Finite Group Databasebeta

← C32×D5×D155 #42124890

Subgroups — C32×D5×D155 #42124890

Order 27900.

288 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 96 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×C31C211yesmaximal, characteristic, complemented
2C32×C5×D155C211yesmaximal, characteristic, complemented
3C32×C5⋊D155C211yesmaximal, characteristic, complemented
4C3×D5×D155C314yesmaximal, direct product factor
5C32×C52×C31C2211yescharacteristic, complemented, Hall
6C2×C32×D155—51nomaximal
7C32×D5×D31—51nomaximal
8C3×C5⋊D155C2×C314yescomplemented
9C3×C5×D155C2×C314yescomplemented
10C3×C5×D5×C31C2×C314yescomplemented
11D5×D155C3211yescharacteristic, direct product factor, Hall
12C32×D155—51no—
13C32×D155—51no—
14C32×D155—102no—
15C32×D155D511yescharacteristic, direct product factor
16C32×D5×C31D511yescharacteristic, complemented
17C32×C5×D31—51no—
18C2×C32×C5×C31—51no—
19C3×C52×C31C22×C314yescomplemented
20C2×C3×D155—54no—
21C3×D5×D31—54no—
22C5⋊D155C2×C3211yescharacteristic, complemented
23C5×D155C2×C3211yescharacteristic, complemented
24C5×D5×C31C2×C3211yescharacteristic, complemented
25C32×C5×C31—22no—
26C32×C5×C31C2×D511yescharacteristic, complemented
27C32×C5×C31C2×D511yescharacteristic, complemented
28C2×C32×D31—251noHall
29C2×C3×C5×C31—54no—
30C3×D155—54no—
31C3×D155—54no—
32C3×D155—108no—
33C3×D155C3×D514yesdirect product factor
34C3×D5×C31C3×D514yescomplemented
35C3×C5×D31—54no—
36C32×D52—311nomaximal, Hall
37C52×C31C22×C3211yescharacteristic, complemented, Hall
38C2×D155—51no—
39D5×D31—51no—
40C2×C32×C31—51no—
41C32×D31—51no—
42C32×D31—251no—
43C3×C5×C31—28no—
44C3×C5×C31C2×C3×D514yescomplemented
45C3×C5×C31C2×C3×D514yescomplemented
46C32×C5⋊D5—311no—
47C32×C5×D5—311no—
48C32×C5×D5D3111yescharacteristic, complemented
49C2×C3×D31—254no—
50C2×C5×C31—51no—
51D155—51no—
52D155—51no—
53D155—102no—
54D155C32×D511yescharacteristic, direct product factor
55C5×D31—51no—
56D5×C31C32×D511yescharacteristic, complemented
57C3×D52—314no—
58C32×C31D5211yescharacteristic, complemented, Hall
59C32×C52C2×D3111yescharacteristic, complemented, Hall
60C2×C3×C31—54no—
61C3×D31—54no—
62C3×D31—254no—
63C2×C32×D5—1551no—
64C2×C32×D5—1551no—
65C5×C31—22no—
66C5×C31C2×C32×D511yescharacteristic, complemented
67C5×C31C2×C32×D511yescharacteristic, complemented
68C3×C5⋊D5—314no—
69C3×C5×D5—314no—
70C3×C5×D5C3×D3114yescomplemented
71C2×D31—251noHall
72D52—311noHall
73C3×C31C3×D5214yescomplemented
74C2×C32×C5—51no—
75C2×C32×C5—1551no—
76C32×D5—311no—
77C32×D5—3102no—
78C32×D5—1551no—
79C32×D5—1551no—
80C32×D5D15511yescharacteristic, direct product factor
81C3×C52C2×C3×D3114yescomplemented
82C2×C31—51no—
83D31—51no—
84D31—251no—
85C2×C3×D5—1554no—
86C2×C3×D5—1554no—
87C5⋊D5—311no—
88C5×D5—311no—
