Finite Group Databasebeta

← C13×#15668724 #50303669

Subgroups — C13×#15668724 #50303669

Order 38220.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C13×#3862C211yesmaximal, characteristic
2C7×C13×Dic35—31nomaximal, Hall
3C5×C13×#3862C411yescharacteristic, complemented, Hall
4C13×#10596868—51nomaximal, Hall
5C2×C5×C72×C13D311yescharacteristic
6C2×C13×#3862D511yescharacteristic
7C5×C72×C13Dic311yescharacteristic, complemented, Hall
8#15668724C1311yesmaximal, characteristic, direct product factor, Hall
9C2×C5×C13×ΓL(1,𝔽8)—141no—
10C7×C13×Dic7—151noHall
11C13×#3862Dic511yescharacteristic, complemented, Hall
12C13×Dic35—31no—
13C7×C13×Dic5—211no—
14C2×C5×#3862C2×C1311yescharacteristic
15C5×C13×ΓL(1,𝔽8)—141no—
16C2×C72×C13D1511yescharacteristic
17C7×Dic35—31noHall
18C2×C5×C7×C13—21no—
19C2×C5×C7×C13—31no—
20C2×C5×C7×C13—31no—
21C13×Dic15—491nomaximal, Hall
22C5×#3862C4×C1311yescharacteristic, complemented, Hall
23C72×C13Dic1511yescharacteristic, complemented, Hall
24#10596868—51noHall
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—1051no—
32C13×Dic7—151no—
33C2×#3862D5×C1311yescharacteristic
34C13×ΓL(1,𝔽8)—141no—
35C13×Dic5—211noHall
36C5×C72Dic3×C1311yescharacteristic, complemented, Hall
37C2×C5×ΓL(1,𝔽8)—141no—
38C7×Dic7—151noHall
39C3×C5×C13—491noHall
40C2×C7×C13—21no—
41C2×C7×C13—31no—
42C2×C7×C13—31no—
43Dic3×C13—2451noHall
44#3862C13×Dic511yescharacteristic, complemented, Hall
45Dic35—31no—
46C7×Dic5—211no—
47C2×C5×C13#6441811yescharacteristic
48C5×ΓL(1,𝔽8)—141no—
49C2×C72C13×D1511yescharacteristic
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, complemented, Hall
58Dic15—491noHall
59C4×C13—1051noHall
60C72C13×Dic1511yescharacteristic, 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—1051no—
68Dic7—151no—
69C2×C13C5⋊#6441811yescharacteristic
70ΓL(1,𝔽8)—141no—
71Dic5—211noHall
72C3×C5—491noHall
73C2×C7—21no—
74C2×C7—31no—
75C2×C7—31no—
76C13#1566872411yescharacteristic, direct product factor, Sylow
77Dic3—2451noHall
78C2×C5C13×#6441811yescharacteristic
79C7—21no—
80C7—31no—
81C7—31no—
82C2×C3—491no—
83C5C13×#1059686811yescharacteristic, complemented, Sylow
84C4—1051noSylow
85C3—491noSylow
86C2C13×C5⋊#6441811yescharacteristic
subgroupG/H
center, hypercenterC2×C13C5⋊#64418
commutator, hypocenterC5×#3862C4×C13
FrattiniC2C13×C5⋊#64418
Fitting, socleC2×C5×C72×C13D3
prime radicalC2×C5×C13×#3862C2
cosocleC2×C5×#3862C2×C13
LCSG ▷ C5×#3862
UCSC1 ◁ C2×C13

Complements

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

NH ≅ G/Ntype
3. C5×C13×#3862C4semidirect
7. C5×C72×C13Dic3semidirect
8. #15668724C13direct (N × H)
11. C13×#3862Dic5semidirect
22. C5×#3862C4×C13semidirect
23. C72×C13Dic15semidirect
36. C5×C72Dic3×C13semidirect
44. #3862C13×Dic5semidirect
57. C5×C13#10596868semidirect
60. C72C13×Dic15semidirect
76. C13#15668724direct (N × H)
83. C5C13×#10596868semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C13×#38622
C7×C13×Dic353
C13×#105968685
#1566872413
C13×Dic1549