Finite Group Databasebeta

← C3×D13⋊C3×D55 #38788070

Subgroups — C3×D13⋊C3×D55 #38788070

Order 25740.

240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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×C13⋊C3×D55C211yesmaximal, characteristic, complemented
2C3×C5⋊(C11⋊(D13⋊C3))C211yesmaximal, characteristic, complemented
3C3×C5×C11×D13⋊C3C211yesmaximal, characteristic, complemented
4C3×D13×D55C311yesmaximal, characteristic, complemented
5D13⋊C3×D55C313yesmaximal, direct product factor
6C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C3×D11×D13⋊C3—51nomaximal, Hall
8C5⋊(C11⋊(D13⋊C3))C2×C313yescomplemented
9C13⋊C3×D55C2×C313yescomplemented
10C5×C11×D13⋊C3C2×C313yescomplemented
11C3×D715C2×C311yescharacteristic, complemented
12C3×C13×D55C2×C311yescharacteristic, complemented
13C3×C5×C11×D13C2×C311yescharacteristic, complemented
14D13×D55C3211yescharacteristic, complemented, Hall
15C3×D11×C13⋊C3—51no—
16C3×C11⋊(D13⋊C3)—51no—
17C3×C11×D13⋊C3D511yescharacteristic, complemented
18C3×D5×D13⋊C3—111nomaximal, Hall
19C5×C11×C13⋊C3C22×C313yescomplemented
20C3×C5×C11×C13C22×C311yescharacteristic, complemented
21C2×C32×D55—131nomaximal, Hall
22C3×D11×D13—51no—
23D11×D13⋊C3—53no—
24D715C2×C3211yescharacteristic, complemented
25C13×D55C2×C3211yescharacteristic, complemented
26C5×C11×D13C2×C3211yescharacteristic, complemented
27C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
28C3×C5⋊(D13⋊C3)—111no—
29C3×D5×C13⋊C3—111no—
30C3×C5×D13⋊C3D1111yescharacteristic, complemented
31C2×C32×C5×C11—131no—
32C32×D55—131no—
33C32×D55—131no—
34C3×D143—51no—
35C3×C13×D11—51no—
36C3×C11×D13C3×D511yescharacteristic, complemented
37C11⋊(D13⋊C3)—53no—
38D11×C13⋊C3—53no—
39C11×D13⋊C3C3×D513yescomplemented
40C3×D5×D13—111no—
41D5×D13⋊C3—113no—
42C5×C11×C13C22×C3211yescharacteristic, complemented, Hall
43C2×C3×D55—133no—
44C2×C3×D55—391no—
45C3×C5×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
46D11×D13—51noHall
47C32×C5×C11—131noHall
48C2×C3×D13⋊C3—551noHall
49C3×C11×C13C2×C3×D511yescharacteristic, complemented
50C11×C13⋊C3C2×C3×D513yescomplemented
51C2×C32×D11—651noHall
52C3×D65—111no—
53C3×D5×C13—111no—
54C3×C5×D13C3×D1111yescharacteristic, complemented
55C5⋊(D13⋊C3)—113no—
56D5×C13⋊C3—113no—
57C5×D13⋊C3C3×D1113yescomplemented
58C2×C3×C5×C11—133no—
59C2×C3×C5×C11—391no—
60C3×D55—133no—
61C3×D55—133no—
62C3×D55—391no—
63C3×D55D13⋊C311yescharacteristic, direct product factor
64D143—51no—
65C11×D13C32×D511yescharacteristic, complemented
66C13×D11—51no—
67D5×D13—111noHall
68C2×C3×C13⋊C3—551no—
69C3×D13⋊C3—551no—
70C3×D13⋊C3D5511yescharacteristic, direct product factor
71C2×D55—391noHall
72C2×C32×C11—131no—
73C32×D11—651no—
74C32×D11—651no—
75C3×C5×C13C2×C3×D1111yescharacteristic, complemented
76C5×C13⋊C3C2×C3×D1113yescomplemented
77C2×C32×D5—1431noHall
78C3×C5×C11—133no—
79C3×C5×C11C2×D13⋊C311yescharacteristic, complemented
80C2×C3×D13—551no—
81C2×D13⋊C3—553no—
82C11×C13C2×C32×D511yescharacteristic, complemented, Hall
83C2×C3×D11—653no—
84C2×C3×D11—1951no—
85D65—111no—
86C5×D13C32×D1111yescharacteristic, complemented
87D5×C13—111no—
88C3×C13⋊C3C2×D5511yescharacteristic, complemented, Hall
89C2×C5×C11—391no—
90D55—391no—
91D55C3×D13⋊C311yescharacteristic, direct product factor
92C32×C11—131noHall
93C2×C32×C5—131no—
94C32×D5—1431no—
95C32×D5—1431no—
96C2×C3×C13—551no—
97C3×D13—551no—
98C3×D13C3×D5511yescharacteristic, complemented
99C2×C13⋊C3—553no—
