Finite Group Databasebeta

← C2×C32×C5×D155 #42124982

Subgroups — C2×C32×C5×D155 #42124982

Order 27900.

288 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 132 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×D155C212yesmaximal, direct product factor
2C2×C32×C52×C31C211yesmaximal, characteristic, complemented
3C2×C3×C5×D155C314yesmaximal, direct product factor
4C32×C52×C31C2211yescharacteristic, complemented, Hall
5C2×C32×C5×D31—51nomaximal
6C2×C32×D155C511yesmaximal, characteristic, direct product factor
7C3×C5×D155C2×C318yesdirect product factor
8C2×C3×C52×C31C2×C314yescomplemented
9C2×C5×D155C3211yescharacteristic, direct product factor, Hall
10C32×D155C2×C512yesdirect product factor
11C32×C5×D31—52no—
12C2×C32×C5×C31—22no—
13C2×C32×C5×C31D511yescharacteristic, complemented
14C2×C32×C5×C31C2×C511yescharacteristic, complemented
15C3×C52×C31C22×C314yescomplemented
16C2×C3×D155C3×C514yesdirect product factor
17C2×C3×C5×D31—54no—
18C2×C52×C31C2×C3211yescharacteristic, complemented
19C5×D155C2×C3212yesdirect product factor
20C32×C5×C31—22no—
21C32×C5×C31C2×D511yescharacteristic, complemented
22C32×C5×C31C22×C511yescharacteristic, complemented
23C2×C32×D31—51noHall
24C2×C3×C5×C31—28no—
25C2×C3×C5×C31C3×D514yescomplemented
26C2×C3×C5×C31C2×C3×C514yescomplemented
27C3×D155C2×C3×C518yesdirect product factor
28C3×C5×D31—58no—
29C2×C32×C5×D5—311nomaximal, Hall
30C52×C31C22×C3211yescharacteristic, complemented, Hall
31C2×D155C32×C511yescharacteristic, direct product factor
32C2×C5×D31—51no—
33C2×C32×C31C5×D511yescharacteristic, complemented
34C32×D31—52no—
35C3×C5×C31—28no—
36C3×C5×C31C2×C3×D514yescomplemented
37C3×C5×C31C22×C3×C514yescomplemented
38C2×C32×C52D3111yescharacteristic, complemented
39C32×C5×D5—312no—
40C2×C3×D31—54no—
41C2×C5×C31—22no—
42C2×C5×C31C32×D511yescharacteristic, complemented
43C2×C5×C31C2×C32×C511yescharacteristic, complemented
44D155C2×C32×C512yesdirect product factor
45C5×D31—52no—
46C2×C3×C5×D5—314no—
47C32×C31C2×C5×D511yescharacteristic, complemented, Hall
48C32×C52C2×D3111yescharacteristic, complemented, Hall
49C2×C3×C31C3×C5×D514yescomplemented
50C3×D31—58no—
51C22×C32×C5—1551no—
52C2×C32×D5—311no—
53C5×C31—22no—
54C5×C31C2×C32×D511yescharacteristic, complemented
55C5×C31C22×C32×C511yescharacteristic, complemented
56C2×C3×C52C3×D3114yescomplemented
57C3×C5×D5—318no—
58C2×D31—51noHall
59C2×C5×D5—311noHall
60C3×C31C2×C3×C5×D514yescomplemented
61C2×C32×C5—22no—
62C2×C32×C5—1552no—
63C2×C32×C5C5×D3111yescharacteristic, complemented
64C2×C32×C5D15511yescharacteristic, direct product factor
65C32×D5—312no—
66C3×C52C2×C3×D3114yescomplemented
67C2×C31C32×C5×D511yescharacteristic, complemented
68D31—52no—
69C22×C3×C5—1554no—
70C2×C3×D5—314no—
71C2×C52C32×D3111yescharacteristic, complemented
72C5×D5—312no—
73C32×C5—22no—
74C32×C5C2×C5×D3111yescharacteristic, complemented
75C32×C5C2×D15511yescharacteristic, direct product factor
76C22×C32—1551noHall
77C31C2×C32×C5×D511yescharacteristic, complemented, Sylow
78C2×C3×C5—28no—
79C2×C3×C5—1558no—
