Finite Group Databasebeta

← C3×(C5⋊(D13⋊C3))⋊D7 #30655384

Subgroups — C3×(C5⋊(D13⋊C3))⋊D7 #30655384

Order 16380.

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

normal subgroups only

This group has 240 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×D35C211yesmaximal, characteristic, complemented
2C3×C7×C5⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
3C3×C5×(C13⋊C3)⋊D7C211yesmaximal, characteristic, complemented
4C3×D35⋊D13C311yesmaximal, characteristic, complemented
5(C5⋊(D13⋊C3))⋊D7C313yesmaximal, direct product factor
6C3×C5×C7×C13⋊C3C2211yescharacteristic, complemented, Hall
7C3×D7×D13⋊C3—51nomaximal, Hall
8C13⋊C3×D35C2×C313yescomplemented
9C7×C5⋊(D13⋊C3)C2×C313yescomplemented
10C5×(C13⋊C3)⋊D7C2×C313yescomplemented
11C3×C13×D35C2×C311yescharacteristic, complemented
12C3×C7×D65C2×C311yescharacteristic, complemented
13C3×C5×D91C2×C311yescharacteristic, complemented
14C3×D5×D13⋊C3—71nomaximal, Hall
15D35⋊D13C3211yescharacteristic, complemented, Hall
16C3×(C13⋊C3)⋊D7D511yescharacteristic, complemented
17C3×D7×C13⋊C3—51no—
18C3×C7×D13⋊C3—51no—
19C3×C5×C7×C13C22×C311yescharacteristic, complemented
20C5×C7×C13⋊C3C22×C313yescomplemented
21C32×D5×D7—131nomaximal, Hall
22C3×C5⋊(D13⋊C3)D711yescharacteristic, complemented
23C3×D5×C13⋊C3—71no—
24C3×C5×D13⋊C3—71no—
25C3×D7×D13—51no—
26D7×D13⋊C3—53no—
27C13×D35C2×C3211yescharacteristic, complemented
28C7×D65C2×C3211yescharacteristic, complemented
29C5×D91C2×C3211yescharacteristic, complemented
30C3×C7×C13⋊C3C2×D511yescharacteristic, complemented, Hall
31C3×D5×D13—71no—
32D5×D13⋊C3—73no—
33C32×D35—131no—
34C32×C7×D5—131no—
35C32×C5×D7—131no—
36C3×C5×C13⋊C3C2×D711yescharacteristic, complemented, Hall
37C3×D91C3×D511yescharacteristic, complemented
38C3×C13×D7—51no—
39C3×C7×D13—51no—
40(C13⋊C3)⋊D7C3×D513yescomplemented
41D7×C13⋊C3—53no—
42C7×D13⋊C3—53no—
43C2×C3×D13⋊C3—351noHall
44C5×C7×C13C22×C3211yescharacteristic, complemented, Hall
45C3×D5×D7—133no—
46C3×D5×D7—391no—
47C3×D65C3×D711yescharacteristic, complemented
48C3×D5×C13—71no—
49C3×C5×D13—71no—
50C5⋊(D13⋊C3)C3×D713yescomplemented
51D5×C13⋊C3—73no—
52C5×D13⋊C3—73no—
53D7×D13—51noHall
54C32×C5×C7—131noHall
55C3×C7×C13C2×C3×D511yescharacteristic, complemented
56C7×C13⋊C3C2×C3×D513yescomplemented
57D5×D13—71noHall
58C2×C32×D7—651noHall
59C2×C3×C13⋊C3—351no—
60C3×D13⋊C3—51no—
61C3×D13⋊C3—71no—
62C3×D35—133no—
63C3×D35D13⋊C311yescharacteristic, complemented
64C3×C7×D5—133no—
65C3×C7×D5—131no—
66C3×C5×D7—133no—
67C3×C5×D7—391no—
68C3×C5×C13C2×C3×D711yescharacteristic, complemented
69C5×C13⋊C3C2×C3×D713yescomplemented
70D91C32×D511yescharacteristic, complemented
71C7×D13—51no—
72C13×D7—51no—
73C2×C32×D5—911noHall
74C2×C3×D13—351no—
75C2×D13⋊C3—353no—
76D5×D7—391noHall
77D65C32×D711yescharacteristic, complemented
78C5×D13—71no—
79D5×C13—71no—
80C2×C32×C7—651no—
81C32×D7—131no—
82C32×D7—651no—
83C3×C13⋊C3D5×D711yescharacteristic, complemented, Hall
84C3×C5×C7—133no—
85C3×C5×C7C2×D13⋊C311yescharacteristic, complemented
86C7×C13C2×C32×D511yescharacteristic, complemented, Hall
87C2×C32×C5—911no—
88C32×D5—131no—
89C32×D5—911no—
90C2×C3×D7—653no—
91C2×C3×D7—1951no—
92C2×C3×C13—351no—
93C3×D13—51no—
