Finite Group Databasebeta

← C3×C5⋊D5×D39 #26043766

Subgroups — C3×C5⋊D5×D39 #26043766

Order 11700.

352 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 92 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×C3⋊(C5⋊D65)C211yesmaximal, characteristic, complemented
2C3×C52×D39C211yesmaximal, characteristic, complemented
3C32×C13×C5⋊D5C211yesmaximal, characteristic, complemented
4C5⋊D5×D39C311yesmaximal, characteristic, direct product factor
5C3×D13×C5⋊D5—31nomaximal
6C32×C52×C13C2211yescharacteristic, complemented, Hall
7C3×D5×D39—56nomaximal
8C3⋊(C5⋊D65)C2×C311yescharacteristic, complemented
9C52×D39C2×C311yescharacteristic, complemented
10C3×C5⋊D65—31no—
11C3×C13×C5⋊D5—21no—
12C3×C13×C5⋊D5D311yescharacteristic, complemented
13C3×C13×C5⋊D5C2×C311yescharacteristic, complemented
14C3×C52×D13—31no—
15D13×C5⋊D5—31noHall
16C3×D195—56no—
17C3×C5×D39D516yescomplemented
18C32×D5×C13—56no—
19C3×C52×C13—21no—
20C3×C52×C13C2×D311yescharacteristic, complemented
21C3×C52×C13C22×C311yescharacteristic, complemented
22C3×D3×C5⋊D5—131nomaximal, Hall
23D5×D39—56no—
24C3×D5×D13—156no—
25C5⋊D65—31no—
26C13×C5⋊D5C3×D311yescharacteristic, complemented
27C52×D13—31no—
28C32×C5×C13C2×D516yescomplemented
29C2×C3×D39—251noHall
30C3×C3⋊(C5⋊D5)—131no—
31C3×C52×D3—131no—
32C32×C5⋊D5D1311yescharacteristic, complemented
33D195—56no—
34C5×D39C3×D516yescomplemented
35C3×D65—156no—
36C3×D5×C13—56no—
37C3×D5×C13—56no—
38C3×D5×C13—106no—
39C3×C5×D13—36no—
40C52×C13C2×C3×D311yescharacteristic, complemented, Hall
41C2×C3×C5⋊D5—391no—
42D3×C5⋊D5—131no—
43D5×D13—156no—
44C2×C32×C13—251no—
45C3×D39—251no—
46C3×D39C5⋊D511yescharacteristic, direct product factor
47C32×C52C2×D1311yescharacteristic, complemented, Hall
48C3×C5×C13—26no—
49C3×C5×C13D3×D516yescomplemented
50C3×C5×C13C2×C3×D516yescomplemented
51C3×D3×D5—656no—
52C2×D39—251no—
53C2×C3×D13—751no—
54C2×C3×C52—391no—
55C3⋊(C5⋊D5)—131no—
56C52×D3—131no—
57C3×C5⋊D5—21no—
58C3×C5⋊D5—391no—
59C3×C5⋊D5C3×D1311yescharacteristic, complemented
60C3×C5⋊D5D3911yescharacteristic, direct product factor
61D65—156no—
62C5×D13—36no—
63D5×C13—56no—
64C32×C13C2×C5⋊D511yescharacteristic, complemented, Hall
65C2×C5⋊D5—391noHall
66C3×D15—656no—
67C3×C5×D3—136no—
68C32×D5—56no—
69C2×C3×C13—251no—
70C2×C3×C13—251no—
71C2×C3×C13—501no—
72D39—251no—
73D39C3×C5⋊D511yescharacteristic, direct product factor
74C3×D13—31no—
75C3×D13—751no—
76C3×C52—21no—
77C3×C52C2×C3×D1311yescharacteristic, complemented
78C3×C52C2×D3911yescharacteristic, complemented
79C5×C13C3×D3×D516yescomplemented
80C2×C3×D5—1956no—
81D3×D5—656no—
82C2×D13—751noHall
83C2×C52—391no—
