Finite Group Databasebeta

← C7×D9×D65 #30655149

Subgroups — C7×D9×D65 #30655149

Order 16380.

120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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×D585C211yesmaximal, characteristic, complemented
2C5×C7×C13×D9C211yesmaximal, characteristic, complemented
3C7×C9×D65C211yesmaximal, characteristic, complemented
4D3×C7×D65—31nomaximal
5C5×C7×C9×C13C2211yescharacteristic, complemented, Hall
6C7×D9×D13—51nomaximal, Hall
7C7×D195—31no—
8C5×D3×C7×C13—31no—
9C3×C7×D65D311yescharacteristic
10D9×D65C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D65—91noHall
12C7×D117—51no—
13C7×C13×D9D511yescharacteristic, complemented
14C7×C9×D13—51no—
15C3×C5×C7×C13C2×D311yescharacteristic
16C7×D5×D9—131nomaximal, Hall
17D585C2×C711yescharacteristic, complemented
18C5×C13×D9C2×C711yescharacteristic, complemented
19C9×D65C2×C711yescharacteristic, complemented
20D3×C7×D13—151no—
21C2×C5×C7×C13—91no—
22C7×D65—91no—
23C7×D65D911yescharacteristic, direct product factor
24C7×C9×C13C2×D511yescharacteristic, complemented, Hall
25D3×D65—31no—
26C7×D45—131no—
27C5×C7×D9D1311yescharacteristic, complemented
28C7×C9×D5—131no—
29C5×C9×C13C22×C711yescharacteristic, complemented, Hall
30C7×D39—151no—
31D3×C7×C13—31no—
32C3×C7×D13—51no—
33D9×D13—51noHall
34C5×C7×C13C2×D911yescharacteristic, complemented, Hall
35D3×C7×D5—391no—
36D195—31no—
37C5×D3×C13—31no—
38C3×D65D3×C711yescharacteristic
39C2×C7×D13—451noHall
40C5×C7×C9C2×D1311yescharacteristic, complemented, Hall
41C3×C7×C13D3×D511yescharacteristic
42C2×D65—91noHall
43C2×C7×D9—651noHall
44D117—51no—
45C9×D13—51no—
46C13×D9C7×D511yescharacteristic, complemented
47C7×D15—391no—
48C5×D3×C7—31no—
49C3×C7×D5—131no—
50C3×C5×C13C2×D3×C711yescharacteristic
51C2×C7×C13—91no—
52C7×D13—51no—
53C7×D13—451no—
54D5×D9—131noHall
55D3×D13—151no—
56C2×C7×D5—1171noHall
57C2×C5×C13—91no—
58D65—91no—
59D65C7×D911yescharacteristic, direct product factor
60C2×C7×C9—651no—
61C7×D9—651no—
62C7×D9D6511yescharacteristic, direct product factor
63C9×C13C2×C7×D511yescharacteristic, complemented, Hall
64C3×C5×C7D3×D1311yescharacteristic
65C7×C13D5×D911yescharacteristic, complemented, Hall
66D45—131no—
67C9×D5—131no—
68C5×D9C7×D1311yescharacteristic, complemented
69C2×D3×C7—1951no—
70D39—151no—
71C3×D13—51no—
72D3×C13—31no—
73C2×C5×C7—91no—
74C7×D5—131no—
75C7×D5—1171no—
76C5×C13C2×C7×D911yescharacteristic, complemented, Hall
77C7×C9C2×D6511yescharacteristic, complemented, Hall
78D3×D5—391no—
79C2×D13—451noHall
80C5×C9C2×C7×D1311yescharacteristic, complemented, Hall
81C2×C3×C7—651no—
82D3×C7—31no—
83D3×C7—1951no—
84C3×C13D3×C7×D511yescharacteristic
85C2×D9—651noHall
86C5×C7D9×D1311yescharacteristic, complemented, Hall
87D15—391no—
88C3×D5—131no—
89C5×D3—31no—
90C22×C7—5851noHall
91C2×C13—91no—
92D13—51no—
93D13—451no—
94C3×C7D3×D6511yescharacteristic
95C2×D5—1171noHall
96C2×C9—651no—
97D9—651no—
98D9C7×D6511yescharacteristic, direct product factor
99C3×C5D3×C7×D1311yescharacteristic
100C2×C7—91no—
101C2×C7—651no—
102C2×C7—5851no—
103C13C7×D5×D911yescharacteristic, complemented, Sylow
104C2×D3—1951no—
105C2×C5—91no—
106D5—131no—
107D5—1171no—
108C9C2×C7×D6511yescharacteristic, complemented, Sylow
109C7D9×D6511yescharacteristic, direct product factor, Sylow
110C2×C3—651no—
111D3—31no—
112D3—1951no—
113C5C7×D9×D1311yescharacteristic, complemented, Sylow
114C22—5851noSylow
115C3D3×C7×D6511yescharacteristic
116C2—91no—
117C2—651no—
118C2—5851no—
subgroupG/H
center, hypercenterC7D9×D65
commutator, cosocle, hypocenterC5×C9×C13C22×C7
FrattiniC3D3×C7×D65
FittingC5×C7×C9×C13C22
socleC3×C5×C7×C13C2×D3
LCSG ▷ C5×C9×C13
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×D585C2semidirect
2. C5×C7×C13×D9C2semidirect
3. C7×C9×D65C2semidirect
5. C5×C7×C9×C13C22semidirect
10. D9×D65C7direct (N × H)
13. C7×C13×D9D5semidirect
17. D585C2×C7semidirect
18. C5×C13×D9C2×C7semidirect
19. C9×D65C2×C7semidirect
23. C7×D65D9direct (N × H)
24. C7×C9×C13C2×D5semidirect
27. C5×C7×D9D13semidirect
29. C5×C9×C13C22×C7semidirect
34. C5×C7×C13C2×D9semidirect
40. C5×C7×C9C2×D13semidirect
46. C13×D9C7×D5semidirect
59. D65C7×D9direct (N × H)
62. C7×D9D65direct (N × H)
63. C9×C13C2×C7×D5semidirect
65. C7×C13D5×D9semidirect
68. C5×D9C7×D13semidirect
76. C5×C13C2×C7×D9semidirect
77. C7×C9C2×D65semidirect
80. C5×C9C2×C7×D13semidirect
86. C5×C7D9×D13semidirect
98. D9C7×D65direct (N × H)
103. C13C7×D5×D9semidirect
108. C9C2×C7×D65semidirect
109. C7D9×D65direct (N × H)
113. C5C7×D9×D13semidirect

Maximal subgroups

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

subgroupindex
C7×D5852
C5×C7×C13×D92
C7×C9×D652
D3×C7×D653
C7×D9×D135
D9×D657
C7×D5×D913