Finite Group Databasebeta

← C5×#63387 #13083830

Subgroups — C5×#63387 #13083830

Order 1440.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C9×Q16C211yesmaximal, characteristic, complemented
2C5×D72C211yesmaximal, characteristic
3C5×C9⋊C16C211yesmaximal, characteristic, complemented
4C5×#828—31nomaximal
5C5×Q8×C9—21no—
6C5×D36—21no—
7C5×C8×C9C2211yescharacteristic
8#63387C511yesmaximal, characteristic, direct product factor, Hall
9C3×C5×Q16D311yescharacteristic
10C5×D24—31no—
11C5×C3⋊C16—31no—
12C2×C5×D9—41no—
13C4×C5×C9—41no—
14C4×C5×C9D411yescharacteristic
15C5×SD32—91noHall
16C9×Q16C2×C511yescharacteristic, complemented
17D72C2×C511yescharacteristic
18C9⋊C16C2×C511yescharacteristic, complemented
19C3×C5×Q8—21no—
20C5×D12—61no—
21C3×C5×C8C2×D311yescharacteristic
22#828—31no—
23C2×C5×C9D811yescharacteristic
24C5×D9—81no—
25C5×Q16D911yescharacteristic, complemented
26C5×D8—91no—
27C5×C16—91no—
28Q8×C9—21no—
29D36—21no—
30C8×C9C22×C511yescharacteristic
31C2×C5×D3—121no—
32C3×C4×C5—41no—
33C3×C4×C5#6711yescharacteristic
34C3×Q16C5×D311yescharacteristic
35D24—31no—
36C3⋊C16—31no—
37C5×C9SD3211yescharacteristic, complemented, Hall
38C5×Q8—21no—
39C5×D4—181no—
40C5×C8C2×D911yescharacteristic
41C2×D9—41no—
42C4×C9—41no—
43C4×C9C5×D411yescharacteristic
44SD32—91noSylow
45C2×C3×C5#21311yescharacteristic
46C5×D3—241no—
47C3×Q8—21no—
48D12—61no—
49C3×C8C2×C5×D311yescharacteristic
50C22×C5—361no—
51C4×C5—41no—
52C4×C5#61111yescharacteristic
53C2×C9C5×D811yescharacteristic
54D9—81no—
55Q16C5×D911yescharacteristic, complemented
56D8—91no—
57C16—91no—
58C3×C5#82811yescharacteristic
59C2×D3—121no—
60C3×C4—41no—
61C3×C4C5×#6711yescharacteristic
62C2×C5—721no—
63C2×C5#367311yescharacteristic
64C9C5×SD3211yescharacteristic, complemented, Sylow
65Q8—21no—
66D4—181no—
67C8C2×C5×D911yescharacteristic
68C2×C3C5×#21311yescharacteristic
69D3—241no—
70C5#6338711yescharacteristic, direct product factor, Sylow
71C22—361no—
72C4—41no—
73C4C5×#61111yescharacteristic
74C3C5×#82811yescharacteristic
75C2—721no—
76C2C5×#367311yescharacteristic
subgroupG/H
centerC2×C5#3673
commutator, cosocleC8×C9C22×C5
FrattiniC3×C8C2×C5×D3
FittingC5×C9×Q16C2
socleC2×C3×C5#213
prime radicalC5×D72C2
hypercenterC5×Q16D9
hypocenterC9C5×SD32
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×Q16

Complements

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

NH ≅ G/Ntype
1. C5×C9×Q16C2semidirect
3. C5×C9⋊C16C2semidirect
8. #63387C5direct (N × H)
16. C9×Q16C2×C5semidirect
18. C9⋊C16C2×C5semidirect
25. C5×Q16D9semidirect
37. C5×C9SD32semidirect
55. Q16C5×D9semidirect
64. C9C5×SD32semidirect
70. C5#63387direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C9×Q162
C5×D722
C5×C9⋊C162
C5×#8283
#633875