Finite Group Databasebeta

← C2×D5×D8 #66088

Subgroups — C2×D5×D8 #66088

Order 320.

338 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 111 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
2C2×C5×D8C211yesmaximal, characteristic, complemented
3C2×#686C212yesmaximal, complemented
4D5×D8C218yesmaximal, direct product factor
5C2×D40C211yesmaximal, characteristic, complemented
6C2×C8×D5C211yesmaximal, characteristic, complemented
7C23×D5—22no—
8C2×C5×D4C2212yescomplemented
9C2×C22⋊D5—22no—
10D4×D5—24no—
11D4×D5C2218yescomplemented
12C2×D20C2212yescomplemented
13C2×C4×D5C2211yescharacteristic
14C5×D8C2214yescomplemented
15C2×C5×C8C2211yescharacteristic, complemented
16#686C2218yescomplemented
17C2×#168C2211yescharacteristic, complemented
18D40C2214yescomplemented
19C8×D5C2214yescomplemented
20C22×D8—51nomaximal, Sylow
21C23×C5—22no—
22C22×D5—22no—
23C22×D5—28no—
24C22×D5—48no—
25C22×D5D411yescharacteristic
26C5×D4—22no—
27C5×D4C2314yescomplemented
28C2×C4×C5C2311yescharacteristic
29C22⋊D5—28no—
30C2×Dic5D411yescharacteristic
31D20—22no—
32D20C2314yescomplemented
33C4×D5D412yes—
34C4×D5C2312yes—
35C5×C8C2312yescomplemented
36#168C2312yescomplemented
37C22×D4—52no—
38C2×D8—52no—
39C2×D8—58no—
40C2×D8—51no—
41C2×D8D511yescharacteristic, direct product factor
42C22×C8—51no—
43C22×C5—24no—
44C22×C5—44no—
45C22×C5C2×D411yescharacteristic
46C2×D5—24no—
47C2×D5—44no—
48C2×D5—416no—
49C2×D5D814yesdirect product factor
50C2×D5C2×D412yes—
51C4×C5C2×D411yescharacteristic
52C4×C5C2411yescharacteristic
53Dic5C2×D412yes—
54C24—102no—
55C2×D4—58no—
56C2×D4—52no—
57C2×D4—104no—
58C2×D4—102no—
59C2×D4C2×D512yescomplemented
60C22×C4—51no—
61D8—58no—
62D8—54no—
63D8C2×D514yesdirect product factor
64C2×C8—51no—
65C2×C8—54no—
66C2×C8C2×D511yescharacteristic, complemented
67C2×C5—44no—
68C2×C5C2×D812yescomplemented
69C2×C5C22×D411yescharacteristic
70D5—44no—
71D5C2×D814yesdirect product factor
72C23—22no—
73C23—51no—
74C23—108no—
75C23—102no—
76C23—208no—
77D4—22no—
78D4—54no—
79D4—108no—
80D4—102no—
81D4C22×D514yescomplemented
82C2×C4—51no—
83C2×C4—52no—
84C2×C4—52no—
85C2×C4C22×D511yescharacteristic
86C8—52no—
87C8C22×D512yescomplemented
88C5C22×D811yescharacteristic, complemented, Sylow
89C22—24no—
90C22—44no—
91C22—52no—
92C22—54no—
93C22—104no—
94C22—2016no—
95C22—204no—
96C22D4×D511yescharacteristic
97C4—52no—
98C4D4×D511yescharacteristic
99C4C23×D511yescharacteristic
100C2—44no—
101C2—54no—
102C2—204no—
103C2D5×D812yesdirect product factor
104C2C2×D4×D511yescharacteristic
subgroupG/H
centerC22D4×D5
commutator, cosocleC4×C5C24
FrattiniC4C23×D5
FittingC2×C5×D8C2
socleC22×C5C2×D4
hypercenterC2×D8D5
hypocenterC5C22×D8
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×D4×D5C2semidirect
2. C2×C5×D8C2semidirect
3. C2×#686C2semidirect
4. D5×D8C2direct (N × H)
5. C2×D40C2semidirect
6. C2×C8×D5C2semidirect
8. C2×C5×D4C22semidirect
11. D4×D5C22semidirect
12. C2×D20C22semidirect
14. C5×D8C22semidirect
15. C2×C5×C8C22semidirect
16. #686C22semidirect
17. C2×#168C22semidirect
18. D40C22semidirect
19. C8×D5C22semidirect
27. C5×D4C23semidirect
32. D20C23semidirect
35. C5×C8C23semidirect
36. #168C23semidirect
41. C2×D8D5direct (N × H)
49. C2×D5D8direct (N × H)
59. C2×D4C2×D5semidirect
63. D8C2×D5direct (N × H)
66. C2×C8C2×D5semidirect
68. C2×C5C2×D8semidirect
71. D5C2×D8direct (N × H)
81. D4C22×D5semidirect
87. C8C22×D5semidirect
88. C5C22×D8semidirect
103. C2D5×D8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D52
C2×C5×D82
C2×#6862
D5×D82
C2×D402
C2×C8×D52
C22×D85