84C5⋊D5—391no—
85C5⋊D5C3×D3911yescharacteristic, direct product factor
86C32×C5D5×D1316yescomplemented
87C3×C13—21no—
88C3×C13D3×C5⋊D511yescharacteristic, complemented
89C3×C13C2×C3×C5⋊D511yescharacteristic, complemented
90C2×C3×D3—3251noHall
91C2×C3×C5—396no—
92D15—656no—
93C3×D5—56no—
94C3×D5—56no—
95C3×D5—106no—
96C3×D5—1956no—
97C5×D3—136no—
98C2×C13—251no—
99D13—31no—
100D13—751no—
101C52C2×C3×D3911yescharacteristic, complemented, Sylow
102C2×D5—1956no—
103C2×C32—251no—
104C3×D3—131no—
105C3×D3—3251no—
106C3×C5—26no—
107C3×C5C3×D5×D1316yescomplemented
108C3×C5D5×D3916yescomplemented
109C13C3×D3×C5⋊D511yescharacteristic, complemented, Sylow
110C22×C3—9751no—
111C2×D3—3251no—
112C2×C5—396no—
113D5—56no—
114D5—1956no—
115C32D13×C5⋊D511yescharacteristic, complemented, Sylow
116C2×C3—251no—
117C2×C3—251no—
118C2×C3—391no—
119C2×C3—501no—
120C2×C3—9751no—
121D3—131no—
122D3—3251no—
123C5C3×D5×D3916yescomplemented
124C22—9751noSylow
125C3—21no—
126C3C3×D13×C5⋊D511yescharacteristic, complemented
127C3C5⋊D5×D3911yescharacteristic, direct product factor
128C2—251no—
129C2—391no—
130C2—9751no—
subgroupG/H
center, hypercenterC3C5⋊D5×D39
commutator, cosocle, hypocenterC3×C52×C13C22×C3
FrattiniC1G
Fitting, socleC32×C52×C13C22
LCSG ▷ C3×C52×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊(C5⋊D65)C2semidirect
2. C3×C52×D39C2semidirect
3. C32×C13×C5⋊D5C2semidirect
4. C5⋊D5×D39C3direct (N × H)
6. C32×C52×C13C22semidirect
8. C3⋊(C5⋊D65)C2×C3semidirect
9. C52×D39C2×C3semidirect
12. C3×C13×C5⋊D5D3semidirect
13. C3×C13×C5⋊D5C2×C3semidirect
17. C3×C5×D39D5semidirect
20. C3×C52×C13C2×D3semidirect
21. C3×C52×C13C22×C3semidirect
26. C13×C5⋊D5C3×D3semidirect
28. C32×C5×C13C2×D5semidirect
32. C32×C5⋊D5D13semidirect
34. C5×D39C3×D5semidirect
40. C52×C13C2×C3×D3semidirect
46. C3×D39C5⋊D5direct (N × H)
47. C32×C52C2×D13semidirect
49. C3×C5×C13D3×D5semidirect
50. C3×C5×C13C2×C3×D5semidirect
59. C3×C5⋊D5C3×D13semidirect
60. C3×C5⋊D5D39direct (N × H)
64. C32×C13C2×C5⋊D5semidirect
73. D39C3×C5⋊D5direct (N × H)
77. C3×C52C2×C3×D13semidirect
78. C3×C52C2×D39semidirect
79. C5×C13C3×D3×D5semidirect
85. C5⋊D5C3×D39direct (N × H)
86. C32×C5D5×D13semidirect
88. C3×C13D3×C5⋊D5semidirect
89. C3×C13C2×C3×C5⋊D5semidirect
101. C52C2×C3×D39semidirect
107. C3×C5C3×D5×D13semidirect
108. C3×C5D5×D39semidirect
109. C13C3×D3×C5⋊D5semidirect
115. C32D13×C5⋊D5semidirect
123. C5C3×D5×D39semidirect
126. C3C3×D13×C5⋊D5semidirect
127. C3C5⋊D5×D39direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C3⋊(C5⋊D65)2
C3×C52×D392
C32×C13×C5⋊D52
C5⋊D5×D393
C3×D13×C5⋊D53
C3×D5×D395
C3×D3×C5⋊D513