Finite Group Databasebeta

← C5×D13⋊C3×C7⋊D7 #50303807

Subgroups — C5×D13⋊C3×C7⋊D7 #50303807

Order 38220.

400 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C5×C13⋊C3×C7⋊D7C211yesmaximal, characteristic, complemented
2C5×(C13⋊C3)⋊(C7⋊D7)C211yesmaximal, characteristic, complemented
3C5×C72×D13⋊C3C211yesmaximal, characteristic, complemented
4C5×D13×C7⋊D7C311yesmaximal, characteristic, complemented, Hall
5C5×C72×C13⋊C3C2211yescharacteristic, complemented, Hall
6D13⋊C3×C7⋊D7C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7⋊D91C2×C311yescharacteristic, complemented
8C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10C5×D7×D13⋊C3—78nomaximal
11C13⋊C3×C7⋊D7C2×C511yescharacteristic, complemented
12(C13⋊C3)⋊(C7⋊D7)C2×C511yescharacteristic, complemented
13C72×D13⋊C3C2×C511yescharacteristic, complemented
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C2×C3×C5×C7⋊D7—131nomaximal, Hall
16C5×(C13⋊C3)⋊D7—78no—
17C5×D7×C13⋊C3—78no—
18C5×C7×D13⋊C3D718yescomplemented
19D13×C7⋊D7C3×C511yescharacteristic, complemented, Hall
20C72×C13⋊C3C22×C511yescharacteristic, complemented, Hall
21C5×D7×D13—78no—
22C2×C3×C5×C72—131no—
23C3×C5×C7⋊D7—131no—
24C3×C5×C7⋊D7—131no—
25C5×C7×C13⋊C3C2×D718yescomplemented
26C7⋊D91C2×C3×C511yescharacteristic, complemented
27C13×C7⋊D7C2×C3×C511yescharacteristic, complemented
28C72×D13C2×C3×C511yescharacteristic, complemented
29D7×D13⋊C3—78no—
30C2×C5×C7⋊D7—131noHall
31C5×D91—78no—
32C5×C13×D7—78no—
33C5×C7×D13C3×D718yescomplemented
34C2×C5×D13⋊C3—491noHall
35C3×C5×C72—131noHall
36C72×C13C22×C3×C511yescharacteristic, complemented, Hall
37C2×C3×C7⋊D7—131noHall
38(C13⋊C3)⋊D7—78no—
39D7×C13⋊C3—78no—
40C7×D13⋊C3C5×D718yescomplemented
41C2×C5×C72—131no—
42C5×C7⋊D7—131no—
43C5×C7⋊D7D13⋊C311yescharacteristic, direct product factor
44C5×C7×C13C2×C3×D718yescomplemented
45C2×C3×C5×D7—918no—
46C2×C5×C13⋊C3—491no—
47C5×D13⋊C3—491no—
48C5×D13⋊C3C7⋊D711yescharacteristic, direct product factor
49D7×D13—78no—
50C2×C3×C72—131no—
51C3×C7⋊D7—131no—
52C3×C7⋊D7—131no—
53C7×C13⋊C3C2×C5×D718yescomplemented
54C2×C5×D13—491noHall
55C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
56C2×C3×C5×C7—138no—
57C3×C5×D7—918no—
58C3×C5×D7—918no—
59C2×C7⋊D7—131noHall
60C5×C13⋊C3C2×C7⋊D711yescharacteristic, complemented, Hall
61D91—78no—
62C7×D13C3×C5×D718yescomplemented
63C13×D7—78no—
64C2×D13⋊C3—491noHall
65C3×C72—131noHall
66C2×C5×D7—918no—
67C2×C5×C13—491no—
68C5×D13—491no—
69C5×D13C3×C7⋊D711yescharacteristic, complemented
70C3×C5×C7—138no—
71C2×C72—131no—
72C7⋊D7—131no—
73C7⋊D7C5×D13⋊C311yescharacteristic, direct product factor
74C7×C13C2×C3×C5×D718yescomplemented
75C2×C3×D7—918no—
76C2×C13⋊C3—491no—
77D13⋊C3—491no—
