Finite Group Databasebeta

← C13×#15668767 #50303912

Subgroups — C13×#15668767 #50303912

Order 38220.

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

normal subgroups only

This group has 144 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×#3861C211yesmaximal, characteristic
2C7×C13×C7⋊AGL(1,𝔽5)C311yesmaximal, characteristic, complemented, Hall
3C5×C13×#3861C411yescharacteristic, complemented, Hall
4C13×#10596873—51nomaximal, Hall
5C72×D5×C13C2×C311yescharacteristic
6C13×AGL(1,𝔽5)×ΓL(1,𝔽8)—71nomaximal
7C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)—71nomaximal
8C2×C13×#3861—51no—
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10#15668767C1311yesmaximal, characteristic, direct product factor, Hall
11D5×C13×ΓL(1,𝔽8)—71no—
12D5×C13×ΓL(1,𝔽8)—71no—
13D5×C13×ΓL(1,𝔽8)—143no—
14C7×C13×Dic7—51noHall
15C13×#3861AGL(1,𝔽5)11yescharacteristic, complemented, Hall
16C13×C7⋊AGL(1,𝔽5)ΓL(1,𝔽8)11yescharacteristic, complemented
17C7×C13×AGL(1,𝔽5)—71no—
18D5×#3861C2×C1311yescharacteristic
19C5×C13×ΓL(1,𝔽8)—71no—
20C5×C13×ΓL(1,𝔽8)—71no—
21C5×C13×ΓL(1,𝔽8)—143no—
22C2×C72×C13—51no—
23C4×C13×ΓL(1,𝔽8)—351no—
24C13×ΓL(1,𝔽8)⋊C4—351no—
25C7×C7⋊AGL(1,𝔽5)C3×C1311yescharacteristic, complemented, Hall
26C7×D5×C13—23no—
27C7×D5×C13AGL(1,𝔽7)11yescharacteristic
28C7×D5×C13C2×ΓL(1,𝔽8)11yescharacteristic
29C3×C13×AGL(1,𝔽5)—491noHall
30C5×#3861C4×C1311yescharacteristic, complemented, Hall
31C72×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
32#10596873—51noHall
33C2×C13×ΓL(1,𝔽8)—351no—
34C2×C13×ΓL(1,𝔽8)—351no—
35C2×C13×ΓL(1,𝔽8)—703no—
36C72×D5C2×C3×C1311yescharacteristic
37C5×C7×C13—23no—
38C5×C7×C13ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
39C5×C7×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
40ΓL(1,𝔽8)⋊AGL(1,𝔽5)—71no—
41AGL(1,𝔽5)×ΓL(1,𝔽8)—71no—
42C3×D5×C13—491no—
43C4×C7×C13—351no—
44C13×Dic7—51no—
45C2×#3861—51no—
46C13×ΓL(1,𝔽8)—71no—
47C13×ΓL(1,𝔽8)—71no—
48C13×ΓL(1,𝔽8)—143no—
49C13×AGL(1,𝔽5)—71noHall
50C5×C72C3×C4×C1311yescharacteristic, complemented, Hall
51D5×ΓL(1,𝔽8)—71no—
52D5×ΓL(1,𝔽8)—71no—
53D5×ΓL(1,𝔽8)—143no—
54C7×Dic7—51noHall
55C3×C5×C13—491noHall
56C2×C7×C13—51no—
57C2×C7×C13—51no—
58C2×C7×C13—103no—
59C3×C4×C13—2451noHall
60#3861C13×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
61C7⋊AGL(1,𝔽5)C13×ΓL(1,𝔽8)11yescharacteristic, complemented
62C7×AGL(1,𝔽5)—71no—
63D5×C13#6442311yescharacteristic
64C5×ΓL(1,𝔽8)—71no—
65C5×ΓL(1,𝔽8)—71no—
66C5×ΓL(1,𝔽8)—143no—
67C2×C72—51no—
68C7×C13—23no—
69C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, complemented
70C7×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
71C4×ΓL(1,𝔽8)—351no—
72ΓL(1,𝔽8)⋊C4—351no—
73C2×C3×C13—2451no—
74C7×D5—23no—
75C7×D5C13×AGL(1,𝔽7)11yescharacteristic
76C7×D5C2×C13×ΓL(1,𝔽8)11yescharacteristic
77C5×C13#1059687311yescharacteristic, complemented, Hall
78C3×AGL(1,𝔽5)—491noHall
79C4×C13—351noHall
80C72C3×C13×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
81C2×ΓL(1,𝔽8)—351no—
82C2×ΓL(1,𝔽8)—351no—
83C2×ΓL(1,𝔽8)—703no—
84C3×C13—491noHall
85C5×C7—23no—
86C5×C7C13×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
87C5×C7C4×C13×ΓL(1,𝔽8)11yescharacteristic, complemented
88C3×D5—491no—
89C4×C7—351no—
90Dic7—51no—
91C2×C13—51no—
92ΓL(1,𝔽8)—71no—
93ΓL(1,𝔽8)—71no—
94ΓL(1,𝔽8)—143no—
95AGL(1,𝔽5)—71noHall
96C3×C5—491noHall
97C2×C7—51no—
98C2×C7—51no—
99C2×C7—103no—
100C13#1566876711yescharacteristic, direct product factor, Sylow
101C3×C4—2451noHall
102D5C13×#6442311yescharacteristic
103C7—23no—
104C7C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)11yescharacteristic, complemented
105C7C13×AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, complemented
106C2×C3—2451no—
107C5C13×#1059687311yescharacteristic, complemented, Sylow
108C4—351noSylow
109C3—491noSylow
110C2—51no—
subgroupG/H
center, hypercenterC13#15668767
commutator, hypocenterC5×C72C3×C4×C13
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalD5×C13×#3861C2
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×#3861C4semidirect
9. C5×C72×C13C3×C4semidirect
10. #15668767C13direct (N × H)
15. C13×#3861AGL(1,𝔽5)semidirect
16. C13×C7⋊AGL(1,𝔽5)ΓL(1,𝔽8)semidirect
25. C7×C7⋊AGL(1,𝔽5)C3×C13semidirect
30. C5×#3861C4×C13semidirect
31. C72×C13C3×AGL(1,𝔽5)semidirect
38. C5×C7×C13ΓL(1,𝔽8)⋊C4semidirect
39. C5×C7×C13C4×ΓL(1,𝔽8)semidirect
50. C5×C72C3×C4×C13semidirect
60. #3861C13×AGL(1,𝔽5)semidirect
61. C7⋊AGL(1,𝔽5)C13×ΓL(1,𝔽8)semidirect
69. C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
70. C7×C13ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
77. C5×C13#10596873semidirect
80. C72C3×C13×AGL(1,𝔽5)semidirect
86. C5×C7C13×ΓL(1,𝔽8)⋊C4semidirect
87. C5×C7C4×C13×ΓL(1,𝔽8)semidirect
100. C13#15668767direct (N × H)
104. C7C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)semidirect
105. C7C13×AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
107. C5C13×#10596873semidirect

Maximal subgroups

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

subgroupindex
D5×C13×#38612
C7×C13×C7⋊AGL(1,𝔽5)3
C13×#105968735
C13×AGL(1,𝔽5)×ΓL(1,𝔽8)7
C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5)7
#1566876713