Finite Group Databasebeta

← C7×D5×C17×D9 #36339263

Subgroups — C7×D5×C17×D9 #36339263

Order 21420.

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 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×C17×D45C211yesmaximal, characteristic, complemented
2C5×C7×C17×D9C211yesmaximal, characteristic, complemented
3C7×C9×D5×C17C211yesmaximal, characteristic, complemented
4D3×C7×D5×C17—31nomaximal
5C5×C7×C9×C17C2211yescharacteristic, complemented, Hall
6C2×C7×C17×D9—51nomaximal, Hall
7C7×C17×D15—31no—
8C5×D3×C7×C17—31no—
9C3×C7×D5×C17D311yescharacteristic
10D5×C17×D9C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D5×C17—91noHall
12C7×C17×D9—51no—
13C7×C17×D9D511yescharacteristic, direct product factor
14C2×C7×C9×C17—51no—
15C3×C5×C7×C17C2×D311yescharacteristic
16C17×D45C2×C711yescharacteristic, complemented
17C5×C17×D9C2×C711yescharacteristic, complemented
18C9×D5×C17C2×C711yescharacteristic, complemented
19C2×D3×C7×C17—151no—
20C7×D5×D9C1711yesmaximal, characteristic, direct product factor, Hall
21C2×C5×C7×C17—91no—
22C7×D5×C17—91no—
23C7×D5×C17D911yescharacteristic, direct product factor
24C7×C9×C17C2×D511yescharacteristic, complemented, Hall
25D3×D5×C17—31no—
26C5×C9×C17C22×C711yescharacteristic, complemented, Hall
27C2×C3×C7×C17—51no—
28D3×C7×C17—31no—
29D3×C7×C17—151no—
30C7×D45C2×C1711yescharacteristic, complemented
31C5×C7×D9C2×C1711yescharacteristic, complemented
32C7×C9×D5C2×C1711yescharacteristic, complemented
33C2×C17×D9—51noHall
34C5×C7×C17C2×D911yescharacteristic, complemented, Hall
35C17×D15—31no—
36C5×D3×C17—31no—
37C3×D5×C17D3×C711yescharacteristic
38C22×C7×C17—451noHall
39D3×C7×D5—31no—
40C3×C7×C17D3×D511yescharacteristic
41C2×D5×C17—91noHall
42C5×C7×C9C22×C1711yescharacteristic, complemented, Hall
43C2×C9×C17—51no—
44C17×D9—51no—
45C17×D9C7×D511yescharacteristic, direct product factor
46C3×C5×C17C2×D3×C711yescharacteristic
47C2×C7×D9—51noHall
48C2×C7×C17—51no—
49C2×C7×C17—91no—
50C2×C7×C17—451no—
51C7×D15—31no—
52C5×D3×C7—31no—
53C3×C7×D5D3×C1711yescharacteristic
54C2×D3×C17—151no—
55D5×D9C7×C1711yescharacteristic, direct product factor, Hall
56C2×C5×C17—91no—
57D5×C17—91no—
58D5×C17C7×D911yescharacteristic, direct product factor
59C9×C17C2×C7×D511yescharacteristic, complemented, Hall
60C2×C7×D5—91noHall
61C2×C7×C9—51no—
62C7×D9—51no—
63C7×D9D5×C1711yescharacteristic, direct product factor
64C7×C17D5×D911yescharacteristic, direct product factor, Hall
65C3×C5×C7C2×D3×C1711yescharacteristic
66C2×C3×C17—51no—
67D3×C17—31no—
68D3×C17—151no—
69D45C2×C7×C1711yescharacteristic, complemented
70C9×D5C2×C7×C1711yescharacteristic, complemented
71C5×D9C2×C7×C1711yescharacteristic, complemented
72C5×C17C2×C7×D911yescharacteristic, complemented, Hall
73C2×D3×C7—151no—
74C2×C5×C7—91no—
75C7×D5—91no—
76C7×D5C17×D911yescharacteristic, direct product factor
77C22×C17—451noHall
78C7×C9C2×D5×C1711yescharacteristic, complemented, Hall
79D3×D5—31no—
80C3×C17D3×C7×D511yescharacteristic
81C5×C9C22×C7×C1711yescharacteristic, complemented, Hall
82C2×C3×C7—51no—
83D3×C7—31no—
84D3×C7—151no—
85C2×D9—51noHall
86C5×C7C2×C17×D911yescharacteristic, complemented, Hall
87C2×C17—51no—
88C2×C17—91no—
89C2×C17—451no—
90D15—31no—
91C3×D5D3×C7×C1711yescharacteristic
92C5×D3—31no—
93C22×C7—451noHall
94C3×C7D3×D5×C1711yescharacteristic
95C2×D5—91noHall
96C2×C9—51no—
97D9—51no—
98D9C7×D5×C1711yescharacteristic, direct product factor
99C17C7×D5×D911yescharacteristic, direct product factor, Sylow
100C3×C5C2×D3×C7×C1711yescharacteristic
101C2×C7—51no—
102C2×C7—91no—
103C2×C7—451no—
104C2×D3—151no—
105C2×C5—91no—
106D5—91no—
107D5C7×C17×D911yescharacteristic, direct product factor
108C9C2×C7×D5×C1711yescharacteristic, complemented, Sylow
109C7D5×C17×D911yescharacteristic, direct product factor, Sylow
110C2×C3—51no—
111D3—31no—
112D3—151no—
113C5C2×C7×C17×D911yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×C7×D5×C1711yescharacteristic
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC7×C17D5×D9
commutator, cosocle, hypocenterC5×C9C22×C7×C17
FrattiniC3D3×C7×D5×C17
FittingC5×C7×C9×C17C22
socleC3×C5×C7×C17C2×D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C17

