Finite Group Databasebeta

← C3×D5×D7×C13⋊C3 #30655385

Subgroups — C3×D5×D7×C13⋊C3 #30655385

Order 16380.

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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×D35C211yesmaximal, characteristic, complemented
2C3×C7×D5×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×C5×D7×C13⋊C3C211yesmaximal, characteristic, complemented
4C3×D5×C13×D7C311yesmaximal, characteristic, complemented
5D5×D7×C13⋊C3C313yesmaximal, direct product factor
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7C2×C3×D7×C13⋊C3—51nomaximal, Hall
8C13⋊C3×D35C2×C313yescomplemented
9C7×D5×C13⋊C3C2×C313yescomplemented
10C5×D7×C13⋊C3C2×C313yescomplemented
11C3×C13×D35C2×C311yescharacteristic, complemented
12C3×C7×D5×C13C2×C311yescharacteristic, complemented
13C3×C5×C13×D7C2×C311yescharacteristic, complemented
14C2×C3×D5×C13⋊C3—71nomaximal, Hall
15D5×C13×D7C3211yescharacteristic, complemented, Hall
16C2×C3×C7×C13⋊C3—51no—
17C3×D7×C13⋊C3—51no—
18C3×D7×C13⋊C3D511yescharacteristic, direct product factor
19C3×C5×C7×C13C22×C311yescharacteristic, complemented
20C5×C7×C13⋊C3C22×C313yescomplemented
21C32×D5×D7—131nomaximal, Hall
22C2×C3×C5×C13⋊C3—71no—
23C3×D5×C13⋊C3—71no—
24C3×D5×C13⋊C3D711yescharacteristic, direct product factor
25C2×C3×C13×D7—51no—
26C2×D7×C13⋊C3—53no—
27C13×D35C2×C3211yescharacteristic, complemented
28C7×D5×C13C2×C3211yescharacteristic, complemented
29C5×C13×D7C2×C3211yescharacteristic, complemented
30C3×C7×C13⋊C3C2×D511yescharacteristic, complemented, Hall
31C2×C3×D5×C13—71no—
32C2×D5×C13⋊C3—73no—
33C32×D35—131no—
34C32×C7×D5—131no—
35C32×C5×D7—131no—
36C3×C5×C13⋊C3C2×D711yescharacteristic, complemented, Hall
37C2×C3×C7×C13—51no—
38C3×C13×D7—51no—
39C3×C13×D7C3×D511yescharacteristic, complemented
40C2×C7×C13⋊C3—53no—
41D7×C13⋊C3—53no—
42D7×C13⋊C3C3×D513yesdirect product factor
43C22×C3×C13⋊C3—351noHall
44C5×C7×C13C22×C3211yescharacteristic, complemented, Hall
45C3×D5×D7—133no—
46C3×D5×D7C13⋊C311yescharacteristic, direct product factor
47C2×C3×C5×C13—71no—
48C3×D5×C13—71no—
49C3×D5×C13C3×D711yescharacteristic, complemented
50C2×C5×C13⋊C3—73no—
51D5×C13⋊C3—73no—
52D5×C13⋊C3C3×D713yesdirect product factor
53C2×C13×D7—51noHall
54C32×C5×C7—131noHall
55C3×C7×C13C2×C3×D511yescharacteristic, complemented
56C7×C13⋊C3C2×C3×D513yescomplemented
57C2×D5×C13—71noHall
58C2×C32×D7—651noHall
59C2×C3×C13⋊C3—51no—
60C2×C3×C13⋊C3—71no—
61C2×C3×C13⋊C3—351no—
62C3×D35—133no—
63C3×D35C2×C13⋊C311yescharacteristic, complemented
64C3×C7×D5—133no—
65C3×C7×D5C2×C13⋊C311yescharacteristic, complemented
66C3×C5×D7—133no—
67C3×C5×D7C2×C13⋊C311yescharacteristic, complemented
68C3×C5×C13C2×C3×D711yescharacteristic, complemented
69C5×C13⋊C3C2×C3×D713yescomplemented
70C2×C7×C13—51no—
71C13×D7—51no—
72C13×D7C32×D511yescharacteristic, complemented
73C2×C32×D5—911noHall
74C22×C3×C13—351no—
75C22×C13⋊C3—353no—
76D5×D7C3×C13⋊C311yescharacteristic, direct product factor, Hall
77C2×C5×C13—71no—
78D5×C13—71no—
79D5×C13C32×D711yescharacteristic, complemented
80C2×C32×C7—651no—
81C32×D7—131no—
82C32×D7—651no—
83C3×C13⋊C3D5×D711yescharacteristic, direct product factor, Hall
84C3×C5×C7—133no—
85C3×C5×C7C22×C13⋊C311yescharacteristic, complemented
86C7×C13C2×C32×D511yescharacteristic, complemented, Hall
87C2×C32×C5—911no—
88C32×D5—131no—
89C32×D5—911no—
90C2×C3×D7—51no—
91C2×C3×D7—653no—
92C2×C3×C13—51no—
93C2×C3×C13—71no—
94C2×C3×C13—351no—
95C2×C13⋊C3—53no—
96C2×C13⋊C3—73no—
97C2×C13⋊C3—353no—
98D35C2×C3×C13⋊C311yescharacteristic, complemented
99C5×D7C2×C3×C13⋊C311yescharacteristic, complemented
100C7×D5C2×C3×C13⋊C311yescharacteristic, complemented
