Finite Group Databasebeta

← C2×C32×C5×D5×C41 #49147205

Subgroups — C2×C32×C5×D5×C41 #49147205

Order 36900.

288 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 168 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×D5×C41C212yesmaximal, direct product factor
2C2×C32×C52×C41C211yesmaximal, characteristic, complemented
3C2×C3×C5×D5×C41C314yesmaximal, direct product factor
4C32×C52×C41C2211yescharacteristic, complemented, Hall
5C2×C32×D5×C41C511yesmaximal, characteristic, direct product factor
6C22×C32×C5×C41—51nomaximal
7C3×C5×D5×C41C2×C318yesdirect product factor
8C2×C3×C52×C41C2×C314yescomplemented
9C2×C5×D5×C41C3211yescharacteristic, direct product factor, Hall
10C32×D5×C41C2×C512yesdirect product factor
11C2×C32×C5×C41—22no—
12C2×C32×C5×C41—52no—
13C2×C32×C5×C41D511yescharacteristic, direct product factor
14C2×C32×C5×C41C2×C511yescharacteristic, complemented
15C3×C52×C41C22×C314yescomplemented
16C2×C3×D5×C41C3×C514yesdirect product factor
17C22×C3×C5×C41—54no—
18C5×D5×C41C2×C3212yesdirect product factor
19C2×C52×C41C2×C3211yescharacteristic, complemented
20C32×C5×C41—22no—
21C32×C5×C41C2×D511yescharacteristic, direct product factor
22C32×C5×C41C22×C511yescharacteristic, complemented
23C22×C32×C41—51noHall
24C2×C3×C5×C41—28no—
25C2×C3×C5×C41—58no—
26C2×C3×C5×C41C3×D514yesdirect product factor
27C2×C3×C5×C41C2×C3×C514yescomplemented
28C3×D5×C41C2×C3×C518yesdirect product factor
29C52×C41C22×C3211yescharacteristic, complemented, Hall
30C2×C32×C5×D5C4111yesmaximal, characteristic, direct product factor, Hall
31C22×C5×C41—51no—
32C2×D5×C41C32×C511yescharacteristic, direct product factor
33C2×C32×C41—52no—
34C2×C32×C41C5×D511yescharacteristic, direct product factor
35C3×C5×C41—28no—
36C3×C5×C41C2×C3×D514yesdirect product factor
37C3×C5×C41C22×C3×C514yescomplemented
38C22×C3×C41—54no—
39C2×C32×C52C2×C4111yescharacteristic, complemented
40C32×C5×D5C2×C4112yesdirect product factor
41C2×C5×C41—22no—
42C2×C5×C41—52no—
43C2×C5×C41C32×D511yescharacteristic, direct product factor
44C2×C5×C41C2×C32×C511yescharacteristic, complemented
45D5×C41C2×C32×C512yesdirect product factor
46C32×C41C2×C5×D511yescharacteristic, direct product factor, Hall
47C2×C3×C5×D5C3×C4114yesdirect product factor
48C2×C3×C41—58no—
49C2×C3×C41C3×C5×D514yesdirect product factor
50C32×C52C22×C4111yescharacteristic, complemented, Hall
51C5×C41—22no—
52C5×C41C2×C32×D511yescharacteristic, direct product factor
53C5×C41C22×C32×C511yescharacteristic, complemented
54C22×C32×C5—51no—
55C2×C32×D5C5×C4111yescharacteristic, direct product factor
56C22×C41—51noHall
57C2×C3×C52C2×C3×C4114yescomplemented
58C3×C5×D5C2×C3×C4118yesdirect product factor
59C3×C41C2×C3×C5×D514yesdirect product factor
60C2×C5×D5C32×C4111yescharacteristic, direct product factor, Hall
61C2×C32×C5—22no—
62C2×C32×C5—52no—
63C2×C32×C5D5×C4111yescharacteristic, direct product factor
64C2×C32×C5C2×C5×C4111yescharacteristic, complemented
65C32×D5C2×C5×C4112yesdirect product factor
66C2×C41—52no—
67C2×C41C32×C5×D511yescharacteristic, direct product factor
68C3×C52C22×C3×C4114yescomplemented
69C22×C3×C5—54no—
70C2×C3×D5C3×C5×C4114yesdirect product factor
71C2×C52C2×C32×C4111yescharacteristic, complemented
72C5×D5C2×C32×C4112yesdirect product factor
73C32×C5—22no—
74C32×C5C2×D5×C4111yescharacteristic, direct product factor
75C32×C5C22×C5×C4111yescharacteristic, complemented
76C41C2×C32×C5×D511yescharacteristic, direct product factor, Sylow
77C22×C32—51noHall
78C2×C3×C5—28no—
79C2×C3×C5—58no—
80C2×C3×C5C3×D5×C4114yesdirect product factor
81C2×C3×C5C2×C3×C5×C4114yescomplemented
82C3×D5C2×C3×C5×C4118yesdirect product factor
83C52C22×C32×C4111yescharacteristic, complemented, Sylow
84C22×C5—51no—
85C2×D5C32×C5×C4111yescharacteristic, direct product factor
86C2×C32—52no—
87C2×C32C5×D5×C4111yescharacteristic, direct product factor
88C3×C5—28no—
89C3×C5C22×C3×C5×C4114yescomplemented
90C3×C5C2×C3×D5×C4114yesdirect product factor
91C22×C3—54no—
92C2×C5—22no—
93C2×C5—52no—
94C2×C5C2×C32×C5×C4111yescharacteristic, complemented
95C2×C5C32×D5×C4111yescharacteristic, direct product factor
96D5C2×C32×C5×C4112yesdirect product factor
97C32C2×C5×D5×C4111yescharacteristic, direct product factor, Sylow
98C2×C3—58no—
99C2×C3C3×C5×D5×C4114yesdirect product factor
100C5—22no—
101C5C22×C32×C5×C4111yescharacteristic, complemented
102C5C2×C32×D5×C4111yescharacteristic, direct product factor
103C22—51noSylow
104C3C2×C3×C5×D5×C4114yesdirect product factor
105C2—52no—
106C2C32×C5×D5×C4111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5×C41D5
commutator, cosocle, hypocenterC5C22×C32×C5×C41
FrattiniC1G
Fitting, socleC2×C32×C52×C41C2
LCSG ▷ C5
UCSC1 ◁ C2×C32×C5×C41

