Finite Group Databasebeta

← D29×C3⋊D105 #49141649

Subgroups — D29×C3⋊D105 #49141649

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×C5×C7×D29C211yesmaximal, characteristic, complemented
2C29×C3⋊D105C211yesmaximal, characteristic, complemented
3C3⋊D3045C211yesmaximal, characteristic, complemented
4D29×D105—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6D29×C3⋊D21—51nomaximal, Hall
7D3045—34no—
8C29×D105—34no—
9C3×C5×C7×D29D314yescomplemented
10D29×C3⋊D15—71nomaximal, Hall
11D29×D35—91noHall
12C3⋊D609—51no—
13C29×C3⋊D21—51no—
14C32×C7×D29D511yescharacteristic, complemented
15C3×C5×C7×C29C2×D314yescomplemented
16C3⋊D435—71no—
17C29×C3⋊D15—71no—
18C32×C5×D29D711yescharacteristic, complemented
19D21×D29—154no—
20D1015—91no—
21C29×D35—91no—
22C5×C7×D29C3⋊D311yescharacteristic, complemented
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D15×D29—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26C2×C3⋊D105—291nomaximal, Hall
27D609—154no—
28C29×D21—154no—
29C3×C7×D29D1514yescomplemented
30C3⋊D3×D29—351noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32D435—214no—
33C29×D15—214no—
34C3×C5×D29D2114yescomplemented
35D7×D29—451noHall
36C2×C32×C5×C7—291no—
37C3⋊D105—291no—
38C3⋊D105D2911yescharacteristic, direct product factor
39C3×C7×C29C2×D1514yescomplemented
40D5×D29—631noHall
41C3⋊D87—351no—
42C3⋊D3×C29—351no—
43C32×D29D3511yescharacteristic, complemented
44C3×C5×C29C2×D2114yescomplemented
45C2×D105—874no—
46D203—451no—
47C7×D29C3⋊D1511yescharacteristic, complemented
48D7×C29—451no—
49D3×D29—1054no—
50C32×C5×C7C2×D2911yescharacteristic, complemented, Hall
51D145—631no—
52C5×D29C3⋊D2111yescharacteristic, complemented
53D5×C29—631no—
54C32×C29C2×D3511yescharacteristic, complemented, Hall
55C2×C3⋊D21—1451noHall
56C2×C3×C5×C7—294no—
57D105—34no—
58D105—874no—
59C7×C29C2×C3⋊D1511yescharacteristic, complemented, Hall
60C2×C3⋊D15—2031noHall
61D87—1054no—
62C3×D29D10514yescomplemented
63D3×C29—1054no—
64C5×C29C2×C3⋊D2111yescharacteristic, complemented, Hall
65C2×D35—2611noHall
66C2×C32×C7—291no—
67C3⋊D21—51no—
68C3⋊D21—1451no—
69C2×D29—3151noHall
70C3×C5×C7D3×D2914yescomplemented
71C2×C32×C5—291no—
72C3⋊D15—71no—
73C3⋊D15—2031no—
74C3×C29C2×D10514yescomplemented
75C2×D21—4354no—
76C2×C5×C7—291no—
77D35—2611no—
78D35—91no—
79C32×C7D5×D2911yescharacteristic, complemented, Hall
80C2×D15—6094no—
81C2×C29—3151no—
82D29—3151no—
83D29C3⋊D10511yescharacteristic, direct product factor
84C32×C5D7×D2911yescharacteristic, complemented, Hall
85C2×C3×C7—294no—
86D21—154no—
87D21—4354no—
88C2×C3⋊D3—10151noHall
89C5×C7C3⋊D3×D2911yescharacteristic, complemented, Hall
90C2×C3×C5—294no—
91D15—214no—
92D15—6094no—
93C29C2×C3⋊D10511yescharacteristic, complemented, Sylow
94C2×D7—13051noHall
95C3×C7D15×D2914yescomplemented
96C2×D5—18271noHall
97C2×C32—291no—
98C3⋊D3—351no—
99C3⋊D3—10151no—
100C3×C5D21×D2914yescomplemented
101C2×C7—291no—
102D7—13051no—
103D7—451no—
104C2×D3—30454no—
105C2×C5—291no—
106D5—18271no—
107D5—631no—
108C32D29×D3511yescharacteristic, complemented, Sylow
109C7D29×C3⋊D1511yescharacteristic, complemented, Sylow
110C2×C3—294no—
111D3—1054no—
112D3—30454no—
113C5D29×C3⋊D2111yescharacteristic, complemented, Sylow
114C22—91351noSylow
115C3D29×D10514yescomplemented
116C2—291no—
117C2—3151no—
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×C5×C7×D29C2semidirect
2. C29×C3⋊D105C2semidirect
3. C3⋊D3045C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C5×C7×D29D3semidirect
14. C32×C7×D29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
18. C32×C5×D29D7semidirect
22. C5×C7×D29C3⋊D3semidirect
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C2×D7semidirect
29. C3×C7×D29D15semidirect
31. C5×C7×C29C2×C3⋊D3semidirect
34. C3×C5×D29D21semidirect
38. C3⋊D105D29direct (N × H)
39. C3×C7×C29C2×D15semidirect
43. C32×D29D35semidirect
44. C3×C5×C29C2×D21semidirect
47. C7×D29C3⋊D15semidirect
50. C32×C5×C7C2×D29semidirect
52. C5×D29C3⋊D21semidirect
54. C32×C29C2×D35semidirect
59. C7×C29C2×C3⋊D15semidirect
62. C3×D29D105semidirect
64. C5×C29C2×C3⋊D21semidirect
70. C3×C5×C7D3×D29semidirect
74. C3×C29C2×D105semidirect
79. C32×C7D5×D29semidirect
83. D29C3⋊D105direct (N × H)
84. C32×C5D7×D29semidirect
89. C5×C7C3⋊D3×D29semidirect
93. C29C2×C3⋊D105semidirect
95. C3×C7D15×D29semidirect
100. C3×C5D21×D29semidirect
108. C32D29×D35semidirect
109. C7D29×C3⋊D15semidirect
113. C5D29×C3⋊D21semidirect
115. C3D29×D105semidirect

Maximal subgroups

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

subgroupindex
C32×C5×C7×D292
C29×C3⋊D1052
C3⋊D30452
D29×D1053
D29×C3⋊D215
D29×C3⋊D157
C2×C3⋊D10529