Finite Group Databasebeta

← C72×D5×D13⋊C3 #50303985

Subgroups — C72×D5×D13⋊C3 #50303985

Order 38220.

400 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 170 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
1C72×D5×C13⋊C3C211yesmaximal, characteristic, complemented
2C72×C5⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C5×C72×D13⋊C3C211yesmaximal, characteristic, complemented
4C72×D5×D13C311yesmaximal, characteristic, complemented, Hall
5C5×C72×C13⋊C3C2211yescharacteristic, complemented, Hall
6C2×C72×D13⋊C3—51nomaximal, Hall
7C72×D65C2×C311yescharacteristic, complemented
8C72×D5×C13C2×C311yescharacteristic, complemented
9C5×C72×D13C2×C311yescharacteristic, complemented
10C7×D5×D13⋊C3C718yesmaximal, direct product factor
11C2×C72×C13⋊C3—51no—
12C72×D13⋊C3—51no—
13C72×D13⋊C3D511yescharacteristic, direct product factor
14C5×C72×C13C22×C311yescharacteristic, complemented, Hall
15C2×C3×C72×D5—131nomaximal, Hall
16C7×C5⋊(D13⋊C3)C2×C718yescomplemented
17C7×D5×C13⋊C3C2×C718yescomplemented
18C5×C7×D13⋊C3C2×C718yescomplemented
19C2×C72×D13—51noHall
20C72×C13⋊C3C2×D511yescharacteristic, complemented, Hall
21C7×D5×D13C3×C718yescomplemented
22C2×C3×C5×C72—131no—
23C3×C72×D5—131no—
24C3×C72×D5—131no—
25C5×C7×C13⋊C3C22×C718yescomplemented
26C2×C72×C13—51no—
27C72×D13—51no—
28C72×D13C3×D511yescharacteristic, complemented
29C2×C7×D13⋊C3—58no—
30C2×C72×D5—131noHall
31C7×D65C2×C3×C718yescomplemented
32C7×D5×C13C2×C3×C718yescomplemented
33C5×C7×D13C2×C3×C718yescomplemented
34D5×D13⋊C3C7211yescharacteristic, direct product factor, Hall
35C3×C5×C72—131noHall
36C72×C13C2×C3×D511yescharacteristic, complemented, Hall
37C22×C3×C72—651noHall
38C2×C7×C13⋊C3—58no—
39C7×D13⋊C3—58no—
40C7×D13⋊C3C7×D518yesdirect product factor
41C2×C5×C72—131no—
42C72×D5—131no—
43C72×D5D13⋊C311yescharacteristic, direct product factor
44C5×C7×C13C22×C3×C718yescomplemented
45C2×C3×C7×D5—138no—
46C5⋊(D13⋊C3)C2×C7211yescharacteristic, complemented
47D5×C13⋊C3C2×C7211yescharacteristic, complemented
48C5×D13⋊C3C2×C7211yescharacteristic, complemented
49C2×C7×D13—58no—
50C2×C3×C72—131no—
51C2×C3×C72—651no—
52C2×C3×C72—651no—
53C7×C13⋊C3C2×C7×D518yescomplemented
54D5×D13C3×C7211yescharacteristic, complemented, Hall
55C5×C72C2×D13⋊C311yescharacteristic, complemented, Hall
56C2×C3×C5×C7—138no—
57C3×C7×D5—138no—
58C3×C7×D5—138no—
59C22×C72—651noHall
60C5×C13⋊C3C22×C7211yescharacteristic, complemented, Hall
61C2×C7×C13—58no—
62C7×D13—58no—
63C7×D13C3×C7×D518yescomplemented
64C2×D13⋊C3—51noHall
65C3×C72—131noHall
66C2×C7×D5—138no—
67D65C2×C3×C7211yescharacteristic, complemented
68C5×D13C2×C3×C7211yescharacteristic, complemented
69D5×C13C2×C3×C7211yescharacteristic, complemented
70C3×C5×C7—138no—
71C2×C72—51no—
72C2×C72—131no—
73C2×C72—651no—
74C7×C13C2×C3×C7×D518yescomplemented
75C22×C3×C7—658no—
76C2×C13⋊C3—51no—
77D13⋊C3—51no—
78D13⋊C3C72×D511yescharacteristic, direct product factor
79C2×C5×C7—138no—
80C7×D5—138no—
81C7×D5C7×D13⋊C318yesdirect product factor
82C5×C13C22×C3×C7211yescharacteristic, complemented, Hall
83C2×C3×D5—131noHall
84C2×D13—51noHall
85C72D5×D13⋊C311yescharacteristic, direct product factor, Sylow
86C2×C3×C7—138no—
87C2×C3×C7—658no—
88C2×C3×C7—658no—
89C13⋊C3C2×C72×D511yescharacteristic, complemented, Hall
90C5×C7C2×C7×D13⋊C318yescomplemented
91C2×C3×C5—131no—
92C3×D5—131no—
93C3×D5—131no—
94C22×C7—658no—
95C2×C13—51no—
96D13—51no—
97D13C3×C72×D511yescharacteristic, complemented
98C3×C7—138no—
99C2×D5—131noHall
100C3×C5—131noHall
101C2×C7—58no—
102C2×C7—138no—
103C2×C7—658no—
104C13C2×C3×C72×D511yescharacteristic, complemented, Sylow
105C22×C3—651noHall
106C2×C5—131no—
107D5—131no—
108D5C72×D13⋊C311yescharacteristic, direct product factor
109C7C7×D5×D13⋊C318yesdirect product factor
110C2×C3—131no—
111C2×C3—651no—
112C2×C3—651no—
113C5C2×C72×D13⋊C311yescharacteristic, complemented, Sylow
114C22—651noSylow
115C3—131noSylow
116C2—51no—
117C2—131no—
118C2—651no—
subgroupG/H
center, hypercenterC72D5×D13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C3×C72
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C5×C13
UCSC1 ◁ C72

