Finite Group Databasebeta

← C3×(C5⋊(D13⋊C3))⋊D13 #44477975

Subgroups — C3×(C5⋊(D13⋊C3))⋊D13 #44477975

Order 30420.

256 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 70 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×D65C211yesmaximal, characteristic, complemented
2C3×C13×C5⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C5×(C13⋊C3)⋊D13C211yesmaximal, characteristic, complemented
4C3×D65⋊D13C311yesmaximal, characteristic, complemented
5(C5⋊(D13⋊C3))⋊D13C313yesmaximal, direct product factor
6C3×C5×C13×C13⋊C3C2211yescharacteristic, complemented, Hall
7C3×D13×D13⋊C3—51nomaximal, Hall
8C3×C13×D65C2×C311yescharacteristic, complemented
9C3×C13×D65C2×C311yescharacteristic, complemented
10C3×C5×C13⋊D13C2×C311yescharacteristic, complemented
11C13⋊C3×D65C2×C313yescomplemented
12C13×C5⋊(D13⋊C3)C2×C313yescomplemented
13C5×(C13⋊C3)⋊D13C2×C313yescomplemented
14D65⋊D13C3211yescharacteristic, complemented, Hall
15C3×D13×C13⋊C3—51no—
16C3×(C13⋊C3)⋊D13D511yescharacteristic, complemented
17C3×C13×D13⋊C3—51no—
18C5×C13×C13⋊C3C22×C313yescomplemented
19C3×C5×C132C22×C311yescharacteristic, complemented
20C32×D5×D13—131nomaximal
21C3×D5×D13⋊C3—131nomaximal
22C3×D132—51no—
23D13×D13⋊C3—53no—
24C13×D65C2×C3211yescharacteristic, complemented
25C13×D65C2×C3211yescharacteristic, complemented
26C5×C13⋊D13C2×C3211yescharacteristic, complemented
27C3×C13×C13⋊C3C2×D511yescharacteristic, complemented, Hall
28C32×D65—131no—
29C32×D5×C13—131no—
30C32×C5×D13—131no—
31C3×C5⋊(D13⋊C3)D1311yescharacteristic, complemented
32C3×D5×C13⋊C3—131no—
33C3×C5×D13⋊C3—131no—
34C3×C13⋊D13C3×D511yescharacteristic, complemented
35C3×C13×D13—51no—
36C3×C13×D13—51no—
37D13×C13⋊C3—53no—
38(C13⋊C3)⋊D13C3×D513yescomplemented
39C13×D13⋊C3—53no—
40C5×C132C22×C3211yescharacteristic, complemented, Hall
41C3×D5×D13—133no—
42C3×D5×D13—131no—
43C3×D5×D13—131no—
44D5×D13⋊C3—133no—
45D132—51noHall
46C32×C5×C13—131no—
47C3×C5×C13⋊C3C2×D1311yescharacteristic, complemented
48C3×C132C2×C3×D511yescharacteristic, complemented
49C13×C13⋊C3C2×C3×D513yescomplemented
50C2×C32×D13—651no—
51C2×C3×D13⋊C3—651no—
52C3×D65—133no—
53C3×D65D13⋊C311yescharacteristic, complemented
54C3×D65C3×D1311yescharacteristic, complemented
55C3×D5×C13—133no—
56C3×D5×C13—131no—
57C3×D5×C13—131no—
58C3×C5×D13—131no—
59C3×C5×D13—133no—
60C3×C5×D13—391no—
61C3×C5×D13—782no—
62C5⋊(D13⋊C3)C3×D1313yescomplemented
63D5×C13⋊C3—133no—
64C5×D13⋊C3—133no—
65C13⋊D13C32×D511yescharacteristic, complemented
66C13×D13—51no—
67C13×D13—51no—
68D5×D13—131no—
69D5×D13—131no—
70C2×C32×C13—651no—
71C32×D13—131no—
72C32×D13—651no—
73C2×C3×C13⋊C3—651no—
74C3×D13⋊C3—51no—
75C3×D13⋊C3—131no—
76C3×C5×C13—62no—
77C3×C5×C13—133no—
78C3×C5×C13C2×D13⋊C311yescharacteristic, complemented
79C3×C5×C13C2×C3×D1311yescharacteristic, complemented
80C5×C13⋊C3C2×C3×D1313yescomplemented
81C2×C32×D5—1691noHall
82C132C2×C32×D511yescharacteristic, complemented, Sylow
83C2×C3×D13—651no—
84C2×C3×D13—653no—
85C2×C3×D13—1951no—
86C2×D13⋊C3—653no—
87D65C3×D13⋊C311yescharacteristic, complemented
88D65C32×D1311yescharacteristic, complemented
89C5×D13—131no—
90C5×D13—391no—
91C5×D13—782no—
92D5×C13—131no—
93D5×C13—131no—
94C32×C13—131no—
95C3×C13⋊C3D5×D1311yescharacteristic, complemented
96C2×C32×C5—1691no—
97C32×D5—131no—
98C32×D5—1691no—
99C2×C3×C13—651no—
100C2×C3×C13—653no—