94C3×D13—71no—
95C2×C13⋊C3—353no—
96D13⋊C3—53no—
97D13⋊C3—73no—
98D35C3×D13⋊C311yescharacteristic, complemented
99C5×D7—391no—
100C7×D5—131no—
101C5×C13C2×C32×D711yescharacteristic, complemented, Hall
102C32×C7—131noHall
103C2×C3×D5—2731no—
104C2×C3×D5—913no—
105C2×D13—351noHall
106C32×C5—131noHall
107C2×C3×C7—653no—
108C2×C3×C7—1951no—
109C3×D7—51no—
110C3×D7—133no—
111C3×D7—391no—
112C3×D7—653no—
113C3×C13C3×D5×D711yescharacteristic, complemented
114C13⋊C3C3×D5×D713yescomplemented
115C22×C32—4551noHall
116C5×C7C2×C3×D13⋊C311yescharacteristic, complemented, Hall
117C2×C3×C5—2731no—
118C2×C3×C5—913no—
119C3×D5—71no—
120C3×D5—133no—
121C3×D5—391no—
122C3×D5—913no—
123C2×D7—1951noHall
124C2×C13—351no—
125D13—51no—
126D13—71no—
127C3×C7—133no—
128C3×C7D5×D13⋊C311yescharacteristic, complemented
129C2×D5—2731noHall
130C2×C32—651no—
131C2×C32—911no—
132C2×C32—4551no—
133C3×C5—133no—
134C3×C5D7×D13⋊C311yescharacteristic, complemented
135C2×C7—1951no—
136D7—51no—
137D7—391no—
138C13C32×D5×D711yescharacteristic, complemented, Sylow
139C22×C3—13651no—
140C22×C3—4553no—
141C2×C5—2731no—
142D5—71no—
143D5—391no—
144C32—131noSylow
145C7C3×D5×D13⋊C311yescharacteristic, complemented, Sylow
146C2×C3—2731no—
147C2×C3—351no—
148C2×C3—653no—
149C2×C3—913no—
150C2×C3—1951no—
151C2×C3—4553no—
152C5C3×D7×D13⋊C311yescharacteristic, complemented, Sylow
153C22—13651noSylow
154C3—133no—
155C3(C5⋊(D13⋊C3))⋊D711yescharacteristic, direct product factor
156C2—2731no—
157C2—351no—
158C2—1951no—
subgroupG/H
center, hypercenterC3(C5⋊(D13⋊C3))⋊D7
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×C5⋊(D13⋊C3)C2semidirect
3. C3×C5×(C13⋊C3)⋊D7C2semidirect
4. C3×D35⋊D13C3semidirect
5. (C5⋊(D13⋊C3))⋊D7C3direct (N × H)
6. C3×C5×C7×C13⋊C3C22semidirect
8. C13⋊C3×D35C2×C3semidirect
9. C7×C5⋊(D13⋊C3)C2×C3semidirect
10. C5×(C13⋊C3)⋊D7C2×C3semidirect
11. C3×C13×D35C2×C3semidirect
12. C3×C7×D65C2×C3semidirect
13. C3×C5×D91C2×C3semidirect
15. D35⋊D13C32semidirect
16. C3×(C13⋊C3)⋊D7D5semidirect
19. C3×C5×C7×C13C22×C3semidirect
20. C5×C7×C13⋊C3C22×C3semidirect
22. C3×C5⋊(D13⋊C3)D7semidirect
27. C13×D35C2×C32semidirect
28. C7×D65C2×C32semidirect
29. C5×D91C2×C32semidirect
30. C3×C7×C13⋊C3C2×D5semidirect
36. C3×C5×C13⋊C3C2×D7semidirect
37. C3×D91C3×D5semidirect
40. (C13⋊C3)⋊D7C3×D5semidirect
44. C5×C7×C13C22×C32semidirect
47. C3×D65C3×D7semidirect
50. C5⋊(D13⋊C3)C3×D7semidirect
55. C3×C7×C13C2×C3×D5semidirect
56. C7×C13⋊C3C2×C3×D5semidirect
63. C3×D35D13⋊C3semidirect
68. C3×C5×C13C2×C3×D7semidirect
69. C5×C13⋊C3C2×C3×D7semidirect
70. D91C32×D5semidirect
77. D65C32×D7semidirect
83. C3×C13⋊C3D5×D7semidirect
85. C3×C5×C7C2×D13⋊C3semidirect
86. C7×C13C2×C32×D5semidirect
98. D35C3×D13⋊C3semidirect
101. C5×C13C2×C32×D7semidirect
113. C3×C13C3×D5×D7semidirect
114. C13⋊C3C3×D5×D7semidirect
116. C5×C7C2×C3×D13⋊C3semidirect
128. C3×C7D5×D13⋊C3semidirect
134. C3×C5D7×D13⋊C3semidirect
138. C13C32×D5×D7semidirect
145. C7C3×D5×D13⋊C3semidirect
152. C5C3×D7×D13⋊C3semidirect
155. C3(C5⋊(D13⋊C3))⋊D7direct (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×C5⋊(D13⋊C3)2
C3×C5×(C13⋊C3)⋊D72
C3×D35⋊D133
(C5⋊(D13⋊C3))⋊D73
C3×D7×D13⋊C35
C3×D5×D13⋊C37
C32×D5×D713