Finite Group Databasebeta

← C2×C5×D4×D7 #11765425

Subgroups — C2×C5×D4×D7 #11765425

Order 1120.

472 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 194 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×C5×D7C212yesmaximal, complemented
2C2×C5×C7×D4C211yesmaximal, characteristic, complemented
3C2×C5×C22⋊D7C212yesmaximal, complemented
4C5×D4×D7C218yesmaximal, direct product factor
5C2×C5×D28C211yesmaximal, characteristic, complemented
6C2×C4×C5×D7C211yesmaximal, characteristic, complemented
7C23×C5×C7C2212yescomplemented
8C22×C5×D7—28no—
9C22×C5×D7C2211yescharacteristic
10C22×C5×D7C2218yescomplemented
11C22×C5×D7C2212yescomplemented
12C5×C7×D4C2214yescomplemented
13C2×C4×C5×C7C2211yescharacteristic, complemented
14C5×C22⋊D7C2218yescomplemented
15C2×C5×Dic7C2211yescharacteristic, complemented
16C5×D28C2214yescomplemented
17C4×C5×D7C2214yescomplemented
18C2×D4×D7C511yesmaximal, characteristic, direct product factor, Hall
19C22×C5×D4—71nomaximal, Hall
20C22×C5×C7—24no—
21C22×C5×C7C2311yescharacteristic
22C22×C5×C7C2314yescomplemented
23C2×C5×D7—24no—
24C2×C5×D7—216no—
25C2×C5×D7D414yesdirect product factor
26C2×C5×D7C2312yes—
27C2×C5×D7C2314yescomplemented
28C4×C5×C7C2312yescomplemented
29C5×Dic7C2312yescomplemented
30C23×D7C2×C512yescomplemented
31C2×C7×D4C2×C511yescharacteristic, complemented
32C2×C22⋊D7C2×C512yescomplemented
33D4×D7C2×C518yesdirect product factor
34C2×D28C2×C511yescharacteristic, complemented
35C2×C4×D7C2×C511yescharacteristic, complemented
36C24×C5—72no—
37C2×C5×D4—72no—
38C2×C5×D4—78no—
39C2×C5×D4—71no—
40C2×C5×D4D711yescharacteristic, direct product factor
41C22×C4×C5—71no—
42C2×C5×C7—24no—
43C2×C5×C7C2×D412yescomplemented
44C2×C5×C7C2411yescharacteristic
45C5×D7—24no—
46C5×D7C2×D414yesdirect product factor
47C23×C7C22×C512yescomplemented
48C22×D7—28no—
49C22×D7C22×C511yescharacteristic
50C22×D7C22×C518yescomplemented
51C22×D7C22×C512yescomplemented
52C7×D4C22×C514yescomplemented
53C2×C4×C7C22×C511yescharacteristic, complemented
54C22⋊D7C22×C518yescomplemented
55C2×Dic7C22×C511yescharacteristic, complemented
56D28C22×C514yescomplemented
57C4×D7C22×C514yescomplemented
58C23×C5—71no—
59C23×C5—72no—
60C23×C5—78no—
61C23×C5—148no—
62C23×C5C2×D712yescomplemented
63C5×D4—78no—
64C5×D4—74no—
65C5×D4C2×D714yesdirect product factor
66C2×C4×C5—71no—
67C2×C4×C5—74no—
68C2×C4×C5C2×D711yescharacteristic, complemented
69C5×C7C22×D411yescharacteristic, complemented, Hall
70C22×D4—71noSylow
71C22×C7—24no—
72C22×C7C23×C511yescharacteristic
73C22×C7C23×C514yescomplemented
74C2×D7—24no—
75C2×D7—216no—
76C2×D7C5×D414yesdirect product factor
77C2×D7C23×C512yes—
78C2×D7C23×C514yescomplemented
79C4×C7C23×C512yescomplemented
80Dic7C23×C512yescomplemented
81C22×C5—24no—
82C22×C5—74no—
83C22×C5—72no—
84C22×C5—74no—
85C22×C5—1416no—
86C22×C5—144no—
87C22×C5C22×D711yescharacteristic
88C22×C5C22×D714yescomplemented
89C4×C5—72no—
90C4×C5C22×D712yescomplemented
91C24—72no—
92C2×D4—72no—
93C2×D4—78no—
94C2×D4—71no—
