Finite Group Databasebeta

← C2×C32×C5×D205 #49147206

Subgroups — C2×C32×C5×D205 #49147206

Order 36900.

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×D205C212yesmaximal, direct product factor
2C2×C32×C52×C41C211yesmaximal, characteristic, complemented
3C2×C3×C5×D205C314yesmaximal, direct product factor
4C32×C52×C41C2211yescharacteristic, complemented, Hall
5C2×C32×C5×D41—51nomaximal
6C2×C32×D205C511yesmaximal, characteristic, direct product factor
7C3×C5×D205C2×C318yesdirect product factor
8C2×C3×C52×C41C2×C314yescomplemented
9C2×C5×D205C3211yescharacteristic, direct product factor, Hall
10C32×D205C2×C512yesdirect product factor
11C32×C5×D41—52no—
12C2×C32×C5×C41—22no—
13C2×C32×C5×C41D511yescharacteristic, complemented
14C2×C32×C5×C41C2×C511yescharacteristic, complemented
15C3×C52×C41C22×C314yescomplemented
16C2×C3×C5×D41—54no—
17C2×C3×D205C3×C514yesdirect product factor
18C5×D205C2×C3212yesdirect product factor
19C2×C52×C41C2×C3211yescharacteristic, complemented
20C32×C5×C41—22no—
21C32×C5×C41C2×D511yescharacteristic, complemented
22C32×C5×C41C22×C511yescharacteristic, complemented
23C2×C32×D41—51noHall
24C2×C3×C5×C41—28no—
25C2×C3×C5×C41C3×D514yescomplemented
26C2×C3×C5×C41C2×C3×C514yescomplemented
27C3×D205C2×C3×C518yesdirect product factor
28C3×C5×D41—58no—
29C52×C41C22×C3211yescharacteristic, complemented, Hall
30C2×C32×C5×D5—411nomaximal, Hall
31C2×D205C32×C511yescharacteristic, direct product factor
32C2×C5×D41—51no—
33C2×C32×C41C5×D511yescharacteristic, complemented
34C32×D41—52no—
35C3×C5×C41—28no—
36C3×C5×C41C2×C3×D514yescomplemented
37C3×C5×C41C22×C3×C514yescomplemented
38C2×C3×D41—54no—
39C2×C32×C52D4111yescharacteristic, complemented
40C32×C5×D5—412no—
41C2×C5×C41—22no—
42C2×C5×C41C32×D511yescharacteristic, complemented
43C2×C5×C41C2×C32×C511yescharacteristic, complemented
44D205C2×C32×C512yesdirect product factor
45C5×D41—52no—
46C32×C41C2×C5×D511yescharacteristic, complemented, Hall
47C2×C3×C5×D5—414no—
48C2×C3×C41C3×C5×D514yescomplemented
49C3×D41—58no—
50C32×C52C2×D4111yescharacteristic, complemented, Hall
51C5×C41—22no—
52C5×C41C2×C32×D511yescharacteristic, complemented
53C5×C41C22×C32×C511yescharacteristic, complemented
54C22×C32×C5—2051no—
55C2×C32×D5—411no—
56C2×D41—51noHall
57C2×C3×C52C3×D4114yescomplemented
58C3×C5×D5—418no—
59C3×C41C2×C3×C5×D514yescomplemented
60C2×C5×D5—411noHall
61C2×C32×C5—22no—
62C2×C32×C5—2052no—
63C2×C32×C5C5×D4111yescharacteristic, complemented
64C2×C32×C5D20511yescharacteristic, direct product factor
65C32×D5—412no—
66C2×C41C32×C5×D511yescharacteristic, complemented
67D41—52no—
68C3×C52C2×C3×D4114yescomplemented
69C22×C3×C5—2054no—
70C2×C3×D5—414no—
71C2×C52C32×D4111yescharacteristic, complemented
72C5×D5—412no—
73C32×C5—22no—
74C32×C5C2×C5×D4111yescharacteristic, complemented
75C32×C5C2×D20511yescharacteristic, direct product factor
76C41C2×C32×C5×D511yescharacteristic, complemented, Sylow
77C22×C32—2051noHall
78C2×C3×C5—28no—
79C2×C3×C5—2058no—
80C2×C3×C5C3×C5×D4114yescomplemented