Complements

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

NH ≅ G/Ntype
1. C72×D5×C13⋊C3C2semidirect
2. C72×C5⋊(D13⋊C3)C2semidirect
3. C5×C72×D13⋊C3C2semidirect
4. C72×D5×D13C3semidirect
5. C5×C72×C13⋊C3C22semidirect
7. C72×D65C2×C3semidirect
8. C72×D5×C13C2×C3semidirect
9. C5×C72×D13C2×C3semidirect
10. C7×D5×D13⋊C3C7direct (N × H)
13. C72×D13⋊C3D5direct (N × H)
14. C5×C72×C13C22×C3semidirect
16. C7×C5⋊(D13⋊C3)C2×C7semidirect
17. C7×D5×C13⋊C3C2×C7semidirect
18. C5×C7×D13⋊C3C2×C7semidirect
20. C72×C13⋊C3C2×D5semidirect
21. C7×D5×D13C3×C7semidirect
25. C5×C7×C13⋊C3C22×C7semidirect
28. C72×D13C3×D5semidirect
31. C7×D65C2×C3×C7semidirect
32. C7×D5×C13C2×C3×C7semidirect
33. C5×C7×D13C2×C3×C7semidirect
34. D5×D13⋊C3C72direct (N × H)
36. C72×C13C2×C3×D5semidirect
40. C7×D13⋊C3C7×D5direct (N × H)
43. C72×D5D13⋊C3direct (N × H)
44. C5×C7×C13C22×C3×C7semidirect
46. C5⋊(D13⋊C3)C2×C72semidirect
47. D5×C13⋊C3C2×C72semidirect
48. C5×D13⋊C3C2×C72semidirect
53. C7×C13⋊C3C2×C7×D5semidirect
54. D5×D13C3×C72semidirect
55. C5×C72C2×D13⋊C3semidirect
60. C5×C13⋊C3C22×C72semidirect
63. C7×D13C3×C7×D5semidirect
67. D65C2×C3×C72semidirect
68. C5×D13C2×C3×C72semidirect
69. D5×C13C2×C3×C72semidirect
74. C7×C13C2×C3×C7×D5semidirect
78. D13⋊C3C72×D5direct (N × H)
81. C7×D5C7×D13⋊C3direct (N × H)
82. C5×C13C22×C3×C72semidirect
85. C72D5×D13⋊C3direct (N × H)
89. C13⋊C3C2×C72×D5semidirect
90. C5×C7C2×C7×D13⋊C3semidirect
97. D13C3×C72×D5semidirect
104. C13C2×C3×C72×D5semidirect
108. D5C72×D13⋊C3direct (N × H)
109. C7C7×D5×D13⋊C3direct (N × H)
113. C5C2×C72×D13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C72×D5×C13⋊C32
C72×C5⋊(D13⋊C3)2
C5×C72×D13⋊C32
C72×D5×D133
C2×C72×D13⋊C35
C7×D5×D13⋊C37
C2×C3×C72×D513