101C5×C13C2×C32×D711yescharacteristic, complemented, Hall
102C32×C7—131noHall
103C2×C3×D5—71no—
104C2×C3×D5—913no—
105C22×C13—351noHall
106C32×C5—131noHall
107C2×C3×C7—51no—
108C2×C3×C7—653no—
109C3×D7—51no—
110C3×D7—133no—
111C3×D7—653no—
112C3×D7D5×C13⋊C311yescharacteristic, direct product factor
113C3×C13C3×D5×D711yescharacteristic, complemented
114C13⋊C3C3×D5×D713yesdirect product factor
115C22×C32—4551noHall
116C5×C7C22×C3×C13⋊C311yescharacteristic, complemented, Hall
117C2×C3×C5—71no—
118C2×C3×C5—913no—
119C3×D5—71no—
120C3×D5—133no—
121C3×D5—913no—
122C3×D5D7×C13⋊C311yescharacteristic, direct product factor
123C2×D7—51noHall
124C2×C13—51no—
125C2×C13—71no—
126C2×C13—351no—
127C3×C7—133no—
128C3×C7C2×D5×C13⋊C311yescharacteristic, complemented
129C2×D5—71noHall
130C2×C32—651no—
131C2×C32—911no—
132C2×C32—4551no—
133C3×C5—133no—
134C3×C5C2×D7×C13⋊C311yescharacteristic, complemented
135C2×C7—51no—
136D7—51no—
137D7C3×D5×C13⋊C311yescharacteristic, direct product factor
138C13C32×D5×D711yescharacteristic, complemented, Sylow
139C22×C3—351no—
140C22×C3—4553no—
141C2×C5—71no—
142D5—71no—
143D5C3×D7×C13⋊C311yescharacteristic, direct product factor
144C32—131noSylow
145C7C2×C3×D5×C13⋊C311yescharacteristic, complemented, Sylow
146C2×C3—51no—
147C2×C3—71no—
148C2×C3—351no—
149C2×C3—653no—
150C2×C3—913no—
151C2×C3—4553no—
152C5C2×C3×D7×C13⋊C311yescharacteristic, complemented, Sylow
153C22—351noSylow
154C3—133no—
155C3D5×D7×C13⋊C311yescharacteristic, direct product factor
156C2—51no—
157C2—71no—
158C2—351no—
subgroupG/H
center, hypercenterC3D5×D7×C13⋊C3
commutator, cosocle, hypocenterC5×C7×C13C22×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C13⋊C3×D35C2semidirect
2. C3×C7×D5×C13⋊C3C2semidirect
3. C3×C5×D7×C13⋊C3C2semidirect
4. C3×D5×C13×D7C3semidirect
5. D5×D7×C13⋊C3C3direct (N × H)
6. C3×C5×C7×C13⋊C3C22semidirect
8. C13⋊C3×D35C2×C3semidirect
9. C7×D5×C13⋊C3C2×C3semidirect
10. C5×D7×C13⋊C3C2×C3semidirect
11. C3×C13×D35C2×C3semidirect
12. C3×C7×D5×C13C2×C3semidirect
13. C3×C5×C13×D7C2×C3semidirect
15. D5×C13×D7C32semidirect
18. C3×D7×C13⋊C3D5direct (N × H)
19. C3×C5×C7×C13C22×C3semidirect
20. C5×C7×C13⋊C3C22×C3semidirect
24. C3×D5×C13⋊C3D7direct (N × H)
27. C13×D35C2×C32semidirect
28. C7×D5×C13C2×C32semidirect
29. C5×C13×D7C2×C32semidirect
30. C3×C7×C13⋊C3C2×D5semidirect
36. C3×C5×C13⋊C3C2×D7semidirect
39. C3×C13×D7C3×D5semidirect
42. D7×C13⋊C3C3×D5direct (N × H)
44. C5×C7×C13C22×C32semidirect
46. C3×D5×D7C13⋊C3direct (N × H)
49. C3×D5×C13C3×D7semidirect
52. D5×C13⋊C3C3×D7direct (N × H)
55. C3×C7×C13C2×C3×D5semidirect
56. C7×C13⋊C3C2×C3×D5semidirect
63. C3×D35C2×C13⋊C3semidirect
65. C3×C7×D5C2×C13⋊C3semidirect
67. C3×C5×D7C2×C13⋊C3semidirect
68. C3×C5×C13C2×C3×D7semidirect
69. C5×C13⋊C3C2×C3×D7semidirect
72. C13×D7C32×D5semidirect
76. D5×D7C3×C13⋊C3direct (N × H)
79. D5×C13C32×D7semidirect
83. C3×C13⋊C3D5×D7direct (N × H)
85. C3×C5×C7C22×C13⋊C3semidirect
86. C7×C13C2×C32×D5semidirect
98. D35C2×C3×C13⋊C3semidirect
99. C5×D7C2×C3×C13⋊C3semidirect
100. C7×D5C2×C3×C13⋊C3semidirect
101. C5×C13C2×C32×D7semidirect
112. C3×D7D5×C13⋊C3direct (N × H)
113. C3×C13C3×D5×D7semidirect
114. C13⋊C3C3×D5×D7direct (N × H)
116. C5×C7C22×C3×C13⋊C3semidirect
122. C3×D5D7×C13⋊C3direct (N × H)
128. C3×C7C2×D5×C13⋊C3semidirect
134. C3×C5C2×D7×C13⋊C3semidirect
137. D7C3×D5×C13⋊C3direct (N × H)
138. C13C32×D5×D7semidirect
143. D5C3×D7×C13⋊C3direct (N × H)
145. C7C2×C3×D5×C13⋊C3semidirect
152. C5C2×C3×D7×C13⋊C3semidirect
155. C3D5×D7×C13⋊C3direct (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×D352
C3×C7×D5×C13⋊C32
C3×C5×D7×C13⋊C32
C3×D5×C13×D73
D5×D7×C13⋊C33
C2×C3×D7×C13⋊C35
C2×C3×D5×C13⋊C37
C32×D5×D713