Finite Group Databasebeta

← D5×C3⋊D609 #49141659

Subgroups — D5×C3⋊D609 #49141659

Order 36540.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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×C7×D5×C29C211yesmaximal, characteristic, complemented
2C5×C3⋊D609C211yesmaximal, characteristic, complemented
3C3⋊D3045C211yesmaximal, characteristic, complemented
4D5×D609—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C2×C3⋊D609—51nomaximal, Hall
7D3045—34no—
8C5×D609—34no—
9C3×C7×D5×C29D314yescomplemented
10D5×C3⋊D87—71nomaximal, Hall
11D5×D203—91noHall
12C3⋊D609—51no—
13C3⋊D609D511yescharacteristic, direct product factor
14C2×C32×C7×C29—51no—
15C3×C5×C7×C29C2×D314yescomplemented
16C3⋊D435—71no—
17C5×C3⋊D87—71no—
18C32×D5×C29D711yescharacteristic, complemented
19C2×D609—154no—
20D1015—91no—
21C7×D5×C29C3⋊D311yescharacteristic, complemented
22C5×D203—91no—
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D5×D87—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26D5×C3⋊D21—291nomaximal, Hall
27C2×C3×C7×C29—54no—
28D609—34no—
29D609—154no—
30C2×C3⋊D87—351noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32D435—214no—
33C5×D87—214no—
34C3×D5×C29D2114yescomplemented
35C2×D203—451noHall
36C3⋊D105—291no—
37C5×C3⋊D21—291no—
38C32×C7×D5D2911yescharacteristic, complemented
39C3×C7×C29D3×D514yescomplemented
40D5×D29—631noHall
41C2×C32×C29—51no—
42C3⋊D87—71no—
43C3⋊D87—351no—
44C3×C5×C29C2×D2114yescomplemented
45D5×D21—874no—
46C2×C7×C29—51no—
47D203—91no—
48D203—451no—
49C2×D87—1054no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51D145—631no—
52C5×D29—631no—
53D5×C29C3⋊D2111yescharacteristic, complemented
54C32×C29D5×D711yescharacteristic, complemented, Hall
55C2×C3⋊D21—1451noHall
56D105—874no—
57C5×D21—874no—
58C3×C7×D5D8714yescomplemented
59C7×C29D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—2031noHall
61C2×C3×C29—54no—
62D87—214no—
63D87—1054no—
64C5×C29C2×C3⋊D2111yescharacteristic, complemented, Hall
65D5×D7—2611noHall
66C2×C32×C7—51no—
67C3⋊D21—291no—
68C3⋊D21—1451no—
69C2×D29—3151noHall
70C3×C5×C7C2×D8714yescomplemented
71C3⋊D15—2031no—
72C5×C3⋊D3—2031no—
73C32×D5D20311yescharacteristic, complemented
74C3×C29D5×D2114yescomplemented
75C2×D21—4354no—
76D35—2611no—
77C5×D7—2611no—
78C7×D5C3⋊D8711yescharacteristic, complemented
79C32×C7D5×D2911yescharacteristic, complemented, Hall
80D3×D5—6094no—
81C2×C29—51no—
82D29—3151no—
83D29—631no—
84C32×C5C2×D20311yescharacteristic, complemented, Hall
85C2×C3×C7—54no—
86D21—874no—
87D21—4354no—
88C2×C3⋊D3—10151noHall
89C5×C7C2×C3⋊D8711yescharacteristic, complemented, Hall
90D15—6094no—
91C3×D5D60914yescomplemented
92C5×D3—6094no—
93C29D5×C3⋊D2111yescharacteristic, complemented, Sylow
94C2×D7—13051noHall
95C3×C7D5×D8714yescomplemented
96C2×D5—18271noHall
97C2×C32—51no—
98C3⋊D3—2031no—
99C3⋊D3—10151no—
100C3×C5C2×D60914yescomplemented
101C2×C7—51no—
102D7—2611no—
103D7—13051no—
104C2×D3—30454no—
105C2×C5—18271no—
106D5—18271no—
107D5C3⋊D60911yescharacteristic, direct product factor
108C32D5×D20311yescharacteristic, complemented, Sylow
109C7D5×C3⋊D8711yescharacteristic, complemented, Sylow
110C2×C3—54no—
111D3—6094no—
112D3—30454no—
113C5C2×C3⋊D60911yescharacteristic, complemented, Sylow
114C22—91351noSylow
115C3D5×D60914yescomplemented
116C2—51no—
117C2—18271no—
118C2—91351no—
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×C7×D5×C29C2semidirect
2. C5×C3⋊D609C2semidirect
3. C3⋊D3045C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C7×D5×C29D3semidirect
13. C3⋊D609D5direct (N × H)
15. C3×C5×C7×C29C2×D3semidirect
18. C32×D5×C29D7semidirect
21. C7×D5×C29C3⋊D3semidirect
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C2×D7semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
34. C3×D5×C29D21semidirect
38. C32×C7×D5D29semidirect
39. C3×C7×C29D3×D5semidirect
44. C3×C5×C29C2×D21semidirect
50. C32×C5×C7C2×D29semidirect
53. D5×C29C3⋊D21semidirect
54. C32×C29D5×D7semidirect
58. C3×C7×D5D87semidirect
59. C7×C29D5×C3⋊D3semidirect
64. C5×C29C2×C3⋊D21semidirect
70. C3×C5×C7C2×D87semidirect
73. C32×D5D203semidirect
74. C3×C29D5×D21semidirect
78. C7×D5C3⋊D87semidirect
79. C32×C7D5×D29semidirect
84. C32×C5C2×D203semidirect
89. C5×C7C2×C3⋊D87semidirect
91. C3×D5D609semidirect
93. C29D5×C3⋊D21semidirect
95. C3×C7D5×D87semidirect
100. C3×C5C2×D609semidirect
107. D5C3⋊D609direct (N × H)
108. C32D5×D203semidirect
109. C7D5×C3⋊D87semidirect
113. C5C2×C3⋊D609semidirect
115. C3D5×D609semidirect

Maximal subgroups

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

subgroupindex
C32×C7×D5×C292
C5×C3⋊D6092
C3⋊D30452
D5×D6093
C2×C3⋊D6095
D5×C3⋊D877
D5×C3⋊D2129