Finite Group Databasebeta

← C3×C5×D4×D7 #13132834

Subgroups — C3×C5×D4×D7 #13132834

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×C3×C5×D7C212yesmaximal, complemented
2C3×C5×C7×D4C211yesmaximal, characteristic, complemented
3C3×C5×C22⋊D7C212yesmaximal, complemented
4C3×C5×D28C211yesmaximal, characteristic, complemented
5C3×C4×C5×D7C211yesmaximal, characteristic, complemented
6C5×D4×D7C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×C7C2212yescomplemented
8C2×C3×C5×D7—24no—
9C2×C3×C5×D7C2211yescharacteristic
10C2×C3×C5×D7C2212yescomplemented
11C3×C4×C5×C7C2211yescharacteristic, complemented
12C3×C5×Dic7C2211yescharacteristic, complemented
13C3×D4×D7C511yesmaximal, characteristic, direct product factor, Hall
14C22×C5×D7C2×C312yescomplemented
15C5×C7×D4C2×C311yescharacteristic, complemented
16C5×C22⋊D7C2×C312yescomplemented
17C5×D28C2×C311yescharacteristic, complemented
18C4×C5×D7C2×C311yescharacteristic, complemented
19C2×C3×C5×D4—71nomaximal, Hall
20C2×C3×C5×C7—22no—
21C2×C3×C5×C7C2311yescharacteristic
22C3×C5×D7—22no—
23C3×C5×D7D412yesdirect product factor
24C22×C3×D7C2×C512yescomplemented
25C3×C7×D4C2×C511yescharacteristic, complemented
26C3×C22⋊D7C2×C512yescomplemented
27C3×D28C2×C511yescharacteristic, complemented
28C3×C4×D7C2×C511yescharacteristic, complemented
29C22×C5×C7C22×C312yescomplemented
30C2×C5×D7—24no—
31C2×C5×D7C22×C311yescharacteristic
32C2×C5×D7C22×C312yescomplemented
33C4×C5×C7C22×C311yescharacteristic, complemented
34C5×Dic7C22×C311yescharacteristic, complemented
35C23×C3×C5—72no—
36C3×C5×D4—72no—
37C3×C5×D4—71no—
38C3×C5×D4D711yescharacteristic, direct product factor
39C2×C3×C4×C5—71no—
40D4×D7C3×C511yescharacteristic, direct product factor, Hall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7C22×C512yescomplemented
43C2×C3×D7—24no—
44C2×C3×D7C22×C511yescharacteristic
45C2×C3×D7C22×C512yescomplemented
46C3×C4×C7C22×C511yescharacteristic, complemented
47C3×Dic7C22×C511yescharacteristic, complemented
48C2×C5×D4—71noHall
49C2×C5×C7—22no—
50C2×C5×C7C23×C311yescharacteristic
51C5×D7—22no—
52C5×D7C3×D412yesdirect product factor
53C22×C3×C5—71no—
54C22×C3×C5—72no—
55C22×C3×C5—144no—
56C22×C3×C5C2×D712yescomplemented
57C3×C4×C5—71no—
58C3×C4×C5C2×D711yescharacteristic, complemented
59C22×D7C2×C3×C512yescomplemented
60C7×D4C2×C3×C511yescharacteristic, complemented
61C22⋊D7C2×C3×C512yescomplemented
62D28C2×C3×C511yescharacteristic, complemented
63C4×D7C2×C3×C511yescharacteristic, complemented
64C2×C3×D4—71noHall
65C2×C3×C7—22no—
66C2×C3×C7C23×C511yescharacteristic
67C3×D7—22no—
68C3×D7C5×D412yesdirect product factor
69C23×C5—72no—
70C5×D4—72no—
71C5×D4—71no—
72C5×D4C3×D711yescharacteristic, direct product factor
73C2×C4×C5—71no—
74C5×C7C2×C3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—22no—
76C2×C3×C5—72no—
77C2×C3×C5—142no—
78C2×C3×C5C22×D711yescharacteristic
79C22×C7C22×C3×C512yescomplemented
80C2×D7—24no—
81C2×D7C22×C3×C511yescharacteristic
82C2×D7C22×C3×C512yescomplemented
83C4×C7C22×C3×C511yescharacteristic, complemented
84Dic7C22×C3×C511yescharacteristic, complemented
85C23×C3—72no—
86C3×D4—72no—
87C3×D4—71no—
88C3×D4C5×D711yescharacteristic, direct product factor
89C2×C3×C4—71no—
90C3×C7C2×C5×D411yescharacteristic, complemented, Hall
91C22×C5—71no—
92C22×C5—72no—
93C22×C5—144no—
