Finite Group Databasebeta

← D5×D29×C7⋊C9 #49141237

Subgroups — D5×D29×C7⋊C9 #49141237

Order 36540.

120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 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⋊C9×D145C211yesmaximal, characteristic, complemented
2D5×C29×C7⋊C9C211yesmaximal, characteristic, complemented
3C5×D29×C7⋊C9C211yesmaximal, characteristic, complemented
4C3×C7×D5×D29C311yesmaximal, characteristic
5C5×C29×C7⋊C9C2211yescharacteristic, complemented, Hall
6C2×D29×C7⋊C9—51nomaximal, Hall
7C3×C7×D145C2×C311yescharacteristic
8C3×C7×D5×C29C2×C311yescharacteristic
9C3×C5×C7×D29C2×C311yescharacteristic
10C9×D5×D29—71nomaximal, Hall
11C7×D5×D29C911yescharacteristic, complemented, Hall
12C2×C29×C7⋊C9—51no—
13D29×C7⋊C9—51no—
14D29×C7⋊C9D511yescharacteristic, direct product factor
15C3×C5×C7×C29C22×C311yescharacteristic
16C9×D145—71no—
17C9×D5×C29—71no—
18C5×C9×D29—71no—
19C2×C3×C7×D29—51no—
20C7×D145C2×C911yescharacteristic, complemented
21C7×D5×C29C2×C911yescharacteristic, complemented
22C5×C7×D29C2×C911yescharacteristic, complemented
23C29×C7⋊C9C2×D511yescharacteristic, complemented, Hall
24C3×D5×D29ΓL(1,𝔽8)11yescharacteristic
25C5×C9×C29—71noHall
26C2×D5×C7⋊C9—291nomaximal, Hall
27C2×C3×C7×C29—51no—
28C3×C7×D29—51no—
29C3×C7×D29C3×D511yescharacteristic
30C2×C9×D29—351noHall
31C5×C7×C29C22×C911yescharacteristic, complemented, Hall
32C3×D145C2×ΓL(1,𝔽8)11yescharacteristic
33C3×D5×C29C2×ΓL(1,𝔽8)11yescharacteristic
34C3×C5×D29C2×ΓL(1,𝔽8)11yescharacteristic
35C2×C7×D29—51noHall
36C2×C5×C7⋊C9—291no—
37D5×C7⋊C9—291no—
38D5×C7⋊C9D2911yescharacteristic, direct product factor
39C3×C7×C29C2×C3×D511yescharacteristic
40D5×D29C7⋊C911yescharacteristic, direct product factor, Hall
41C2×C9×C29—351no—
42C9×D29—71no—
43C9×D29—351no—
44C3×C5×C29C22×ΓL(1,𝔽8)11yescharacteristic
45C2×C3×C7×D5—291no—
46C2×C7×C29—51no—
47C7×D29—51no—
48C7×D29C9×D511yescharacteristic, complemented
49C2×C3×D29—51no—
50C5×C7⋊C9C2×D2911yescharacteristic, complemented, Hall
51D145C2×C7⋊C911yescharacteristic, complemented
52C5×D29C2×C7⋊C911yescharacteristic, complemented
53D5×C29C2×C7⋊C911yescharacteristic, complemented
54C9×C29—71noHall
55C22×C7⋊C9—1451noHall
56C2×C3×C5×C7—291no—
57C3×C7×D5—291no—
58C3×C7×D5C3×D2911yescharacteristic
59C7×C29C2×C9×D511yescharacteristic, complemented, Hall
60C2×C9×D5—2031noHall
61C2×C3×C29—51no—
62C3×D29—51no—
63C3×D29D5×ΓL(1,𝔽8)11yescharacteristic
64C5×C29C22×C7⋊C911yescharacteristic, complemented, Hall
65C2×C7×D5—291noHall
66C2×C7⋊C9—51no—
67C2×C7⋊C9—291no—