100D13⋊C3—553no—
101D13⋊C3C3×D5513yesdirect product factor
102C2×C3×C11—133no—
103C2×C3×C11—391no—
104C3×D11—51no—
105C3×D11—653no—
106C3×D11—653no—
107C3×D11—1951no—
108C5×C13C2×C32×D1111yescharacteristic, complemented, Hall
109C2×C3×D5—1433no—
110C2×C3×D5—4291no—
111C5×C11C2×C3×D13⋊C311yescharacteristic, complemented, Hall
112C2×D13—551noHall
113C32×C5—131noHall
114C2×D11—1951noHall
115C3×C13C2×C3×D5511yescharacteristic, complemented
116C13⋊C3C2×C3×D5513yescomplemented
117C22×C32—7151noHall
118C3×C11—133no—
119C3×C11D5×D13⋊C311yescharacteristic, complemented
120C2×C3×C5—133no—
121C2×C3×C5—391no—
122C3×D5—111no—
123C3×D5—1433no—
124C3×D5—1433no—
125C3×D5—4291no—
126C2×C13—551no—
127D13—551no—
128D13C32×D5511yescharacteristic, complemented
129C2×C11—391no—
130D11—51no—
131D11—1951no—
132C2×D5—4291noHall
133C2×C32—131no—
134C2×C32—7151no—
135C2×C32—7151no—
136C3×C5—133no—
137C3×C5D11×D13⋊C311yescharacteristic, complemented
138C13C2×C32×D5511yescharacteristic, complemented, Sylow
139C22×C3—21451no—
140C22×C3—7153no—
141C11C3×D5×D13⋊C311yescharacteristic, complemented, Sylow
142C2×C5—391no—
143D5—111no—
144D5—4291no—
145C32—131noSylow
146C2×C3—133no—
147C2×C3—391no—
148C2×C3—551no—
149C2×C3—21451no—
150C2×C3—7153no—
151C2×C3—7153no—
152C5C3×D11×D13⋊C311yescharacteristic, complemented, Sylow
153C22—21451noSylow
154C3—133no—
155C3D13⋊C3×D5511yescharacteristic, direct product factor
156C2—391no—
157C2—551no—
158C2—21451no—
subgroupG/H
center, hypercenterC3D13⋊C3×D55
commutator, cosocle, hypocenterC5×C11×C13C22×C32
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22×C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C13⋊C3×D55C2semidirect
2. C3×C5⋊(C11⋊(D13⋊C3))C2semidirect
3. C3×C5×C11×D13⋊C3C2semidirect
4. C3×D13×D55C3semidirect
5. D13⋊C3×D55C3direct (N × H)
6. C3×C5×C11×C13⋊C3C22semidirect
8. C5⋊(C11⋊(D13⋊C3))C2×C3semidirect
9. C13⋊C3×D55C2×C3semidirect
10. C5×C11×D13⋊C3C2×C3semidirect
11. C3×D715C2×C3semidirect
12. C3×C13×D55C2×C3semidirect
13. C3×C5×C11×D13C2×C3semidirect
14. D13×D55C32semidirect
17. C3×C11×D13⋊C3D5semidirect
19. C5×C11×C13⋊C3C22×C3semidirect
20. C3×C5×C11×C13C22×C3semidirect
24. D715C2×C32semidirect
25. C13×D55C2×C32semidirect
26. C5×C11×D13C2×C32semidirect
27. C3×C11×C13⋊C3C2×D5semidirect
30. C3×C5×D13⋊C3D11semidirect
36. C3×C11×D13C3×D5semidirect
39. C11×D13⋊C3C3×D5semidirect
42. C5×C11×C13C22×C32semidirect
45. C3×C5×C13⋊C3C2×D11semidirect
49. C3×C11×C13C2×C3×D5semidirect
50. C11×C13⋊C3C2×C3×D5semidirect
54. C3×C5×D13C3×D11semidirect
57. C5×D13⋊C3C3×D11semidirect
63. C3×D55D13⋊C3direct (N × H)
65. C11×D13C32×D5semidirect
70. C3×D13⋊C3D55direct (N × H)
75. C3×C5×C13C2×C3×D11semidirect
76. C5×C13⋊C3C2×C3×D11semidirect
79. C3×C5×C11C2×D13⋊C3semidirect
82. C11×C13C2×C32×D5semidirect
86. C5×D13C32×D11semidirect
88. C3×C13⋊C3C2×D55semidirect
91. D55C3×D13⋊C3direct (N × H)
98. C3×D13C3×D55semidirect
101. D13⋊C3C3×D55direct (N × H)
108. C5×C13C2×C32×D11semidirect
111. C5×C11C2×C3×D13⋊C3semidirect
115. C3×C13C2×C3×D55semidirect
116. C13⋊C3C2×C3×D55semidirect
119. C3×C11D5×D13⋊C3semidirect
128. D13C32×D55semidirect
137. C3×C5D11×D13⋊C3semidirect
138. C13C2×C32×D55semidirect
141. C11C3×D5×D13⋊C3semidirect
152. C5C3×D11×D13⋊C3semidirect
155. C3D13⋊C3×D55direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C13⋊C3×D552
C3×C5⋊(C11⋊(D13⋊C3))2
C3×C5×C11×D13⋊C32
C3×D13×D553
D13⋊C3×D553
C3×D11×D13⋊C35
C3×D5×D13⋊C311
C2×C32×D5513