94C22×C5C2×C3×D712yescomplemented
95C4×C5—71no—
96C4×C5C2×C3×D711yescharacteristic, complemented
97C2×D4—71noSylow
98C3×C5D4×D711yescharacteristic, direct product factor, Hall
99C2×C7—22no—
100C2×C7C23×C3×C511yescharacteristic
101D7—22no—
102D7C3×C5×D412yesdirect product factor
103C22×C3—71no—
104C22×C3—72no—
105C22×C3—144no—
106C22×C3C2×C5×D712yescomplemented
107C3×C4—71no—
108C3×C4C2×C5×D711yescharacteristic, complemented
109C2×C5—22no—
110C2×C5—72no—
111C2×C5—142no—
112C2×C5C22×C3×D711yescharacteristic
113C23—72no—
114D4—72no—
115D4—71no—
116D4C3×C5×D711yescharacteristic, direct product factor
117C2×C4—71no—
118C7C2×C3×C5×D411yescharacteristic, complemented, Sylow
119C2×C3—22no—
120C2×C3—72no—
121C2×C3—142no—
122C2×C3C22×C5×D711yescharacteristic
123C5C3×D4×D711yescharacteristic, direct product factor, Sylow
124C22—71no—
125C22—72no—
126C22—144no—
127C22C2×C3×C5×D712yescomplemented
128C4—71no—
129C4C2×C3×C5×D711yescharacteristic, complemented
130C3C5×D4×D711yescharacteristic, direct product factor, Sylow
131C2—22no—
132C2—72no—
133C2—142no—
134C2C22×C3×C5×D711yescharacteristic
subgroupG/H
centerC2×C3×C5C22×D7
commutator, cosocleC2×C7C23×C3×C5
FrattiniC2C22×C3×C5×D7
FittingC3×C5×C7×D4C2
socleC2×C3×C5×C7C23
hypercenterC3×C5×D4D7
hypocenterC7C2×C3×C5×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3×C5 ◁ C3×C5×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×D7C2semidirect
2. C3×C5×C7×D4C2semidirect
3. C3×C5×C22⋊D7C2semidirect
4. C3×C5×D28C2semidirect
5. C3×C4×C5×D7C2semidirect
6. C5×D4×D7C3direct (N × H)
7. C22×C3×C5×C7C22semidirect
10. C2×C3×C5×D7C22semidirect
11. C3×C4×C5×C7C22semidirect
12. C3×C5×Dic7C22semidirect
13. C3×D4×D7C5direct (N × H)
14. C22×C5×D7C2×C3semidirect
15. C5×C7×D4C2×C3semidirect
16. C5×C22⋊D7C2×C3semidirect
17. C5×D28C2×C3semidirect
18. C4×C5×D7C2×C3semidirect
23. C3×C5×D7D4direct (N × H)
24. C22×C3×D7C2×C5semidirect
25. C3×C7×D4C2×C5semidirect
26. C3×C22⋊D7C2×C5semidirect
27. C3×D28C2×C5semidirect
28. C3×C4×D7C2×C5semidirect
29. C22×C5×C7C22×C3semidirect
32. C2×C5×D7C22×C3semidirect
33. C4×C5×C7C22×C3semidirect
34. C5×Dic7C22×C3semidirect
38. C3×C5×D4D7direct (N × H)
40. D4×D7C3×C5direct (N × H)
41. C3×C5×C7C2×D4semidirect
42. C22×C3×C7C22×C5semidirect
45. C2×C3×D7C22×C5semidirect
46. C3×C4×C7C22×C5semidirect
47. C3×Dic7C22×C5semidirect
52. C5×D7C3×D4direct (N × H)
56. C22×C3×C5C2×D7semidirect
58. C3×C4×C5C2×D7semidirect
59. C22×D7C2×C3×C5semidirect
60. C7×D4C2×C3×C5semidirect
61. C22⋊D7C2×C3×C5semidirect
62. D28C2×C3×C5semidirect
63. C4×D7C2×C3×C5semidirect
68. C3×D7C5×D4direct (N × H)
72. C5×D4C3×D7direct (N × H)
74. C5×C7C2×C3×D4semidirect
79. C22×C7C22×C3×C5semidirect
82. C2×D7C22×C3×C5semidirect
83. C4×C7C22×C3×C5semidirect
84. Dic7C22×C3×C5semidirect
88. C3×D4C5×D7direct (N × H)
90. C3×C7C2×C5×D4semidirect
94. C22×C5C2×C3×D7semidirect
96. C4×C5C2×C3×D7semidirect
98. C3×C5D4×D7direct (N × H)
102. D7C3×C5×D4direct (N × H)
106. C22×C3C2×C5×D7semidirect
108. C3×C4C2×C5×D7semidirect
116. D4C3×C5×D7direct (N × H)
118. C7C2×C3×C5×D4semidirect
123. C5C3×D4×D7direct (N × H)
127. C22C2×C3×C5×D7semidirect
129. C4C2×C3×C5×D7semidirect
130. C3C5×D4×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×D72
C3×C5×C7×D42
C3×C5×C22⋊D72
C3×C5×D282
C3×C4×C5×D72
C5×D4×D73
C3×D4×D75
C2×C3×C5×D47