Finite Group Databasebeta

← C5×D3×C7×D4 #13132864

Subgroups — C5×D3×C7×D4 #13132864

Order 1680.

216 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C22×C5×D3×C7C212yesmaximal, complemented
2C3×C5×C7×D4C211yesmaximal, characteristic, complemented
3C5×C7×#67C212yesmaximal, complemented
4C5×C7×D12C211yesmaximal, characteristic, complemented
5C4×C5×D3×C7C211yesmaximal, characteristic, complemented
6C2×C5×C7×D4—31nomaximal, Hall
7C22×C3×C5×C7C2212yescomplemented
8C2×C5×D3×C7—24no—
9C2×C5×D3×C7C2211yescharacteristic
10C2×C5×D3×C7C2212yescomplemented
11C3×C4×C5×C7C2211yescharacteristic, complemented
12C5×C7×Dic3C2211yescharacteristic, complemented
13D3×C7×D4C511yesmaximal, characteristic, direct product factor, Hall
14C23×C5×C7—32no—
15C5×C7×D4—32no—
16C5×C7×D4—31no—
17C5×C7×D4D311yescharacteristic, direct product factor
18C2×C4×C5×C7—31no—
19C5×D3×D4C711yesmaximal, characteristic, direct product factor, Hall
20C2×C3×C5×C7—22no—
21C2×C3×C5×C7C2311yescharacteristic
22C5×D3×C7—22no—
23C5×D3×C7D412yesdirect product factor
24C22×D3×C7C2×C512yescomplemented
25C3×C7×D4C2×C511yescharacteristic, complemented
26C7×#67C2×C512yescomplemented
27C7×D12C2×C511yescharacteristic, complemented
28C4×D3×C7C2×C511yescharacteristic, complemented
29C22×C5×C7—31no—
30C22×C5×C7—32no—
31C22×C5×C7—64no—
32C22×C5×C7C2×D312yescomplemented
33C4×C5×C7—31no—
34C4×C5×C7C2×D311yescharacteristic, complemented
35C22×C5×D3C2×C712yescomplemented
36C3×C5×D4C2×C711yescharacteristic, complemented
37C5×#67C2×C712yescomplemented
38C5×D12C2×C711yescharacteristic, complemented
39C4×C5×D3C2×C711yescharacteristic, complemented
40C2×C7×D4—31noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7C22×C512yescomplemented
43C2×D3×C7—24no—
44C2×D3×C7C22×C511yescharacteristic
45C2×D3×C7C22×C512yescomplemented
46C3×C4×C7C22×C511yescharacteristic, complemented
47C7×Dic3C22×C511yescharacteristic, complemented
48C2×C5×D4—31noHall
49C2×C5×C7—22no—
50C2×C5×C7—32no—
51C2×C5×C7—62no—
52C2×C5×C7C22×D311yescharacteristic
53C22×C3×C5C22×C712yescomplemented
54C2×C5×D3—24no—
55C2×C5×D3C22×C711yescharacteristic
56C2×C5×D3C22×C712yescomplemented
57C3×C4×C5C22×C711yescharacteristic, complemented
58C5×Dic3C22×C711yescharacteristic, complemented
59C23×C7—32no—
60C7×D4—32no—
61C7×D4—31no—
62C7×D4C5×D311yescharacteristic, direct product factor
63C2×C4×C7—31no—
64D3×D4C5×C711yescharacteristic, direct product factor, Hall
65C2×C3×C7—22no—
66C2×C3×C7C23×C511yescharacteristic
67D3×C7—22no—
68D3×C7C5×D412yesdirect product factor
69C23×C5—32no—
70C5×D4—32no—
71C5×D4—31no—
72C5×D4D3×C711yescharacteristic, direct product factor
73C2×C4×C5—31no—
74C5×C7D3×D411yescharacteristic, direct product factor, Hall
75C2×C3×C5—22no—
76C2×C3×C5C23×C711yescharacteristic
77C5×D3—22no—
78C5×D3C7×D412yesdirect product factor
79C22×C7—31no—
80C22×C7—32no—
81C22×C7—64no—
82C22×C7C2×C5×D312yescomplemented
83C4×C7—31no—
84C4×C7C2×C5×D311yescharacteristic, complemented
85C22×D3C2×C5×C712yescomplemented
86C3×D4C2×C5×C711yescharacteristic, complemented
87#67C2×C5×C712yescomplemented
88D12C2×C5×C711yescharacteristic, complemented
89C4×D3C2×C5×C711yescharacteristic, complemented
90C3×C7C2×C5×D411yescharacteristic, complemented, Hall
91C22×C5—31no—
92C22×C5—32no—
93C22×C5—64no—
94C22×C5C2×D3×C712yescomplemented
95C4×C5—31no—
96C4×C5C2×D3×C711yescharacteristic, complemented
97C2×D4—31noSylow
98C3×C5C2×C7×D411yescharacteristic, complemented, Hall
99C2×C7—22no—
100C2×C7—32no—
101C2×C7—62no—
102C2×C7C22×C5×D311yescharacteristic
103C22×C3C22×C5×C712yescomplemented
104C2×D3—24no—
105C2×D3C22×C5×C711yescharacteristic
106C2×D3C22×C5×C712yescomplemented
107C3×C4C22×C5×C711yescharacteristic, complemented
108Dic3C22×C5×C711yescharacteristic, complemented
109C2×C5—22no—
110C2×C5—32no—
111C2×C5—62no—
112C2×C5C22×D3×C711yescharacteristic
113C23—32no—
114D4—32no—
115D4—31no—
116D4C5×D3×C711yescharacteristic, direct product factor
117C2×C4—31no—
118C7C5×D3×D411yescharacteristic, direct product factor, Sylow
119C2×C3—22no—
120C2×C3C23×C5×C711yescharacteristic
121D3—22no—
122D3C5×C7×D412yesdirect product factor
123C5D3×C7×D411yescharacteristic, direct product factor, Sylow
124C22—31no—
125C22—32no—
126C22—64no—
127C22C2×C5×D3×C712yescomplemented
128C4—31no—
129C4C2×C5×D3×C711yescharacteristic, complemented
130C3C2×C5×C7×D411yescharacteristic, complemented, Sylow
131C2—22no—
132C2—32no—
133C2—62no—
134C2C22×C5×D3×C711yescharacteristic
subgroupG/H
centerC2×C5×C7C22×D3
commutator, cosocleC2×C3C23×C5×C7
FrattiniC2C22×C5×D3×C7
FittingC3×C5×C7×D4C2
socleC2×C3×C5×C7C23
hypercenterC5×C7×D4D3
hypocenterC3C2×C5×C7×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5×C7 ◁ C5×C7×D4

