Finite Group Databasebeta

← #50304111

Subgroups — #50304111

Order 38220.

400 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 65 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
1D65×#3861C211yesmaximal, characteristic, complemented
2C13×C5⋊#64424C211yesmaximal, characteristic, complemented
3C5×#16838450C211yesmaximal, characteristic, complemented
4D65⋊(C7⋊D7)C311yesmaximal, characteristic, complemented, Hall
5C5×C13×#3861C2211yescharacteristic, complemented, Hall
6D13×#64424—51nomaximal, Hall
7C13×C5⋊(C7⋊D7)C2×C311yescharacteristic, complemented
8C72×D65C2×C311yescharacteristic, complemented
9C5×C7⋊D91C2×C311yescharacteristic, complemented
10(C5⋊AGL(1,𝔽7))⋊D13—78nomaximal
11D13×#3861—51no—
12#16838450D511yescharacteristic, complemented
13C13×#64424—51no—
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15D5×#64424—131nomaximal, Hall
16C13×C5⋊AGL(1,𝔽7)—78no—
17ΓL(1,𝔽8)×D65—78no—
18C5×ΓL(1,𝔽8)⋊D13—78no—
19D13×C7⋊D7—51noHall
20C13×#3861C2×D511yescharacteristic, complemented, Hall
21D35⋊D13—78no—
22D5×#3861—131no—
23C5⋊#64424D1311yescharacteristic, complemented
24C5×#64424—131no—
25C5×C13×ΓL(1,𝔽8)—78no—
26C7⋊D91C3×D511yescharacteristic, complemented
27C13×C7⋊D7—51no—
28C72×D13—51no—
29D13×AGL(1,𝔽7)—358no—
30D5×C7⋊D7—131noHall
31C13×D35—78no—
32C7×D65AGL(1,𝔽7)18yescomplemented
33C5×D91—78no—
34C3×D5×D13—491noHall
35C5×#3861C2×D1311yescharacteristic, complemented, Hall
36C72×C13C2×C3×D511yescharacteristic, complemented, Hall
37C2×#64424—651noHall
38ΓL(1,𝔽8)⋊D13—78no—
39C13×AGL(1,𝔽7)—358no—
40ΓL(1,𝔽8)×D13—358no—
41C5⋊(C7⋊D7)C3×D1311yescharacteristic, complemented
42C72×D5—131no—
43C5×C7⋊D7—131no—
44C5×C7×C13C2×AGL(1,𝔽7)18yescomplemented
45D5×AGL(1,𝔽7)—918no—
46C3×D65—491no—
47C3×D5×C13—491no—
48C3×C5×D13—491no—
49D7×D13—358no—
50C2×#3861—651no—
51#64424—51no—
52#64424—131no—
53C13×ΓL(1,𝔽8)—78no—
54D5×D13—491noHall
55C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
56C5⋊AGL(1,𝔽7)—78no—
57D5×ΓL(1,𝔽8)—918no—
58C5×AGL(1,𝔽7)—918no—
59C2×C7⋊D7—651noHall
60C3×C5×C13—491noHall
61D91—78no—
62C7×D13—58no—
63C13×D7—358no—
64C2×C3×D13—2451noHall
65#3861D5×D1311yescharacteristic, complemented, Hall
66D5×D7—918no—
67D65#6442411yescharacteristic, complemented
68C5×D13—491no—
69D5×C13—491no—
70C5×ΓL(1,𝔽8)—78no—
71C2×C72—651no—
72C7⋊D7—51no—
73C7⋊D7—131no—
74C7×C13D5×AGL(1,𝔽7)18yescomplemented
75C2×AGL(1,𝔽7)—4558no—
76C2×C3×C13—2451no—
77C3×D13—491no—
78C3×D13—2451no—
79D35—78no—
80C5×D7—918no—
81C7×D5—138no—
82C5×C13C2×#6442411yescharacteristic, complemented, Hall
83C2×C3×D5—6371noHall
84C2×D13—2451noHall
85C72C3×D5×D1311yescharacteristic, complemented, Sylow
86C2×ΓL(1,𝔽8)—4558no—
87AGL(1,𝔽7)—358no—
88AGL(1,𝔽7)—918no—
89C3×C13—491noHall
90C5×C7D13×AGL(1,𝔽7)18yescomplemented
91C2×C3×C5—6371no—
92C3×D5—491no—
93C3×D5—6371no—
94C2×D7—4558no—
95C2×C13—2451no—
96D13—51no—
97D13—491no—
98ΓL(1,𝔽8)—78no—
99C2×D5—6371noHall
100C3×C5—491noHall
101C2×C7—658no—
102D7—358no—
103D7—918no—
104C13D5×#6442411yescharacteristic, complemented, Sylow
105C22×C3—31851noHall
106C2×C5—6371no—
107D5—131no—
108D5—491no—
109C7(C5⋊AGL(1,𝔽7))⋊D1318yescomplemented
110C2×C3—31851no—
111C2×C3—6371no—
112C2×C3—2451no—
113C5D13×#6442411yescharacteristic, complemented, Sylow
114C22—31851noSylow
115C3—491noSylow
116C2—651no—
117C2—6371no—
118C2—2451no—
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. D65×#3861C2semidirect
2. C13×C5⋊#64424C2semidirect
3. C5×#16838450C2semidirect
4. D65⋊(C7⋊D7)C3semidirect
5. C5×C13×#3861C22semidirect
7. C13×C5⋊(C7⋊D7)C2×C3semidirect
8. C72×D65C2×C3semidirect
9. C5×C7⋊D91C2×C3semidirect
12. #16838450D5semidirect
14. C5×C72×C13C22×C3semidirect
20. C13×#3861C2×D5semidirect
23. C5⋊#64424D13semidirect
26. C7⋊D91C3×D5semidirect
32. C7×D65AGL(1,𝔽7)semidirect
35. C5×#3861C2×D13semidirect
36. C72×C13C2×C3×D5semidirect
41. C5⋊(C7⋊D7)C3×D13semidirect
44. C5×C7×C13C2×AGL(1,𝔽7)semidirect
55. C5×C72C2×C3×D13semidirect
65. #3861D5×D13semidirect
67. D65#64424semidirect
74. C7×C13D5×AGL(1,𝔽7)semidirect
82. C5×C13C2×#64424semidirect
85. C72C3×D5×D13semidirect
90. C5×C7D13×AGL(1,𝔽7)semidirect
104. C13D5×#64424semidirect
109. C7(C5⋊AGL(1,𝔽7))⋊D13semidirect
113. C5D13×#64424semidirect

Maximal subgroups

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

subgroupindex
D65×#38612
C13×C5⋊#644242
C5×#168384502
D65⋊(C7⋊D7)3
D13×#644245
(C5⋊AGL(1,𝔽7))⋊D137
D5×#6442413