Finite Group Databasebeta

← C13×#15668782 #50304188

Subgroups — C13×#15668782 #50304188

Order 38220.

168 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C13×C5⋊#64422C212yesmaximal, complemented
2C5×C13×#64425C211yesmaximal, characteristic, complemented
3C13×D35⋊D7C311yesmaximal, characteristic, complemented, Hall
4C5×C13×#3862C2211yescharacteristic, complemented, Hall
5C13×#64422⋊C2—51nomaximal, Hall
6C7×C13×D35C2×C312yescomplemented
7C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
8D5×C13×AGL(1,𝔽7)—72nomaximal
9C13×#64422—52no—
10C13×#64425D511yescharacteristic, complemented
11C5×C72×C13C22×C311yescharacteristic, complemented, Hall
12#15668782C1311yesmaximal, characteristic, direct product factor, Hall
13C13×C5⋊AGL(1,𝔽7)—72no—
14D5×C13×ΓL(1,𝔽8)—72no—
15C5×C13×AGL(1,𝔽7)—72no—
16C13×D72—51noHall
17C13×#3862C2×D511yescharacteristic, complemented, Hall
18D5×C13×D7—72no—
19C5⋊#64422C2×C1312yescomplemented
20C5×#64425C2×C1311yescharacteristic, complemented
21C5×C13×ΓL(1,𝔽8)—72no—
22C13×C7⋊D7C3×D511yescharacteristic, complemented
23C7×C13×D7—52no—
24C2×C13×AGL(1,𝔽7)—352no—
25D35⋊D7C3×C1311yescharacteristic, complemented, Hall
26C13×D35AGL(1,𝔽7)12yescomplemented
27C7×D5×C13—72no—
28C5×C13×D7—72no—
29C5×C13×D7—421no—
30C2×C3×D5×C13—491noHall
31C5×#3862C22×C1311yescharacteristic, complemented, Hall
32C72×C13C2×C3×D511yescharacteristic, complemented, Hall
33#64422⋊C2—51noHall
34C2×C13×ΓL(1,𝔽8)—352no—
35C13×AGL(1,𝔽7)—72no—
36C13×AGL(1,𝔽7)—352no—
37C7×D35C2×C3×C1312yescomplemented
38C5×C7⋊D7C2×C3×C1311yescharacteristic, complemented
39C5×C7×C13—61no—
40C5×C7×C13C2×AGL(1,𝔽7)12yescomplemented
41D5×AGL(1,𝔽7)—72no—
42C2×C3×C5×C13—491no—
43C3×D5×C13—492no—
44C2×C13×D7—352no—
45#64425D5×C1311yescharacteristic, complemented
46#64422—52no—
47C13×ΓL(1,𝔽8)—72no—
48C2×D5×C13—491noHall
49C5×C72C22×C3×C1311yescharacteristic, complemented, Hall
50C5⋊AGL(1,𝔽7)—72no—
51D5×ΓL(1,𝔽8)—72no—
52C5×AGL(1,𝔽7)—72no—
53D72—51noHall
54C3×C5×C13—491noHall
55C2×C7×C13—352no—
56C13×D7—52no—
57C13×D7—72no—
58C13×D7—421no—
59C22×C3×C13—2451noHall
60#3862C2×D5×C1311yescharacteristic, complemented, Hall
61D5×D7—72no—
62C2×C5×C13—491no—
63D5×C13—72no—
64C5×ΓL(1,𝔽8)—72no—
65C7⋊D7C3×D5×C1311yescharacteristic, complemented
66C7×D7—52no—
67C7×C13—61no—
68C7×C13D5×AGL(1,𝔽7)12yescomplemented
69C2×AGL(1,𝔽7)—352no—
70C2×C3×C13—491no—
71C2×C3×C13—2452no—
72D35C13×AGL(1,𝔽7)12yescomplemented
73C5×D7—72no—
74C5×D7—421no—
75C7×D5—72no—
76C5×C13#64422⋊C211yescharacteristic, complemented, Hall
77C2×C3×D5—491noHall
78C22×C13—2451noHall
79C72C2×C3×D5×C1311yescharacteristic, complemented, Sylow
80C2×ΓL(1,𝔽8)—352no—
81AGL(1,𝔽7)—72no—
82AGL(1,𝔽7)—352no—
83C3×C13—491noHall
84C5×C7—61no—
85C5×C7C2×C13×AGL(1,𝔽7)12yescomplemented
86C2×C3×C5—491no—
87C3×D5—492no—
88C2×D7—352no—
89C2×C13—352no—
90C2×C13—491no—
91ΓL(1,𝔽8)—72no—
92C2×D5—491noHall
93C3×C5—491noHall
94C2×C7—352no—
95D7—52no—
96D7—72no—
97D7—421no—
98C13#1566878211yescharacteristic, direct product factor, Sylow
99C22×C3—2451noHall
100C2×C5—491no—
101D5—72no—
102C7—61no—
103C7D5×C13×AGL(1,𝔽7)12yescomplemented
104C2×C3—491no—
105C2×C3—2452no—
106C5C13×#64422⋊C211yescharacteristic, complemented, Sylow
107C22—2451noSylow
108C3—491noSylow
109C2—352no—
110C2—491no—
subgroupG/H
center, hypercenterC13#15668782
commutator, cosocle, hypocenterC5×C72C22×C3×C13
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C5×C72
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C13×C5⋊#64422C2semidirect
2. C5×C13×#64425C2semidirect
3. C13×D35⋊D7C3semidirect
4. C5×C13×#3862C22semidirect
6. C7×C13×D35C2×C3semidirect
7. C5×C13×C7⋊D7C2×C3semidirect
10. C13×#64425D5semidirect
11. C5×C72×C13C22×C3semidirect
12. #15668782C13direct (N × H)
17. C13×#3862C2×D5semidirect
19. C5⋊#64422C2×C13semidirect
20. C5×#64425C2×C13semidirect
22. C13×C7⋊D7C3×D5semidirect
25. D35⋊D7C3×C13semidirect
26. C13×D35AGL(1,𝔽7)semidirect
31. C5×#3862C22×C13semidirect
32. C72×C13C2×C3×D5semidirect
37. C7×D35C2×C3×C13semidirect
38. C5×C7⋊D7C2×C3×C13semidirect
40. C5×C7×C13C2×AGL(1,𝔽7)semidirect
45. #64425D5×C13semidirect
49. C5×C72C22×C3×C13semidirect
60. #3862C2×D5×C13semidirect
65. C7⋊D7C3×D5×C13semidirect
68. C7×C13D5×AGL(1,𝔽7)semidirect
72. D35C13×AGL(1,𝔽7)semidirect
76. C5×C13#64422⋊C2semidirect
79. C72C2×C3×D5×C13semidirect
85. C5×C7C2×C13×AGL(1,𝔽7)semidirect
98. C13#15668782direct (N × H)
103. C7D5×C13×AGL(1,𝔽7)semidirect
106. C5C13×#64422⋊C2semidirect

Maximal subgroups

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

subgroupindex
C13×C5⋊#644222
C5×C13×#644252
C13×D35⋊D73
C13×#64422⋊C25
D5×C13×AGL(1,𝔽7)7
#1566878213