Finite Group Databasebeta

← C2×C5×C9×D155 #42124590

Subgroups — C2×C5×C9×D155 #42124590

Order 27900.

144 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 66 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×C9×D155C212yesmaximal, direct product factor
2C2×C52×C9×C31C211yesmaximal, characteristic, complemented
3C2×C3×C5×D155C311yesmaximal, characteristic
4C52×C9×C31C2211yescharacteristic, complemented, Hall
5C2×C9×D155C511yesmaximal, characteristic, direct product factor
6C2×C5×C9×D31—51nomaximal
7C3×C5×D155C2×C312yes—
8C2×C3×C52×C31C2×C311yescharacteristic
9C2×C5×D155C911yescharacteristic, direct product factor, Hall
10C9×D155C2×C512yesdirect product factor
11C5×C9×D31—52no—
12C2×C5×C9×C31—22no—
13C2×C5×C9×C31D511yescharacteristic, complemented
14C2×C5×C9×C31C2×C511yescharacteristic, complemented
15C3×C52×C31C22×C311yescharacteristic
16C2×C3×D155C3×C511yescharacteristic
17C2×C3×C5×D31—51no—
18C2×C52×C31C2×C911yescharacteristic, complemented
19C5×D155C2×C912yesdirect product factor
20C5×C9×C31—22no—
21C5×C9×C31C2×D511yescharacteristic, complemented
22C5×C9×C31C22×C511yescharacteristic, complemented
23C2×C9×D31—51noHall
24C2×C3×C5×C31—22no—
25C2×C3×C5×C31C3×D511yescharacteristic
26C2×C3×C5×C31C2×C3×C511yescharacteristic
27C3×D155C2×C3×C512yes—
28C3×C5×D31—52no—
29C2×C5×C9×D5—311nomaximal, Hall
30C52×C31C22×C911yescharacteristic, complemented, Hall
31C2×D155C5×C911yescharacteristic, direct product factor
32C2×C5×D31—51no—
33C2×C9×C31C5×D511yescharacteristic, complemented
34C9×D31—52no—
35C3×C5×C31—22no—
36C3×C5×C31C2×C3×D511yescharacteristic
37C3×C5×C31C22×C3×C511yescharacteristic
38C2×C52×C9D3111yescharacteristic, complemented
39C5×C9×D5—312no—
40C2×C3×D31—51no—
41C2×C5×C31—22no—
42C2×C5×C31C9×D511yescharacteristic, complemented
43C2×C5×C31C2×C5×C911yescharacteristic, complemented
44D155C2×C5×C912yesdirect product factor
45C5×D31—52no—
46C2×C3×C5×D5—311no—
47C9×C31C2×C5×D511yescharacteristic, complemented, Hall
48C52×C9C2×D3111yescharacteristic, complemented, Hall
49C2×C3×C31C3×C5×D511yescharacteristic
50C3×D31—52no—
51C22×C5×C9—1551no—
52C2×C9×D5—311no—
53C5×C31—22no—
54C5×C31C2×C9×D511yescharacteristic, complemented
55C5×C31C22×C5×C911yescharacteristic, complemented
56C2×C3×C52C3×D3111yescharacteristic
57C3×C5×D5—312no—
58C2×D31—51noHall
59C2×C5×D5—311noHall
60C3×C31C2×C3×C5×D511yescharacteristic
61C2×C5×C9—22no—
62C2×C5×C9—1552no—
63C2×C5×C9C5×D3111yescharacteristic, complemented
64C2×C5×C9D15511yescharacteristic, direct product factor
65C9×D5—312no—
66C3×C52C2×C3×D3111yescharacteristic
67C2×C31C5×C9×D511yescharacteristic, complemented
68D31—52no—
69C22×C3×C5—1551no—
70C2×C3×D5—311no—
71C2×C52C9×D3111yescharacteristic, complemented
72C5×D5—312no—
73C5×C9—22no—
74C5×C9C2×C5×D3111yescharacteristic, complemented
75C5×C9C2×D15511yescharacteristic, direct product factor
76C22×C9—1551noHall
77C31C2×C5×C9×D511yescharacteristic, complemented, Sylow
78C2×C3×C5—22no—
79C2×C3×C5—1552no—
80C2×C3×C5C3×C5×D3111yescharacteristic
81C2×C3×C5C3×D15511yescharacteristic
82C3×D5—312no—
83C52C2×C9×D3111yescharacteristic, complemented, Sylow
84C22×C5—1551no—
85C2×D5—311no—
86C2×C9—1552no—
87C2×C9C5×D15511yescharacteristic, direct product factor
88C3×C5—22no—
89C3×C5C2×C3×C5×D3111yescharacteristic
90C3×C5C2×C3×D15511yescharacteristic
91C22×C3—1551no—
92C2×C5—22no—
93C2×C5—1552no—
94C2×C5C5×C9×D3111yescharacteristic, complemented
95C2×C5C9×D15511yescharacteristic, direct product factor
96D5—312no—
97C9C2×C5×D15511yescharacteristic, direct product factor, Sylow
98C2×C3—1552no—
99C2×C3C3×C5×D15511yescharacteristic
100C5—22no—
101C5C2×C5×C9×D3111yescharacteristic, complemented
102C5C2×C9×D15511yescharacteristic, direct product factor
103C22—1551noSylow
104C3C2×C3×C5×D15511yescharacteristic
105C2—1552no—
106C2C5×C9×D15511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5×C9D155
commutator, hypocenterC5×C31C22×C5×C9
FrattiniC3C2×C3×C5×D155
FittingC2×C52×C9×C31C2
socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C5×D155C3
cosocleC3×C5×C31C22×C3×C5
LCSG ▷ C5×C31
UCSC1 ◁ C2×C5×C9

