Finite Group Databasebeta

← C3×C5×D13×C7⋊D7 #50304346

Subgroups — C3×C5×D13×C7⋊D7 #50304346

Order 38220.

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

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 136 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
1C3×C5×C72×D13C211yesmaximal, characteristic, complemented
2C3×C5×C13×C7⋊D7C211yesmaximal, characteristic, complemented
3C3×C5×C7⋊D91C211yesmaximal, characteristic, complemented
4C5×D13×C7⋊D7C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6C3×D13×C7⋊D7C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7⋊D91C2×C311yescharacteristic, complemented
8C5×C13×C7⋊D7C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10C3×C5×D7×D13—78nomaximal
11C3×C7⋊D91C2×C511yescharacteristic, complemented
12C3×C13×C7⋊D7C2×C511yescharacteristic, complemented
13C3×C72×D13C2×C511yescharacteristic, complemented
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C2×C3×C5×C7⋊D7—131nomaximal, Hall
16C3×C5×D91—78no—
17C3×C5×C13×D7—78no—
18C3×C5×C7×D13D718yescomplemented
19D13×C7⋊D7C3×C511yescharacteristic, direct product factor, Hall
20C3×C72×C13C22×C511yescharacteristic, complemented, Hall
21C5×D7×D13—78no—
22C2×C3×C5×C72—131no—
23C3×C5×C7⋊D7—131no—
24C3×C5×C7⋊D7D1311yescharacteristic, direct product factor
25C3×C5×C7×C13C2×D718yescomplemented
26C7⋊D91C2×C3×C511yescharacteristic, complemented
27C13×C7⋊D7C2×C3×C511yescharacteristic, complemented
28C72×D13C2×C3×C511yescharacteristic, complemented
29C3×D7×D13—78no—
30C2×C5×C7⋊D7—131noHall
31C5×D91—78no—
32C5×C13×D7—78no—
33C5×C7×D13C3×D718yescomplemented
34C2×C3×C5×D13—491noHall
35C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
36C72×C13C22×C3×C511yescharacteristic, complemented, Hall
37C2×C3×C7⋊D7—131noHall
38C3×D91—78no—
39C3×C13×D7—78no—
40C3×C7×D13C5×D718yescomplemented
41C2×C5×C72—131no—
42C5×C7⋊D7—131no—
43C5×C7⋊D7C3×D1311yescharacteristic, direct product factor
44C5×C7×C13C2×C3×D718yescomplemented
45C2×C3×C5×D7—918no—
46C2×C3×C5×C13—491no—
47C3×C5×D13—491no—
48C3×C5×D13C7⋊D711yescharacteristic, direct product factor
49D7×D13—78no—
50C2×C3×C72—131no—
51C3×C7⋊D7—131no—
52C3×C7⋊D7C5×D1311yescharacteristic, direct product factor
53C3×C7×C13C2×C5×D718yescomplemented
54C2×C5×D13—491noHall
55C5×C72C2×C3×D1311yescharacteristic, complemented, Hall
56C2×C3×C5×C7—138no—
57C3×C5×D7—78no—
58C3×C5×D7—918no—
59C2×C7⋊D7—131noHall
60C3×C5×C13C2×C7⋊D711yescharacteristic, complemented, Hall
61D91—78no—
62C7×D13C3×C5×D718yescomplemented
63C13×D7—78no—
64C2×C3×D13—491noHall
65C3×C72C2×C5×D1311yescharacteristic, complemented, Hall
66C2×C5×D7—918no—
67C2×C5×C13—491no—
68C5×D13—491no—
69C5×D13C3×C7⋊D711yescharacteristic, direct product factor
70C3×C5×C7D7×D1318yescomplemented
71C2×C72—131no—
72C7⋊D7—131no—
73C7⋊D7C3×C5×D1311yescharacteristic, direct product factor
74C7×C13C2×C3×C5×D718yescomplemented
