Finite Group Databasebeta

← C3×C5⋊#1113 #13108549

Subgroups — C3×C5⋊#1113 #13108549

Order 1620.

348 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C32×C3⋊D15C212yesmaximal, complemented
2C32×C5×C3⋊D3C211yesmaximal, characteristic, complemented
3C5⋊#1113C311yesmaximal, characteristic, direct product factor
4C3×(C3⋊D3)⋊D5—31nomaximal
5C3×D3×D15—32nomaximal
6C34×C5C2211yescharacteristic, complemented, Hall
7C3×#1113—51nomaximal, Hall
8C3×C3⋊D15—22no—
9C3×C3⋊D15D312yescomplemented
10C3×C3⋊D15C2×C312yescomplemented
11C3×C5×C3⋊D3—21no—
12C3×C5×C3⋊D3D311yescharacteristic, complemented
13C3×C5×C3⋊D3C2×C311yescharacteristic, complemented
14C32×D15—32no—
15C32×D15—32no—
16C32×D15—62no—
17C32×C5×D3—32no—
18C32×C5×D3—61no—
19C2×C3×D15—91no—
20(C3⋊D3)⋊D5—31no—
21D3×D15—32no—
22C3×D3×D5—92no—
23C32×C3⋊D3—52no—
24C32×C3⋊D3D511yescharacteristic, complemented
25C33×C5—21no—
26C33×C5—22no—
27C33×C5—21no—
28C33×C5—22no—
29C33×C5—42no—
30C33×C5—42no—
31C33×C5—41no—
32C33×C5—41no—
33C33×C5C2×D312yescomplemented
34C33×C5C2×D311yescharacteristic, complemented
35C33×C5C22×C311yescharacteristic, complemented
36#1113—51no—
37C3×D32—152no—
38C3×D32—151no—
39C2×C32×C5—91no—
40C3⋊D15C3×D312yescomplemented
41C5×C3⋊D3C3×D311yescharacteristic, complemented
42C3×D15—32no—
43C3×D15—32no—
44C3×D15—32no—
45C3×D15—32no—
46C3×D15—62no—
47C3×D15—62no—
48C3×D15—62no—
49C3×D15—62no—
50C3×D15—64no—
51C3×C5×D3—32no—
52C3×C5×D3—32no—
53C3×C5×D3—62no—
54C3×C5×D3—61no—
55C3×C5×D3—61no—
56C3×C5×D3—62no—
57C32×D5—92no—
58C34C2×D511yescharacteristic, complemented, Sylow
59C2×D15—91no—
60C2×C3×D5—271no—
61D3×D5—92no—
62C3×C3⋊D3—21no—
63C3×C3⋊D3—52no—
64C3×C3⋊D3—52no—
65C3×C3⋊D3—102no—
66C3×C3⋊D3C3×D511yescharacteristic, complemented
67C3×C3⋊D3D1511yescharacteristic, complemented
68C32×D3—32no—
69C32×D3—61no—
70C32×D3—152no—
71C32×D3—152no—
72C32×D3—302no—
73C32×C5—22no—
74C32×C5—24no—
75C32×C5—22no—
76C32×C5—21no—
77C32×C5—22no—
78C32×C5—22no—
79C32×C5—22no—
80C32×C5—21no—
81C32×C5—22no—
82C32×C5—42no—
83C32×C5—41no—
84C32×C5—41no—
85C32×C5—42no—
86C32×C5—44no—
87C32×C5—44no—
88C32×C5—42no—
89C32×C5—42no—
90C32×C5—42no—
91C32×C5—41no—
92C32×C5—41no—
93C32×C5D3212yescomplemented
94C32×C5D3211yescharacteristic, complemented
95C32×C5C2×C3×D312yescomplemented
96C32×C5C2×C3×D311yescharacteristic, complemented
97C2×C3×D3—452no—
98C2×C3×D3—451no—
99D32—152no—
100D32—151no—
101C2×C3×C5—91no—
102C2×C3×C5—91no—
103C2×C3×C5—181no—
104D15—32no—
105D15—32no—
106D15—62no—
107C3×D5—92no—
108C3×D5—92no—
109C3×D5—182no—
110C5×D3—32no—
111C5×D3—61no—
112C33—22no—
113C33—22no—
114C33—21no—
115C33—21no—
116C33—42no—
117C33—42no—
118C33—41no—
119C33—41no—
120C33D3×D512yescomplemented
121C33C2×C3×D511yescharacteristic, complemented
122C33C2×D1511yescharacteristic, complemented
123C2×D5—271noHall
124C2×C32—91no—