Complements

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

NH ≅ G/Ntype
1. C5×C9×D155C2direct (N × H)
2. C2×C52×C9×C31C2semidirect
4. C52×C9×C31C22semidirect
5. C2×C9×D155C5direct (N × H)
9. C2×C5×D155C9direct (N × H)
10. C9×D155C2×C5direct (N × H)
13. C2×C5×C9×C31D5semidirect
14. C2×C5×C9×C31C2×C5semidirect
18. C2×C52×C31C2×C9semidirect
19. C5×D155C2×C9direct (N × H)
21. C5×C9×C31C2×D5semidirect
22. C5×C9×C31C22×C5semidirect
30. C52×C31C22×C9semidirect
31. C2×D155C5×C9direct (N × H)
33. C2×C9×C31C5×D5semidirect
38. C2×C52×C9D31semidirect
42. C2×C5×C31C9×D5semidirect
43. C2×C5×C31C2×C5×C9semidirect
44. D155C2×C5×C9direct (N × H)
47. C9×C31C2×C5×D5semidirect
48. C52×C9C2×D31semidirect
54. C5×C31C2×C9×D5semidirect
55. C5×C31C22×C5×C9semidirect
63. C2×C5×C9C5×D31semidirect
64. C2×C5×C9D155direct (N × H)
67. C2×C31C5×C9×D5semidirect
71. C2×C52C9×D31semidirect
74. C5×C9C2×C5×D31semidirect
75. C5×C9C2×D155direct (N × H)
77. C31C2×C5×C9×D5semidirect
83. C52C2×C9×D31semidirect
87. C2×C9C5×D155direct (N × H)
94. C2×C5C5×C9×D31semidirect
95. C2×C5C9×D155direct (N × H)
97. C9C2×C5×D155direct (N × H)
101. C5C2×C5×C9×D31semidirect
102. C5C2×C9×D155direct (N × H)
106. C2C5×C9×D155direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C9×D1552
C2×C52×C9×C312
C2×C3×C5×D1553
C2×C9×D1555
C2×C5×C9×D315
C2×C5×C9×D531