Finite Group Databasebeta

← C2×C3×C7×C22⋊D5 #13132849

Subgroups — C2×C3×C7×C22⋊D5 #13132849

Order 1680.

216 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C23×C3×C5×C7C211yesmaximal, characteristic, complemented
2C22×C3×C7×D5C211yesmaximal, characteristic, complemented
3C3×C7×C22⋊D5C214yesmaximal, direct product factor
4C2×C3×C7×Dic5C211yesmaximal, characteristic, complemented
5C2×C7×C22⋊D5C311yesmaximal, characteristic, direct product factor, Hall
6C22×C3×C5×C7—22no—
7C22×C3×C5×C7C2211yescharacteristic
8C22×C3×C5×C7C2212yescomplemented
9C2×C3×C7×D5—22no—
10C2×C3×C7×D5C2212yescomplemented
11C3×C7×Dic5C2212yescomplemented
12C2×C3×C7×D4—51nomaximal, Hall
13C23×C5×C7C2×C311yescharacteristic, complemented
14C22×C7×D5C2×C311yescharacteristic, complemented
15C7×C22⋊D5C2×C314yesdirect product factor
16C2×C7×Dic5C2×C311yescharacteristic, complemented
17C2×C3×C22⋊D5C711yesmaximal, characteristic, direct product factor, Hall
18C2×C3×C5×C7—22no—
19C2×C3×C5×C7D412yescomplemented
20C2×C3×C5×C7C2311yescharacteristic
21C3×C7×D5—22no—
22C23×C3×C7—51no—
23C23×C3×C7D511yescharacteristic, complemented
24C3×C7×D4—54no—
25C2×C3×C4×C7—51no—
26C22×C5×C7—22no—
27C22×C5×C7C22×C311yescharacteristic
28C22×C5×C7C22×C312yescomplemented
29C2×C7×D5—22no—
30C2×C7×D5C22×C312yescomplemented
31C7×Dic5C22×C312yescomplemented
32C23×C3×C5C2×C711yescharacteristic, complemented
33C22×C3×D5C2×C711yescharacteristic, complemented
34C3×C22⋊D5C2×C714yesdirect product factor
35C2×C3×Dic5C2×C711yescharacteristic, complemented
36C2×C7×D4—51noHall
37C3×C5×C7C2×D411yescharacteristic, complemented, Hall
38C22×C3×C7—22no—
39C22×C3×C7—52no—
40C22×C3×C7—102no—
41C22×C3×C7C2×D511yescharacteristic
42C22×C3×C7C2×D512yescomplemented
43C3×C4×C7—52no—
44C2×C22⋊D5C3×C711yescharacteristic, direct product factor, Hall
45C2×C5×C7—22no—
46C2×C5×C7C3×D412yescomplemented
47C2×C5×C7C23×C311yescharacteristic
48C7×D5—22no—
49C22×C3×C5—22no—
50C22×C3×C5C22×C711yescharacteristic
51C22×C3×C5C22×C712yescomplemented
52C2×C3×D5—22no—
53C2×C3×D5C22×C712yescomplemented
54C3×Dic5C22×C712yescomplemented
55C23×C7—51no—
56C23×C7C3×D511yescharacteristic, complemented
57C7×D4—54no—
58C2×C4×C7—51no—
59C2×C3×D4—51noHall
60C2×C3×C7—22no—
61C2×C3×C7—102no—
62C2×C3×C7C22⋊D512yesdirect product factor
63C2×C3×C7C22×D511yescharacteristic
64C23×C5C2×C3×C711yescharacteristic, complemented
65C22×D5C2×C3×C711yescharacteristic, complemented
66C22⋊D5C2×C3×C714yesdirect product factor
67C2×Dic5C2×C3×C711yescharacteristic, complemented
68C5×C7C2×C3×D411yescharacteristic, complemented, Hall
69C2×C3×C5—22no—
70C2×C3×C5C7×D412yescomplemented
71C2×C3×C5C23×C711yescharacteristic
72C3×D5—22no—
73C22×C7—22no—
74C22×C7—52no—
75C22×C7—102no—
76C22×C7C2×C3×D511yescharacteristic
77C22×C7C2×C3×D512yescomplemented
78C4×C7—52no—
79C23×C3—51no—
80C23×C3C7×D511yescharacteristic, complemented
81C3×D4—54no—
82C2×C3×C4—51no—
83C3×C7C2×C22⋊D511yescharacteristic, direct product factor, Hall
84C22×C5—22no—
85C22×C5C22×C3×C711yescharacteristic
86C22×C5C22×C3×C712yescomplemented
87C2×D5—22no—
88C2×D5C22×C3×C712yescomplemented
89Dic5C22×C3×C712yescomplemented
90C2×D4—51noSylow
91C3×C5C2×C7×D411yescharacteristic, complemented, Hall
92C2×C7—22no—
93C2×C7—102no—
94C2×C7C3×C22⋊D512yesdirect product factor
95C2×C7C22×C3×D511yescharacteristic
96C22×C3—22no—
97C22×C3—52no—
98C22×C3—102no—
99C22×C3C2×C7×D511yescharacteristic
100C22×C3C2×C7×D512yescomplemented
101C3×C4—52no—
102C2×C5—22no—
103C2×C5C3×C7×D412yescomplemented
104C2×C5C23×C3×C711yescharacteristic
105D5—22no—
106C23—51no—
107C23C3×C7×D511yescharacteristic, complemented
108D4—54no—
109C2×C4—51no—
110C7C2×C3×C22⋊D511yescharacteristic, direct product factor, Sylow
111C2×C3—22no—
112C2×C3—102no—
113C2×C3C7×C22⋊D512yesdirect product factor
114C2×C3C22×C7×D511yescharacteristic
115C5C2×C3×C7×D411yescharacteristic, complemented, Sylow
116C22—22no—
117C22—52no—
118C22—102no—
119C22C2×C3×C7×D511yescharacteristic
120C22C2×C3×C7×D512yescomplemented
121C4—52no—
122C3C2×C7×C22⋊D511yescharacteristic, direct product factor, Sylow
123C2—22no—
124C2—102no—
125C2C3×C7×C22⋊D512yesdirect product factor
126C2C22×C3×C7×D511yescharacteristic
subgroupG/H
centerC22×C3×C7C2×D5
commutator, cosocleC2×C5C23×C3×C7
FrattiniC2C22×C3×C7×D5
FittingC23×C3×C5×C7C2
socleC22×C3×C5×C7C22
hypercenterC23×C3×C7D5
hypocenterC5C2×C3×C7×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C7 ◁ C23×C3×C7