101C2×C3×C13—1951no—
102C3×D13—51no—
103C3×D13—51no—
104C3×D13—133no—
105C3×D13—131no—
106C3×D13—391no—
107C3×D13—653no—
108C3×D13—782no—
109C2×C13⋊C3—653no—
110D13⋊C3—53no—
111D13⋊C3—133no—
112C5×C13—62no—
113C5×C13C2×C3×D13⋊C311yescharacteristic, complemented
114C5×C13C2×C32×D1311yescharacteristic, complemented
115C2×C3×D5—1693no—
116C2×C3×D5—1691no—
117C2×D13—651no—
118C2×D13—1951no—
119C32×C5—131noHall
120C3×C13—62no—
121C3×C13—133no—
122C3×C13D5×D13⋊C311yescharacteristic, complemented
123C3×C13C3×D5×D1311yescharacteristic, complemented
124C13⋊C3C3×D5×D1313yescomplemented
125C22×C32—8451noHall
126C2×C3×C5—1693no—
127C2×C3×C5—1691no—
128C3×D5—133no—
129C3×D5—131no—
130C3×D5—131no—
131C3×D5—1693no—
132C2×C13—651no—
133C2×C13—1951no—
134D13—51no—
135D13—51no—
136D13—131no—
137D13—391no—
138D13—782no—
139C2×D5—1691noHall
140C2×C32—651no—
141C2×C32—8451no—
142C2×C32—1691no—
143C3×C5—133no—
144C3×C5D13×D13⋊C311yescharacteristic, complemented
145C13—62no—
146C13C3×D5×D13⋊C311yescharacteristic, complemented
147C13C32×D5×D1311yescharacteristic, complemented
148C22×C3—8453no—
149C22×C3—25351no—
150C2×C5—1691no—
151D5—131no—
152D5—131no—
153C32—131noSylow
154C2×C3—651no—
155C2×C3—653no—
156C2×C3—8453no—
157C2×C3—1693no—
158C2×C3—1951no—
159C2×C3—5071no—
160C5C3×D13×D13⋊C311yescharacteristic, complemented, Sylow
161C22—25351noSylow
162C3—133no—
163C3(C5⋊(D13⋊C3))⋊D1311yescharacteristic, direct product factor
164C2—651no—
165C2—1951no—
166C2—5071no—
subgroupG/H
center, hypercenterC3(C5⋊(D13⋊C3))⋊D13
commutator, cosocle, hypocenterC5×C132C22×C32
FrattiniC1G
Fitting, socleC3×C5×C132C22×C3
LCSG ▷ C5×C132
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C13⋊C3×D65C2semidirect
2. C3×C13×C5⋊(D13⋊C3)C2semidirect
3. C3×C5×(C13⋊C3)⋊D13C2semidirect
4. C3×D65⋊D13C3semidirect
5. (C5⋊(D13⋊C3))⋊D13C3direct (N × H)
6. C3×C5×C13×C13⋊C3C22semidirect
8. C3×C13×D65C2×C3semidirect
9. C3×C13×D65C2×C3semidirect
10. C3×C5×C13⋊D13C2×C3semidirect
11. C13⋊C3×D65C2×C3semidirect
12. C13×C5⋊(D13⋊C3)C2×C3semidirect
13. C5×(C13⋊C3)⋊D13C2×C3semidirect
14. D65⋊D13C32semidirect
16. C3×(C13⋊C3)⋊D13D5semidirect
18. C5×C13×C13⋊C3C22×C3semidirect
19. C3×C5×C132C22×C3semidirect
24. C13×D65C2×C32semidirect
25. C13×D65C2×C32semidirect
26. C5×C13⋊D13C2×C32semidirect
27. C3×C13×C13⋊C3C2×D5semidirect
31. C3×C5⋊(D13⋊C3)D13semidirect
34. C3×C13⋊D13C3×D5semidirect
38. (C13⋊C3)⋊D13C3×D5semidirect
40. C5×C132C22×C32semidirect
47. C3×C5×C13⋊C3C2×D13semidirect
48. C3×C132C2×C3×D5semidirect
49. C13×C13⋊C3C2×C3×D5semidirect
53. C3×D65D13⋊C3semidirect
54. C3×D65C3×D13semidirect
62. C5⋊(D13⋊C3)C3×D13semidirect
65. C13⋊D13C32×D5semidirect
78. C3×C5×C13C2×D13⋊C3semidirect
79. C3×C5×C13C2×C3×D13semidirect
80. C5×C13⋊C3C2×C3×D13semidirect
82. C132C2×C32×D5semidirect
87. D65C3×D13⋊C3semidirect
88. D65C32×D13semidirect
95. C3×C13⋊C3D5×D13semidirect
113. C5×C13C2×C3×D13⋊C3semidirect
114. C5×C13C2×C32×D13semidirect
122. C3×C13D5×D13⋊C3semidirect
123. C3×C13C3×D5×D13semidirect
124. C13⋊C3C3×D5×D13semidirect
144. C3×C5D13×D13⋊C3semidirect
146. C13C3×D5×D13⋊C3semidirect
147. C13C32×D5×D13semidirect
160. C5C3×D13×D13⋊C3semidirect
163. C3(C5⋊(D13⋊C3))⋊D13direct (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×D652
C3×C13×C5⋊(D13⋊C3)2
C3×C5×(C13⋊C3)⋊D132
C3×D65⋊D133
(C5⋊(D13⋊C3))⋊D133
C3×D13×D13⋊C35
C32×D5×D1313
C3×D5×D13⋊C313