78D13⋊C3C5×C7⋊D711yescharacteristic, direct product factor
79C2×C5×C7—138no—
80C5×D7—78no—
81C5×D7—918no—
82C5×C13C2×C3×C7⋊D711yescharacteristic, complemented, Hall
83C22×C3×C5—6371noHall
84C2×D13—491noHall
85C72C2×C5×D13⋊C311yescharacteristic, complemented, Sylow
86C2×C3×C7—138no—
87C3×D7—918no—
88C3×D7—918no—
89C13⋊C3C2×C5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7D7×D13⋊C318yescomplemented
91C2×C3×C5—131no—
92C2×C3×C5—6371no—
93C2×C3×C5—6371no—
94C2×D7—918no—
95C2×C13—491no—
96D13—491no—
97D13C3×C5×C7⋊D711yescharacteristic, complemented
98C3×C7—138no—
99C22×C5—6371noHall
100C3×C5—131noHall
101C2×C7—138no—
102D7—78no—
103D7—918no—
104C13C2×C3×C5×C7⋊D711yescharacteristic, complemented, Sylow
105C22×C3—6371noHall
106C2×C5—131no—
107C2×C5—491no—
108C2×C5—6371no—
109C7C5×D7×D13⋊C318yescomplemented
110C2×C3—131no—
111C2×C3—6371no—
112C2×C3—6371no—
113C5D13⋊C3×C7⋊D711yescharacteristic, direct product factor, Sylow
114C22—6371noSylow
115C3—131noSylow
116C2—131no—
117C2—491no—
118C2—6371no—
subgroupG/H
center, hypercenterC5D13⋊C3×C7⋊D7
commutator, cosocle, hypocenterC72×C13C22×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C72×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C13⋊C3×C7⋊D7C2semidirect
2. C5×(C13⋊C3)⋊(C7⋊D7)C2semidirect
3. C5×C72×D13⋊C3C2semidirect
4. C5×D13×C7⋊D7C3semidirect
5. C5×C72×C13⋊C3C22semidirect
6. D13⋊C3×C7⋊D7C5direct (N × H)
7. C5×C7⋊D91C2×C3semidirect
8. C5×C13×C7⋊D7C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
11. C13⋊C3×C7⋊D7C2×C5semidirect
12. (C13⋊C3)⋊(C7⋊D7)C2×C5semidirect
13. C72×D13⋊C3C2×C5semidirect
14. C5×C72×C13C22×C3semidirect
18. C5×C7×D13⋊C3D7semidirect
19. D13×C7⋊D7C3×C5semidirect
20. C72×C13⋊C3C22×C5semidirect
25. C5×C7×C13⋊C3C2×D7semidirect
26. C7⋊D91C2×C3×C5semidirect
27. C13×C7⋊D7C2×C3×C5semidirect
28. C72×D13C2×C3×C5semidirect
33. C5×C7×D13C3×D7semidirect
36. C72×C13C22×C3×C5semidirect
40. C7×D13⋊C3C5×D7semidirect
43. C5×C7⋊D7D13⋊C3direct (N × H)
44. C5×C7×C13C2×C3×D7semidirect
48. C5×D13⋊C3C7⋊D7direct (N × H)
53. C7×C13⋊C3C2×C5×D7semidirect
55. C5×C72C2×D13⋊C3semidirect
60. C5×C13⋊C3C2×C7⋊D7semidirect
62. C7×D13C3×C5×D7semidirect
69. C5×D13C3×C7⋊D7semidirect
73. C7⋊D7C5×D13⋊C3direct (N × H)
74. C7×C13C2×C3×C5×D7semidirect
78. D13⋊C3C5×C7⋊D7direct (N × H)
82. C5×C13C2×C3×C7⋊D7semidirect
85. C72C2×C5×D13⋊C3semidirect
89. C13⋊C3C2×C5×C7⋊D7semidirect
90. C5×C7D7×D13⋊C3semidirect
97. D13C3×C5×C7⋊D7semidirect
104. C13C2×C3×C5×C7⋊D7semidirect
109. C7C5×D7×D13⋊C3semidirect
113. C5D13⋊C3×C7⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C13⋊C3×C7⋊D72
C5×(C13⋊C3)⋊(C7⋊D7)2
C5×C72×D13⋊C32
C5×D13×C7⋊D73
D13⋊C3×C7⋊D75
C5×D7×D13⋊C37
C2×C3×C5×C7⋊D713