89C5×D5C32×D3111yescharacteristic, complemented
90C32×C5—22no—
91C32×C5D5×D3111yescharacteristic, complemented
92C32×C5C2×D15511yescharacteristic, complemented
93C22×C32—7751noHall
94C31C32×D5211yescharacteristic, complemented, Sylow
95C2×C3×C5—54no—
96C2×C3×C5—1554no—
97C3×D5—314no—
98C3×D5—3108no—
99C3×D5—1554no—
100C3×D5—1554no—
101C3×D5C3×D15514yesdirect product factor
102C52C2×C32×D3111yescharacteristic, complemented, Sylow
103C2×D5—1551no—
104C2×D5—1551no—
105C2×C32—51no—
106C2×C32—7751no—
107C2×C32—1551no—
108C3×C5—28no—
109C3×C5C3×D5×D3114yescomplemented
110C3×C5C2×C3×D15514yescomplemented
111C22×C3—7754no—
112C2×C5—51no—
113C2×C5—1551no—
114D5—311no—
115D5—3102no—
116D5—1551no—
117D5—1551no—
118D5C32×D15511yescharacteristic, direct product factor
119C32D5×D15511yescharacteristic, direct product factor, Sylow
120C2×C3—54no—
121C2×C3—7754no—
122C2×C3—1554no—
123C5—22no—
124C5C32×D5×D3111yescharacteristic, complemented
125C5C2×C32×D15511yescharacteristic, complemented
126C22—7751noSylow
127C3C3×D5×D15514yesdirect product factor
128C2—51no—
129C2—7751no—
130C2—1551no—
subgroupG/H
center, hypercenterC32D5×D155
commutator, cosocle, hypocenterC52×C31C22×C32
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C52×C31
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C31C2semidirect
2. C32×C5×D155C2semidirect
3. C32×C5⋊D155C2semidirect
4. C3×D5×D155C3direct (N × H)
5. C32×C52×C31C22semidirect
8. C3×C5⋊D155C2×C3semidirect
9. C3×C5×D155C2×C3semidirect
10. C3×C5×D5×C31C2×C3semidirect
11. D5×D155C32direct (N × H)
15. C32×D155D5direct (N × H)
16. C32×D5×C31D5semidirect
19. C3×C52×C31C22×C3semidirect
22. C5⋊D155C2×C32semidirect
23. C5×D155C2×C32semidirect
24. C5×D5×C31C2×C32semidirect
26. C32×C5×C31C2×D5semidirect
27. C32×C5×C31C2×D5semidirect
33. C3×D155C3×D5direct (N × H)
34. C3×D5×C31C3×D5semidirect
37. C52×C31C22×C32semidirect
44. C3×C5×C31C2×C3×D5semidirect
45. C3×C5×C31C2×C3×D5semidirect
48. C32×C5×D5D31semidirect
54. D155C32×D5direct (N × H)
56. D5×C31C32×D5semidirect
58. C32×C31D52semidirect
59. C32×C52C2×D31semidirect
66. C5×C31C2×C32×D5semidirect
67. C5×C31C2×C32×D5semidirect
70. C3×C5×D5C3×D31semidirect
73. C3×C31C3×D52semidirect
80. C32×D5D155direct (N × H)
81. C3×C52C2×C3×D31semidirect
89. C5×D5C32×D31semidirect
91. C32×C5D5×D31semidirect
92. C32×C5C2×D155semidirect
94. C31C32×D52semidirect
101. C3×D5C3×D155direct (N × H)
102. C52C2×C32×D31semidirect
109. C3×C5C3×D5×D31semidirect
110. C3×C5C2×C3×D155semidirect
118. D5C32×D155direct (N × H)
119. C32D5×D155direct (N × H)
124. C5C32×D5×D31semidirect
125. C5C2×C32×D155semidirect
127. C3C3×D5×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×D5×C312
C32×C5×D1552
C32×C5⋊D1552
C3×D5×D1553
C2×C32×D1555
C32×D5×D315
C32×D5231