91no—
75C7×D5C13×C3⋊D311yescharacteristic, direct product factor
76C5×C13C2×C7×C3⋊D311yescharacteristic, complemented, Hall
77C32×C7C2×D5×C1311yescharacteristic, complemented, Hall
78D3×D5—34no—
79C22×C13—451noHall
80C32×C5C22×C7×C1311yescharacteristic, complemented, Hall
81C2×C3×C7—54no—
82D3×C7—34no—
83D3×C7—154no—
84C3×C13D3×C7×D514yescomplemented
85C2×C3⋊D3—51noHall
86C5×C7C2×C13×C3⋊D311yescharacteristic, complemented, Hall
87D15—34no—
88C3×D5D3×C7×C1314yescomplemented
89C5×D3—34no—
90C22×C7—451noHall
91C2×C13—51no—
92C2×C13—91no—
93C2×C13—451no—
94C3×C7D3×D5×C1314yescomplemented
95C2×D5—91noHall
96C2×C32—51no—
97C3⋊D3—51no—
98C3⋊D3C7×D5×C1311yescharacteristic, direct product factor
99C3×C5C2×D3×C7×C1314yescomplemented
100C2×C7—51no—
101C2×C7—91no—
102C2×C7—451no—
103C13C7×D5×C3⋊D311yescharacteristic, direct product factor, Sylow
104C2×D3—154no—
105C2×C5—91no—
106D5—91no—
107D5C7×C13×C3⋊D311yescharacteristic, direct product factor
108C32C2×C7×D5×C1311yescharacteristic, complemented, Sylow
109C7D5×C13×C3⋊D311yescharacteristic, direct product factor, Sylow
110C2×C3—54no—
111D3—34no—
112D3—154no—
113C5C2×C7×C13×C3⋊D311yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×C7×D5×C1314yescomplemented
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC7×C13D5×C3⋊D3
commutator, cosocle, hypocenterC32×C5C22×C7×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C32×C5
UCSC1 ◁ C7×C13

Complements

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

NH ≅ G/Ntype
1. C7×C13×C3⋊D15C2semidirect
2. C5×C7×C13×C3⋊D3C2semidirect
3. C32×C7×D5×C13C2semidirect
5. C32×C5×C7×C13C22semidirect
9. C3×C7×D5×C13D3semidirect
10. D5×C13×C3⋊D3C7direct (N × H)
14. C7×C13×C3⋊D3D5direct (N × H)
15. C3×C5×C7×C13C2×D3semidirect
16. C7×D5×C3⋊D3C13direct (N × H)
17. C13×C3⋊D15C2×C7semidirect
18. C5×C13×C3⋊D3C2×C7semidirect
19. C32×D5×C13C2×C7semidirect
23. C7×D5×C13C3⋊D3direct (N × H)
24. C32×C7×C13C2×D5semidirect
26. C7×C3⋊D15C2×C13semidirect
27. C5×C7×C3⋊D3C2×C13semidirect
28. C32×C7×D5C2×C13semidirect
29. C32×C5×C13C22×C7semidirect
34. C5×C7×C13C2×C3⋊D3semidirect
38. C3×D5×C13D3×C7semidirect
40. C32×C5×C7C22×C13semidirect
41. C3×C7×C13D3×D5semidirect
46. C13×C3⋊D3C7×D5direct (N × H)
49. C3×C7×D5D3×C13semidirect
50. C3×C5×C13C2×D3×C7semidirect
54. D5×C3⋊D3C7×C13direct (N × H)
59. D5×C13C7×C3⋊D3direct (N × H)
62. C7×C3⋊D3D5×C13direct (N × H)
63. C32×C13C2×C7×D5semidirect
64. C3×C5×C7C2×D3×C13semidirect
65. C7×C13D5×C3⋊D3direct (N × H)
66. C3⋊D15C2×C7×C13semidirect
67. C5×C3⋊D3C2×C7×C13semidirect
68. C32×D5C2×C7×C13semidirect
75. C7×D5C13×C3⋊D3direct (N × H)
76. C5×C13C2×C7×C3⋊D3semidirect
77. C32×C7C2×D5×C13semidirect
80. C32×C5C22×C7×C13semidirect
84. C3×C13D3×C7×D5semidirect
86. C5×C7C2×C13×C3⋊D3semidirect
88. C3×D5D3×C7×C13semidirect
94. C3×C7D3×D5×C13semidirect
98. C3⋊D3C7×D5×C13direct (N × H)
99. C3×C5C2×D3×C7×C13semidirect
103. C13C7×D5×C3⋊D3direct (N × H)
107. D5C7×C13×C3⋊D3direct (N × H)
108. C32C2×C7×D5×C13semidirect
109. C7D5×C13×C3⋊D3direct (N × H)
113. C5C2×C7×C13×C3⋊D3semidirect
115. C3D3×C7×D5×C13semidirect

Maximal subgroups

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

subgroupindex
C7×C13×C3⋊D152
C5×C7×C13×C3⋊D32
C32×C7×D5×C132
D3×C7×D5×C133
C2×C7×C13×C3⋊D35
D5×C13×C3⋊D37
C7×D5×C3⋊D313