75C2×C3×D7—918no—
76C2×C3×C13—491no—
77C3×D13—491no—
78C3×D13C5×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×C3×C5×D1311yescharacteristic, complemented, Sylow
86C2×C3×C7—138no—
87C3×D7—78no—
88C3×D7—918no—
89C3×C13C2×C5×C7⋊D711yescharacteristic, complemented, Hall
90C5×C7C3×D7×D1318yescomplemented
91C2×C3×C5—131no—
92C2×C3×C5—491no—
93C2×C3×C5—6371no—
94C2×D7—918no—
95C2×C13—491no—
96D13—491no—
97D13C3×C5×C7⋊D711yescharacteristic, direct product factor
98C3×C7C5×D7×D1318yescomplemented
99C22×C5—6371noHall
100C3×C5D13×C7⋊D711yescharacteristic, direct product factor, Hall
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—
109C7C3×C5×D7×D1318yescomplemented
110C2×C3—131no—
111C2×C3—491no—
112C2×C3—6371no—
113C5C3×D13×C7⋊D711yescharacteristic, direct product factor, Sylow
114C22—6371noSylow
115C3C5×D13×C7⋊D711yescharacteristic, direct product factor, Sylow
116C2—131no—
117C2—491no—
118C2—6371no—
subgroupG/H
center, hypercenterC3×C5D13×C7⋊D7
commutator, cosocle, hypocenterC72×C13C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C72×C13
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×D13C2semidirect
2. C3×C5×C13×C7⋊D7C2semidirect
3. C3×C5×C7⋊D91C2semidirect
4. C5×D13×C7⋊D7C3direct (N × H)
5. C3×C5×C72×C13C22semidirect
6. C3×D13×C7⋊D7C5direct (N × H)
7. C5×C7⋊D91C2×C3semidirect
8. C5×C13×C7⋊D7C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
11. C3×C7⋊D91C2×C5semidirect
12. C3×C13×C7⋊D7C2×C5semidirect
13. C3×C72×D13C2×C5semidirect
14. C5×C72×C13C22×C3semidirect
18. C3×C5×C7×D13D7semidirect
19. D13×C7⋊D7C3×C5direct (N × H)
20. C3×C72×C13C22×C5semidirect
24. C3×C5×C7⋊D7D13direct (N × H)
25. C3×C5×C7×C13C2×D7semidirect
26. C7⋊D91C2×C3×C5semidirect
27. C13×C7⋊D7C2×C3×C5semidirect
28. C72×D13C2×C3×C5semidirect
33. C5×C7×D13C3×D7semidirect
35. C3×C5×C72C2×D13semidirect
36. C72×C13C22×C3×C5semidirect
40. C3×C7×D13C5×D7semidirect
43. C5×C7⋊D7C3×D13direct (N × H)
44. C5×C7×C13C2×C3×D7semidirect
48. C3×C5×D13C7⋊D7direct (N × H)
52. C3×C7⋊D7C5×D13direct (N × H)
53. C3×C7×C13C2×C5×D7semidirect
55. C5×C72C2×C3×D13semidirect
60. C3×C5×C13C2×C7⋊D7semidirect
62. C7×D13C3×C5×D7semidirect
65. C3×C72C2×C5×D13semidirect
69. C5×D13C3×C7⋊D7direct (N × H)
70. C3×C5×C7D7×D13semidirect
73. C7⋊D7C3×C5×D13direct (N × H)
74. C7×C13C2×C3×C5×D7semidirect
78. C3×D13C5×C7⋊D7direct (N × H)
82. C5×C13C2×C3×C7⋊D7semidirect
85. C72C2×C3×C5×D13semidirect
89. C3×C13C2×C5×C7⋊D7semidirect
90. C5×C7C3×D7×D13semidirect
97. D13C3×C5×C7⋊D7direct (N × H)
98. C3×C7C5×D7×D13semidirect
100. C3×C5D13×C7⋊D7direct (N × H)
104. C13C2×C3×C5×C7⋊D7semidirect
109. C7C3×C5×D7×D13semidirect
113. C5C3×D13×C7⋊D7direct (N × H)
115. C3C5×D13×C7⋊D7direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C72×D132
C3×C5×C13×C7⋊D72
C3×C5×C7⋊D912
C5×D13×C7⋊D73
C3×D13×C7⋊D75
C3×C5×D7×D137
C2×C3×C5×C7⋊D713