Finite Group Databasebeta

← C72×D13×D15 #50304431

Subgroups — C72×D13×D15 #50304431

Order 38220.

400 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 160 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
2C72×C13×D15C211yesmaximal, characteristic, complemented
3C72×D195C211yesmaximal, characteristic, complemented
4C72×D5×D13—31nomaximal, Hall
5C3×C5×C72×C13C2211yescharacteristic, complemented, Hall
6D3×C72×D13—51nomaximal, Hall
7C72×D65—31no—
8C72×D5×C13—31no—
9C5×C72×D13D311yescharacteristic, complemented
10C7×D13×D15C718yesmaximal, direct product factor
11C72×D39—51no—
12D3×C72×C13—51no—
13C3×C72×D13D511yescharacteristic, complemented
14C5×C72×C13C2×D311yescharacteristic, complemented, Hall
15C2×C72×D15—131nomaximal, Hall
16C7×D195C2×C718yescomplemented
17C7×C13×D15C2×C718yescomplemented
18C3×C5×C7×D13C2×C718yescomplemented
19C2×C72×D13—151noHall
20C3×C72×C13C2×D511yescharacteristic, complemented, Hall
21C7×D5×D13—38no—
22C2×C3×C5×C72—131no—
23C72×D15—131no—
24C72×D15D1311yescharacteristic, direct product factor
25C3×C5×C7×C13C22×C718yescomplemented
26C2×C72×C13—151no—
27C72×D13—151no—
28C72×D13D1511yescharacteristic, direct product factor
29D3×C7×D13—58no—
30C2×C72×D5—391noHall
31C7×D65—38no—
32C7×D5×C13—38no—
33C5×C7×D13D3×C718yescomplemented
34D13×D15C7211yescharacteristic, direct product factor, Hall
35C3×C5×C72C2×D1311yescharacteristic, complemented, Hall
36C72×C13C2×D1511yescharacteristic, complemented, Hall
37C2×D3×C72—651noHall
38C7×D39—58no—
39D3×C7×C13—58no—
40C3×C7×D13C7×D518yescomplemented
41C2×C5×C72—131no—
42C72×D5—31no—
43C72×D5—391no—
44C5×C7×C13C2×D3×C718yescomplemented
45C2×C7×D15—138no—
46D195C2×C7211yescharacteristic, complemented
47C13×D15C2×C7211yescharacteristic, complemented
48C3×C5×D13C2×C7211yescharacteristic, complemented
49C2×C7×D13—158no—
50C2×C3×C72—131no—
51D3×C72—51no—
52D3×C72—651no—
53C3×C7×C13C2×C7×D518yescomplemented
54D5×D13—31noHall
55C5×C72D3×D1311yescharacteristic, complemented, Hall
56C2×C3×C5×C7—138no—
57C7×D15—138no—
58C7×D15C7×D1318yesdirect product factor
59C22×C72—1951noHall
60C3×C5×C13C22×C7211yescharacteristic, complemented, Hall
61C2×C7×C13—158no—
62C7×D13—158no—
63C7×D13C7×D1518yesdirect product factor
64D3×D13—51noHall
65C3×C72D5×D1311yescharacteristic, complemented, Hall
66C2×C7×D5—398no—
67D65—31no—
68C5×D13D3×C7211yescharacteristic, complemented
69D5×C13—31no—
70C3×C5×C7C2×C7×D1318yescomplemented
71C2×C72—131no—
72C2×C72—151no—
73C2×C72—1951no—
74C7×C13C2×C7×D1518yescomplemented
75C2×D3×C7—658no—
76D39—51no—
77C3×D13C72×D511yescharacteristic, complemented
78D3×C13—51no—
79C2×C5×C7—138no—
80C7×D5—38no—
81C7×D5—398no—
82C5×C13C2×D3×C7211yescharacteristic, complemented, Hall
83C2×D15—131noHall
84C2×D13—151noHall
85C72D13×D1511yescharacteristic, direct product factor, Sylow
86C2×C3×C7—138no—
87D3×C7—58no—
88D3×C7—658no—
89C3×C13C2×C72×D511yescharacteristic, complemented, Hall
90C5×C7D3×C7×D1318yescomplemented
91C2×C3×C5—131no—
92D15—131no—
93D15C72×D1311yescharacteristic, direct product factor
94C22×C7—1958no—
95C2×C13—151no—
96D13—151no—
97D13C72×D1511yescharacteristic, direct product factor
98C3×C7C7×D5×D1318yescomplemented
99C2×D5—391noHall
100C3×C5C2×C72×D1311yescharacteristic, complemented, Hall
101C2×C7—138no—
102C2×C7—158no—
103C2×C7—1958no—
104C13C2×C72×D1511yescharacteristic, complemented, Sylow
105C2×D3—651noHall
106C2×C5—131no—
107D5—31no—
108D5—391no—
109C7C7×D13×D1518yesdirect product factor
110C2×C3—131no—
111D3—51no—
112D3—651no—
113C5D3×C72×D1311yescharacteristic, complemented, Sylow
114C22—1951noSylow
115C3C72×D5×D1311yescharacteristic, complemented, Sylow
116C2—131no—
117C2—151no—
118C2—1951no—
subgroupG/H
center, hypercenterC72D13×D15
commutator, cosocle, hypocenterC3×C5×C13C22×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C72

Complements

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

NH ≅ G/Ntype
1. C3×C5×C72×D13C2semidirect
2. C72×C13×D15C2semidirect
3. C72×D195C2semidirect
5. C3×C5×C72×C13C22semidirect
9. C5×C72×D13D3semidirect
10. C7×D13×D15C7direct (N × H)
13. C3×C72×D13D5semidirect
14. C5×C72×C13C2×D3semidirect
16. C7×D195C2×C7semidirect
17. C7×C13×D15C2×C7semidirect
18. C3×C5×C7×D13C2×C7semidirect
20. C3×C72×C13C2×D5semidirect
24. C72×D15D13direct (N × H)
25. C3×C5×C7×C13C22×C7semidirect
28. C72×D13D15direct (N × H)
33. C5×C7×D13D3×C7semidirect
34. D13×D15C72direct (N × H)
35. C3×C5×C72C2×D13semidirect
36. C72×C13C2×D15semidirect
40. C3×C7×D13C7×D5semidirect
44. C5×C7×C13C2×D3×C7semidirect
46. D195C2×C72semidirect
47. C13×D15C2×C72semidirect
48. C3×C5×D13C2×C72semidirect
53. C3×C7×C13C2×C7×D5semidirect
55. C5×C72D3×D13semidirect
58. C7×D15C7×D13direct (N × H)
60. C3×C5×C13C22×C72semidirect
63. C7×D13C7×D15direct (N × H)
65. C3×C72D5×D13semidirect
68. C5×D13D3×C72semidirect
70. C3×C5×C7C2×C7×D13semidirect
74. C7×C13C2×C7×D15semidirect
77. C3×D13C72×D5semidirect
82. C5×C13C2×D3×C72semidirect
85. C72D13×D15direct (N × H)
89. C3×C13C2×C72×D5semidirect
90. C5×C7D3×C7×D13semidirect
93. D15C72×D13direct (N × H)
97. D13C72×D15direct (N × H)
98. C3×C7C7×D5×D13semidirect
100. C3×C5C2×C72×D13semidirect
104. C13C2×C72×D15semidirect
109. C7C7×D13×D15direct (N × H)
113. C5D3×C72×D13semidirect
115. C3C72×D5×D13semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C72×D132
C72×C13×D152
C72×D1952
C72×D5×D133
D3×C72×D135
C7×D13×D157
C2×C72×D1513