Finite Group Databasebeta

← C5×C3⋊D3×D91 #30655680

Subgroups — C5×C3⋊D3×D91 #30655680

Order 16380.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C5×C3⋊D273C211yesmaximal, characteristic, complemented
2C5×C7×C13×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C5×D91C211yesmaximal, characteristic, complemented
4C5×D3×D91—34nomaximal
5C32×C5×C7×C13C2211yescharacteristic, complemented, Hall
6C3⋊D3×D91C511yesmaximal, characteristic, direct product factor, Hall
7C5×D273—34no—
8C5×D3×C7×C13—34no—
9C3×C5×D91D314yescomplemented
10C5×C3⋊D3×D13—71nomaximal, Hall
11C2×C5×D91—91noHall
12C3⋊D273C2×C511yescharacteristic, complemented
13C7×C13×C3⋊D3C2×C511yescharacteristic, complemented
14C32×D91C2×C511yescharacteristic, complemented
15C3×C5×C7×C13C2×D314yescomplemented
16C5×D7×C3⋊D3—131nomaximal, Hall
17C5×C3⋊D39—71no—
18C5×C13×C3⋊D3D711yescharacteristic, complemented
19C32×C5×D13—71no—
20D3×D91—34no—
21C2×C5×C7×C13—91no—
22C5×D91—91no—
23C5×D91C3⋊D311yescharacteristic, direct product factor
24C32×C7×C13C22×C511yescharacteristic, complemented, Hall
25C5×D3×D13—214no—
26C5×C3⋊D21—131no—
27C5×C7×C3⋊D3D1311yescharacteristic, complemented
28C32×C5×D7—131no—
29C32×C5×C13C2×D711yescharacteristic, complemented, Hall
30D273—34no—
31D3×C7×C13—34no—
32C3×D91C5×D314yescomplemented
33C3⋊D3×D13—71noHall
34C5×C7×C13C2×C3⋊D311yescharacteristic, complemented, Hall
35C5×D3×D7—394no—
36C5×D39—214no—
37C5×D3×C13—34no—
38C3×C5×D13—74no—
39C2×D91—91noHall
40C32×C5×C7C2×D1311yescharacteristic, complemented, Hall
41C3×C7×C13C2×C5×D314yescomplemented
42C2×C5×D13—631noHall
43D7×C3⋊D3—131noHall
44C3⋊D39—71no—
45C13×C3⋊D3C5×D711yescharacteristic, complemented
46C32×D13—71no—
47C5×D21—394no—
48C5×D3×C7—34no—
49C3×C5×D7—134no—
50C3×C5×C13D3×D714yescomplemented
51C2×C7×C13—91no—
52D91—91no—
53D91C5×C3⋊D311yescharacteristic, direct product factor
54C2×C5×C3⋊D3—911noHall
55D3×D13—214no—
56C2×C5×D7—1171noHall
57C2×C5×C13—91no—
58C5×D13—71no—
59C5×D13—631no—
60C3⋊D21—131no—
61C7×C3⋊D3C5×D1311yescharacteristic, complemented
62C32×D7—131no—
63C32×C13C2×C5×D711yescharacteristic, complemented, Hall
64C3×C5×C7D3×D1314yescomplemented
65C7×C13C2×C5×C3⋊D311yescharacteristic, complemented, Hall
66C2×C32×C5—911no—
67C5×C3⋊D3—911no—
68C5×C3⋊D3D9111yescharacteristic, direct product factor
69D3×D7—394no—
70D39—214no—
71C3×D13—74no—
72D3×C13—34no—
73C2×C5×C7—91no—
74C5×D7—131no—
75C5×D7—1171no—
76C5×C13D7×C3⋊D311yescharacteristic, complemented, Hall