81C2×C3×C5C3×D20514yesdirect product factor
82C3×D5—418no—
83C52C2×C32×D4111yescharacteristic, complemented, Sylow
84C22×C5—2051no—
85C2×D5—411no—
86C2×C32—2052no—
87C2×C32C5×D20511yescharacteristic, direct product factor
88C3×C5—28no—
89C3×C5C2×C3×D20514yesdirect product factor
90C3×C5C2×C3×C5×D4114yescomplemented
91C22×C3—2054no—
92C2×C5—22no—
93C2×C5—2052no—
94C2×C5C32×C5×D4111yescharacteristic, complemented
95C2×C5C32×D20511yescharacteristic, direct product factor
96D5—412no—
97C32C2×C5×D20511yescharacteristic, direct product factor, Sylow
98C2×C3—2058no—
99C2×C3C3×C5×D20514yesdirect product factor
100C5—22no—
101C5C2×C32×D20511yescharacteristic, direct product factor
102C5C2×C32×C5×D4111yescharacteristic, complemented
103C22—2051noSylow
104C3C2×C3×C5×D20514yesdirect product factor
105C2—2052no—
106C2C32×C5×D20511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5D205
commutator, cosocle, hypocenterC5×C41C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C41C2
LCSG ▷ C5×C41
UCSC1 ◁ C2×C32×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D205C2direct (N × H)
2. C2×C32×C52×C41C2semidirect
3. C2×C3×C5×D205C3direct (N × H)
4. C32×C52×C41C22semidirect
6. C2×C32×D205C5direct (N × H)
7. C3×C5×D205C2×C3direct (N × H)
8. C2×C3×C52×C41C2×C3semidirect
9. C2×C5×D205C32direct (N × H)
10. C32×D205C2×C5direct (N × H)
13. C2×C32×C5×C41D5semidirect
14. C2×C32×C5×C41C2×C5semidirect
15. C3×C52×C41C22×C3semidirect
17. C2×C3×D205C3×C5direct (N × H)
18. C5×D205C2×C32direct (N × H)
19. C2×C52×C41C2×C32semidirect
21. C32×C5×C41C2×D5semidirect
22. C32×C5×C41C22×C5semidirect
25. C2×C3×C5×C41C3×D5semidirect
26. C2×C3×C5×C41C2×C3×C5semidirect
27. C3×D205C2×C3×C5direct (N × H)
29. C52×C41C22×C32semidirect
31. C2×D205C32×C5direct (N × H)
33. C2×C32×C41C5×D5semidirect
36. C3×C5×C41C2×C3×D5semidirect
37. C3×C5×C41C22×C3×C5semidirect
39. C2×C32×C52D41semidirect
42. C2×C5×C41C32×D5semidirect
43. C2×C5×C41C2×C32×C5semidirect
44. D205C2×C32×C5direct (N × H)
46. C32×C41C2×C5×D5semidirect
48. C2×C3×C41C3×C5×D5semidirect
50. C32×C52C2×D41semidirect
52. C5×C41C2×C32×D5semidirect
53. C5×C41C22×C32×C5semidirect
57. C2×C3×C52C3×D41semidirect
59. C3×C41C2×C3×C5×D5semidirect
63. C2×C32×C5C5×D41semidirect
64. C2×C32×C5D205direct (N × H)
66. C2×C41C32×C5×D5semidirect
68. C3×C52C2×C3×D41semidirect
71. C2×C52C32×D41semidirect
74. C32×C5C2×C5×D41semidirect
75. C32×C5C2×D205direct (N × H)
76. C41C2×C32×C5×D5semidirect
80. C2×C3×C5C3×C5×D41semidirect
81. C2×C3×C5C3×D205direct (N × H)
83. C52C2×C32×D41semidirect
87. C2×C32C5×D205direct (N × H)
89. C3×C5C2×C3×D205direct (N × H)
90. C3×C5C2×C3×C5×D41semidirect
94. C2×C5C32×C5×D41semidirect
95. C2×C5C32×D205direct (N × H)
97. C32C2×C5×D205direct (N × H)
99. C2×C3C3×C5×D205direct (N × H)
101. C5C2×C32×D205direct (N × H)
102. C5C2×C32×C5×D41semidirect
104. C3C2×C3×C5×D205direct (N × H)
106. C2C32×C5×D205direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D2052
C2×C32×C52×C412
C2×C3×C5×D2053
C2×C32×C5×D415
C2×C32×D2055
C2×C32×C5×D541