Finite Group Databasebeta

← C2×C5×C13×#64418 #50304217

Subgroups — C2×C5×C13×#64418 #50304217

Order 38220.

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

normal subgroups only

This group has 136 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
1C2×C5×C13×#3862C211yesmaximal, characteristic, complemented
2C5×C13×#64418C212yesmaximal, direct product factor
3C2×C5×C7×C13×D7—31nomaximal, Hall
4C5×C13×#3862C2211yescharacteristic, complemented, Hall
5C2×C13×#64418C511yesmaximal, characteristic, direct product factor, Hall
6C5×C7×C13×D7—32no—
7C2×C5×C72×C13D311yescharacteristic, complemented
8C2×C13×#3862C2×C511yescharacteristic, complemented
9C13×#64418C2×C512yesdirect product factor
10C5×C72×C13C2×D311yescharacteristic, complemented, Hall
11C2×C5×#64418C1311yesmaximal, characteristic, direct product factor, Hall
12C2×C5×C13×ΓL(1,𝔽8)—141no—
13C2×C7×C13×D7—31noHall
14C13×#3862C22×C511yescharacteristic, complemented, Hall
15C22×C5×C7×C13—211no—
16C2×C5×C13×D7—31no—
17C2×C5×#3862C2×C1311yescharacteristic, complemented
18C5×#64418C2×C1312yesdirect product factor
19C5×C13×ΓL(1,𝔽8)—141no—
20C2×C72×C13C5×D311yescharacteristic, complemented
21C7×C13×D7—32no—
22C2×C5×C7×D7—31noHall
23C2×C5×C7×C13—21no—
24C2×C5×C7×C13—31no—
25C2×C5×C7×C13—31no—
26C2×C5×C7×C13—212no—
27C5×C13×D7—32no—
28C2×C5×D3×C13—491nomaximal, Hall
29C5×#3862C22×C1311yescharacteristic, complemented, Hall
30C72×C13C2×C5×D311yescharacteristic, complemented, Hall
31C2×#64418C5×C1311yescharacteristic, direct product factor, Hall
32C2×C13×ΓL(1,𝔽8)—141no—
33C2×C5×C72D3×C1311yescharacteristic, complemented
34C5×C7×D7—32no—
35C5×C7×C13—21no—
36C5×C7×C13—31no—
37C5×C7×C13—31no—
38C2×C3×C5×C13—491no—
39C5×D3×C13—492no—
40C22×C7×C13—211no—
41C2×C13×D7—31no—
42C2×#3862C2×C5×C1311yescharacteristic, complemented
43#64418C2×C5×C1312yesdirect product factor
44C13×ΓL(1,𝔽8)—141no—
45C22×C5×C13—211noHall
46C5×C72C2×D3×C1311yescharacteristic, complemented, Hall
47C2×C5×ΓL(1,𝔽8)—141no—
48C2×C7×D7—31noHall
49C3×C5×C13—491noHall
50C2×C7×C13—21no—
51C2×C7×C13—31no—
52C2×C7×C13—31no—
53C2×C7×C13—212no—
54C13×D7—32no—
55C2×D3×C13—491noHall
56#3862C22×C5×C1311yescharacteristic, complemented, Hall
57C22×C5×C7—211no—
58C2×C5×D7—31no—
59C2×C5×C13—212no—
60C2×C5×C13#6441811yescharacteristic, direct product factor
61C5×ΓL(1,𝔽8)—141no—
62C2×C72C5×D3×C1311yescharacteristic, complemented
63C7×D7—32no—
64C7×C13—21no—
65C7×C13—31no—
66C7×C13—31no—
67C2×C3×C13—491no—
68D3×C13—492no—
69C2×C5×C7—21no—
70C2×C5×C7—31no—
71C2×C5×C7—31no—
72C2×C5×C7—212no—
73C5×D7—32no—
74C5×C13C2×#6441811yescharacteristic, direct product factor, Hall
75C2×C5×D3—491noHall
76C22×C13—211noHall
77C72C2×C5×D3×C1311yescharacteristic, complemented, Sylow
78C2×ΓL(1,𝔽8)—141no—
79C3×C13—491noHall
80C5×C7—21no—
81C5×C7—31no—
82C5×C7—31no—
83C2×C3×C5—491no—
84C5×D3—492no—
85C22×C7—211no—
86C2×D7—31no—
87C2×C13—212no—
88C2×C13C5×#6441811yescharacteristic, direct product factor
89ΓL(1,𝔽8)—141no—
90C22×C5—211noHall
91C3×C5—491noHall
92C2×C7—21no—
93C2×C7—31no—
94C2×C7—31no—
95C2×C7—212no—
96D7—32no—
97C13C2×C5×#6441811yescharacteristic, direct product factor, Sylow
98C2×D3—491noHall
99C2×C5—212no—
100C2×C5C13×#6441811yescharacteristic, direct product factor
101C7—21no—
102C7—31no—
103C7—31no—
104C2×C3—491no—
105D3—492no—
106C5C2×C13×#6441811yescharacteristic, direct product factor, Sylow
107C22—211noSylow
108C3—491noSylow
109C2—212no—
110C2C5×C13×#6441811yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C13#64418
commutator, cosocle, hypocenter#3862C22×C5×C13
FrattiniC1G
Fitting, socleC2×C5×C72×C13D3
LCSG ▷ #3862
UCSC1 ◁ C2×C5×C13

Complements

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

NH ≅ G/Ntype
1. C2×C5×C13×#3862C2semidirect
2. C5×C13×#64418C2direct (N × H)
4. C5×C13×#3862C22semidirect
5. C2×C13×#64418C5direct (N × H)
7. C2×C5×C72×C13D3semidirect
8. C2×C13×#3862C2×C5semidirect
9. C13×#64418C2×C5direct (N × H)
10. C5×C72×C13C2×D3semidirect
11. C2×C5×#64418C13direct (N × H)
14. C13×#3862C22×C5semidirect
17. C2×C5×#3862C2×C13semidirect
18. C5×#64418C2×C13direct (N × H)
20. C2×C72×C13C5×D3semidirect
29. C5×#3862C22×C13semidirect
30. C72×C13C2×C5×D3semidirect
31. C2×#64418C5×C13direct (N × H)
33. C2×C5×C72D3×C13semidirect
42. C2×#3862C2×C5×C13semidirect
43. #64418C2×C5×C13direct (N × H)
46. C5×C72C2×D3×C13semidirect
56. #3862C22×C5×C13semidirect
60. C2×C5×C13#64418direct (N × H)
62. C2×C72C5×D3×C13semidirect
74. C5×C13C2×#64418direct (N × H)
77. C72C2×C5×D3×C13semidirect
88. C2×C13C5×#64418direct (N × H)
97. C13C2×C5×#64418direct (N × H)
100. C2×C5C13×#64418direct (N × H)
106. C5C2×C13×#64418direct (N × H)
110. C2C5×C13×#64418direct (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×#38622
C5×C13×#644182
C2×C5×C7×C13×D73
C2×C13×#644185
C2×C5×#6441813
C2×C5×D3×C1349