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C41C2direct (N × H)
2. C2×C32×C52×C41C2semidirect
3. C2×C3×C5×D5×C41C3direct (N × H)
4. C32×C52×C41C22semidirect
5. C2×C32×D5×C41C5direct (N × H)
7. C3×C5×D5×C41C2×C3direct (N × H)
8. C2×C3×C52×C41C2×C3semidirect
9. C2×C5×D5×C41C32direct (N × H)
10. C32×D5×C41C2×C5direct (N × H)
13. C2×C32×C5×C41D5direct (N × H)
14. C2×C32×C5×C41C2×C5semidirect
15. C3×C52×C41C22×C3semidirect
16. C2×C3×D5×C41C3×C5direct (N × H)
18. C5×D5×C41C2×C32direct (N × H)
19. C2×C52×C41C2×C32semidirect
21. C32×C5×C41C2×D5direct (N × H)
22. C32×C5×C41C22×C5semidirect
26. C2×C3×C5×C41C3×D5direct (N × H)
27. C2×C3×C5×C41C2×C3×C5semidirect
28. C3×D5×C41C2×C3×C5direct (N × H)
29. C52×C41C22×C32semidirect
30. C2×C32×C5×D5C41direct (N × H)
32. C2×D5×C41C32×C5direct (N × H)
34. C2×C32×C41C5×D5direct (N × H)
36. C3×C5×C41C2×C3×D5direct (N × H)
37. C3×C5×C41C22×C3×C5semidirect
39. C2×C32×C52C2×C41semidirect
40. C32×C5×D5C2×C41direct (N × H)
43. C2×C5×C41C32×D5direct (N × H)
44. C2×C5×C41C2×C32×C5semidirect
45. D5×C41C2×C32×C5direct (N × H)
46. C32×C41C2×C5×D5direct (N × H)
47. C2×C3×C5×D5C3×C41direct (N × H)
49. C2×C3×C41C3×C5×D5direct (N × H)
50. C32×C52C22×C41semidirect
52. C5×C41C2×C32×D5direct (N × H)
53. C5×C41C22×C32×C5semidirect
55. C2×C32×D5C5×C41direct (N × H)
57. C2×C3×C52C2×C3×C41semidirect
58. C3×C5×D5C2×C3×C41direct (N × H)
59. C3×C41C2×C3×C5×D5direct (N × H)
60. C2×C5×D5C32×C41direct (N × H)
63. C2×C32×C5D5×C41direct (N × H)
64. C2×C32×C5C2×C5×C41semidirect
65. C32×D5C2×C5×C41direct (N × H)
67. C2×C41C32×C5×D5direct (N × H)
68. C3×C52C22×C3×C41semidirect
70. C2×C3×D5C3×C5×C41direct (N × H)
71. C2×C52C2×C32×C41semidirect
72. C5×D5C2×C32×C41direct (N × H)
74. C32×C5C2×D5×C41direct (N × H)
75. C32×C5C22×C5×C41semidirect
76. C41C2×C32×C5×D5direct (N × H)
80. C2×C3×C5C3×D5×C41direct (N × H)
81. C2×C3×C5C2×C3×C5×C41semidirect
82. C3×D5C2×C3×C5×C41direct (N × H)
83. C52C22×C32×C41semidirect
85. C2×D5C32×C5×C41direct (N × H)
87. C2×C32C5×D5×C41direct (N × H)
89. C3×C5C22×C3×C5×C41semidirect
90. C3×C5C2×C3×D5×C41direct (N × H)
94. C2×C5C2×C32×C5×C41semidirect
95. C2×C5C32×D5×C41direct (N × H)
96. D5C2×C32×C5×C41direct (N × H)
97. C32C2×C5×D5×C41direct (N × H)
99. C2×C3C3×C5×D5×C41direct (N × H)
101. C5C22×C32×C5×C41semidirect
102. C5C2×C32×D5×C41direct (N × H)
104. C3C2×C3×C5×D5×C41direct (N × H)
106. C2C32×C5×D5×C41direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D5×C412
C2×C32×C52×C412
C2×C3×C5×D5×C413
C2×C32×D5×C415
C22×C32×C5×C415
C2×C32×C5×D541