Finite Group Databasebeta

← C3×D5×C11×D13⋊C3 #38788068

Subgroups — C3×D5×C11×D13⋊C3 #38788068

Order 25740.

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

normal subgroups only

This group has 240 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
1C3×D5×C11×C13⋊C3C211yesmaximal, characteristic, complemented
2C3×C11×C5⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C5×C11×D13⋊C3C211yesmaximal, characteristic, complemented
4C3×D5×C11×D13C311yesmaximal, characteristic, complemented
5D5×C11×D13⋊C3C313yesmaximal, direct product factor
6C3×C5×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×C3×C11×D13⋊C3—51nomaximal, Hall
8C11×C5⋊(D13⋊C3)C2×C313yescomplemented
9D5×C11×C13⋊C3C2×C313yescomplemented
10C5×C11×D13⋊C3C2×C313yescomplemented
11C3×C11×D65C2×C311yescharacteristic, complemented
12C3×D5×C11×C13C2×C311yescharacteristic, complemented
13C3×C5×C11×D13C2×C311yescharacteristic, complemented
14D5×C11×D13C3211yescharacteristic, complemented, Hall
15C2×C3×C11×C13⋊C3—51no—
16C3×C11×D13⋊C3—51no—
17C3×C11×D13⋊C3D511yescharacteristic, direct product factor
18C3×D5×D13⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
19C5×C11×C13⋊C3C22×C313yescomplemented
20C3×C5×C11×C13C22×C311yescharacteristic, complemented
21C2×C32×D5×C11—131nomaximal, Hall
22C2×C3×C11×D13—51no—
23C2×C11×D13⋊C3—53no—
24C11×D65C2×C3211yescharacteristic, complemented
25D5×C11×C13C2×C3211yescharacteristic, complemented
26C5×C11×D13C2×C3211yescharacteristic, complemented
27C3×C11×C13⋊C3C2×D511yescharacteristic, complemented, Hall
28C3×C5⋊(D13⋊C3)C2×C1111yescharacteristic, complemented
29C3×D5×C13⋊C3C2×C1111yescharacteristic, complemented
30C3×C5×D13⋊C3C2×C1111yescharacteristic, complemented
31C2×C32×C5×C11—131no—
32C32×D5×C11—131no—
33C32×D5×C11—131no—
34C2×C3×C11×C13—51no—
35C3×C11×D13—51no—
36C3×C11×D13C3×D511yescharacteristic, complemented
37C2×C11×C13⋊C3—53no—
38C11×D13⋊C3—53no—
39C11×D13⋊C3C3×D513yesdirect product factor
40C3×D5×D13C3×C1111yescharacteristic, complemented
41D5×D13⋊C3C3×C1113yesdirect product factor
42C5×C11×C13C22×C3211yescharacteristic, complemented, Hall
43C2×C3×D5×C11—133no—
44C2×C3×D5×C11—131no—
45C3×C5×C13⋊C3C22×C1111yescharacteristic, complemented, Hall
46C2×C11×D13—51noHall
47C32×C5×C11—131noHall
48C2×C3×D13⋊C3—51noHall
49C3×C11×C13C2×C3×D511yescharacteristic, complemented
50C11×C13⋊C3C2×C3×D513yescomplemented
51C22×C32×C11—651noHall
52C3×D65C2×C3×C1111yescharacteristic, complemented
53C3×D5×C13C2×C3×C1111yescharacteristic, complemented
54C3×C5×D13C2×C3×C1111yescharacteristic, complemented
55C5⋊(D13⋊C3)C2×C3×C1113yescomplemented
56D5×C13⋊C3C2×C3×C1113yescomplemented
57C5×D13⋊C3C2×C3×C1113yescomplemented
58C2×C3×C5×C11—133no—
