Finite Group Databasebeta

← C5×C11×#10597479 #46778039

Subgroups — C5×C11×#10597479 #46778039

Order 33660.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C11×C3⋊D51C211yesmaximal, characteristic
2C32×C5×C11×C17C411yescharacteristic, complemented, Hall
3C11×#10597479C511yesmaximal, characteristic, direct product factor, Hall
4C5×C11×D51—62no—
5C5×C11×#595—91nomaximal, Hall
6C11×C3⋊D51C2×C511yescharacteristic
7C5×#10597479C1111yesmaximal, characteristic, direct product factor, Hall
8C3×C5×C11×C17—22no—
9C5×C11×#157—171nomaximal, Hall
10C5×C11×D17—91no—
11C32×C11×C17C4×C511yescharacteristic, complemented, Hall
12C5×C3⋊D51C2×C1111yescharacteristic
13C11×D51—62no—
14C5×C11×C3⋊D3—171no—
15C5×C11×C17#15711yescharacteristic, complemented, Hall
16C32×C5×C17C4×C1111yescharacteristic, complemented, Hall
17C11×#595—91noHall
18#10597479C5×C1111yescharacteristic, direct product factor, Hall
19C3×C11×C17—22no—
20C5×D51—62no—
21C32×C5×C11#59511yescharacteristic, complemented, Hall
22C11×#157—171noHall
23C11×D17—91no—
24C5×#595—91noHall
25C5×D3×C11—1022no—
26C3⋊D51C2×C5×C1111yescharacteristic
27C3×C5×C17—22no—
28C4×C5×C11—1531noHall
29C11×C3⋊D3—171no—
30C11×C17C5×#15711yescharacteristic, complemented, Hall
31C5×#157—171noHall
32C5×D17—91no—
33C3×C5×C11—22no—
34C32×C17C4×C5×C1111yescharacteristic, complemented, Hall
35C2×C5×C11—1531no—
36D51—62no—
37C32×C11C5×#59511yescharacteristic, complemented, Hall
38C5×C3⋊D3—171no—
39C5×C17C11×#15711yescharacteristic, complemented, Hall
40#595—91noHall
41D3×C11—1022no—
42C5×C11#1059747911yescharacteristic, direct product factor, Hall
43C3×C17—22no—
44C32×C5C11×#59511yescharacteristic, complemented, Hall
45C4×C11—1531noHall
46#157—171noHall
47D17—91no—
48C3×C11—22no—
49C5×D3—1022no—
50C2×C11—1531no—
51C4×C5—1531noHall
52C3⋊D3—171no—
53C17C5×C11×#15711yescharacteristic, complemented, Sylow
54C3×C5—22no—
55C11C5×#1059747911yescharacteristic, direct product factor, Sylow
56C2×C5—1531no—
57C32C5×C11×#59511yescharacteristic, complemented, Sylow
58D3—1022no—
59C5C11×#1059747911yescharacteristic, direct product factor, Sylow
60C4—1531noSylow
61C3—22no—
62C2—1531no—
subgroupG/H
center, hypercenterC5×C11#10597479
commutator, hypocenterC32×C17C4×C5×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC5×C11×C3⋊D51C2
cosocleC3⋊D51C2×C5×C11
LCSG ▷ C32×C17
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
2. C32×C5×C11×C17C4semidirect
3. C11×#10597479C5direct (N × H)
7. C5×#10597479C11direct (N × H)
11. C32×C11×C17C4×C5semidirect
15. C5×C11×C17#157semidirect
16. C32×C5×C17C4×C11semidirect
18. #10597479C5×C11direct (N × H)
21. C32×C5×C11#595semidirect
30. C11×C17C5×#157semidirect
34. C32×C17C4×C5×C11semidirect
37. C32×C11C5×#595semidirect
39. C5×C17C11×#157semidirect
42. C5×C11#10597479direct (N × H)
44. C32×C5C11×#595semidirect
53. C17C5×C11×#157semidirect
55. C11C5×#10597479direct (N × H)
57. C32C5×C11×#595semidirect
59. C5C11×#10597479direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×C3⋊D512
C11×#105974795
C5×C11×#5959
C5×#1059747911
C5×C11×#15717