Finite Group Databasebeta

← C5×C3⋊D3×D15 #72247709

Subgroups — C5×C3⋊D3×D15 #72247709

Order 2700.

368 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C5×C3⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
2C3×C52×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×C5×D15C211yesmaximal, characteristic, complemented
4C5×D3×D15—34nomaximal
5C5×D5×C3⋊D3—31nomaximal
6C33×C52C2211yescharacteristic, complemented, Hall
7C3⋊D3×D15C511yesmaximal, characteristic, direct product factor
8C5×D3×C3⋊D3—51nomaximal
9C5×C3⋊D15—31no—
10C5×C3⋊D15—34no—
11C5×C3⋊D15—64no—
12C52×C3⋊D3D311yescharacteristic, complemented
13C3×C5×D15D314yescomplemented
14C3×C52×D3—34no—
15C32×C5×D5—31no—
16C2×C5×D15—91no—
17C5×D3×D5—94no—
18C3⋊(C3⋊D15)C2×C511yescharacteristic, complemented
19C5×C3⋊(C3⋊D3)—51no—
20C3×C5×C3⋊D3—22no—
21C3×C5×C3⋊D3D511yescharacteristic, complemented
22C3×C5×C3⋊D3C2×C511yescharacteristic, complemented
23C32×D15C2×C511yescharacteristic, complemented
24C32×C5×D3—51no—
25C32×C52—24no—
26C32×C52C2×D314yescomplemented
27C32×C52C2×D311yescharacteristic, complemented
28C2×C5×C3⋊D3—151no—
29D3×D15—34no—
30C5×D32—154no—
31D5×C3⋊D3—31no—
32C2×C3×C52—91no—
33C5×D15—94no—
34C5×D15—91no—
35C5×D15—184no—
36C5×D15C3⋊D311yescharacteristic, direct product factor
37C52×D3—34no—
38C3×C5×D5—34no—
39C33×C5—22no—
40C33×C5C2×D511yescharacteristic, complemented
41C33×C5C22×C511yescharacteristic, complemented
42D3×C3⋊D3—51noHall
43C2×C5×D5—271noHall
44C2×C32×C5—151no—
45C3⋊D15—31no—
46C3⋊D15—34no—
47C3⋊D15—64no—
48C5×C3⋊D3—22no—
49C5×C3⋊D3—151no—
50C5×C3⋊D3—154no—
51C5×C3⋊D3—304no—
52C5×C3⋊D3C5×D311yescharacteristic, complemented
53C5×C3⋊D3D1511yescharacteristic, direct product factor
54C3×D15C5×D314yescomplemented
55C3×C5×D3—34no—
56C3×C5×D3—34no—
57C3×C5×D3—54no—
58C3×C5×D3—68no—
59C32×D5—31no—
60C3×C52—24no—
61C3×C52D3214yescomplemented
62C3×C52C2×C3⋊D311yescharacteristic, complemented
63C2×D15—91no—
64C2×C5×D3—454no—
65C2×C5×D3—451no—
66D3×D5—94no—
67C3⋊(C3⋊D3)—51no—
68C3×C3⋊D3C5×D511yescharacteristic, complemented
69C32×D3—51no—
70C2×C52—91no—
71C5×D5—31no—
72C5×D5—271no—
73C32×C5—24no—
74C32×C5—24no—
75C32×C5—28no—
76C32×C5—22no—
77C32×C5—48no—
78C32×C5D3×D514yescomplemented
79C32×C5C2×C5×D314yescomplemented
80C32×C5C2×C5×D311yescharacteristic, complemented
81C32×C5C2×D1511yescharacteristic, complemented
82C2×C3⋊D3—151no—
83D32—154no—
84C2×C3×C5—91no—
85C2×C3×C5—91no—
86C2×C3×C5—154no—
87C2×C3×C5—182no—
88D15—94no—
89D15—91no—
90D15—184no—
91D15C5×C3⋊D311yescharacteristic, direct product factor
92C3×D5—34no—
93C5×D3—34no—
94C5×D3—34no—
95C5×D3—51no—
96C5×D3—68no—
97C5×D3—451no—
