Finite Group Databasebeta

← C2×C5×#1094 #11761997

Subgroups — C2×C5×#1094 #11761997

Order 1080.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1094C211yesmaximal, characteristic, direct product factor
2C23×C32×C5C311yesmaximal, characteristic
3C2×C5×C22⋊C9C313yesmaximal, complemented
4C2×C5×3−1+2—41nomaximal
5C2×#1094C511yesmaximal, characteristic, direct product factor, Hall
6C22×C32×C5—31no—
7C22×C32×C5—31no—
8C22×C32×C5C2×C311yescharacteristic
9C5×C22⋊C9C2×C313yescomplemented
10C5×3−1+2—41noHall
11C23×C3×C5—31no—
12C23×C3×C5C3211yescharacteristic
13#1094C2×C511yescharacteristic, direct product factor
14C2×C32×C5—31no—
15C2×C32×C5—31no—
16C2×C32×C5A411yescharacteristic
17C2×C5×C9—43no—
18C23×C32C3×C511yescharacteristic
19C2×C22⋊C9C3×C513yescomplemented
20C22×C3×C5—31no—
21C22×C3×C5—33no—
22C22×C3×C5—33no—
23C22×C3×C5—31no—
24C22×C3×C5—31no—
25C22×C3×C5C2×C3211yescharacteristic
26C2×3−1+2—41no—
27C32×C5C2×A411yescharacteristic
28C5×C9—43no—
29C23×C53−1+211yescharacteristic, complemented, Hall
30C22×C32—31no—
31C22×C32—31no—
32C22×C32C2×C3×C511yescharacteristic
33C22⋊C9C2×C3×C513yescomplemented
34C2×C3×C5—33no—
35C2×C3×C5—33no—
36C2×C3×C5—31no—
37C2×C3×C5—31no—
38C2×C3×C5—31no—
39C2×C3×C5C3×A411yescharacteristic
403−1+2—41noSylow
41C23×C3—31no—
42C23×C3C32×C511yescharacteristic
43C22×C5—31no—
44C22×C5—31no—
45C22×C5C2×3−1+211yescharacteristic, complemented
46C2×C32—31no—
47C2×C32—31no—
48C2×C32C5×A411yescharacteristic
49C2×C9—43no—
50C3×C5—31no—
51C3×C5C2×C3×A411yescharacteristic
52C22×C3—31no—
53C22×C3—33no—
54C22×C3—33no—
55C22×C3—31no—
56C22×C3—31no—
57C22×C3C2×C32×C511yescharacteristic
58C2×C5—31no—
59C2×C5—31no—
60C2×C5#109411yescharacteristic, direct product factor
61C32C2×C5×A411yescharacteristic
62C9—43no—
63C23C5×3−1+211yescharacteristic, complemented, Sylow
64C2×C3—33no—
65C2×C3—33no—
66C2×C3—31no—
67C2×C3—31no—
68C2×C3—31no—
69C2×C3C3×C5×A411yescharacteristic
70C5C2×#109411yescharacteristic, direct product factor, Sylow
71C22—31no—
72C22—31no—
73C22C2×C5×3−1+211yescharacteristic, complemented
74C3—31no—
75C3C2×C3×C5×A411yescharacteristic
76C2—31no—
77C2—31no—
78C2C5×#109411yescharacteristic, direct product factor
subgroupG/H
centerC2×C3×C5C3×A4
commutator, cosocleC22×C3C2×C32×C5
FrattiniC3C2×C3×C5×A4
Fitting, prime radicalC23×C32×C5C3
socleC23×C3×C5C32
hypercenterC2×C32×C5A4
hypocenterC22C2×C5×3−1+2
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C3×C5 ◁ C2×C32×C5

Complements

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

NH ≅ G/Ntype
1. C5×#1094C2direct (N × H)
3. C2×C5×C22⋊C9C3semidirect
5. C2×#1094C5direct (N × H)
9. C5×C22⋊C9C2×C3semidirect
13. #1094C2×C5direct (N × H)
19. C2×C22⋊C9C3×C5semidirect
29. C23×C53−1+2semidirect
33. C22⋊C9C2×C3×C5semidirect
45. C22×C5C2×3−1+2semidirect
60. C2×C5#1094direct (N × H)
63. C23C5×3−1+2semidirect
70. C5C2×#1094direct (N × H)
73. C22C2×C5×3−1+2semidirect
78. C2C5×#1094direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#10942
C23×C32×C53
C2×C5×C22⋊C93
C2×C5×3−1+24
C2×#10945