Finite Group Databasebeta

← #30655713

Subgroups — #30655713

Order 16380.

240 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C7×C13×C3⋊D15C211yesmaximal, characteristic, complemented
2C5×C3⋊D273C211yesmaximal, characteristic, complemented
3C32×D455C211yesmaximal, characteristic, complemented
4D15⋊D91—34nomaximal
5C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
6C3⋊D3×D91—51nomaximal, Hall
7C7×C13×D15—34no—
8C5×D273—34no—
9C3×D455D314yescomplemented
10D65⋊(C3⋊D3)—71nomaximal, Hall
11D5×D91—91noHall
12C3⋊D273D511yescharacteristic, complemented
13C7×C13×C3⋊D3—51no—
14C32×D91—51no—
15C3×C5×C7×C13C2×D314yescomplemented
16D35⋊(C3⋊D3)—131nomaximal, Hall
17C13×C3⋊D15D711yescharacteristic, complemented
18C5×C3⋊D39—71no—
19C32×D65—71no—
20D3×D91—154no—
21D455C3⋊D311yescharacteristic, complemented
22C7×D5×C13—91no—
23C5×D91—91no—
24C32×C7×C13C2×D511yescharacteristic, complemented, Hall
25D15⋊D13—214no—
26C7×C3⋊D15D1311yescharacteristic, complemented
27C5×C3⋊D21—131no—
28C32×D35—131no—
29C32×C5×C13C2×D711yescharacteristic, complemented, Hall
30D273—34no—
31D3×C7×C13—154no—
32C3×D91—54no—
33C3⋊D3×D13—351noHall
34C5×C7×C13C2×C3⋊D311yescharacteristic, complemented, Hall
35D15⋊D7—394no—
36C13×D15—34no—
37C5×D39—214no—
38C3×D65—74no—
39C2×D91—451noHall
40C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
41C3×C7×C13D3×D514yescomplemented
42D5×D13—631noHall
43D7×C3⋊D3—651noHall
44C3⋊D39—71no—
45C13×C3⋊D3—51no—
46C32×D13—351no—
47C7×D15—34no—
48C5×D21—394no—
49C3×D35—134no—
50C3×C5×C13D3×D714yescomplemented
51C2×C7×C13—451no—
52D91—51no—
53D91—91no—
54D5×C3⋊D3—911noHall
55D3×D13—1054no—
56D5×D7—1171noHall
57D65—71no—
58C5×D13—631no—
59D5×C13—91no—
60C3⋊D21—131no—
61C7×C3⋊D3—51no—
62C32×D7—651no—
63C32×C13D5×D711yescharacteristic, complemented, Hall
64C3×C5×C7D3×D1314yescomplemented
65C7×C13D5×C3⋊D311yescharacteristic, complemented, Hall
66C3⋊D15D9111yescharacteristic, complemented
67C5×C3⋊D3—911no—
68C32×D5—911no—
69D3×D7—1954no—
70D39—214no—
71C3×D13—354no—
72D3×C13—154no—
73D35—131no—
74C5×D7—1171no—
75C7×D5—91no—
76C5×C13D7×C3⋊D311yescharacteristic, complemented, Hall
77C32×C7D5×D1311yescharacteristic, complemented, Hall
78D3×D5—2734no—
79C2×D13—3151noHall
80C32×C5C2×D9111yescharacteristic, complemented, Hall
81D21—394no—
82C3×D7—654no—
83D3×C7—154no—
84C3×C13D15⋊D714yescomplemented
85C2×C3⋊D3—4551noHall
86C5×C7C3⋊D3×D1311yescharacteristic, complemented, Hall
87D15—34no—
88C3×D5—914no—
89C5×D3—2734no—
90C2×D7—5851noHall
91C2×C13—451no—
92D13—351no—
93D13—631no—
94C3×C7D15⋊D1314yescomplemented
95C2×D5—8191noHall
96C2×C32—4551no—
97C3⋊D3—51no—
98C3⋊D3—911no—
99C3×C5D3×D9114yescomplemented
100C2×C7—451no—
101D7—651no—
102D7—1171no—
103C13D35⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
104C2×D3—13654no—
105C2×C5—8191no—
106D5—91no—
107D5—911no—
108C32D5×D9111yescharacteristic, complemented, Sylow
109C7D65⋊(C3⋊D3)11yescharacteristic, complemented, Sylow
110C2×C3—4554no—
111D3—154no—
112D3—2734no—
113C5C3⋊D3×D9111yescharacteristic, complemented, Sylow
114C22—40951noSylow
115C3D15⋊D9114yescomplemented
116C2—451no—
117C2—8191no—
118C2—4551no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C13C22
LCSG ▷ C32×C5×C7×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. C7×C13×C3⋊D15C2semidirect
2. C5×C3⋊D273C2semidirect
3. C32×D455C2semidirect
5. C32×C5×C7×C13C22semidirect
9. C3×D455D3semidirect
12. C3⋊D273D5semidirect
15. C3×C5×C7×C13C2×D3semidirect
17. C13×C3⋊D15D7semidirect
21. D455C3⋊D3semidirect
24. C32×C7×C13C2×D5semidirect
26. C7×C3⋊D15D13semidirect
29. C32×C5×C13C2×D7semidirect
34. C5×C7×C13C2×C3⋊D3semidirect
40. C32×C5×C7C2×D13semidirect
41. C3×C7×C13D3×D5semidirect
50. C3×C5×C13D3×D7semidirect
63. C32×C13D5×D7semidirect
64. C3×C5×C7D3×D13semidirect
65. C7×C13D5×C3⋊D3semidirect
66. C3⋊D15D91semidirect
76. C5×C13D7×C3⋊D3semidirect
77. C32×C7D5×D13semidirect
80. C32×C5C2×D91semidirect
84. C3×C13D15⋊D7semidirect
86. C5×C7C3⋊D3×D13semidirect
94. C3×C7D15⋊D13semidirect
99. C3×C5D3×D91semidirect
103. C13D35⋊(C3⋊D3)semidirect
108. C32D5×D91semidirect
109. C7D65⋊(C3⋊D3)semidirect
113. C5C3⋊D3×D91semidirect
115. C3D15⋊D91semidirect

Maximal subgroups

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

subgroupindex
C7×C13×C3⋊D152
C5×C3⋊D2732
C32×D4552
D15⋊D913
C3⋊D3×D915
D65⋊(C3⋊D3)7
D35⋊(C3⋊D3)13