Finite Group Databasebeta

← C2×C5⋊#16838417 #50303457

Subgroups — C2×C5⋊#16838417 #50303457

Order 38220.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5⋊#16838417C212yesmaximal, direct product factor
2C2×C5×#14274254C211yesmaximal, characteristic, complemented
3C2×C13×D245C311yesmaximal, characteristic, complemented, Hall
4C5×#14274254C2211yescharacteristic, complemented, Hall
5C2×#16838417—51nomaximal, Hall
6C13×D245C2×C312yescomplemented
7C2×C5×C13×C49C2×C311yescharacteristic, complemented
8C2×C5⋊#10587720—71nomaximal
9C2×#14274254D511yescharacteristic, complemented
10#16838417—52no—
11C5×C13×C49C22×C311yescharacteristic, complemented, Hall
12C2×C5⋊(D49⋊C3)—131nomaximal, Hall
13C5⋊#10587720—72no—
14C2×C5×#63270—71no—
15C2×C13×D49—51noHall
16#14274254C2×D511yescharacteristic, complemented, Hall
17C2×C13×D35—71no—
18C2×C5×C49⋊C3—131no—
19C5⋊(D49⋊C3)—132no—
20C5×#63270—71no—
21C2×C13×C49C3×D511yescharacteristic, complemented
22C13×D49—52no—
23C2×#10587720—351no—
24C2×D245C13⋊C311yescharacteristic, complemented, Hall
25C2×C5×C7×C13AGL(1,𝔽7)11yescharacteristic
26C13×D35—72no—
27C2×D5×C13⋊C3—491noHall
28C5×C49⋊C3—131noHall
29C13×C49C2×C3×D511yescharacteristic, complemented, Hall
30C2×D49⋊C3—651noHall
31C2×#63270—71no—
32#10587720—352no—
33C2×C5×C49C2×C13⋊C311yescharacteristic, complemented
34D245C2×C13⋊C312yescomplemented
35C5×C7×C13C2×AGL(1,𝔽7)11yescharacteristic
36C2×C5⋊AGL(1,𝔽7)—911no—
37C2×C5×C13⋊C3—491no—
38D5×C13⋊C3—492no—
39C2×C13×D7—351no—
40C2×C49⋊C3—131no—
41D49⋊C3—652no—
42#63270—71no—
43C2×D5×C13—491noHall
44C5×C49C22×C13⋊C311yescharacteristic, complemented, Hall
45C2×C5×ΓL(1,𝔽8)—911no—
46C5⋊AGL(1,𝔽7)—912no—
47C2×D49—51noHall
48C5×C13⋊C3—491noHall
49C2×C7×C13C5⋊AGL(1,𝔽7)11yescharacteristic
50C13×D7—352no—
51C22×C13⋊C3—2451noHall
52C49⋊C3—131noHall
53C2×D35—71no—
54C2×C5×C13D49⋊C311yescharacteristic, complemented
55D5×C13—492no—
56C5×ΓL(1,𝔽8)—911no—
57C2×C49D5×C13⋊C311yescharacteristic, complemented
58D49—52no—
59C7×C13C2×C5⋊AGL(1,𝔽7)11yescharacteristic
60C2×AGL(1,𝔽7)—4551no—
61C2×C13⋊C3—491no—
62C2×C13⋊C3—2452no—
63C2×C5×C7#1058772011yescharacteristic
64D35—72no—
65C5×C13C2×D49⋊C311yescharacteristic, complemented, Hall
66C2×C3×D5—6371noHall
67C22×C13—2451noHall
68C49C2×D5×C13⋊C311yescharacteristic, complemented, Sylow
69C2×ΓL(1,𝔽8)—911no—
70AGL(1,𝔽7)—4552no—
71C13⋊C3—491noHall
72C5×C7C2×#1058772011yescharacteristic
73C2×C3×C5—6371no—
74C3×D5—6372no—
75C2×D7—351no—
76C2×C13—2452no—
77C2×C13C5⋊(D49⋊C3)11yescharacteristic, complemented
78ΓL(1,𝔽8)—911no—
79C2×D5—491noHall
80C3×C5—6371noHall
81C2×C7C5⋊#1058772011yescharacteristic
82D7—352no—
83C13C2×C5⋊(D49⋊C3)11yescharacteristic, complemented, Sylow
84C22×C3—31851noHall
85C2×C5#1683841711yescharacteristic, complemented
86D5—492no—
87C7C2×C5⋊#1058772011yescharacteristic
88C2×C3—31852no—
89C2×C3—6371no—
90C5C2×#1683841711yescharacteristic, complemented, Sylow
91C22—2451noSylow
92C3—6371noSylow
93C2—2452no—
94C2C5⋊#1683841711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C5⋊#16838417
commutator, cosocle, hypocenterC5×C13×C49C22×C3
FrattiniC7C2×C5⋊#10587720
FittingC2×C5×C13×C49C2×C3
socleC2×C5×C7×C13AGL(1,𝔽7)
LCSG ▷ C5×C13×C49
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C5⋊#16838417C2direct (N × H)
2. C2×C5×#14274254C2semidirect
3. C2×C13×D245C3semidirect
4. C5×#14274254C22semidirect
6. C13×D245C2×C3semidirect
7. C2×C5×C13×C49C2×C3semidirect
9. C2×#14274254D5semidirect
11. C5×C13×C49C22×C3semidirect
16. #14274254C2×D5semidirect
21. C2×C13×C49C3×D5semidirect
24. C2×D245C13⋊C3semidirect
29. C13×C49C2×C3×D5semidirect
33. C2×C5×C49C2×C13⋊C3semidirect
34. D245C2×C13⋊C3semidirect
44. C5×C49C22×C13⋊C3semidirect
54. C2×C5×C13D49⋊C3semidirect
57. C2×C49D5×C13⋊C3semidirect
65. C5×C13C2×D49⋊C3semidirect
68. C49C2×D5×C13⋊C3semidirect
77. C2×C13C5⋊(D49⋊C3)semidirect
83. C13C2×C5⋊(D49⋊C3)semidirect
85. C2×C5#16838417semidirect
90. C5C2×#16838417semidirect
94. C2C5⋊#16838417direct (N × H)

Maximal subgroups

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

subgroupindex
C5⋊#168384172
C2×C5×#142742542
C2×C13×D2453
C2×#168384175
C2×C5⋊#105877207
C2×C5⋊(D49⋊C3)13