Finite Group Databasebeta

← C5×C13×#10596868 #50303605

Subgroups — C5×C13×#10596868 #50303605

Order 38220.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C13×#3862C211yesmaximal, characteristic
2C5×C7×C13×Dic7—31nomaximal, Hall
3C5×C13×#3862C411yescharacteristic, complemented, Hall
4C13×#10596868C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C72×C13D311yescharacteristic
6C2×C13×#3862C2×C511yescharacteristic
7C5×C72×C13Dic311yescharacteristic, complemented, Hall
8C5×#10596868C1311yesmaximal, characteristic, direct product factor, Hall
9C2×C5×C13×ΓL(1,𝔽8)—141no—
10C7×C13×Dic7—31noHall
11C13×#3862C4×C511yescharacteristic, complemented, Hall
12C4×C5×C7×C13—211no—
13C5×C13×Dic7—31no—
14C2×C5×#3862C2×C1311yescharacteristic
15C5×C13×ΓL(1,𝔽8)—141no—
16C2×C72×C13C5×D311yescharacteristic
17C5×C7×Dic7—31noHall
18C2×C5×C7×C13—21no—
19C2×C5×C7×C13—31no—
20C2×C5×C7×C13—31no—
21C5×Dic3×C13—491nomaximal, Hall
22C5×#3862C4×C1311yescharacteristic, complemented, Hall
23C72×C13C5×Dic311yescharacteristic, complemented, Hall
24#10596868C5×C1311yescharacteristic, direct product factor, Hall
25C2×C13×ΓL(1,𝔽8)—141no—
26C2×C5×C72D3×C1311yescharacteristic
27C5×C7×C13—21no—
28C5×C7×C13—31no—
29C5×C7×C13—31no—
30C2×C3×C5×C13—491no—
31C4×C7×C13—211no—
32C13×Dic7—31no—
33C2×#3862C2×C5×C1311yescharacteristic
34C13×ΓL(1,𝔽8)—141no—
35C4×C5×C13—211noHall
36C5×C72Dic3×C1311yescharacteristic, complemented, Hall
37C2×C5×ΓL(1,𝔽8)—141no—
38C7×Dic7—31noHall
39C3×C5×C13—491noHall
40C2×C7×C13—21no—
41C2×C7×C13—31no—
42C2×C7×C13—31no—
43Dic3×C13—491noHall
44#3862C4×C5×C1311yescharacteristic, complemented, Hall
45C4×C5×C7—211no—
46C5×Dic7—31no—
47C2×C5×C13#6441811yescharacteristic
48C5×ΓL(1,𝔽8)—141no—
49C2×C72C5×D3×C1311yescharacteristic
50C7×C13—21no—
51C7×C13—31no—
52C7×C13—31no—
53C2×C3×C13—491no—
54C2×C5×C7—21no—
55C2×C5×C7—31no—
56C2×C5×C7—31no—
57C5×C13#1059686811yescharacteristic, direct product factor, Hall
58C5×Dic3—491noHall
59C4×C13—211noHall
60C72C5×Dic3×C1311yescharacteristic, complemented, Sylow
61C2×ΓL(1,𝔽8)—141no—
62C3×C13—491noHall
63C5×C7—21no—
64C5×C7—31no—
65C5×C7—31no—
66C2×C3×C5—491no—
67C4×C7—211no—
68Dic7—31no—
69C2×C13C5×#6441811yescharacteristic
70ΓL(1,𝔽8)—141no—
71C4×C5—211noHall
72C3×C5—491noHall
73C2×C7—21no—
74C2×C7—31no—
75C2×C7—31no—
76C13C5×#1059686811yescharacteristic, direct product factor, Sylow
77Dic3—491noHall
78C2×C5C13×#6441811yescharacteristic
79C7—21no—
80C7—31no—
81C7—31no—
82C2×C3—491no—
83C5C13×#1059686811yescharacteristic, direct product factor, Sylow
84C4—211noSylow
85C3—491noSylow
86C2C5×C13×#6441811yescharacteristic
subgroupG/H
center, hypercenterC2×C5×C13#64418
commutator, hypocenter#3862C4×C5×C13
FrattiniC2C5×C13×#64418
Fitting, socleC2×C5×C72×C13D3
prime radicalC2×C5×C13×#3862C2
cosocleC2×#3862C2×C5×C13
LCSG ▷ #3862
UCSC1 ◁ C2×C5×C13

Complements

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

NH ≅ G/Ntype
3. C5×C13×#3862C4semidirect
4. C13×#10596868C5direct (N × H)
7. C5×C72×C13Dic3semidirect
8. C5×#10596868C13direct (N × H)
11. C13×#3862C4×C5semidirect
22. C5×#3862C4×C13semidirect
23. C72×C13C5×Dic3semidirect
24. #10596868C5×C13direct (N × H)
36. C5×C72Dic3×C13semidirect
44. #3862C4×C5×C13semidirect
57. C5×C13#10596868direct (N × H)
60. C72C5×Dic3×C13semidirect
76. C13C5×#10596868direct (N × H)
83. C5C13×#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×C13×#38622
C5×C7×C13×Dic73
C13×#105968685
C5×#1059686813
C5×Dic3×C1349