Complements

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

NH ≅ G/Ntype
1. C7×C17×D45C2semidirect
2. C5×C7×C17×D9C2semidirect
3. C7×C9×D5×C17C2semidirect
5. C5×C7×C9×C17C22semidirect
10. D5×C17×D9C7direct (N × H)
13. C7×C17×D9D5direct (N × H)
16. C17×D45C2×C7semidirect
17. C5×C17×D9C2×C7semidirect
18. C9×D5×C17C2×C7semidirect
20. C7×D5×D9C17direct (N × H)
23. C7×D5×C17D9direct (N × H)
24. C7×C9×C17C2×D5semidirect
26. C5×C9×C17C22×C7semidirect
30. C7×D45C2×C17semidirect
31. C5×C7×D9C2×C17semidirect
32. C7×C9×D5C2×C17semidirect
34. C5×C7×C17C2×D9semidirect
42. C5×C7×C9C22×C17semidirect
45. C17×D9C7×D5direct (N × H)
55. D5×D9C7×C17direct (N × H)
58. D5×C17C7×D9direct (N × H)
59. C9×C17C2×C7×D5semidirect
63. C7×D9D5×C17direct (N × H)
64. C7×C17D5×D9direct (N × H)
69. D45C2×C7×C17semidirect
70. C9×D5C2×C7×C17semidirect
71. C5×D9C2×C7×C17semidirect
72. C5×C17C2×C7×D9semidirect
76. C7×D5C17×D9direct (N × H)
78. C7×C9C2×D5×C17semidirect
81. C5×C9C22×C7×C17semidirect
86. C5×C7C2×C17×D9semidirect
98. D9C7×D5×C17direct (N × H)
99. C17C7×D5×D9direct (N × H)
107. D5C7×C17×D9direct (N × H)
108. C9C2×C7×D5×C17semidirect
109. C7D5×C17×D9direct (N × H)
113. C5C2×C7×C17×D9semidirect

Maximal subgroups

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

subgroupindex
C7×C17×D452
C5×C7×C17×D92
C7×C9×D5×C172
D3×C7×D5×C173
C2×C7×C17×D95
D5×C17×D97
C7×D5×D917