Finite Group Databasebeta

← C3⋊D3×D1015 #49141664

Subgroups — C3⋊D3×D1015 #49141664

Order 36540.

240 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C32×D1015C211yesmaximal, characteristic, complemented
2C5×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C3⋊D3045C211yesmaximal, characteristic, complemented
4D3×D1015—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C3⋊D3×D203—51nomaximal, Hall
7D3045—34no—
8C5×D3×C7×C29—34no—
9C3×D1015D314yescomplemented
10C3⋊D3×D145—71nomaximal, Hall
11C2×D1015—91noHall
12C3⋊D609—51no—
13C7×C3⋊D3×C29D511yescharacteristic, complemented
14C32×D203—51no—
15C3×C5×C7×C29C2×D314yescomplemented
16C3⋊D435—71no—
17C5×C3⋊D3×C29D711yescharacteristic, complemented
18C32×D145—71no—
19D3×D203—154no—
20D1015—91no—
21D1015C3⋊D311yescharacteristic, direct product factor
22C2×C5×C7×C29—91no—
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D3×D145—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26C3⋊D3×D35—291nomaximal, Hall
27D609—154no—
28D3×C7×C29—34no—
29C3×D203—54no—
30C3⋊D3×D29—351noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32D435—214no—
33C5×D3×C29—34no—
34C3×D145—74no—
35C2×D203—451noHall
36C3⋊D105—291no—
37C5×C7×C3⋊D3D2911yescharacteristic, complemented
38C32×D35—291no—
39C3×C7×C29D3×D514yescomplemented
40C2×D145—631noHall
41C3⋊D87—351no—
42C3⋊D3×C29D3511yescharacteristic, complemented
43C32×D29—351no—
44C3×C5×C29D3×D714yescomplemented
45D3×D35—874no—
46C2×C7×C29—91no—
47D203—51no—
48D203—451no—
49D3×D29—1054no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51C2×C5×C29—91no—
52D145—71no—
53D145—631no—
54C32×C29C2×D3511yescharacteristic, complemented, Hall
55D7×C3⋊D3—1451noHall
56D105—874no—
57C5×D3×C7—34no—
58C3×D35—294no—
59C7×C29D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—2031noHall
61D87—1054no—
62C3×D29—354no—
63D3×C29—34no—
64C5×C29D7×C3⋊D311yescharacteristic, complemented, Hall
65C2×D35—2611noHall
66C3⋊D21—1451no—
67C7×C3⋊D3D14511yescharacteristic, complemented
68C32×D7—1451no—
69C2×D29—3151noHall
70C3×C5×C7D3×D2914yescomplemented
71C3⋊D15—2031no—
72C5×C3⋊D3D20311yescharacteristic, complemented
73C32×D5—2031no—
74C3×C29D3×D3514yescomplemented
75D3×D7—4354no—
76C2×C5×C7—91no—
77D35—2611no—
78D35—291no—
79C32×C7C2×D14511yescharacteristic, complemented, Hall
80D3×D5—6094no—
81C2×C29—91no—
82D29—351no—
83D29—3151no—
84C32×C5C2×D20311yescharacteristic, complemented, Hall
85D21—4354no—
86C3×D7—1454no—
87D3×C7—34no—
88C2×C3⋊D3—10151noHall
89C5×C7C3⋊D3×D2911yescharacteristic, complemented, Hall
90D15—6094no—
91C3×D5—2034no—
92C5×D3—34no—
93C29C3⋊D3×D3511yescharacteristic, complemented, Sylow
94C2×D7—13051noHall
95C3×C7D3×D14514yescomplemented
96C2×D5—18271noHall
97C2×C32—10151no—
98C3⋊D3—10151no—
99C3⋊D3D101511yescharacteristic, direct product factor
100C3×C5D3×D20314yescomplemented
101C2×C7—91no—
102D7—13051no—
103D7—1451no—
104C2×D3—30454no—
105C2×C5—91no—
106D5—18271no—
107D5—2031no—
108C32C2×D101511yescharacteristic, complemented, Sylow
109C7C3⋊D3×D14511yescharacteristic, complemented, Sylow
110C2×C3—10154no—
111D3—34no—
112D3—30454no—
113C5C3⋊D3×D20311yescharacteristic, complemented, Sylow
114C22—91351noSylow
115C3D3×D101514yescomplemented
116C2—91no—
117C2—91351no—
118C2—10151no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×D1015C2semidirect
2. C5×C7×C3⋊D3×C29C2semidirect
3. C3⋊D3045C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×D1015D3semidirect
13. C7×C3⋊D3×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
17. C5×C3⋊D3×C29D7semidirect
21. D1015C3⋊D3direct (N × H)
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C2×D7semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
37. C5×C7×C3⋊D3D29semidirect
39. C3×C7×C29D3×D5semidirect
42. C3⋊D3×C29D35semidirect
44. C3×C5×C29D3×D7semidirect
50. C32×C5×C7C2×D29semidirect
54. C32×C29C2×D35semidirect
59. C7×C29D5×C3⋊D3semidirect
64. C5×C29D7×C3⋊D3semidirect
67. C7×C3⋊D3D145semidirect
70. C3×C5×C7D3×D29semidirect
72. C5×C3⋊D3D203semidirect
74. C3×C29D3×D35semidirect
79. C32×C7C2×D145semidirect
84. C32×C5C2×D203semidirect
89. C5×C7C3⋊D3×D29semidirect
93. C29C3⋊D3×D35semidirect
95. C3×C7D3×D145semidirect
99. C3⋊D3D1015direct (N × H)
100. C3×C5D3×D203semidirect
108. C32C2×D1015semidirect
109. C7C3⋊D3×D145semidirect
113. C5C3⋊D3×D203semidirect
115. C3D3×D1015semidirect

Maximal subgroups

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

subgroupindex
C32×D10152
C5×C7×C3⋊D3×C292
C3⋊D30452
D3×D10153
C3⋊D3×D2035
C3⋊D3×D1457
C3⋊D3×D3529