Complements

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

NH ≅ G/Ntype
1. C23×C3×C5×C7C2semidirect
2. C22×C3×C7×D5C2semidirect
3. C3×C7×C22⋊D5C2direct (N × H)
4. C2×C3×C7×Dic5C2semidirect
5. C2×C7×C22⋊D5C3direct (N × H)
8. C22×C3×C5×C7C22semidirect
10. C2×C3×C7×D5C22semidirect
11. C3×C7×Dic5C22semidirect
13. C23×C5×C7C2×C3semidirect
14. C22×C7×D5C2×C3semidirect
15. C7×C22⋊D5C2×C3direct (N × H)
16. C2×C7×Dic5C2×C3semidirect
17. C2×C3×C22⋊D5C7direct (N × H)
19. C2×C3×C5×C7D4semidirect
23. C23×C3×C7D5semidirect
28. C22×C5×C7C22×C3semidirect
30. C2×C7×D5C22×C3semidirect
31. C7×Dic5C22×C3semidirect
32. C23×C3×C5C2×C7semidirect
33. C22×C3×D5C2×C7semidirect
34. C3×C22⋊D5C2×C7direct (N × H)
35. C2×C3×Dic5C2×C7semidirect
37. C3×C5×C7C2×D4semidirect
42. C22×C3×C7C2×D5semidirect
44. C2×C22⋊D5C3×C7direct (N × H)
46. C2×C5×C7C3×D4semidirect
51. C22×C3×C5C22×C7semidirect
53. C2×C3×D5C22×C7semidirect
54. C3×Dic5C22×C7semidirect
56. C23×C7C3×D5semidirect
62. C2×C3×C7C22⋊D5direct (N × H)
64. C23×C5C2×C3×C7semidirect
65. C22×D5C2×C3×C7semidirect
66. C22⋊D5C2×C3×C7direct (N × H)
67. C2×Dic5C2×C3×C7semidirect
68. C5×C7C2×C3×D4semidirect
70. C2×C3×C5C7×D4semidirect
77. C22×C7C2×C3×D5semidirect
80. C23×C3C7×D5semidirect
83. C3×C7C2×C22⋊D5direct (N × H)
86. C22×C5C22×C3×C7semidirect
88. C2×D5C22×C3×C7semidirect
89. Dic5C22×C3×C7semidirect
91. C3×C5C2×C7×D4semidirect
94. C2×C7C3×C22⋊D5direct (N × H)
100. C22×C3C2×C7×D5semidirect
103. C2×C5C3×C7×D4semidirect
107. C23C3×C7×D5semidirect
110. C7C2×C3×C22⋊D5direct (N × H)
113. C2×C3C7×C22⋊D5direct (N × H)
115. C5C2×C3×C7×D4semidirect
120. C22C2×C3×C7×D5semidirect
122. C3C2×C7×C22⋊D5direct (N × H)
125. C2C3×C7×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C5×C72
C22×C3×C7×D52
C3×C7×C22⋊D52
C2×C3×C7×Dic52
C2×C7×C22⋊D53
C2×C3×C7×D45
C2×C3×C22⋊D57