Finite Group Databasebeta

← C2×D7×D20 #11765382

Subgroups — C2×D7×D20 #11765382

Order 1120.

472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 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×D5×D7C212yesmaximal, complemented
2C2×D140C211yesmaximal, characteristic, complemented
3C2×C7×D20C211yesmaximal, characteristic, complemented
4C2×C4×C5×D7C211yesmaximal, characteristic, complemented
5C2×#63307C212yesmaximal, complemented
6D7×D20C218yesmaximal, direct product factor
7C22×D35C2212yescomplemented
8C22×C7×D5C2212yescomplemented
9C22×C5×D7C2211yescharacteristic
10C2×D5×D7—28no—
11C2×D5×D7C2218yescomplemented
12C2×C4×C5×C7C2211yescharacteristic, complemented
13D140C2214yescomplemented
14C7×D20C2214yescomplemented
15C2×C5×Dic7C2211yescharacteristic, complemented
16C4×C5×D7C2214yescomplemented
17#63307C2218yescomplemented
18C2×D4×D7—51nomaximal, Hall
19C22×D20—71nomaximal, Hall
20C22×C5×C7C2311yescharacteristic
21C2×D35—24no—
22C2×D35C2314yescomplemented
23C2×C7×D5—24no—
24C2×C7×D5C2314yescomplemented
25C2×C5×D7D414yescomplemented
26C2×C5×D7C2312yes—
27D5×D7—216no—
28C4×C5×C7C2312yescomplemented
29C5×Dic7C2312yescomplemented
30C23×D7—52no—
31C2×C7×D4—51no—
32C2×C22⋊D7—52no—
33D4×D7—58no—
34C2×D28—51no—
35C2×C4×D7D511yescharacteristic, complemented
36C23×D5—72no—
37C22×C4×C5—71no—
38C2×D20—72no—
39C2×D20—71no—
40C2×D20—78no—
41C2×D20D711yescharacteristic, direct product factor
42C2×C5×C7C2×D412yescomplemented
43C2×C5×C7C2411yescharacteristic
44D35—24no—
45C5×D7C2×D414yescomplemented
46C7×D5—24no—
47C23×C7—52no—
48C22×D7—52no—
49C22×D7—58no—
50C22×D7—108no—
51C22×D7C2×D511yescharacteristic
52C7×D4—54no—
53C2×C4×C7C2×D511yescharacteristic, complemented
54C22⋊D7—58no—
55C2×Dic7C2×D511yescharacteristic, complemented
56D28—54no—
57C4×D7C2×D514yescomplemented
58C23×C5—71no—
59C22×D5—72no—
60C22×D5—78no—
61C22×D5—148no—
62C22×D5C2×D712yescomplemented
63C2×C4×C5—71no—
64C2×C4×C5—74no—
65C2×C4×C5C2×D711yescharacteristic, complemented
66D20—78no—
67D20—74no—
68D20C2×D714yesdirect product factor
69C5×C7C22×D411yescharacteristic, complemented, Hall
70C22×D4—351noSylow
71C22×C7—54no—
72C22×C7—104no—
73C22×C7C22×D511yescharacteristic
74C2×D7—54no—
75C2×D7—104no—
76C2×D7—1016no—
77C2×D7D2014yesdirect product factor
78C2×D7C22×D512yes—
79C4×C7C22×D512yescomplemented
80Dic7C22×D512yescomplemented
81C22×C5—74no—
82C22×C5—72no—
83C22×C5C22×D711yescharacteristic
84C2×D5—24no—
85C2×D5—74no—
86C2×D5—1416no—
87C2×D5—144no—
88C2×D5C22×D714yescomplemented
89C4×C5—72no—
90C4×C5C22×D712yescomplemented
91C24—352no—
92C2×D4—51no—
93C2×D4—358no—
94C2×D4—352no—
95C2×D4—351no—
96C22×C4—71no—
97C2×C7—104no—
98C2×C7C2×D2012yescomplemented
99C2×C7C23×D511yescharacteristic
100D7—104no—
101D7C2×D2014yesdirect product factor
102C2×C5—74no—
103C2×C5D4×D712yescomplemented
104C2×C5C23×D711yescharacteristic
105D5—24no—
106D5—144no—
107C23—52no—
108C23—71no—
109C23—358no—
110C23—352no—
111C23—708no—
112D4—54no—
113D4—358no—
114D4—354no—
115C2×C4—71no—
116C2×C4—74no—
117C2×C4D5×D711yescharacteristic, complemented
118C7C22×D2011yescharacteristic, complemented, Sylow
119C5C2×D4×D711yescharacteristic, complemented, Sylow
120C22—54no—
121C22—74no—
122C22—72no—
123C22—104no—
124C22—354no—
125C22—7016no—
126C22—704no—
127C22C2×D5×D711yescharacteristic
128C4—72no—
129C4C2×D5×D712yescomplemented
130C2—74no—
131C2—104no—
132C2—704no—
133C2D7×D2012yesdirect product factor
134C2C22×D5×D711yescharacteristic
subgroupG/H
centerC22C2×D5×D7
commutator, cosocleC2×C5×C7C24
FrattiniC2C22×D5×D7
FittingC2×C4×C5×C7C22
socleC22×C5×C7C23
hypercenterC2×C4D5×D7
hypocenterC5×C7C22×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×D7C2semidirect
2. C2×D140C2semidirect
3. C2×C7×D20C2semidirect
4. C2×C4×C5×D7C2semidirect
5. C2×#63307C2semidirect
6. D7×D20C2direct (N × H)
7. C22×D35C22semidirect
8. C22×C7×D5C22semidirect
11. C2×D5×D7C22semidirect
12. C2×C4×C5×C7C22semidirect
13. D140C22semidirect
14. C7×D20C22semidirect
15. C2×C5×Dic7C22semidirect
16. C4×C5×D7C22semidirect
17. #63307C22semidirect
22. C2×D35C23semidirect
24. C2×C7×D5C23semidirect
25. C2×C5×D7D4semidirect
28. C4×C5×C7C23semidirect
29. C5×Dic7C23semidirect
35. C2×C4×D7D5semidirect
41. C2×D20D7direct (N × H)
42. C2×C5×C7C2×D4semidirect
45. C5×D7C2×D4semidirect
53. C2×C4×C7C2×D5semidirect
55. C2×Dic7C2×D5semidirect
57. C4×D7C2×D5semidirect
62. C22×D5C2×D7semidirect
65. C2×C4×C5C2×D7semidirect
68. D20C2×D7direct (N × H)
69. C5×C7C22×D4semidirect
77. C2×D7D20direct (N × H)
79. C4×C7C22×D5semidirect
80. Dic7C22×D5semidirect
88. C2×D5C22×D7semidirect
90. C4×C5C22×D7semidirect
98. C2×C7C2×D20semidirect
101. D7C2×D20direct (N × H)
103. C2×C5D4×D7semidirect
117. C2×C4D5×D7semidirect
118. C7C22×D20semidirect
119. C5C2×D4×D7semidirect
129. C4C2×D5×D7semidirect
133. C2D7×D20direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×D72
C2×D1402
C2×C7×D202
C2×C4×C5×D72
C2×#633072
D7×D202
C2×D4×D75
C22×D207