Finite Group Databasebeta

← C2×#4057 #66089

Subgroups — C2×#4057 #66089

Order 320.

298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#711C211yesmaximal, characteristic, complemented
2C2×D4×D5C211yesmaximal, characteristic, complemented
3C2×C5×D8C211yesmaximal, characteristic, complemented
4C2×#687C211yesmaximal, characteristic, complemented
5C2×#686C211yesmaximal, characteristic, complemented
6#4057C218yesmaximal, direct product factor
7C2×#677C211yesmaximal, characteristic, complemented
8C2×#676C211yesmaximal, characteristic, complemented
9C23×D5—21no—
10C2×C5×D4C2211yescharacteristic
11C2×C5×D4C2211yescharacteristic, complemented
12C2×C22⋊D5—21no—
13C2×C22⋊D5—21no—
14C22×Dic5—21no—
15#711—22no—
16#711C2214yescomplemented
17D4×D5—22no—
18D4×D5C2214yescomplemented
19C2×D20C2211yescharacteristic
20C2×C4×D5C2211yescharacteristic
21C2×Dic10C2211yescharacteristic, complemented
22C5×D8C2214yescomplemented
23C2×C5×C8C2211yescharacteristic, complemented
24#687C2214yescomplemented
25#686C2214yescomplemented
26C2×#168C2211yescharacteristic, complemented
27#677C2214yescomplemented
28#676C2214yescomplemented
29C2×AGL(1,ℤ/8)—51nomaximal, Sylow
30C23×C5—21no—
31C23×C5—21no—
32C22×D5—21no—
33C22×D5—24no—
34C22×D5—44no—
35C22×D5D411yescharacteristic
36C5×D4—21no—
37C5×D4—21no—
38C5×D4C2312yes—
39C5×D4C2312yescomplemented
40C2×C4×C5C2311yescharacteristic
41C22⋊D5—24no—
42C22⋊D5—24no—
43C2×Dic5—21no—
44C2×Dic5—24no—
45C2×Dic5D411yescharacteristic
46D20—21no—
47D20C2312yes—
48C4×D5D412yes—
49C4×D5C2312yes—
50Dic10—21no—
51Dic10C2312yescomplemented
52C5×C8C2312yescomplemented
53#168C2312yescomplemented
54C2×#41—51no—
55C22×D4—51no—
56AGL(1,ℤ/8)—58no—
57C2×SD16—51no—
58C2×SD16—51no—
59C2×D8—51no—
60C2×D8D511yescharacteristic, complemented
61C2×M16—51no—
62C22×C5—22no—
63C22×C5—22no—
64C22×C5—42no—
65C22×C5—42no—
66C22×C5C2×D411yescharacteristic
67C2×D5—22no—
68C2×D5—22no—
69C2×D5—48no—
70C2×D5—42no—
71C2×D5C2×D412yes—
72C4×C5C2×D411yescharacteristic
73C4×C5C2411yescharacteristic
74Dic5—22no—
75Dic5C2×D412yes—
76C24—101no—
77#41—54no—
78#41—102no—
79C2×Q8—51no—
80C2×D4—54no—
81C2×D4—51no—
82C2×D4—102no—
83C2×D4—101no—
84C2×D4—101no—
85C2×D4C2×D511yescharacteristic
86C2×D4C2×D511yescharacteristic, complemented
87C22×C4—51no—
88C22×C4—101no—
89SD16—54no—
90SD16—54no—
91D8—54no—
92D8C2×D514yescomplemented
93M16—54no—
94C2×C8—51no—
95C2×C8C2×D511yescharacteristic, complemented
96C2×C5—42no—
97C2×C5—42no—
98C2×C5AGL(1,ℤ/8)12yescomplemented
99C2×C5C22×D411yescharacteristic
100D5—22no—
101D5—42no—
102C23—21no—
103C23—21no—
104C23—51no—
105C23—104no—
106C23—101no—
107C23—204no—
108Q8—52no—
109Q8—101no—
110D4—21no—
111D4—21no—
112D4—52no—
113D4—104no—
114D4—104no—
115D4—101no—
116D4C22×D512yes—
117D4C22×D512yescomplemented
118C2×C4—51no—
119C2×C4—52no—
120C2×C4—52no—
121C2×C4—104no—
122C2×C4—101no—
123C2×C4C22×D511yescharacteristic
124C8—52no—
125C8C22×D512yescomplemented
126C5C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
127C22—22no—
128C22—22no—
129C22—42no—
130C22—42no—
131C22—52no—
132C22—102no—
133C22—102no—
134C22—208no—
135C22—202no—
136C22D4×D511yescharacteristic
137C4—52no—
138C4—102no—
139C4D4×D511yescharacteristic
140C4C23×D511yescharacteristic
141C2—42no—
142C2—42no—
143C2—102no—
144C2—202no—
145C2#405712yesdirect product factor
146C2C2×D4×D511yescharacteristic
subgroupG/H
centerC22D4×D5
commutator, cosocleC4×C5C24
FrattiniC4C23×D5
FittingC2×C5×D8C2
socleC22×C5C2×D4
hypercenterC2×D8D5
hypocenterC5C2×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#711C2semidirect
2. C2×D4×D5C2semidirect
3. C2×C5×D8C2semidirect
4. C2×#687C2semidirect
5. C2×#686C2semidirect
6. #4057C2direct (N × H)
7. C2×#677C2semidirect
8. C2×#676C2semidirect
11. C2×C5×D4C22semidirect
16. #711C22semidirect
18. D4×D5C22semidirect
21. C2×Dic10C22semidirect
22. C5×D8C22semidirect
23. C2×C5×C8C22semidirect
24. #687C22semidirect
25. #686C22semidirect
26. C2×#168C22semidirect
27. #677C22semidirect
28. #676C22semidirect
39. C5×D4C23semidirect
51. Dic10C23semidirect
52. C5×C8C23semidirect
53. #168C23semidirect
60. C2×D8D5semidirect
86. C2×D4C2×D5semidirect
92. D8C2×D5semidirect
95. C2×C8C2×D5semidirect
98. C2×C5AGL(1,ℤ/8)semidirect
117. D4C22×D5semidirect
125. C8C22×D5semidirect
126. C5C2×AGL(1,ℤ/8)semidirect
145. C2#4057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#7112
C2×D4×D52
C2×C5×D82
C2×#6872
C2×#6862
#40572
C2×#6772
C2×#6762
C2×AGL(1,ℤ/8)5