Finite Group Databasebeta

← #50304193

Subgroups — #50304193

Order 38220.

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

normal subgroups only

This group has 168 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
1C5⋊#16838466C212yesmaximal, complemented
2C5×C13×#64425C211yesmaximal, characteristic, complemented
3(C7⋊D7)⋊D65C311yesmaximal, characteristic, complemented, Hall
4C5×C13×#3862C2211yescharacteristic, complemented, Hall
5#21439622—51nomaximal, Hall
6C7×D455C2×C312yescomplemented
7C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
8AGL(1,𝔽7)×D65—72nomaximal
9#16838466—52no—
10C13×#64425D511yescharacteristic, complemented
11C5×C72×C13C22×C311yescharacteristic, complemented, Hall
12#15668782—131nomaximal, Hall
13C5⋊(ΓL(1,𝔽8)⋊D13)—72no—
14ΓL(1,𝔽8)×D65—72no—
15C5×C13×AGL(1,𝔽7)—72no—
16(C7⋊D7)⋊D13—51noHall
17C13×#3862C2×D511yescharacteristic, complemented, Hall
18D7×D65—72no—
19C5⋊#64422—132no—
20C5×#64425D1311yescharacteristic, complemented
21C5×C13×ΓL(1,𝔽8)—72no—
22C13×C7⋊D7C3×D511yescharacteristic, complemented
23C7×D91—52no—
24D13×AGL(1,𝔽7)—352no—
25D35⋊D7—131noHall
26D455AGL(1,𝔽7)12yescomplemented
27C7×D65—72no—
28C5×C13×D7—72no—
29C5×C13×D7—421no—
30C2×C3×D65—491noHall
31C5×#3862C2×D1311yescharacteristic, complemented, Hall
32C72×C13C2×C3×D511yescharacteristic, complemented, Hall
33#64422⋊C2—651noHall
34ΓL(1,𝔽8)⋊D13—352no—
35C13×AGL(1,𝔽7)—72no—
36ΓL(1,𝔽8)×D13—352no—
37C7×D35—132no—
38C5×C7⋊D7C3×D1311yescharacteristic, complemented
39C5×C7×C13—61no—
40C5×C7×C13C2×AGL(1,𝔽7)12yescomplemented
41D5×AGL(1,𝔽7)—912no—
42C2×C3×C5×C13—491no—
43C3×D65—492no—
44D7×D13—352no—
45#64425D6511yescharacteristic, complemented
46#64422—652no—
47C13×ΓL(1,𝔽8)—72no—
48C2×D65—491noHall
49C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
50C5⋊AGL(1,𝔽7)—912no—
51D5×ΓL(1,𝔽8)—912no—
52C5×AGL(1,𝔽7)—72no—
53D72—651noHall
54C3×C5×C13—491noHall
55D91—52no—
56C7×D13—352no—
57C13×D7—72no—
58C13×D7—421no—
59C2×C3×D13—2451noHall
60#3862C2×D6511yescharacteristic, complemented, Hall
61D5×D7—912no—
62C2×C5×C13—491no—
63D65—72no—
64C5×ΓL(1,𝔽8)—72no—
65C7⋊D7C3×D6511yescharacteristic, complemented
66C7×D7—652no—
67C7×C13—61no—
68C7×C13D5×AGL(1,𝔽7)12yescomplemented
69C2×AGL(1,𝔽7)—4552no—
70C2×C3×C13—491no—
71C3×D13—2452no—
72D35—132no—
73C5×D7—72no—
74C5×D7—421no—
75C7×D5—912no—
76C5×C13#64422⋊C211yescharacteristic, complemented, Hall
77C2×C3×D5—6371noHall
78C2×D13—2451noHall
79C72C2×C3×D6511yescharacteristic, complemented, Sylow
80C2×ΓL(1,𝔽8)—4552no—
81AGL(1,𝔽7)—72no—
82AGL(1,𝔽7)—4552no—
83C3×C13—491noHall
84C5×C7—61no—
85C5×C7D13×AGL(1,𝔽7)12yescomplemented
86C2×C3×C5—491no—
87C3×D5—6372no—
88C2×D7—4552no—
89C2×C13—491no—
90D13—352no—
91ΓL(1,𝔽8)—72no—
92C2×D5—6371noHall
93C3×C5—491noHall
94C2×C7—4552no—
95D7—72no—
96D7—421no—
97D7—652no—
98C13#1566878211yescharacteristic, complemented, Sylow
99C22×C3—31851noHall
100C2×C5—491no—
101D5—912no—
102C7—61no—
103C7AGL(1,𝔽7)×D6512yescomplemented
104C2×C3—491no—
105C2×C3—31852no—
106C5#2143962211yescharacteristic, complemented, Sylow
107C22—31851noSylow
108C3—491noSylow
109C2—491no—
110C2—4552no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C13C22×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5⋊#16838466C2semidirect
2. C5×C13×#64425C2semidirect
3. (C7⋊D7)⋊D65C3semidirect
4. C5×C13×#3862C22semidirect
6. C7×D455C2×C3semidirect
7. C5×C13×C7⋊D7C2×C3semidirect
10. C13×#64425D5semidirect
11. C5×C72×C13C22×C3semidirect
17. C13×#3862C2×D5semidirect
20. C5×#64425D13semidirect
22. C13×C7⋊D7C3×D5semidirect
26. D455AGL(1,𝔽7)semidirect
31. C5×#3862C2×D13semidirect
32. C72×C13C2×C3×D5semidirect
38. C5×C7⋊D7C3×D13semidirect
40. C5×C7×C13C2×AGL(1,𝔽7)semidirect
45. #64425D65semidirect
49. C5×C72C2×C3×D13semidirect
60. #3862C2×D65semidirect
65. C7⋊D7C3×D65semidirect
68. C7×C13D5×AGL(1,𝔽7)semidirect
76. C5×C13#64422⋊C2semidirect
79. C72C2×C3×D65semidirect
85. C5×C7D13×AGL(1,𝔽7)semidirect
98. C13#15668782semidirect
103. C7AGL(1,𝔽7)×D65semidirect
106. C5#21439622semidirect

Maximal subgroups

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

subgroupindex
C5⋊#168384662
C5×C13×#644252
(C7⋊D7)⋊D653
#214396225
AGL(1,𝔽7)×D657
#1566878213