Finite Group Databasebeta

← C3×C7×D4×D5 #13132844

Subgroups — C3×C7×D4×D5 #13132844

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×C7×D5C212yesmaximal, complemented
2C3×C5×C7×D4C211yesmaximal, characteristic, complemented
3C3×C7×C22⋊D5C212yesmaximal, complemented
4C3×C7×D20C211yesmaximal, characteristic, complemented
5C3×C4×C7×D5C211yesmaximal, characteristic, complemented
6C7×D4×D5C311yesmaximal, characteristic, direct product factor, Hall
7C22×C3×C5×C7C2212yescomplemented
8C2×C3×C7×D5—24no—
9C2×C3×C7×D5C2211yescharacteristic
10C2×C3×C7×D5C2212yescomplemented
11C3×C4×C5×C7C2211yescharacteristic, complemented
12C3×C7×Dic5C2211yescharacteristic, complemented
13C2×C3×C7×D4—51nomaximal, Hall
14C22×C7×D5C2×C312yescomplemented
15C5×C7×D4C2×C311yescharacteristic, complemented
16C7×C22⋊D5C2×C312yescomplemented
17C7×D20C2×C311yescharacteristic, complemented
18C4×C7×D5C2×C311yescharacteristic, complemented
19C3×D4×D5C711yesmaximal, characteristic, direct product factor, Hall
20C2×C3×C5×C7—22no—
21C2×C3×C5×C7C2311yescharacteristic
22C3×C7×D5—22no—
23C3×C7×D5D412yesdirect product factor
24C23×C3×C7—52no—
25C3×C7×D4—52no—
26C3×C7×D4—51no—
27C3×C7×D4D511yescharacteristic, direct product factor
28C2×C3×C4×C7—51no—
29C22×C5×C7C22×C312yescomplemented
30C2×C7×D5—24no—
31C2×C7×D5C22×C311yescharacteristic
32C2×C7×D5C22×C312yescomplemented
33C4×C5×C7C22×C311yescharacteristic, complemented
34C7×Dic5C22×C311yescharacteristic, complemented
35C22×C3×D5C2×C712yescomplemented
36C3×C5×D4C2×C711yescharacteristic, complemented
37C3×C22⋊D5C2×C712yescomplemented
38C3×D20C2×C711yescharacteristic, complemented
39C3×C4×D5C2×C711yescharacteristic, complemented
40C2×C7×D4—51noHall
41C3×C5×C7C2×D411yescharacteristic, complemented, Hall
42C22×C3×C7—51no—
43C22×C3×C7—52no—
44C22×C3×C7—104no—
45C22×C3×C7C2×D512yescomplemented
46C3×C4×C7—51no—
47C3×C4×C7C2×D511yescharacteristic, complemented
48D4×D5C3×C711yescharacteristic, direct product factor, Hall
49C2×C5×C7—22no—
50C2×C5×C7C23×C311yescharacteristic
51C7×D5—22no—
52C7×D5C3×D412yesdirect product factor
53C22×C3×C5C22×C712yescomplemented
54C2×C3×D5—24no—
55C2×C3×D5C22×C711yescharacteristic
56C2×C3×D5C22×C712yescomplemented
57C3×C4×C5C22×C711yescharacteristic, complemented
58C3×Dic5C22×C711yescharacteristic, complemented
59C23×C7—52no—
60C7×D4—52no—
61C7×D4—51no—
62C7×D4C3×D511yescharacteristic, direct product factor
63C2×C4×C7—51no—
64C2×C3×D4—51noHall
65C2×C3×C7—22no—
66C2×C3×C7—52no—
67C2×C3×C7—102no—
68C2×C3×C7C22×D511yescharacteristic
69C22×D5C2×C3×C712yescomplemented
70C5×D4C2×C3×C711yescharacteristic, complemented
71C22⋊D5C2×C3×C712yescomplemented
72D20C2×C3×C711yescharacteristic, complemented
73C4×D5C2×C3×C711yescharacteristic, complemented
74C5×C7C2×C3×D411yescharacteristic, complemented, Hall
75C2×C3×C5—22no—
76C2×C3×C5C23×C711yescharacteristic
77C3×D5—22no—
78C3×D5C7×D412yesdirect product factor
79C22×C7—51no—
80C22×C7—52no—
81C22×C7—104no—
82C22×C7C2×C3×D512yescomplemented
83C4×C7—51no—
84C4×C7C2×C3×D511yescharacteristic, complemented
85C23×C3—52no—
86C3×D4—52no—
87C3×D4—51no—
88C3×D4C7×D511yescharacteristic, direct product factor
89C2×C3×C4—51no—
90C3×C7D4×D511yescharacteristic, direct product factor, Hall
91C22×C5C22×C3×C712yescomplemented
92C2×D5—24no—
93C2×D5C22×C3×C711yescharacteristic
