Finite Group Databasebeta

← C3×D25×D31⋊C3 #42124397

Subgroups — C3×D25×D31⋊C3 #42124397

Order 27900.

180 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C3×D25×C31⋊C3C211yesmaximal, characteristic, complemented
2C3×C25⋊(D31⋊C3)C211yesmaximal, characteristic, complemented
3C3×C25×D31⋊C3C211yesmaximal, characteristic, complemented
4C3×D25×D31C311yesmaximal, characteristic, complemented
5D25×D31⋊C3C313yesmaximal, direct product factor
6C3×C25×C31⋊C3C2211yescharacteristic, complemented, Hall
7C3×D5×D31⋊C3—51nomaximal
8C3×D775C2×C311yescharacteristic, complemented
9C3×C31×D25C2×C311yescharacteristic, complemented
10C3×C25×D31C2×C311yescharacteristic, complemented
11C25⋊(D31⋊C3)C2×C313yescomplemented
12D25×C31⋊C3C2×C313yescomplemented
13C25×D31⋊C3C2×C313yescomplemented
14D25×D31C3211yescharacteristic, complemented, Hall
15C3×D5×C31⋊C3—51no—
16C3×C5⋊(D31⋊C3)—51no—
17C3×C5×D31⋊C3D511yescharacteristic
18C25×C31⋊C3C22×C313yescomplemented
19C3×C25×C31C22×C311yescharacteristic, complemented
20C3×D5×D31—51no—
21D5×D31⋊C3—53no—
22D775C2×C3211yescharacteristic, complemented
23C25×D31C2×C3211yescharacteristic, complemented
24C31×D25C2×C3211yescharacteristic, complemented
25C3×C5×C31⋊C3C2×D511yescharacteristic
26C2×C3×D31⋊C3—251noHall
27C3×D155—51no—
28C3×D5×C31—51no—
29C3×C5×D31C3×D511yescharacteristic
30C5⋊(D31⋊C3)—53no—
31D5×C31⋊C3—53no—
32C5×D31⋊C3C3×D513yes—
33C2×C32×D25—311nomaximal, Hall
34C25×C31C22×C3211yescharacteristic, complemented, Hall
35D5×D31—51no—
36C2×C3×C31⋊C3—251no—
37C3×D31⋊C3—251no—
38C3×D31⋊C3D2511yescharacteristic, direct product factor
39C3×C5×C31C2×C3×D511yescharacteristic
40C5×C31⋊C3C2×C3×D513yes—
41C2×C32×C25—311no—
42C32×D25—311no—
43C32×D25—311no—
44C2×C3×D31—251no—
45C2×D31⋊C3—253no—
46D155—51no—
47C5×D31C32×D511yescharacteristic
48D5×C31—51no—
49C2×C3×D25—313no—
50C2×C3×D25—311no—
51C3×C31⋊C3C2×D2511yescharacteristic, complemented, Hall
52C32×C25—311noHall
53C2×C3×C31—251no—
54C3×D31—251no—
55C3×D31C3×D2511yescharacteristic, complemented
56C2×C31⋊C3—253no—
57D31⋊C3—253no—
58D31⋊C3C3×D2513yesdirect product factor
59C2×C32×D5—1551no—
60C5×C31C2×C32×D511yescharacteristic
61C2×C3×C25—313no—
62C2×C3×C25—311no—
63C3×D25—313no—
64C3×D25—313no—
65C3×D25—311no—
66C3×D25D31⋊C311yescharacteristic, direct product factor
67C2×D31—251noHall
68C2×D25—311noHall
69C3×C31C2×C3×D2511yescharacteristic, complemented
70C31⋊C3C2×C3×D2513yescomplemented
71C2×C32×C5—311no—
72C32×D5—1551no—
73C32×D5—1551no—
74C3×C25—313no—
75C3×C25C2×D31⋊C311yescharacteristic, complemented
76C2×C31—251no—
77D31—251no—
78D31C32×D2511yescharacteristic, complemented
79C2×C3×D5—1551no—
80C2×C3×D5—1553no—
81C2×C25—311no—
82D25—311no—
83D25C3×D31⋊C311yescharacteristic, direct product factor
84C32×C5—311no—
85C22×C32—7751noHall
86C31C2×C32×D2511yescharacteristic, complemented, Sylow
87C2×C3×C5—313no—
88C2×C3×C5—311no—
89C3×D5—51no—
90C3×D5—1553no—
91C3×D5—1553no—
92C3×D5—1551no—
93C25C2×C3×D31⋊C311yescharacteristic, complemented, Sylow
94C2×D5—1551no—
95C2×C32—7751no—
96C2×C32—7751no—
97C2×C32—311no—
98C3×C5—313no—
99C3×C5D5×D31⋊C311yescharacteristic
100C22×C3—7753no—
101C22×C3—7751no—
102C2×C5—311no—
103D5—51no—
104D5—1551no—
105C32—311noSylow
106C2×C3—7753no—
107C2×C3—7751no—
108C2×C3—7753no—
109C2×C3—251no—
110C2×C3—313no—
111C2×C3—311no—
112C5C3×D5×D31⋊C311yescharacteristic
113C22—7751noSylow
114C3—313no—
115C3D25×D31⋊C311yescharacteristic, direct product factor
116C2—7751no—
117C2—251no—
118C2—311no—
subgroupG/H
center, hypercenterC3D25×D31⋊C3
commutator, cosocle, hypocenterC25×C31C22×C32
FrattiniC5C3×D5×D31⋊C3
FittingC3×C25×C31C22×C3
socleC3×C5×C31C2×C3×D5
LCSG ▷ C25×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D25×C31⋊C3C2semidirect
2. C3×C25⋊(D31⋊C3)C2semidirect
3. C3×C25×D31⋊C3C2semidirect
4. C3×D25×D31C3semidirect
5. D25×D31⋊C3C3direct (N × H)
6. C3×C25×C31⋊C3C22semidirect
8. C3×D775C2×C3semidirect
9. C3×C31×D25C2×C3semidirect
10. C3×C25×D31C2×C3semidirect
11. C25⋊(D31⋊C3)C2×C3semidirect
12. D25×C31⋊C3C2×C3semidirect
13. C25×D31⋊C3C2×C3semidirect
14. D25×D31C32semidirect
18. C25×C31⋊C3C22×C3semidirect
19. C3×C25×C31C22×C3semidirect
22. D775C2×C32semidirect
23. C25×D31C2×C32semidirect
24. C31×D25C2×C32semidirect
34. C25×C31C22×C32semidirect
38. C3×D31⋊C3D25direct (N × H)
51. C3×C31⋊C3C2×D25semidirect
55. C3×D31C3×D25semidirect
58. D31⋊C3C3×D25direct (N × H)
66. C3×D25D31⋊C3direct (N × H)
69. C3×C31C2×C3×D25semidirect
70. C31⋊C3C2×C3×D25semidirect
75. C3×C25C2×D31⋊C3semidirect
78. D31C32×D25semidirect
83. D25C3×D31⋊C3direct (N × H)
86. C31C2×C32×D25semidirect
93. C25C2×C3×D31⋊C3semidirect
115. C3D25×D31⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D25×C31⋊C32
C3×C25⋊(D31⋊C3)2
C3×C25×D31⋊C32
C3×D25×D313
D25×D31⋊C33
C3×D5×D31⋊C35
C2×C32×D2531