Finite Group Databasebeta

← C5×C11×#10596868 #44568488

Subgroups — C5×C11×#10596868 #44568488

Order 32340.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×#3862C211yesmaximal, characteristic
2C5×C7×C11×Dic7—31nomaximal, Hall
3C5×C11×#3862C411yescharacteristic, complemented, Hall
4C11×#10596868C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C72×C11D311yescharacteristic
6C2×C11×#3862C2×C511yescharacteristic
7C5×#10596868C1111yesmaximal, characteristic, direct product factor, Hall
8C5×C72×C11Dic311yescharacteristic, complemented, Hall
9C2×C5×C11×ΓL(1,𝔽8)—141no—
10C7×C11×Dic7—31noHall
11C11×#3862C4×C511yescharacteristic, complemented, Hall
12C4×C5×C7×C11—211no—
13C5×C11×Dic7—31no—
14C2×C5×#3862C2×C1111yescharacteristic
15C5×C11×ΓL(1,𝔽8)—141no—
16C2×C72×C11C5×D311yescharacteristic
17C5×C7×Dic7—31noHall
18C2×C5×C7×C11—21no—
19C2×C5×C7×C11—31no—
20C2×C5×C7×C11—31no—
21C5×#3862C4×C1111yescharacteristic, complemented, Hall
22C5×C11×Dic3—491nomaximal, Hall
23#10596868C5×C1111yescharacteristic, direct product factor, Hall
24C72×C11C5×Dic311yescharacteristic, complemented, Hall
25C2×C5×C72D3×C1111yescharacteristic
26C2×C11×ΓL(1,𝔽8)—141no—
27C5×C7×C11—21no—
28C5×C7×C11—31no—
29C5×C7×C11—31no—
30C2×C3×C5×C11—491no—
31C4×C7×C11—211no—
32C11×Dic7—31no—
33C2×#3862C2×C5×C1111yescharacteristic
34C5×C72C11×Dic311yescharacteristic, complemented, Hall
35C11×ΓL(1,𝔽8)—141no—
36C4×C5×C11—211noHall
37C2×C5×ΓL(1,𝔽8)—141no—
38C7×Dic7—31noHall
39C3×C5×C11—491noHall
40C2×C7×C11—21no—
41C2×C7×C11—31no—
42C2×C7×C11—31no—
43#3862C4×C5×C1111yescharacteristic, complemented, Hall
44C4×C5×C7—211no—
45C5×Dic7—31no—
46C11×Dic3—491noHall
47C2×C5×C11#6441811yescharacteristic
48C5×ΓL(1,𝔽8)—141no—
49C2×C72C5×D3×C1111yescharacteristic
50C7×C11—21no—
51C7×C11—31no—
52C7×C11—31no—
53C2×C5×C7—21no—
54C2×C5×C7—31no—
55C2×C5×C7—31no—
56C2×C3×C11—491no—
57C5×Dic3—491noHall
58C5×C11#1059686811yescharacteristic, direct product factor, Hall
59C72C5×C11×Dic311yescharacteristic, complemented, Sylow
60C4×C11—211noHall
61C2×ΓL(1,𝔽8)—141no—
62C5×C7—21no—
63C5×C7—31no—
64C5×C7—31no—
65C3×C11—491noHall
66C2×C3×C5—491no—
67C4×C7—211no—
68Dic7—31no—
69C2×C11C5×#6441811yescharacteristic
70ΓL(1,𝔽8)—141no—
71C4×C5—211noHall
72C3×C5—491noHall
73C2×C7—21no—
74C2×C7—31no—
75C2×C7—31no—
76Dic3—491noHall
77C11C5×#1059686811yescharacteristic, direct product factor, Sylow
78C2×C5C11×#6441811yescharacteristic
79C7—21no—
80C7—31no—
81C7—31no—
82C2×C3—491no—
83C5C11×#1059686811yescharacteristic, direct product factor, Sylow
84C4—211noSylow
85C3—491noSylow
86C2C5×C11×#6441811yescharacteristic
subgroupG/H
center, hypercenterC2×C5×C11#64418
commutator, hypocenter#3862C4×C5×C11
FrattiniC2C5×C11×#64418
Fitting, socleC2×C5×C72×C11D3
prime radicalC2×C5×C11×#3862C2
cosocleC2×#3862C2×C5×C11
LCSG ▷ #3862
UCSC1 ◁ C2×C5×C11

Complements

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

NH ≅ G/Ntype
3. C5×C11×#3862C4semidirect
4. C11×#10596868C5direct (N × H)
7. C5×#10596868C11direct (N × H)
8. C5×C72×C11Dic3semidirect
11. C11×#3862C4×C5semidirect
21. C5×#3862C4×C11semidirect
23. #10596868C5×C11direct (N × H)
24. C72×C11C5×Dic3semidirect
34. C5×C72C11×Dic3semidirect
43. #3862C4×C5×C11semidirect
58. C5×C11#10596868direct (N × H)
59. C72C5×C11×Dic3semidirect
77. C11C5×#10596868direct (N × H)
83. C5C11×#10596868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C11×#38622
C5×C7×C11×Dic73
C11×#105968685
C5×#1059686811
C5×C11×Dic349