98C5×D3—454no—
99C5×D3—904no—
100C33C2×C5×D511yescharacteristic, complemented, Sylow
101C52D3×C3⋊D311yescharacteristic, complemented, Sylow
102C22×C5—1351no—
103C2×D5—271no—
104C2×C32—151no—
105C3⋊D3—151no—
106C3⋊D3—154no—
107C3⋊D3—304no—
108C3⋊D3C5×D1511yescharacteristic, direct product factor
109C3×D3—34no—
110C3×D3—54no—
111C3×C5—24no—
112C3×C5—24no—
113C3×C5—22no—
114C3×C5—28no—
115C3×C5—48no—
116C3×C5D5×C3⋊D311yescharacteristic, complemented
117C3×C5C5×D3214yescomplemented
118C3×C5D3×D1514yescomplemented
119C3×C5C2×C5×C3⋊D311yescharacteristic, complemented
120C2×D3—454no—
121C2×D3—451no—
122C2×C5—91no—
123C2×C5—91no—
124C2×C5—151no—
125C2×C5—182no—
126C2×C5—1351no—
127D5—31no—
128D5—271no—
129C32—24no—
130C32C5×D3×D514yescomplemented
131C32C2×C5×D1511yescharacteristic, complemented
132C2×C3—91no—
133C2×C3—154no—
134D3—34no—
135D3—51no—
136D3—451no—
137D3—454no—
138D3—904no—
139C5—22no—
140C5C5×D3×C3⋊D311yescharacteristic, complemented
141C5C3⋊D3×D1511yescharacteristic, direct product factor
142C22—1351noSylow
143C3—24no—
144C3C5×D5×C3⋊D311yescharacteristic, complemented
145C3C5×D3×D1514yescomplemented
146C2—91no—
147C2—151no—
148C2—1351no—
subgroupG/H
center, hypercenterC5C3⋊D3×D15
commutator, cosocle, hypocenterC33×C5C22×C5
FrattiniC1G
Fitting, socleC33×C52C22
LCSG ▷ C33×C5
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C3⋊(C3⋊D15)C2semidirect
2. C3×C52×C3⋊D3C2semidirect
3. C32×C5×D15C2semidirect
6. C33×C52C22semidirect
7. C3⋊D3×D15C5direct (N × H)
12. C52×C3⋊D3D3semidirect
13. C3×C5×D15D3semidirect
18. C3⋊(C3⋊D15)C2×C5semidirect
21. C3×C5×C3⋊D3D5semidirect
22. C3×C5×C3⋊D3C2×C5semidirect
23. C32×D15C2×C5semidirect
26. C32×C52C2×D3semidirect
27. C32×C52C2×D3semidirect
36. C5×D15C3⋊D3direct (N × H)
40. C33×C5C2×D5semidirect
41. C33×C5C22×C5semidirect
52. C5×C3⋊D3C5×D3semidirect
53. C5×C3⋊D3D15direct (N × H)
54. C3×D15C5×D3semidirect
61. C3×C52D32semidirect
62. C3×C52C2×C3⋊D3semidirect
68. C3×C3⋊D3C5×D5semidirect
78. C32×C5D3×D5semidirect
79. C32×C5C2×C5×D3semidirect
80. C32×C5C2×C5×D3semidirect
81. C32×C5C2×D15semidirect
91. D15C5×C3⋊D3direct (N × H)
100. C33C2×C5×D5semidirect
101. C52D3×C3⋊D3semidirect
108. C3⋊D3C5×D15direct (N × H)
116. C3×C5D5×C3⋊D3semidirect
117. C3×C5C5×D32semidirect
118. C3×C5D3×D15semidirect
119. C3×C5C2×C5×C3⋊D3semidirect
130. C32C5×D3×D5semidirect
131. C32C2×C5×D15semidirect
140. C5C5×D3×C3⋊D3semidirect
141. C5C3⋊D3×D15direct (N × H)
144. C3C5×D5×C3⋊D3semidirect
145. C3C5×D3×D15semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊(C3⋊D15)2
C3×C52×C3⋊D32
C32×C5×D152
C5×D3×D153
C5×D5×C3⋊D33
C3⋊D3×D155
C5×D3×C3⋊D35