Finite Group Databasebeta

← C2×C5⋊#16838450 #50304313

Subgroups — C2×C5⋊#16838450 #50304313

Order 38220.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C13×#3861C211yesmaximal, characteristic, complemented
2C5⋊#16838450C212yesmaximal, direct product factor
3C2×C5⋊(C7⋊D91)C311yesmaximal, characteristic, complemented, Hall
4C5×C13×#3861C2211yescharacteristic, complemented, Hall
5C2×#16838450—51nomaximal, Hall
6C5⋊(C7⋊D91)C2×C312yescomplemented
7C2×C5×C72×C13C2×C311yescharacteristic, complemented
8C2×C5⋊(ΓL(1,𝔽8)⋊D13)—78nomaximal
9C2×C13×#3861D511yescharacteristic, complemented
10#16838450—52no—
11C5×C72×C13C22×C311yescharacteristic, complemented, Hall
12C2×C5⋊#64424—131nomaximal, Hall
13C5⋊(ΓL(1,𝔽8)⋊D13)—716no—
14C2×C5×C13×ΓL(1,𝔽8)—78no—
15C2×C7⋊D91—51noHall
16C13×#3861C2×D511yescharacteristic, complemented, Hall
17C2×D455—78no—
18C2×C5×#3861D1311yescharacteristic, complemented
19C5⋊#64424—132no—
20C5×C13×ΓL(1,𝔽8)—78no—
21C2×C72×C13C3×D511yescharacteristic, complemented
22C7⋊D91—52no—
23C2×ΓL(1,𝔽8)⋊D13—358no—
24C2×C5⋊(C7⋊D7)—131noHall
25C2×C5×C7×C13AGL(1,𝔽7)18yescomplemented
26D455—716no—
27C2×C3×D65—491noHall
28C5×#3861C2×D1311yescharacteristic, complemented, Hall
29C72×C13C2×C3×D511yescharacteristic, complemented, Hall
30C2×#64424—651noHall
31C2×C13×ΓL(1,𝔽8)—78no—
32ΓL(1,𝔽8)⋊D13—3516no—
33C2×C5×C72C3×D1311yescharacteristic, complemented
34C5⋊(C7⋊D7)—132no—
35C5×C7×C13C2×AGL(1,𝔽7)18yescomplemented
36C2×C5⋊AGL(1,𝔽7)—918no—
37C2×C3×C5×C13—491no—
38C3×D65—492no—
39C2×D91—358no—
40C2×#3861D6511yescharacteristic, complemented
41#64424—652no—
42C13×ΓL(1,𝔽8)—78no—
43C2×D65—491noHall
44C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
45C2×C5×ΓL(1,𝔽8)—78no—
46C5⋊AGL(1,𝔽7)—9116no—
47C2×C7⋊D7—651noHall
48C3×C5×C13—491noHall
49C2×C7×C13C5⋊AGL(1,𝔽7)18yescomplemented
50D91—3516no—
51C2×C3×D13—2451noHall
52#3861C2×D6511yescharacteristic, complemented, Hall
53C2×D35—918no—
54C2×C5×C13#6442411yescharacteristic, complemented
55D65—492no—
56C5×ΓL(1,𝔽8)—78no—
57C2×C72C3×D6511yescharacteristic, complemented
58C7⋊D7—652no—
59C7×C13C2×C5⋊AGL(1,𝔽7)18yescomplemented
60C2×AGL(1,𝔽7)—4558no—
61C2×C3×C13—491no—
62C3×D13—2452no—
63C2×C5×C7ΓL(1,𝔽8)⋊D1318yescomplemented
64D35—9116no—
65C5×C13C2×#6442411yescharacteristic, complemented, Hall
66C2×C3×D5—6371noHall
67C2×D13—2451noHall
68C72C2×C3×D6511yescharacteristic, complemented, Sylow
69C2×ΓL(1,𝔽8)—78no—
70AGL(1,𝔽7)—45516no—
71C3×C13—491noHall
72C5×C7C2×ΓL(1,𝔽8)⋊D1318yescomplemented
73C2×C3×C5—491no—
74C3×D5—6372no—
75C2×D7—4558no—
76C2×C13C5⋊#6442411yescharacteristic, complemented
77D13—2452no—
78ΓL(1,𝔽8)—78no—
79C2×D5—6371noHall
80C3×C5—491noHall
81C2×C7C5⋊(ΓL(1,𝔽8)⋊D13)18yescomplemented
82D7—45516no—
83C13C2×C5⋊#6442411yescharacteristic, complemented, Sylow
84C22×C3—31851noHall
85C2×C5#1683845011yescharacteristic, complemented
86D5—6372no—
87C7C2×C5⋊(ΓL(1,𝔽8)⋊D13)18yescomplemented
88C2×C3—491no—
89C2×C3—31852no—
90C5C2×#1683845011yescharacteristic, complemented, Sylow
91C22—31851noSylow
92C3—491noSylow
93C2—31852no—
94C2C5⋊#1683845011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C5⋊#16838450
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. C5⋊#16838450C2direct (N × H)
3. C2×C5⋊(C7⋊D91)C3semidirect
4. C5×C13×#3861C22semidirect
6. C5⋊(C7⋊D91)C2×C3semidirect
7. C2×C5×C72×C13C2×C3semidirect
9. C2×C13×#3861D5semidirect
11. C5×C72×C13C22×C3semidirect
16. C13×#3861C2×D5semidirect
18. C2×C5×#3861D13semidirect
21. C2×C72×C13C3×D5semidirect
25. C2×C5×C7×C13AGL(1,𝔽7)semidirect
28. C5×#3861C2×D13semidirect
29. C72×C13C2×C3×D5semidirect
33. C2×C5×C72C3×D13semidirect
35. C5×C7×C13C2×AGL(1,𝔽7)semidirect
40. C2×#3861D65semidirect
44. C5×C72C2×C3×D13semidirect
49. C2×C7×C13C5⋊AGL(1,𝔽7)semidirect
52. #3861C2×D65semidirect
54. C2×C5×C13#64424semidirect
57. C2×C72C3×D65semidirect
59. C7×C13C2×C5⋊AGL(1,𝔽7)semidirect
63. C2×C5×C7ΓL(1,𝔽8)⋊D13semidirect
65. C5×C13C2×#64424semidirect
68. C72C2×C3×D65semidirect
72. C5×C7C2×ΓL(1,𝔽8)⋊D13semidirect
76. C2×C13C5⋊#64424semidirect
81. C2×C7C5⋊(ΓL(1,𝔽8)⋊D13)semidirect
83. C13C2×C5⋊#64424semidirect
85. C2×C5#16838450semidirect
87. C7C2×C5⋊(ΓL(1,𝔽8)⋊D13)semidirect
90. C5C2×#16838450semidirect
94. C2C5⋊#16838450direct (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
C5⋊#168384502
C2×C5⋊(C7⋊D91)3
C2×#168384505
C2×C5⋊(ΓL(1,𝔽8)⋊D13)7
C2×C5⋊#6442413