125C2×C32—452no—
126C3⋊D3—52no—
127C3⋊D3C3×D1511yescharacteristic, complemented
128C3×D3—32no—
129C3×D3—32no—
130C3×D3—62no—
131C3×D3—61no—
132C3×D3—61no—
133C3×D3—62no—
134C3×D3—152no—
135C3×D3—152no—
136C3×D3—152no—
137C3×D3—152no—
138C3×D3—302no—
139C3×D3—302no—
140C3×D3—302no—
141C3×D3—302no—
142C3×D3—304no—
143C3×C5—21no—
144C3×C5—22no—
145C3×C5—22no—
146C3×C5—21no—
147C3×C5—42no—
148C3×C5—42no—
149C3×C5—41no—
150C3×C5—41no—
151C3×C5C3×D3212yescomplemented
152C3×C5C3×D3211yescharacteristic, complemented
153C3×C5#111311yescharacteristic, complemented
154C22×C3—1351no—
155C2×D3—452no—
156C2×D3—451no—
157C2×C5—91no—
158D5—92no—
159C32—22no—
160C32—24no—
161C32—22no—
162C32—22no—
163C32—22no—
164C32—21no—
165C32—22no—
166C32—21no—
167C32—22no—
168C32—42no—
169C32—41no—
170C32—41no—
171C32—42no—
172C32—44no—
173C32—42no—
174C32—44no—
175C32—42no—
176C32—42no—
177C32—41no—
178C32—41no—
179C32C3×D3×D512yescomplemented
180C32D3×D1512yescomplemented
181C32(C3⋊D3)⋊D511yescharacteristic, complemented
182C32C2×C3×D1511yescharacteristic, complemented
183C2×C3—91no—
184C2×C3—91no—
185C2×C3—181no—
186C2×C3—452no—
187C2×C3—452no—
188C2×C3—902no—
189D3—32no—
190D3—61no—
191D3—152no—
192D3—152no—
193D3—302no—
194C5C3×#111311yescharacteristic, complemented, Sylow
195C22—1351noSylow
196C3—21no—
197C3—22no—
198C3—21no—
199C3—22no—
200C3—42no—
201C3—42no—
202C3—41no—
203C3—41no—
204C3C3×D3×D1512yescomplemented
205C3C3×(C3⋊D3)⋊D511yescharacteristic, complemented
206C3C5⋊#111311yescharacteristic, direct product factor
207C2—91no—
208C2—452no—
subgroupG/H
center, hypercenterC3C5⋊#1113
commutator, cosocle, hypocenterC33×C5C22×C3
FrattiniC1G
Fitting, socleC34×C5C22
LCSG ▷ C33×C5
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C3⋊D15C2semidirect
2. C32×C5×C3⋊D3C2semidirect
3. C5⋊#1113C3direct (N × H)
6. C34×C5C22semidirect
9. C3×C3⋊D15D3semidirect
10. C3×C3⋊D15C2×C3semidirect
12. C3×C5×C3⋊D3D3semidirect
13. C3×C5×C3⋊D3C2×C3semidirect
24. C32×C3⋊D3D5semidirect
33. C33×C5C2×D3semidirect
34. C33×C5C2×D3semidirect
35. C33×C5C22×C3semidirect
40. C3⋊D15C3×D3semidirect
41. C5×C3⋊D3C3×D3semidirect
58. C34C2×D5semidirect
66. C3×C3⋊D3C3×D5semidirect
67. C3×C3⋊D3D15semidirect
93. C32×C5D32semidirect
94. C32×C5D32semidirect
95. C32×C5C2×C3×D3semidirect
96. C32×C5C2×C3×D3semidirect
120. C33D3×D5semidirect
121. C33C2×C3×D5semidirect
122. C33C2×D15semidirect
127. C3⋊D3C3×D15semidirect
151. C3×C5C3×D32semidirect
152. C3×C5C3×D32semidirect
153. C3×C5#1113semidirect
179. C32C3×D3×D5semidirect
180. C32D3×D15semidirect
181. C32(C3⋊D3)⋊D5semidirect
182. C32C2×C3×D15semidirect
194. C5C3×#1113semidirect
204. C3C3×D3×D15semidirect
205. C3C3×(C3⋊D3)⋊D5semidirect
206. C3C5⋊#1113direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C3⋊D152
C32×C5×C3⋊D32
C5⋊#11133
C3×(C3⋊D3)⋊D53
C3×D3×D153
C3×#11135