Finite Group Databasebeta

← D4×D20 #65883

Subgroups — D4×D20 #65883

Order 320.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C2×D4×D5C212yesmaximal, complemented
2C22×D20C212yesmaximal, complemented
3C4×C5×D4C211yesmaximal, characteristic, complemented
4#4076C212yesmaximal, complemented
5#4041C212yesmaximal, complemented
6#4028C214yesmaximal, complemented
7#4020C211yesmaximal, characteristic, complemented
8C4×D20C211yesmaximal, characteristic, complemented
9C23×D5C2214yescomplemented
10C2×C5×D4C2211yescharacteristic
11C22×C4×C5C2212yescomplemented
12C2×C22⋊D5C2214yescomplemented
13D4×D5—28no—
14C2×D20—28no—
15C2×D20C2211yescharacteristic
16C2×D20C2212yescomplemented
17C2×D20C2214yescomplemented
18C2×D20C2212yescomplemented
19C2×D20C2212yescomplemented
20C2×C4×D5C2212yescomplemented
21C5×C4⋊C4C2211yescharacteristic, complemented
22C5×C22⋊C4C2212yescomplemented
23C42×C5C2211yescharacteristic, complemented
24#685C2212yescomplemented
25#685C2214yescomplemented
26C4⋊Dic5C2211yescharacteristic, complemented
27D42—51nomaximal, Sylow
28C23×C5C2312yes—
29C22×D5—28no—
30C22×D5—28no—
31C22×D5—44no—
32C22×D5C2314yes—
33C22×D5C2312yes—
34C5×D4D414yescomplemented
35C2×C4×C5—24no—
36C2×C4×C5C2311yescharacteristic
37C2×C4×C5C2312yes—
38C2×C4×C5C2311yescharacteristic
39C2×C4×C5C2311yescharacteristic
40C22⋊D5—28no—
41C2×Dic5C2312yes—
42D20—28no—
43D20—24no—
44D20—24no—
45D20—42no—
46D20D414yesdirect product factor
47C4×D5—24no—
48C22×D4—52no—
49C22×D4—52no—
50#127—51no—
51#121—52no—
52#121—52no—
53#120—54no—
54C4×D4—51no—
55C4×D4D511yescharacteristic, complemented
56C22×C5—22no—
57C22×C5—22no—
58C22×C5C2×D414yescomplemented
59C22×C5C2411yescharacteristic
60C2×D5—22no—
61C2×D5—22no—
62C2×D5—24no—
63C2×D5—24no—
64C2×D5—24no—
65C2×D5—416no—
66C2×D5C2×D414yescomplemented
67C4×C5—22no—
68C4×C5—21no—
69C4×C5C2×D412yescomplemented
70C4×C5C2×D412yescomplemented
71Dic5—22no—
72C24—54no—
73C2×D4—54no—
74C2×D4—51no—
75C2×D4—54no—
76C2×D4—52no—
77C2×D4—52no—
78C2×D4—52no—
79C2×D4—108no—
80C2×D4—108no—
81C2×D4C2×D511yescharacteristic
82C22×C4—52no—
83C22×C4C2×D512yescomplemented
84C4⋊C4—51no—
85C4⋊C4C2×D511yescharacteristic, complemented
86C22⋊C4—52no—
87C22⋊C4—54no—
88C22⋊C4C2×D512yescomplemented
89C42C2×D511yescharacteristic, complemented
90C2×C5—24no—
91C2×C5C22×D411yescharacteristic
92C2×C5C22×D411yescharacteristic
93C2×C5H(5,𝔽2)11yescharacteristic
94D5—24no—
95D5—44no—
96C23—52no—
97C23—54no—
98C23—108no—
99C23—108no—
100C23—204no—
101C23C22×D512yes—
102D4—54no—
103D4—108no—
104D4—108no—
105D4—104no—
106D4—104no—
107D4—202no—
108D4D2014yesdirect product factor
109C2×C4—24no—
110C2×C4—52no—
111C2×C4—104no—
112C2×C4C22×D511yescharacteristic
113C2×C4C22×D512yes—
114C2×C4C22×D511yescharacteristic
115C2×C4C22×D511yescharacteristic
116C5D4211yescharacteristic, complemented, Sylow
117C22—22no—
118C22—22no—
119C22—54no—
120C22—102no—
121C22—102no—
122C22—104no—
123C22—104no—
124C22—104no—
125C22—2016no—
126C22C2×D2014yescomplemented
127C22C23×D511yescharacteristic
128C4—22no—
129C4—21no—
130C4—102no—
131C4C2×D2012yescomplemented
132C4D4×D512yescomplemented
133C2—24no—
134C2—104no—
135C2—204no—
136C2C22×D2011yescharacteristic
137C2C2×D4×D511yescharacteristic
138C2#414911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D5
commutator, socle, cosocleC22×C5C24
FittingC4×C5×D4C2
hypercenterC4×D4D5
hypocenterC5D42
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×D5C2semidirect
2. C22×D20C2semidirect
3. C4×C5×D4C2semidirect
4. #4076C2semidirect
5. #4041C2semidirect
6. #4028C2semidirect
7. #4020C2semidirect
8. C4×D20C2semidirect
9. C23×D5C22semidirect
11. C22×C4×C5C22semidirect
12. C2×C22⋊D5C22semidirect
16. C2×D20C22semidirect
17. C2×D20C22semidirect
18. C2×D20C22semidirect
19. C2×D20C22semidirect
20. C2×C4×D5C22semidirect
21. C5×C4⋊C4C22semidirect
22. C5×C22⋊C4C22semidirect
23. C42×C5C22semidirect
24. #685C22semidirect
25. #685C22semidirect
26. C4⋊Dic5C22semidirect
34. C5×D4D4semidirect
46. D20D4direct (N × H)
55. C4×D4D5semidirect
58. C22×C5C2×D4semidirect
66. C2×D5C2×D4semidirect
69. C4×C5C2×D4semidirect
70. C4×C5C2×D4semidirect
83. C22×C4C2×D5semidirect
85. C4⋊C4C2×D5semidirect
88. C22⋊C4C2×D5semidirect
89. C42C2×D5semidirect
108. D4D20direct (N × H)
116. C5D42semidirect
126. C22C2×D20semidirect
131. C4C2×D20semidirect
132. C4D4×D5semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D52
C22×D202
C4×C5×D42
#40762
#40412
#40282
#40202
C4×D202
D425