77C32×C7C2×C5×D1311yescharacteristic, complemented, Hall
78C2×C5×D3—2734no—
79C2×D13—631noHall
80C32×C5C2×D9111yescharacteristic, complemented, Hall
81D21—394no—
82C3×D7—134no—
83D3×C7—34no—
84C3×C13C5×D3×D714yescomplemented
85C2×C3⋊D3—911noHall
86C5×C7C3⋊D3×D1311yescharacteristic, complemented, Hall
87C2×C3×C5—914no—
88C5×D3—34no—
89C5×D3—2734no—
90C2×D7—1171noHall
91C2×C13—91no—
92D13—71no—
93D13—631no—
94C3×C7C5×D3×D1314yescomplemented
95C22×C5—8191noHall
96C2×C32—911no—
97C3⋊D3—911no—
98C3⋊D3C5×D9111yescharacteristic, direct product factor
99C3×C5D3×D9114yescomplemented
100C2×C7—91no—
101D7—131no—
102D7—1171no—
103C13C5×D7×C3⋊D311yescharacteristic, complemented, Sylow
104C2×D3—2734no—
105C2×C5—91no—
106C2×C5—8191no—
107C2×C5—911no—
108C32C2×C5×D9111yescharacteristic, complemented, Sylow
109C7C5×C3⋊D3×D1311yescharacteristic, complemented, Sylow
110C2×C3—914no—
111D3—34no—
112D3—2734no—
113C5C3⋊D3×D9111yescharacteristic, direct product factor, Sylow
114C22—8191noSylow
115C3C5×D3×D9114yescomplemented
116C2—91no—
117C2—8191no—
118C2—911no—
subgroupG/H
center, hypercenterC5C3⋊D3×D91
commutator, cosocle, hypocenterC32×C7×C13C22×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊D273C2semidirect
2. C5×C7×C13×C3⋊D3C2semidirect
3. C32×C5×D91C2semidirect
5. C32×C5×C7×C13C22semidirect
6. C3⋊D3×D91C5direct (N × H)
9. C3×C5×D91D3semidirect
12. C3⋊D273C2×C5semidirect
13. C7×C13×C3⋊D3C2×C5semidirect
14. C32×D91C2×C5semidirect
15. C3×C5×C7×C13C2×D3semidirect
18. C5×C13×C3⋊D3D7semidirect
23. C5×D91C3⋊D3direct (N × H)
24. C32×C7×C13C22×C5semidirect
27. C5×C7×C3⋊D3D13semidirect
29. C32×C5×C13C2×D7semidirect
32. C3×D91C5×D3semidirect
34. C5×C7×C13C2×C3⋊D3semidirect
40. C32×C5×C7C2×D13semidirect
41. C3×C7×C13C2×C5×D3semidirect
45. C13×C3⋊D3C5×D7semidirect
50. C3×C5×C13D3×D7semidirect
53. D91C5×C3⋊D3direct (N × H)
61. C7×C3⋊D3C5×D13semidirect
63. C32×C13C2×C5×D7semidirect
64. C3×C5×C7D3×D13semidirect
65. C7×C13C2×C5×C3⋊D3semidirect
68. C5×C3⋊D3D91direct (N × H)
76. C5×C13D7×C3⋊D3semidirect
77. C32×C7C2×C5×D13semidirect
80. C32×C5C2×D91semidirect
84. C3×C13C5×D3×D7semidirect
86. C5×C7C3⋊D3×D13semidirect
94. C3×C7C5×D3×D13semidirect
98. C3⋊D3C5×D91direct (N × H)
99. C3×C5D3×D91semidirect
103. C13C5×D7×C3⋊D3semidirect
108. C32C2×C5×D91semidirect
109. C7C5×C3⋊D3×D13semidirect
113. C5C3⋊D3×D91direct (N × H)
115. C3C5×D3×D91semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊D2732
C5×C7×C13×C3⋊D32
C32×C5×D912
C5×D3×D913
C3⋊D3×D915
C5×C3⋊D3×D137
C5×D7×C3⋊D313