Finite Group Databasebeta

← C2×D65×#3861 #50304307

Subgroups — C2×D65×#3861 #50304307

Order 38220.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C13×#3861C211yesmaximal, characteristic, complemented
2D65×#3861C212yesmaximal, direct product factor
3C2×C72×D65C311yesmaximal, characteristic, complemented, Hall
4C5×C13×#3861C2211yescharacteristic, complemented, Hall
5C2×D13×#3861—51nomaximal, Hall
6C72×D65C2×C312yescomplemented
7C2×C5×C72×C13C2×C311yescharacteristic, complemented
8C2×ΓL(1,𝔽8)×D65—78nomaximal
9C2×C13×#3861D511yescharacteristic, complemented
10D13×#3861—52no—
11C5×C72×C13C22×C311yescharacteristic, complemented, Hall
12C2×D5×#3861—131nomaximal, Hall
13ΓL(1,𝔽8)×D65—716no—
14C2×C5×C13×ΓL(1,𝔽8)—78no—
15C2×C72×D13—51noHall
16C13×#3861C2×D511yescharacteristic, complemented, Hall
17C2×C7×D65ΓL(1,𝔽8)18yescomplemented
18C2×C5×#3861D1311yescharacteristic, complemented
19D5×#3861—132no—
20C5×C13×ΓL(1,𝔽8)—78no—
21C2×C72×C13C3×D511yescharacteristic, complemented
22C72×D13—52no—
23C2×ΓL(1,𝔽8)×D13—358no—
24C2×C72×D5—131noHall
25C2×C5×C7×C13C2×ΓL(1,𝔽8)18yescomplemented
26C7×D65C2×ΓL(1,𝔽8)116yescomplemented
27C2×C3×D65—491noHall
28C5×#3861C2×D1311yescharacteristic, complemented, Hall
29C72×C13C2×C3×D511yescharacteristic, complemented, Hall
30C22×#3861—651noHall
31C2×C13×ΓL(1,𝔽8)—78no—
32ΓL(1,𝔽8)×D13—3516no—
33C2×C5×C72C3×D1311yescharacteristic, complemented
34C72×D5—132no—
35C5×C7×C13C22×ΓL(1,𝔽8)18yescomplemented
36C2×D5×ΓL(1,𝔽8)—918no—
37C2×C3×C5×C13—491no—
38C3×D65—492no—
39C2×C7×D13—58no—
40C2×#3861—652no—
41C2×#3861D6511yescharacteristic, direct product factor
42C13×ΓL(1,𝔽8)—78no—
43C2×D65#386111yescharacteristic, direct product factor, Hall
44C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
45C2×C5×ΓL(1,𝔽8)—78no—
46D5×ΓL(1,𝔽8)—9116no—
47C22×C72—651noHall
48C3×C5×C13—491noHall
49C2×C7×C13D5×ΓL(1,𝔽8)18yescomplemented
50C7×D13—516no—
51C2×C3×D13—2451noHall
52#3861C2×D6511yescharacteristic, direct product factor, Hall
53C2×C7×D5—138no—
54C2×C5×C13C2×#386111yescharacteristic, complemented
55D65C2×#386112yesdirect product factor
56C5×ΓL(1,𝔽8)—78no—
57C2×C72—652no—
58C2×C72C3×D6511yescharacteristic, complemented
59C7×C13C2×D5×ΓL(1,𝔽8)18yescomplemented
60C22×ΓL(1,𝔽8)—4558no—
61C2×C3×C13—491no—
62C3×D13—2452no—
63C2×C5×C7ΓL(1,𝔽8)×D1318yescomplemented
64C7×D5—1316no—
65C5×C13C22×#386111yescharacteristic, complemented, Hall
66C2×C3×D5—6371noHall
67C2×D13—51noHall
68C72C2×C3×D6511yescharacteristic, complemented, Sylow
69C2×ΓL(1,𝔽8)—78no—
70C2×ΓL(1,𝔽8)—45516no—
71C3×C13—491noHall
72C5×C7C2×ΓL(1,𝔽8)×D1318yescomplemented
73C2×C3×C5—491no—
74C3×D5—6372no—
75C22×C7—658no—
76C2×C13D5×#386111yescharacteristic, complemented
77D13—52no—
78ΓL(1,𝔽8)—78no—
79C2×D5—131noHall
80C3×C5—491noHall
81C2×C7—6516no—
82C2×C7ΓL(1,𝔽8)×D6518yescomplemented
83C13C2×D5×#386111yescharacteristic, complemented, Sylow
84C22×C3—31851noHall
85C2×C5D13×#386111yescharacteristic, complemented
86D5—132no—
87C7C2×ΓL(1,𝔽8)×D6518yescomplemented
88C2×C3—491no—
89C2×C3—31852no—
90C5C2×D13×#386111yescharacteristic, complemented, Sylow
91C22—651noSylow
92C3—491noSylow
93C2—652no—
94C2D65×#386111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D65×#3861
commutator, cosocle, hypocenterC5×C72×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C72×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C5×C13×#3861C2semidirect
2. D65×#3861C2direct (N × H)
3. C2×C72×D65C3semidirect
4. C5×C13×#3861C22semidirect
6. C72×D65C2×C3semidirect
7. C2×C5×C72×C13C2×C3semidirect
9. C2×C13×#3861D5semidirect
11. C5×C72×C13C22×C3semidirect
16. C13×#3861C2×D5semidirect
17. C2×C7×D65ΓL(1,𝔽8)semidirect
18. C2×C5×#3861D13semidirect
21. C2×C72×C13C3×D5semidirect
25. C2×C5×C7×C13C2×ΓL(1,𝔽8)semidirect
26. C7×D65C2×ΓL(1,𝔽8)semidirect
28. C5×#3861C2×D13semidirect
29. C72×C13C2×C3×D5semidirect
33. C2×C5×C72C3×D13semidirect
35. C5×C7×C13C22×ΓL(1,𝔽8)semidirect
41. C2×#3861D65direct (N × H)
43. C2×D65#3861direct (N × H)
44. C5×C72C2×C3×D13semidirect
49. C2×C7×C13D5×ΓL(1,𝔽8)semidirect
52. #3861C2×D65direct (N × H)
54. C2×C5×C13C2×#3861semidirect
55. D65C2×#3861direct (N × H)
58. C2×C72C3×D65semidirect
59. C7×C13C2×D5×ΓL(1,𝔽8)semidirect
63. C2×C5×C7ΓL(1,𝔽8)×D13semidirect
65. C5×C13C22×#3861semidirect
68. C72C2×C3×D65semidirect
72. C5×C7C2×ΓL(1,𝔽8)×D13semidirect
76. C2×C13D5×#3861semidirect
82. C2×C7ΓL(1,𝔽8)×D65semidirect
83. C13C2×D5×#3861semidirect
85. C2×C5D13×#3861semidirect
87. C7C2×ΓL(1,𝔽8)×D65semidirect
90. C5C2×D13×#3861semidirect
94. C2D65×#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C13×#38612
D65×#38612
C2×C72×D653
C2×D13×#38615
C2×ΓL(1,𝔽8)×D657
C2×D5×#386113