Finite Group Databasebeta

← C13×#64424⋊D5 #50304149

Subgroups — C13×#64424⋊D5 #50304149

Order 38220.

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

normal subgroups only

This group has 208 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⋊#64423C212yesmaximal, complemented
2C5×C13×#64424C211yesmaximal, characteristic, complemented
3C13×D35⋊D7C311yesmaximal, characteristic, complemented, Hall
4C5×C13×#3861C2211yescharacteristic, complemented, Hall
5C13×#64423⋊C2—51nomaximal, Hall
6C7×C13×D35C2×C312yescomplemented
7C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
8D5×C13×AGL(1,𝔽7)—72nomaximal
9C13×#64423—52no—
10C13×#64424D511yescharacteristic, complemented
11C5×C72×C13C22×C311yescharacteristic, complemented, Hall
12#64424⋊D5C1311yesmaximal, characteristic, direct product factor, Hall
13C13×C5⋊AGL(1,𝔽7)—72no—
14D5×C13×ΓL(1,𝔽8)—72no—
15C5×C13×AGL(1,𝔽7)—72no—
16C5×C13×AGL(1,𝔽7)—143no—
17C13×D72—51noHall
18C13×#3861C2×D511yescharacteristic, complemented, Hall
19D5×C13×D7—72no—
20C5⋊#64423C2×C1312yescomplemented
21C5×#64424C2×C1311yescharacteristic, complemented
22C5×C13×ΓL(1,𝔽8)—72no—
23C5×C13×ΓL(1,𝔽8)—143no—
24C13×C7⋊D7C3×D511yescharacteristic, complemented
25C7×C13×D7—52no—
26C2×C13×AGL(1,𝔽7)—352no—
27D35⋊D7C3×C1311yescharacteristic, complemented, Hall
28C13×D35AGL(1,𝔽7)12yescomplemented
29C7×D5×C13—72no—
30C5×C13×D7—72no—
31C5×C13×D7—143no—
32C2×C3×D5×C13—491noHall
33C5×#3861C22×C1311yescharacteristic, complemented, Hall
34C72×C13C2×C3×D511yescharacteristic, complemented, Hall
35#64423⋊C2—51noHall
36C2×C13×ΓL(1,𝔽8)—352no—
37C13×AGL(1,𝔽7)—72no—
38C13×AGL(1,𝔽7)—143no—
39C13×AGL(1,𝔽7)—352no—
40C7×D35C2×C3×C1312yescomplemented
41C5×C7⋊D7C2×C3×C1311yescharacteristic, complemented
42C5×C7×C13—23no—
43C5×C7×C13C2×AGL(1,𝔽7)12yescomplemented
44D5×AGL(1,𝔽7)—72no—
45C2×C3×C5×C13—491no—
46C3×D5×C13—492no—
47C2×C13×D7—352no—
48#64424D5×C1311yescharacteristic, complemented
49#64423—52no—
50C13×ΓL(1,𝔽8)—72no—
51C13×ΓL(1,𝔽8)—143no—
52C2×D5×C13—491noHall
53C5×C72C22×C3×C1311yescharacteristic, complemented, Hall
54C5⋊AGL(1,𝔽7)—72no—
55D5×ΓL(1,𝔽8)—72no—
56C5×AGL(1,𝔽7)—72no—
57C5×AGL(1,𝔽7)—143no—
58D72—51noHall
59C3×C5×C13—491noHall
60C2×C7×C13—352no—
61C13×D7—52no—
62C13×D7—72no—
63C13×D7—143no—
64C22×C3×C13—2451noHall
65#3861C2×D5×C1311yescharacteristic, complemented, Hall
66D5×D7—72no—
67C2×C5×C13—491no—
68D5×C13—72no—
69C5×ΓL(1,𝔽8)—72no—
70C5×ΓL(1,𝔽8)—143no—
71C7⋊D7C3×D5×C1311yescharacteristic, complemented
72C7×D7—52no—
73C7×C13—23no—
74C7×C13D5×AGL(1,𝔽7)12yescomplemented
75C2×AGL(1,𝔽7)—352no—
76C2×C3×C13—491no—
77C2×C3×C13—2452no—
78D35C13×AGL(1,𝔽7)12yescomplemented
79C5×D7—72no—
80C5×D7—143no—
81C7×D5—72no—
82C5×C13#64423⋊C211yescharacteristic, complemented, Hall
83C2×C3×D5—491noHall
84C22×C13—2451noHall
85C72C2×C3×D5×C1311yescharacteristic, complemented, Sylow
86C2×ΓL(1,𝔽8)—352no—
87AGL(1,𝔽7)—72no—
88AGL(1,𝔽7)—143no—
89AGL(1,𝔽7)—352no—
90C3×C13—491noHall
91C5×C7—23no—
92C5×C7C2×C13×AGL(1,𝔽7)12yescomplemented
93C2×C3×C5—491no—
94C3×D5—492no—
95C2×D7—352no—
96C2×C13—352no—
97C2×C13—491no—
98ΓL(1,𝔽8)—72no—
99ΓL(1,𝔽8)—143no—
100C2×D5—491noHall
101C3×C5—491noHall
102C2×C7—352no—
103D7—52no—
104D7—72no—
105D7—143no—
106C13#64424⋊D511yescharacteristic, direct product factor, Sylow
107C22×C3—2451noHall
108C2×C5—491no—
109D5—72no—
110C7—23no—
111C7D5×C13×AGL(1,𝔽7)12yescomplemented
112C2×C3—491no—
113C2×C3—2452no—
114C5C13×#64423⋊C211yescharacteristic, complemented, Sylow
115C22—2451noSylow
116C3—491noSylow
117C2—352no—
118C2—491no—
subgroupG/H
center, hypercenterC13#64424⋊D5
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⋊#64423C2semidirect
2. C5×C13×#64424C2semidirect
3. C13×D35⋊D7C3semidirect
4. C5×C13×#3861C22semidirect
6. C7×C13×D35C2×C3semidirect
7. C5×C13×C7⋊D7C2×C3semidirect
10. C13×#64424D5semidirect
11. C5×C72×C13C22×C3semidirect
12. #64424⋊D5C13direct (N × H)
18. C13×#3861C2×D5semidirect
20. C5⋊#64423C2×C13semidirect
21. C5×#64424C2×C13semidirect
24. C13×C7⋊D7C3×D5semidirect
27. D35⋊D7C3×C13semidirect
28. C13×D35AGL(1,𝔽7)semidirect
33. C5×#3861C22×C13semidirect
34. C72×C13C2×C3×D5semidirect
40. C7×D35C2×C3×C13semidirect
41. C5×C7⋊D7C2×C3×C13semidirect
43. C5×C7×C13C2×AGL(1,𝔽7)semidirect
48. #64424D5×C13semidirect
53. C5×C72C22×C3×C13semidirect
65. #3861C2×D5×C13semidirect
71. C7⋊D7C3×D5×C13semidirect
74. C7×C13D5×AGL(1,𝔽7)semidirect
78. D35C13×AGL(1,𝔽7)semidirect
82. C5×C13#64423⋊C2semidirect
85. C72C2×C3×D5×C13semidirect
92. C5×C7C2×C13×AGL(1,𝔽7)semidirect
106. C13#64424⋊D5direct (N × H)
111. C7D5×C13×AGL(1,𝔽7)semidirect
114. C5C13×#64423⋊C2semidirect

Maximal subgroups

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

subgroupindex
C13×C5⋊#644232
C5×C13×#644242
C13×D35⋊D73
C13×#64423⋊C25
D5×C13×AGL(1,𝔽7)7
#64424⋊D513