59C2×C3×C5×C11—131no—
60C3×D5×C11—133no—
61C3×D5×C11—131no—
62C3×D5×C11—133no—
63C3×D5×C11D13⋊C311yescharacteristic, direct product factor
64C2×C11×C13—51no—
65C11×D13—51no—
66C11×D13C32×D511yescharacteristic, complemented
67D5×D13C32×C1111yescharacteristic, complemented, Hall
68C2×C3×C13⋊C3—51no—
69C3×D13⋊C3—51no—
70C3×D13⋊C3D5×C1111yescharacteristic, direct product factor
71C2×D5×C11—131noHall
72C2×C32×C11—131no—
73C2×C32×C11—651no—
74C2×C32×C11—651no—
75C3×C5×C13C22×C3×C1111yescharacteristic, complemented
76C5×C13⋊C3C22×C3×C1113yescomplemented
77C2×C32×D5—131noHall
78C3×C5×C11—133no—
79C3×C5×C11C2×D13⋊C311yescharacteristic, complemented
80C2×C3×D13—51no—
81C2×D13⋊C3—53no—
82C11×C13C2×C32×D511yescharacteristic, complemented, Hall
83C22×C3×C11—651no—
84C22×C3×C11—653no—
85D65C2×C32×C1111yescharacteristic, complemented
86C5×D13C2×C32×C1111yescharacteristic, complemented
87D5×C13C2×C32×C1111yescharacteristic, complemented
88C3×C13⋊C3C2×D5×C1111yescharacteristic, complemented, Hall
89C2×C5×C11—131no—
90D5×C11—131no—
91D5×C11C3×D13⋊C311yescharacteristic, direct product factor
92C32×C11—131noHall
93C2×C32×C5—131no—
94C32×D5—131no—
95C32×D5—131no—
96C2×C3×C13—51no—
97C3×D13—51no—
98C3×D13C3×D5×C1111yescharacteristic, complemented
99C2×C13⋊C3—53no—
100D13⋊C3—53no—
101D13⋊C3C3×D5×C1113yesdirect product factor
102C2×C3×C11—51no—
103C2×C3×C11—133no—
104C2×C3×C11—131no—
105C2×C3×C11—653no—
106C2×C3×C11—653no—
107C2×C3×C11—651no—
108C5×C13C22×C32×C1111yescharacteristic, complemented, Hall
109C2×C3×D5—133no—
110C2×C3×D5—131no—
111C5×C11C2×C3×D13⋊C311yescharacteristic, complemented, Hall
112C2×D13—51noHall
113C32×C5—131noHall
114C22×C11—651noHall
115C3×C13C2×C3×D5×C1111yescharacteristic, complemented
116C13⋊C3C2×C3×D5×C1113yescomplemented
117C22×C32—651noHall
118C3×C11—133no—
119C3×C11D5×D13⋊C311yescharacteristic, direct product factor
120C2×C3×C5—133no—
121C2×C3×C5—131no—
122C3×D5—133no—
123C3×D5—131no—
124C3×D5—133no—
125C3×D5C11×D13⋊C311yescharacteristic, direct product factor
126C2×C13—51no—
127D13—51no—
128D13C32×D5×C1111yescharacteristic, complemented
129C2×C11—51no—
130C2×C11—131no—
131C2×C11—651no—
132C2×D5—131noHall
133C2×C32—131no—
134C2×C32—651no—
135C2×C32—651no—
136C3×C5—133no—
137C3×C5C2×C11×D13⋊C311yescharacteristic, complemented
138C13C2×C32×D5×C1111yescharacteristic, complemented, Sylow
139C22×C3—651no—
140C22×C3—653no—
141C11C3×D5×D13⋊C311yescharacteristic, direct product factor, Sylow
142C2×C5—131no—
143D5—131no—
144D5C3×C11×D13⋊C311yescharacteristic, direct product factor
145C32—131noSylow
146C2×C3—51no—
147C2×C3—133no—
148C2×C3—131no—
149C2×C3—653no—
150C2×C3—653no—
151C2×C3—651no—
152C5C2×C3×C11×D13⋊C311yescharacteristic, complemented, Sylow
