Finite Group Databasebeta

← C52×D13×D21 #41031964

Subgroups — C52×D13×D21 #41031964

Order 27300.

320 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 128 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×C52×C7×D13C211yesmaximal, characteristic, complemented
2C52×C13×D21C211yesmaximal, characteristic, complemented
3C52×D273C211yesmaximal, characteristic, complemented
4C52×D7×D13—31nomaximal, Hall
5C3×C52×C7×C13C2211yescharacteristic, complemented, Hall
6C5×D13×D21C516yesmaximal, direct product factor
7C52×D91—31no—
8C52×C13×D7—31no—
9C52×C7×D13D311yescharacteristic, complemented
10C52×D3×D13—71nomaximal, Hall
11C5×D273C2×C516yescomplemented
12C5×C13×D21C2×C516yescomplemented
13C3×C5×C7×D13C2×C516yescomplemented
14C52×C7×C13C2×D311yescharacteristic, complemented, Hall
15C2×C52×D21—131nomaximal, Hall
16C52×D39—71no—
17C52×D3×C13—71no—
18C3×C52×D13D711yescharacteristic, complemented
19C5×D7×D13—36no—
20C3×C5×C7×C13C22×C516yescomplemented
21C2×C52×D13—211noHall
22D13×D21C5211yescharacteristic, direct product factor, Hall
23C2×C3×C52×C7—131no—
24C52×D21—131no—
25C52×D21D1311yescharacteristic, direct product factor
26C3×C52×C13C2×D711yescharacteristic, complemented, Hall
27C5×D91—36no—
28C5×C13×D7—36no—
29C5×C7×D13C5×D316yescomplemented
30C5×D3×D13—76no—
31C2×C52×D7—391noHall
32C2×C52×C13—211no—
33C52×D13—211no—
34C52×D13D2111yescharacteristic, direct product factor
35D273C2×C5211yescharacteristic, complemented
36C13×D21C2×C5211yescharacteristic, complemented
37C3×C7×D13C2×C5211yescharacteristic, complemented
38C3×C52×C7C2×D1311yescharacteristic, complemented, Hall
39C5×C7×C13C2×C5×D316yescomplemented
40C2×C5×D21—136no—
41C5×D39—76no—
42C5×D3×C13—76no—
43C3×C5×D13C5×D716yescomplemented
44D7×D13—31noHall
45C2×C52×C7—131no—
46C52×D7—31no—
47C52×D7—391no—
48C52×C13C2×D2111yescharacteristic, complemented, Hall
49C2×C52×D3—911noHall
50C3×C7×C13C22×C5211yescharacteristic, complemented, Hall
51C2×C5×D13—216no—
52C2×C3×C5×C7—136no—
53C5×D21—136no—
54C5×D21C5×D1316yesdirect product factor
55C3×C5×C13C2×C5×D716yescomplemented
56D91—31no—
57C7×D13C52×D311yescharacteristic, complemented
58C13×D7—31no—
59C52×C7D3×D1311yescharacteristic, complemented, Hall
60D3×D13—71noHall
61C2×C3×C52—131no—
62C52×D3—71no—
63C52×D3—911no—
64C2×C5×D7—396no—
65C2×C5×C13—216no—
66C5×D13—216no—
67C5×D13C5×D2116yesdirect product factor
68C3×C5×C7C2×C5×D1316yescomplemented
69C22×C52—2731noHall
70C7×C13C2×C52×D311yescharacteristic, complemented, Hall
71C2×D21—131noHall
72D39—71no—
73C3×D13C52×D711yescharacteristic, complemented
74D3×C13—71no—
75C3×C52D7×D1311yescharacteristic, complemented, Hall
76C2×C5×C7—136no—
77C5×D7—36no—
78C5×D7—396no—
79C5×C13C2×C5×D2116yescomplemented
80C2×C5×D3—916no—
81C2×D13—211noHall
82C2×C52—131no—
83C2×C52—2731no—
84C2×C52—211no—
85C2×C3×C7—131no—
86D21—131no—
87D21C52×D1311yescharacteristic, direct product factor
88C3×C13C2×C52×D711yescharacteristic, complemented, Hall
89C5×C7C5×D3×D1316yescomplemented
90C2×C3×C5—136no—
91C5×D3—76no—
92C5×D3—916no—
93C2×D7—391noHall
94C2×C13—211no—
95D13—211no—
96D13C52×D2111yescharacteristic, direct product factor
97C52D13×D2111yescharacteristic, direct product factor, Sylow
98C3×C7C2×C52×D1311yescharacteristic, complemented, Hall
99C22×C5—2736no—
100C3×C5C5×D7×D1316yescomplemented
101C2×C7—131no—
102D7—31no—
103D7—391no—
104C13C2×C52×D2111yescharacteristic, complemented, Sylow
105C2×D3—911noHall
106C2×C5—136no—
107C2×C5—2736no—
108C2×C5—216no—
109C7C52×D3×D1311yescharacteristic, complemented, Sylow
110C2×C3—131no—
111D3—71no—
112D3—911no—
113C5C5×D13×D2116yesdirect product factor
114C22—2731noSylow
115C3C52×D7×D1311yescharacteristic, complemented, Sylow
116C2—131no—
117C2—2731no—
118C2—211no—
subgroupG/H
center, hypercenterC52D13×D21
commutator, cosocle, hypocenterC3×C7×C13C22×C52
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C7×C13
UCSC1 ◁ C52

