Finite Group Databasebeta

← D5×SD32 #65202

Subgroups — D5×SD32 #65202

Order 320.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×Q16C211yesmaximal, characteristic, complemented
2D5×D8C211yesmaximal, characteristic
3C5×SD32C211yesmaximal, characteristic, complemented
4#3960C211yesmaximal, characteristic, complemented
5#3959C211yesmaximal, characteristic, complemented
6#3932C211yesmaximal, characteristic, complemented
7D5×C16C211yesmaximal, characteristic, complemented
8Q8×D5—21no—
9D4×D5—21no—
10C5×Q16C2211yescharacteristic, complemented
11C5×D8C2211yescharacteristic
12#689—21no—
13#686—21no—
14Dic20C2211yescharacteristic, complemented
15D40C2211yescharacteristic
16C8×D5C2211yescharacteristic
17C5×C16C2211yescharacteristic, complemented
18#672C2211yescharacteristic, complemented
19C2×SD32—51nomaximal, Sylow
20C22×D5—41no—
21C5×Q8—21no—
22C5×D4—21no—
23C22⋊D5—41no—
24D20—21no—
25C4×D5—41no—
26C4×D5D411yescharacteristic
27Dic10—21no—
28Dic10—41no—
29C5×C8C2311yescharacteristic
30#168D411yescharacteristic
31C2×Q16—51no—
32C2×D8—51no—
33SD32—51no—
34SD32—51no—
35SD32—51no—
36SD32D511yescharacteristic, direct product factor
37C2×C16—51no—
38C22×C5—41no—
39C2×D5—41no—
40C2×D5—82no—
41C2×D5D811yescharacteristic
42C4×C5—41no—
43C4×C5C2×D411yescharacteristic
44Dic5—41no—
45Dic5D811yescharacteristic
46C2×Q8—101no—
47C2×D4—101no—
48Q16—51no—
49Q16—101no—
50Q16C2×D511yescharacteristic, complemented
51D8—51no—
52D8—101no—
53D8C2×D511yescharacteristic
54C2×C8—51no—
55C16—51no—
56C16C2×D511yescharacteristic, complemented
57C2×C5—81no—
58C2×C5C2×D811yescharacteristic
59D5—81no—
60D5SD3212yesdirect product factor
61C23—201no—
62Q8—21no—
63Q8—101no—
64Q8—201no—
65D4—21no—
66D4—101no—
67D4—201no—
68C2×C4—51no—
69C2×C4—201no—
70C8—51no—
71C8C22×D511yescharacteristic
72C5C2×SD3211yescharacteristic, complemented, Sylow
73C22—41no—
74C22—51no—
75C22—201no—
76C22—402no—
77C4—41no—
78C4—51no—
79C4—201no—
80C4D4×D511yescharacteristic
81C2—52no—
82C2—81no—
83C2—401no—
84C2D5×D811yescharacteristic
subgroupG/H
centerC2D5×D8
commutator, cosocleC5×C8C23
FrattiniC8C22×D5
FittingC5×SD32C2
socleC2×C5C2×D8
prime radicalD5×D8C2
hypercenterSD32D5
hypocenterC5C2×SD32
LCSG ▷ C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. D5×Q16C2semidirect
3. C5×SD32C2semidirect
4. #3960C2semidirect
5. #3959C2semidirect
6. #3932C2semidirect
7. D5×C16C2semidirect
10. C5×Q16C22semidirect
14. Dic20C22semidirect
17. C5×C16C22semidirect
18. #672C22semidirect
36. SD32D5direct (N × H)
50. Q16C2×D5semidirect
56. C16C2×D5semidirect
60. D5SD32direct (N × H)
72. C5C2×SD32semidirect

Maximal subgroups

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

subgroupindex
D5×Q162
D5×D82
C5×SD322
#39602
#39592
#39322
D5×C162
C2×SD325