68C2×C7⋊C9—1451no—
69C2×D29—51noHall
70C3×C5×C7C2×C3×D2911yescharacteristic
71C2×C5×C9—2031no—
72C9×D5—71no—
73C9×D5—2031no—
74C3×C29C2×D5×ΓL(1,𝔽8)11yescharacteristic
75C22×C3×C7—1451no—
76C2×C5×C7—291no—
77C7×D5—291no—
78C7×D5C9×D2911yescharacteristic, complemented
79C7⋊C9D5×D2911yescharacteristic, direct product factor, Hall
80C2×C3×D5—291no—
81C2×C29—51no—
82D29—51no—
83D29D5×C7⋊C911yescharacteristic, direct product factor
84C5×C9—71noHall
85C2×C3×C7—51no—
86C2×C3×C7—291no—
87C2×C3×C7—1451no—
88C22×C9—10151noHall
89C5×C7C2×C9×D2911yescharacteristic, complemented, Hall
90C2×C3×C5—291no—
91C3×D5—291no—
92C3×D5ΓL(1,𝔽8)×D2911yescharacteristic
93C29C2×D5×C7⋊C911yescharacteristic, complemented, Sylow
94C22×C7—1451noHall
95C3×C7C3×D5×D2911yescharacteristic
96C2×D5—291noHall
97C2×C9—351no—
98C2×C9—2031no—
99C2×C9—10151no—
100C3×C5C2×ΓL(1,𝔽8)×D2911yescharacteristic
101C2×C7—51no—
102C2×C7—291no—
103C2×C7—1451no—
104C22×C3—1451no—
105C2×C5—291no—
106D5—291no—
107D5D29×C7⋊C911yescharacteristic, direct product factor
108C9—71noSylow
109C7C9×D5×D2911yescharacteristic, complemented, Sylow
110C2×C3—51no—
111C2×C3—291no—
112C2×C3—1451no—
113C5C2×D29×C7⋊C911yescharacteristic, complemented, Sylow
114C22—1451noSylow
115C3D5×ΓL(1,𝔽8)×D2911yescharacteristic
116C2—51no—
117C2—291no—
118C2—1451no—
subgroupG/H
center, Frattini, hypercenterC3D5×ΓL(1,𝔽8)×D29
commutator, hypocenterC5×C7×C29C22×C9
Fitting, socle, cosocleC3×C5×C7×C29C22×C3
prime radicalC3×C7×D5×D29C3
LCSG ▷ C5×C7×C29
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C7⋊C9×D145C2semidirect
2. D5×C29×C7⋊C9C2semidirect
3. C5×D29×C7⋊C9C2semidirect
5. C5×C29×C7⋊C9C22semidirect
11. C7×D5×D29C9semidirect
14. D29×C7⋊C9D5direct (N × H)
20. C7×D145C2×C9semidirect
21. C7×D5×C29C2×C9semidirect
22. C5×C7×D29C2×C9semidirect
23. C29×C7⋊C9C2×D5semidirect
31. C5×C7×C29C22×C9semidirect
38. D5×C7⋊C9D29direct (N × H)
40. D5×D29C7⋊C9direct (N × H)
48. C7×D29C9×D5semidirect
50. C5×C7⋊C9C2×D29semidirect
51. D145C2×C7⋊C9semidirect
52. C5×D29C2×C7⋊C9semidirect
53. D5×C29C2×C7⋊C9semidirect
59. C7×C29C2×C9×D5semidirect
64. C5×C29C22×C7⋊C9semidirect
78. C7×D5C9×D29semidirect
79. C7⋊C9D5×D29direct (N × H)
83. D29D5×C7⋊C9direct (N × H)
89. C5×C7C2×C9×D29semidirect
93. C29C2×D5×C7⋊C9semidirect
107. D5D29×C7⋊C9direct (N × H)
109. C7C9×D5×D29semidirect
113. C5C2×D29×C7⋊C9semidirect

Maximal subgroups

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

subgroupindex
C7⋊C9×D1452
D5×C29×C7⋊C92
C5×D29×C7⋊C92
C3×C7×D5×D293
C2×D29×C7⋊C95
C9×D5×D297
C2×D5×C7⋊C929