Complements

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

NH ≅ G/Ntype
1. C22×C5×D3×C7C2semidirect
2. C3×C5×C7×D4C2semidirect
3. C5×C7×#67C2semidirect
4. C5×C7×D12C2semidirect
5. C4×C5×D3×C7C2semidirect
7. C22×C3×C5×C7C22semidirect
10. C2×C5×D3×C7C22semidirect
11. C3×C4×C5×C7C22semidirect
12. C5×C7×Dic3C22semidirect
13. D3×C7×D4C5direct (N × H)
17. C5×C7×D4D3direct (N × H)
19. C5×D3×D4C7direct (N × H)
23. C5×D3×C7D4direct (N × H)
24. C22×D3×C7C2×C5semidirect
25. C3×C7×D4C2×C5semidirect
26. C7×#67C2×C5semidirect
27. C7×D12C2×C5semidirect
28. C4×D3×C7C2×C5semidirect
32. C22×C5×C7C2×D3semidirect
34. C4×C5×C7C2×D3semidirect
35. C22×C5×D3C2×C7semidirect
36. C3×C5×D4C2×C7semidirect
37. C5×#67C2×C7semidirect
38. C5×D12C2×C7semidirect
39. C4×C5×D3C2×C7semidirect
41. C3×C5×C7C2×D4semidirect
42. C22×C3×C7C22×C5semidirect
45. C2×D3×C7C22×C5semidirect
46. C3×C4×C7C22×C5semidirect
47. C7×Dic3C22×C5semidirect
53. C22×C3×C5C22×C7semidirect
56. C2×C5×D3C22×C7semidirect
57. C3×C4×C5C22×C7semidirect
58. C5×Dic3C22×C7semidirect
62. C7×D4C5×D3direct (N × H)
64. D3×D4C5×C7direct (N × H)
68. D3×C7C5×D4direct (N × H)
72. C5×D4D3×C7direct (N × H)
74. C5×C7D3×D4direct (N × H)
78. C5×D3C7×D4direct (N × H)
82. C22×C7C2×C5×D3semidirect
84. C4×C7C2×C5×D3semidirect
85. C22×D3C2×C5×C7semidirect
86. C3×D4C2×C5×C7semidirect
87. #67C2×C5×C7semidirect
88. D12C2×C5×C7semidirect
89. C4×D3C2×C5×C7semidirect
90. C3×C7C2×C5×D4semidirect
94. C22×C5C2×D3×C7semidirect
96. C4×C5C2×D3×C7semidirect
98. C3×C5C2×C7×D4semidirect
103. C22×C3C22×C5×C7semidirect
106. C2×D3C22×C5×C7semidirect
107. C3×C4C22×C5×C7semidirect
108. Dic3C22×C5×C7semidirect
116. D4C5×D3×C7direct (N × H)
118. C7C5×D3×D4direct (N × H)
122. D3C5×C7×D4direct (N × H)
123. C5D3×C7×D4direct (N × H)
127. C22C2×C5×D3×C7semidirect
129. C4C2×C5×D3×C7semidirect
130. C3C2×C5×C7×D4semidirect

Maximal subgroups

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

subgroupindex
C22×C5×D3×C72
C3×C5×C7×D42
C5×C7×#672
C5×C7×D122
C4×C5×D3×C72
C2×C5×C7×D43
D3×C7×D45
C5×D3×D47