153C22—651noSylow
154C3—133no—
155C3D5×C11×D13⋊C311yescharacteristic, direct product factor
156C2—51no—
157C2—131no—
158C2—651no—
subgroupG/H
center, hypercenterC3×C11D5×D13⋊C3
commutator, cosocle, hypocenterC5×C13C22×C32×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22×C3
LCSG ▷ C5×C13
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C3×D5×C11×C13⋊C3C2semidirect
2. C3×C11×C5⋊(D13⋊C3)C2semidirect
3. C3×C5×C11×D13⋊C3C2semidirect
4. C3×D5×C11×D13C3semidirect
5. D5×C11×D13⋊C3C3direct (N × H)
6. C3×C5×C11×C13⋊C3C22semidirect
8. C11×C5⋊(D13⋊C3)C2×C3semidirect
9. D5×C11×C13⋊C3C2×C3semidirect
10. C5×C11×D13⋊C3C2×C3semidirect
11. C3×C11×D65C2×C3semidirect
12. C3×D5×C11×C13C2×C3semidirect
13. C3×C5×C11×D13C2×C3semidirect
14. D5×C11×D13C32semidirect
17. C3×C11×D13⋊C3D5direct (N × H)
18. C3×D5×D13⋊C3C11direct (N × H)
19. C5×C11×C13⋊C3C22×C3semidirect
20. C3×C5×C11×C13C22×C3semidirect
24. C11×D65C2×C32semidirect
25. D5×C11×C13C2×C32semidirect
26. C5×C11×D13C2×C32semidirect
27. C3×C11×C13⋊C3C2×D5semidirect
28. C3×C5⋊(D13⋊C3)C2×C11semidirect
29. C3×D5×C13⋊C3C2×C11semidirect
30. C3×C5×D13⋊C3C2×C11semidirect
36. C3×C11×D13C3×D5semidirect
39. C11×D13⋊C3C3×D5direct (N × H)
40. C3×D5×D13C3×C11semidirect
41. D5×D13⋊C3C3×C11direct (N × H)
42. C5×C11×C13C22×C32semidirect
45. C3×C5×C13⋊C3C22×C11semidirect
49. C3×C11×C13C2×C3×D5semidirect
50. C11×C13⋊C3C2×C3×D5semidirect
52. C3×D65C2×C3×C11semidirect
53. C3×D5×C13C2×C3×C11semidirect
54. C3×C5×D13C2×C3×C11semidirect
55. C5⋊(D13⋊C3)C2×C3×C11semidirect
56. D5×C13⋊C3C2×C3×C11semidirect
57. C5×D13⋊C3C2×C3×C11semidirect
63. C3×D5×C11D13⋊C3direct (N × H)
66. C11×D13C32×D5semidirect
67. D5×D13C32×C11semidirect
70. C3×D13⋊C3D5×C11direct (N × H)
75. C3×C5×C13C22×C3×C11semidirect
76. C5×C13⋊C3C22×C3×C11semidirect
79. C3×C5×C11C2×D13⋊C3semidirect
82. C11×C13C2×C32×D5semidirect
85. D65C2×C32×C11semidirect
86. C5×D13C2×C32×C11semidirect
87. D5×C13C2×C32×C11semidirect
88. C3×C13⋊C3C2×D5×C11semidirect
91. D5×C11C3×D13⋊C3direct (N × H)
98. C3×D13C3×D5×C11semidirect
101. D13⋊C3C3×D5×C11direct (N × H)
108. C5×C13C22×C32×C11semidirect
111. C5×C11C2×C3×D13⋊C3semidirect
115. C3×C13C2×C3×D5×C11semidirect
116. C13⋊C3C2×C3×D5×C11semidirect
119. C3×C11D5×D13⋊C3direct (N × H)
125. C3×D5C11×D13⋊C3direct (N × H)
128. D13C32×D5×C11semidirect
137. C3×C5C2×C11×D13⋊C3semidirect
138. C13C2×C32×D5×C11semidirect
141. C11C3×D5×D13⋊C3direct (N × H)
144. D5C3×C11×D13⋊C3direct (N × H)
152. C5C2×C3×C11×D13⋊C3semidirect
155. C3D5×C11×D13⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D5×C11×C13⋊C32
C3×C11×C5⋊(D13⋊C3)2
C3×C5×C11×D13⋊C32
C3×D5×C11×D133
D5×C11×D13⋊C33
C2×C3×C11×D13⋊C35
C3×D5×D13⋊C311
C2×C32×D5×C1113