Finite Group Databasebeta

← C13×#15668768 #50303924

Subgroups — C13×#15668768 #50303924

Order 38220.

104 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C13×#3862C211yesmaximal, characteristic
2C7×C13×C7⋊AGL(1,𝔽5)C311yesmaximal, characteristic, complemented, Hall
3C5×C13×#3862C411yescharacteristic, complemented, Hall
4C13×#10596872—51nomaximal, Hall
5C72×D5×C13C2×C311yescharacteristic
6C13×AGL(1,𝔽5)×ΓL(1,𝔽8)—71nomaximal
7C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)—71nomaximal
8C2×C13×#3862—51no—
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10#15668768C1311yesmaximal, characteristic, direct product factor, Hall
11D5×C13×ΓL(1,𝔽8)—71no—
12D5×C13×ΓL(1,𝔽8)—71no—
13C7×C13×Dic7—51noHall
14C13×#3862AGL(1,𝔽5)11yescharacteristic, complemented, Hall
15C13×C7⋊AGL(1,𝔽5)ΓL(1,𝔽8)11yescharacteristic, complemented
16C7×C13×AGL(1,𝔽5)—71no—
17D5×#3862C2×C1311yescharacteristic
18C5×C13×ΓL(1,𝔽8)—71no—
19C5×C13×ΓL(1,𝔽8)—71no—
20C2×C72×C13—51no—
21C4×C13×ΓL(1,𝔽8)—351no—
22C13×ΓL(1,𝔽8)⋊C4—351no—
23C7×C7⋊AGL(1,𝔽5)C3×C1311yescharacteristic, complemented, Hall
24C7×D5×C13—61no—
25C7×D5×C13AGL(1,𝔽7)11yescharacteristic
26C7×D5×C13C2×ΓL(1,𝔽8)11yescharacteristic
27C3×C13×AGL(1,𝔽5)—491noHall
28C5×#3862C4×C1311yescharacteristic, complemented, Hall
29C72×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
30#10596872—51noHall
31C2×C13×ΓL(1,𝔽8)—351no—
32C2×C13×ΓL(1,𝔽8)—351no—
33C72×D5C2×C3×C1311yescharacteristic
34C5×C7×C13—61no—
35C5×C7×C13ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
36C5×C7×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
37ΓL(1,𝔽8)⋊AGL(1,𝔽5)—71no—
38AGL(1,𝔽5)×ΓL(1,𝔽8)—71no—
39C3×D5×C13—491no—
40C4×C7×C13—351no—
41C13×Dic7—51no—
42C2×#3862—51no—
43C13×ΓL(1,𝔽8)—71no—
44C13×ΓL(1,𝔽8)—71no—
45C13×AGL(1,𝔽5)—71noHall
46C5×C72C3×C4×C1311yescharacteristic, complemented, Hall
47D5×ΓL(1,𝔽8)—71no—
48D5×ΓL(1,𝔽8)—71no—
49C7×Dic7—51noHall
50C3×C5×C13—491noHall
51C2×C7×C13—51no—
52C2×C7×C13—51no—
53C2×C7×C13—301no—
54C3×C4×C13—2451noHall
55#3862C13×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
56C7⋊AGL(1,𝔽5)C13×ΓL(1,𝔽8)11yescharacteristic, complemented
57C7×AGL(1,𝔽5)—71no—
58D5×C13#6442211yescharacteristic
59C5×ΓL(1,𝔽8)—71no—
60C5×ΓL(1,𝔽8)—71no—
61C2×C72—51no—
62C7×C13—61no—
63C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, complemented
64C7×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
65C4×ΓL(1,𝔽8)—351no—
66ΓL(1,𝔽8)⋊C4—351no—
67C2×C3×C13—2451no—
68C7×D5—61no—
69C7×D5C13×AGL(1,𝔽7)11yescharacteristic
70C7×D5C2×C13×ΓL(1,𝔽8)11yescharacteristic
71C5×C13#1059687211yescharacteristic, complemented, Hall
72C3×AGL(1,𝔽5)—491noHall
73C4×C13—351noHall
74C72C3×C13×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
75C2×ΓL(1,𝔽8)—351no—
76C2×ΓL(1,𝔽8)—351no—
77C3×C13—491noHall
78C5×C7—61no—
79C5×C7C13×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
80C5×C7C4×C13×ΓL(1,𝔽8)11yescharacteristic, complemented
81C3×D5—491no—
82C4×C7—351no—
83Dic7—51no—
84C2×C13—51no—
85ΓL(1,𝔽8)—71no—
86ΓL(1,𝔽8)—71no—
87AGL(1,𝔽5)—71noHall
88C3×C5—491noHall
89C2×C7—51no—
90C2×C7—51no—
91C2×C7—301no—
92C13#1566876811yescharacteristic, direct product factor, Sylow
93C3×C4—2451noHall
94D5C13×#6442211yescharacteristic
95C7—61no—
96C7C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
97C7C13×AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, complemented
98C2×C3—2451no—
99C5C13×#1059687211yescharacteristic, complemented, Sylow
100C4—351noSylow
101C3—491noSylow
102C2—51no—
subgroupG/H
center, hypercenterC13#15668768
commutator, hypocenterC5×C72C3×C4×C13
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalD5×C13×#3862C2
cosocleC72×D5C2×C3×C13
LCSG ▷ C5×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
2. C7×C13×C7⋊AGL(1,𝔽5)C3semidirect
3. C5×C13×#3862C4semidirect
9. C5×C72×C13C3×C4semidirect
10. #15668768C13direct (N × H)
14. C13×#3862AGL(1,𝔽5)semidirect
15. C13×C7⋊AGL(1,𝔽5)ΓL(1,𝔽8)semidirect
23. C7×C7⋊AGL(1,𝔽5)C3×C13semidirect
28. C5×#3862C4×C13semidirect
29. C72×C13C3×AGL(1,𝔽5)semidirect
35. C5×C7×C13ΓL(1,𝔽8)⋊C4semidirect
36. C5×C7×C13C4×ΓL(1,𝔽8)semidirect
46. C5×C72C3×C4×C13semidirect
55. #3862C13×AGL(1,𝔽5)semidirect
56. C7⋊AGL(1,𝔽5)C13×ΓL(1,𝔽8)semidirect
63. C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
64. C7×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
71. C5×C13#10596872semidirect
74. C72C3×C13×AGL(1,𝔽5)semidirect
79. C5×C7C13×ΓL(1,𝔽8)⋊C4semidirect
80. C5×C7C4×C13×ΓL(1,𝔽8)semidirect
92. C13#15668768direct (N × H)
96. C7C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
97. C7C13×AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
99. C5C13×#10596872semidirect

Maximal subgroups

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

subgroupindex
D5×C13×#38622
C7×C13×C7⋊AGL(1,𝔽5)3
C13×#105968725
C13×AGL(1,𝔽5)×ΓL(1,𝔽8)7
C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)7
#1566876813