Finite Group Databasebeta

← C5×#327 #64794

Subgroups — C5×#327 #64794

Order 320.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#121C211yesmaximal, characteristic
2C5×C22⋊C8C211yesmaximal, characteristic, complemented
3C5×#95C211yesmaximal, characteristic, complemented
4C2×C5×D4—21no—
5C2×C5×D4C411yescharacteristic, complemented
6C22×C4×C5—21no—
7C22×C4×C5C2211yescharacteristic
8C2×C5×C8—21no—
9C5×C4⋊C4C411yescharacteristic, complemented
10C5×C22⋊C4—21no—
11#327C511yesmaximal, characteristic, direct product factor, Sylow
12C23×C5—21no—
13C23×C5D411yescharacteristic
14C5×D4—41no—
15C5×D4—41no—
16C5×D4—41no—
17C2×C4×C5—22no—
18C2×C4×C5—21no—
19C2×C4×C5—41no—
20C2×C4×C5—41no—
21C2×C4×C5—41no—
22C2×C4×C5C2×C411yescharacteristic
23C2×C4×C5D411yescharacteristic
24C5×C8—41no—
25#121C2×C511yescharacteristic
26C22⋊C8C2×C511yescharacteristic, complemented
27#95C2×C511yescharacteristic, complemented
28C22×C5—21no—
29C22×C5—21no—
30C22×C5—41no—
31C22×C5—41no—
32C22×C5—41no—
33C22×C5C22⋊C411yescharacteristic
34C22×C5D811yescharacteristic
35C22×C5SD1611yescharacteristic
36C4×C5—21no—
37C4×C5—21no—
38C4×C5—42no—
39C4×C5—41no—
40C2×D4—21no—
41C2×D4C4×C511yescharacteristic, complemented
42C22×C4—21no—
43C22×C4C22×C511yescharacteristic
44C2×C8—21no—
45C4⋊C4C4×C511yescharacteristic, complemented
46C22⋊C4—21no—
47C2×C5—21no—
48C2×C5—21no—
49C2×C5—81no—
50C2×C5#9911yescharacteristic
51C2×C5#10211yescharacteristic
52C2×C5#10411yescharacteristic
53C23—21no—
54C23C5×D411yescharacteristic
55D4—41no—
56D4—41no—
57D4—41no—
58C2×C4—22no—
59C2×C4—21no—
60C2×C4—41no—
61C2×C4—41no—
62C2×C4—41no—
63C2×C4C2×C4×C511yescharacteristic
64C2×C4C5×D411yescharacteristic
65C8—41no—
66C5#32711yescharacteristic, direct product factor, Sylow
67C22—21no—
68C22—21no—
69C22—41no—
70C22—41no—
71C22—41no—
72C22C5×C22⋊C411yescharacteristic
73C22C5×D811yescharacteristic
74C22C5×SD1611yescharacteristic
75C4—21no—
76C4—21no—
77C4—42no—
78C4—41no—
79C2—21no—
80C2—21no—
81C2—81no—
82C2C5×#9911yescharacteristic
83C2C5×#10211yescharacteristic
84C2C5×#10411yescharacteristic
subgroupG/H
center, socleC22×C5C22⋊C4
commutatorC2×C4C2×C4×C5
Frattini, cosocleC22×C4C22×C5
prime radicalC5×#121C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×C22⋊C8C2semidirect
3. C5×#95C2semidirect
5. C2×C5×D4C4semidirect
9. C5×C4⋊C4C4semidirect
11. #327C5direct (N × H)
26. C22⋊C8C2×C5semidirect
27. #95C2×C5semidirect
41. C2×D4C4×C5semidirect
45. C4⋊C4C4×C5semidirect
66. C5#327direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#1212
C5×C22⋊C82
C5×#952
#3275