80C2×C3×C5C3×C5×D3114yescomplemented
81C2×C3×C5C3×D15514yesdirect product factor
82C3×D5—318no—
83C52C2×C32×D3111yescharacteristic, complemented, Sylow
84C22×C5—1551no—
85C2×D5—311no—
86C2×C32—1552no—
87C2×C32C5×D15511yescharacteristic, direct product factor
88C3×C5—28no—
89C3×C5C2×C3×C5×D3114yescomplemented
90C3×C5C2×C3×D15514yesdirect product factor
91C22×C3—1554no—
92C2×C5—22no—
93C2×C5—1552no—
94C2×C5C32×C5×D3111yescharacteristic, complemented
95C2×C5C32×D15511yescharacteristic, direct product factor
96D5—312no—
97C32C2×C5×D15511yescharacteristic, direct product factor, Sylow
98C2×C3—1558no—
99C2×C3C3×C5×D15514yesdirect product factor
100C5—22no—
101C5C2×C32×D15511yescharacteristic, direct product factor
102C5C2×C32×C5×D3111yescharacteristic, complemented
103C22—1551noSylow
104C3C2×C3×C5×D15514yesdirect product factor
105C2—1552no—
106C2C32×C5×D15511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5D155
commutator, cosocle, hypocenterC5×C31C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C31C2
LCSG ▷ C5×C31
UCSC1 ◁ C2×C32×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D155C2direct (N × H)
2. C2×C32×C52×C31C2semidirect
3. C2×C3×C5×D155C3direct (N × H)
4. C32×C52×C31C22semidirect
6. C2×C32×D155C5direct (N × H)
7. C3×C5×D155C2×C3direct (N × H)
8. C2×C3×C52×C31C2×C3semidirect
9. C2×C5×D155C32direct (N × H)
10. C32×D155C2×C5direct (N × H)
13. C2×C32×C5×C31D5semidirect
14. C2×C32×C5×C31C2×C5semidirect
15. C3×C52×C31C22×C3semidirect
16. C2×C3×D155C3×C5direct (N × H)
18. C2×C52×C31C2×C32semidirect
19. C5×D155C2×C32direct (N × H)
21. C32×C5×C31C2×D5semidirect
22. C32×C5×C31C22×C5semidirect
25. C2×C3×C5×C31C3×D5semidirect
26. C2×C3×C5×C31C2×C3×C5semidirect
27. C3×D155C2×C3×C5direct (N × H)
30. C52×C31C22×C32semidirect
31. C2×D155C32×C5direct (N × H)
33. C2×C32×C31C5×D5semidirect
36. C3×C5×C31C2×C3×D5semidirect
37. C3×C5×C31C22×C3×C5semidirect
38. C2×C32×C52D31semidirect
42. C2×C5×C31C32×D5semidirect
43. C2×C5×C31C2×C32×C5semidirect
44. D155C2×C32×C5direct (N × H)
47. C32×C31C2×C5×D5semidirect
48. C32×C52C2×D31semidirect
49. C2×C3×C31C3×C5×D5semidirect
54. C5×C31C2×C32×D5semidirect
55. C5×C31C22×C32×C5semidirect
56. C2×C3×C52C3×D31semidirect
60. C3×C31C2×C3×C5×D5semidirect
63. C2×C32×C5C5×D31semidirect
64. C2×C32×C5D155direct (N × H)
66. C3×C52C2×C3×D31semidirect
67. C2×C31C32×C5×D5semidirect
71. C2×C52C32×D31semidirect
74. C32×C5C2×C5×D31semidirect
75. C32×C5C2×D155direct (N × H)
77. C31C2×C32×C5×D5semidirect
80. C2×C3×C5C3×C5×D31semidirect
81. C2×C3×C5C3×D155direct (N × H)
83. C52C2×C32×D31semidirect
87. C2×C32C5×D155direct (N × H)
89. C3×C5C2×C3×C5×D31semidirect
90. C3×C5C2×C3×D155direct (N × H)
94. C2×C5C32×C5×D31semidirect
95. C2×C5C32×D155direct (N × H)
97. C32C2×C5×D155direct (N × H)
99. C2×C3C3×C5×D155direct (N × H)
101. C5C2×C32×D155direct (N × H)
102. C5C2×C32×C5×D31semidirect
104. C3C2×C3×C5×D155direct (N × H)
106. C2C32×C5×D155direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D1552
C2×C32×C52×C312
C2×C3×C5×D1553
C2×C32×C5×D315
C2×C32×D1555
C2×C32×C5×D531