94C2×D5C22×C3×C712yescomplemented
95C4×C5C22×C3×C711yescharacteristic, complemented
96Dic5C22×C3×C711yescharacteristic, complemented
97C2×D4—51noSylow
98C3×C5C2×C7×D411yescharacteristic, complemented, Hall
99C2×C7—22no—
100C2×C7—52no—
101C2×C7—102no—
102C2×C7C22×C3×D511yescharacteristic
103C22×C3—51no—
104C22×C3—52no—
105C22×C3—104no—
106C22×C3C2×C7×D512yescomplemented
107C3×C4—51no—
108C3×C4C2×C7×D511yescharacteristic, complemented
109C2×C5—22no—
110C2×C5C23×C3×C711yescharacteristic
111D5—22no—
112D5C3×C7×D412yesdirect product factor
113C23—52no—
114D4—52no—
115D4—51no—
116D4C3×C7×D511yescharacteristic, direct product factor
117C2×C4—51no—
118C7C3×D4×D511yescharacteristic, direct product factor, Sylow
119C2×C3—22no—
120C2×C3—52no—
121C2×C3—102no—
122C2×C3C22×C7×D511yescharacteristic
123C5C2×C3×C7×D411yescharacteristic, complemented, Sylow
124C22—51no—
125C22—52no—
126C22—104no—
127C22C2×C3×C7×D512yescomplemented
128C4—51no—
129C4C2×C3×C7×D511yescharacteristic, complemented
130C3C7×D4×D511yescharacteristic, direct product factor, Sylow
131C2—22no—
132C2—52no—
133C2—102no—
134C2C22×C3×C7×D511yescharacteristic
subgroupG/H
centerC2×C3×C7C22×D5
commutator, cosocleC2×C5C23×C3×C7
FrattiniC2C22×C3×C7×D5
FittingC3×C5×C7×D4C2
socleC2×C3×C5×C7C23
hypercenterC3×C7×D4D5
hypocenterC5C2×C3×C7×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C7 ◁ C3×C7×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C7×D5C2semidirect
2. C3×C5×C7×D4C2semidirect
3. C3×C7×C22⋊D5C2semidirect
4. C3×C7×D20C2semidirect
5. C3×C4×C7×D5C2semidirect
6. C7×D4×D5C3direct (N × H)
7. C22×C3×C5×C7C22semidirect
10. C2×C3×C7×D5C22semidirect
11. C3×C4×C5×C7C22semidirect
12. C3×C7×Dic5C22semidirect
14. C22×C7×D5C2×C3semidirect
15. C5×C7×D4C2×C3semidirect
16. C7×C22⋊D5C2×C3semidirect
17. C7×D20C2×C3semidirect
18. C4×C7×D5C2×C3semidirect
19. C3×D4×D5C7direct (N × H)
23. C3×C7×D5D4direct (N × H)
27. C3×C7×D4D5direct (N × H)
29. C22×C5×C7C22×C3semidirect
32. C2×C7×D5C22×C3semidirect
33. C4×C5×C7C22×C3semidirect
34. C7×Dic5C22×C3semidirect
35. C22×C3×D5C2×C7semidirect
36. C3×C5×D4C2×C7semidirect
37. C3×C22⋊D5C2×C7semidirect
38. C3×D20C2×C7semidirect
39. C3×C4×D5C2×C7semidirect
41. C3×C5×C7C2×D4semidirect
45. C22×C3×C7C2×D5semidirect
47. C3×C4×C7C2×D5semidirect
48. D4×D5C3×C7direct (N × H)
52. C7×D5C3×D4direct (N × H)
53. C22×C3×C5C22×C7semidirect
56. C2×C3×D5C22×C7semidirect
57. C3×C4×C5C22×C7semidirect
58. C3×Dic5C22×C7semidirect
62. C7×D4C3×D5direct (N × H)
69. C22×D5C2×C3×C7semidirect
70. C5×D4C2×C3×C7semidirect
71. C22⋊D5C2×C3×C7semidirect
72. D20C2×C3×C7semidirect
73. C4×D5C2×C3×C7semidirect
74. C5×C7C2×C3×D4semidirect
78. C3×D5C7×D4direct (N × H)
82. C22×C7C2×C3×D5semidirect
84. C4×C7C2×C3×D5semidirect
88. C3×D4C7×D5direct (N × H)
90. C3×C7D4×D5direct (N × H)
91. C22×C5C22×C3×C7semidirect
94. C2×D5C22×C3×C7semidirect
95. C4×C5C22×C3×C7semidirect
96. Dic5C22×C3×C7semidirect
98. C3×C5C2×C7×D4semidirect
106. C22×C3C2×C7×D5semidirect
108. C3×C4C2×C7×D5semidirect
112. D5C3×C7×D4direct (N × H)
116. D4C3×C7×D5direct (N × H)
118. C7C3×D4×D5direct (N × H)
123. C5C2×C3×C7×D4semidirect
127. C22C2×C3×C7×D5semidirect
129. C4C2×C3×C7×D5semidirect
130. C3C7×D4×D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C7×D52
C3×C5×C7×D42
C3×C7×C22⋊D52
C3×C7×D202
C3×C4×C7×D52
C7×D4×D53
C2×C3×C7×D45
C3×D4×D57