95C2×D4C5×D711yescharacteristic, direct product factor
96C22×C4—71no—
97C2×C7—24no—
98C2×C7C2×C5×D412yescomplemented
99C2×C7C24×C511yescharacteristic
100D7—24no—
101D7C2×C5×D414yesdirect product factor
102C2×C5—24no—
103C2×C5—74no—
104C2×C5—144no—
105C2×C5D4×D712yesdirect product factor
106C2×C5C23×D711yescharacteristic
107C23—71no—
108C23—72no—
109C23—78no—
110C23—148no—
111C23C2×C5×D712yescomplemented
112D4—78no—
113D4—74no—
114D4C2×C5×D714yesdirect product factor
115C2×C4—71no—
116C2×C4—74no—
117C2×C4C2×C5×D711yescharacteristic, complemented
118C7C22×C5×D411yescharacteristic, complemented, Sylow
119C5C2×D4×D711yescharacteristic, direct product factor, Sylow
120C22—24no—
121C22—74no—
122C22—72no—
123C22—74no—
124C22—1416no—
125C22—144no—
126C22C22×C5×D711yescharacteristic
127C22C22×C5×D714yescomplemented
128C4—72no—
129C4C22×C5×D712yescomplemented
130C2—24no—
131C2—74no—
132C2—144no—
133C2C5×D4×D712yesdirect product factor
134C2C23×C5×D711yescharacteristic
subgroupG/H
centerC22×C5C22×D7
commutator, cosocleC2×C7C24×C5
FrattiniC2C23×C5×D7
FittingC2×C5×C7×D4C2
socleC22×C5×C7C23
hypercenterC2×C5×D4D7
hypocenterC7C22×C5×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
1. C23×C5×D7C2semidirect
2. C2×C5×C7×D4C2semidirect
3. C2×C5×C22⋊D7C2semidirect
4. C5×D4×D7C2direct (N × H)
5. C2×C5×D28C2semidirect
6. C2×C4×C5×D7C2semidirect
7. C23×C5×C7C22semidirect
10. C22×C5×D7C22semidirect
11. C22×C5×D7C22semidirect
12. C5×C7×D4C22semidirect
13. C2×C4×C5×C7C22semidirect
14. C5×C22⋊D7C22semidirect
15. C2×C5×Dic7C22semidirect
16. C5×D28C22semidirect
17. C4×C5×D7C22semidirect
18. C2×D4×D7C5direct (N × H)
22. C22×C5×C7C23semidirect
25. C2×C5×D7D4direct (N × H)
27. C2×C5×D7C23semidirect
28. C4×C5×C7C23semidirect
29. C5×Dic7C23semidirect
30. C23×D7C2×C5semidirect
31. C2×C7×D4C2×C5semidirect
32. C2×C22⋊D7C2×C5semidirect
33. D4×D7C2×C5direct (N × H)
34. C2×D28C2×C5semidirect
35. C2×C4×D7C2×C5semidirect
40. C2×C5×D4D7direct (N × H)
43. C2×C5×C7C2×D4semidirect
46. C5×D7C2×D4direct (N × H)
47. C23×C7C22×C5semidirect
50. C22×D7C22×C5semidirect
51. C22×D7C22×C5semidirect
52. C7×D4C22×C5semidirect
53. C2×C4×C7C22×C5semidirect
54. C22⋊D7C22×C5semidirect
55. C2×Dic7C22×C5semidirect
56. D28C22×C5semidirect
57. C4×D7C22×C5semidirect
62. C23×C5C2×D7semidirect
65. C5×D4C2×D7direct (N × H)
68. C2×C4×C5C2×D7semidirect
69. C5×C7C22×D4semidirect
73. C22×C7C23×C5semidirect
76. C2×D7C5×D4direct (N × H)
78. C2×D7C23×C5semidirect
79. C4×C7C23×C5semidirect
80. Dic7C23×C5semidirect
88. C22×C5C22×D7semidirect
90. C4×C5C22×D7semidirect
95. C2×D4C5×D7direct (N × H)
98. C2×C7C2×C5×D4semidirect
101. D7C2×C5×D4direct (N × H)
105. C2×C5D4×D7direct (N × H)
111. C23C2×C5×D7semidirect
114. D4C2×C5×D7direct (N × H)
117. C2×C4C2×C5×D7semidirect
118. C7C22×C5×D4semidirect
119. C5C2×D4×D7direct (N × H)
127. C22C22×C5×D7semidirect
129. C4C22×C5×D7semidirect
133. C2C5×D4×D7direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×D72
C2×C5×C7×D42
C2×C5×C22⋊D72
C5×D4×D72
C2×C5×D282
C2×C4×C5×D72
C2×D4×D75
C22×C5×D47