Complements

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

NH ≅ G/Ntype
1. C3×C52×C7×D13C2semidirect
2. C52×C13×D21C2semidirect
3. C52×D273C2semidirect
5. C3×C52×C7×C13C22semidirect
6. C5×D13×D21C5direct (N × H)
9. C52×C7×D13D3semidirect
11. C5×D273C2×C5semidirect
12. C5×C13×D21C2×C5semidirect
13. C3×C5×C7×D13C2×C5semidirect
14. C52×C7×C13C2×D3semidirect
18. C3×C52×D13D7semidirect
20. C3×C5×C7×C13C22×C5semidirect
22. D13×D21C52direct (N × H)
25. C52×D21D13direct (N × H)
26. C3×C52×C13C2×D7semidirect
29. C5×C7×D13C5×D3semidirect
34. C52×D13D21direct (N × H)
35. D273C2×C52semidirect
36. C13×D21C2×C52semidirect
37. C3×C7×D13C2×C52semidirect
38. C3×C52×C7C2×D13semidirect
39. C5×C7×C13C2×C5×D3semidirect
43. C3×C5×D13C5×D7semidirect
48. C52×C13C2×D21semidirect
50. C3×C7×C13C22×C52semidirect
54. C5×D21C5×D13direct (N × H)
55. C3×C5×C13C2×C5×D7semidirect
57. C7×D13C52×D3semidirect
59. C52×C7D3×D13semidirect
67. C5×D13C5×D21direct (N × H)
68. C3×C5×C7C2×C5×D13semidirect
70. C7×C13C2×C52×D3semidirect
73. C3×D13C52×D7semidirect
75. C3×C52D7×D13semidirect
79. C5×C13C2×C5×D21semidirect
87. D21C52×D13direct (N × H)
88. C3×C13C2×C52×D7semidirect
89. C5×C7C5×D3×D13semidirect
96. D13C52×D21direct (N × H)
97. C52D13×D21direct (N × H)
98. C3×C7C2×C52×D13semidirect
100. C3×C5C5×D7×D13semidirect
104. C13C2×C52×D21semidirect
109. C7C52×D3×D13semidirect
113. C5C5×D13×D21direct (N × H)
115. C3C52×D7×D13semidirect

Maximal subgroups

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

subgroupindex
C3×C52×C7×D132
C52×C13×D212
C52×D2732
C52×D7×D133
C5×D13×D215
C52×D3×D137
C2×C52×D2113