Finite Group Databasebeta

← A4×D15⋊D5 #72231285

Subgroups — A4×D15⋊D5 #72231285

Order 3600.

392 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 45 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×A4×D15C212yesmaximal, complemented
2C3×A4×C5⋊D5C211yesmaximal, characteristic, complemented
3C22×D15⋊D5C311yesmaximal, characteristic, complemented
4D52×A4—31nomaximal
5C3×C52×A4C2211yescharacteristic, complemented
6C3×D15⋊D5—41nomaximal
7D3×D5×A4—52nomaximal
8C22×C5×D15C2×C312yescomplemented
9C22×C3×C5⋊D5C2×C311yescharacteristic, complemented
10C2×D15⋊D5—31no—
11C2×D15⋊D5—32no—
12C2×D15⋊D5—31no—
13A4×C5⋊D5—21no—
14A4×C5⋊D5D311yescharacteristic, complemented
15C5×D5×A4—32no—
16C3×C5×D15—42no—
17C32×C5⋊D5—41no—
18C22×D52—31noHall
19A4×D15D512yescomplemented
20C5×D3×A4—52no—
21C3×D5×A4—52no—
22C3×D5×A4—102no—
23C22×C3×C52C22×C311yescharacteristic, complemented
24C2×C5×D15—32no—
25C2×C5×D15—32no—
26C2×C3×C5⋊D5—31no—
27C2×C3×C5⋊D5—31no—
28C52×A4—21no—
29C52×A4C2×D311yescharacteristic, complemented
30D15⋊D5—32no—
31D15⋊D5—32no—
32D15⋊D5—31no—
33D15⋊D5A411yescharacteristic, direct product factor
34C3×D52—121no—
35C22×D3×D5—52no—
36C2×D5×A4—152no—
37C32×C52—41noHall
38C22×C5⋊D5C3×D311yescharacteristic, complemented
39C22×C5×D5—32no—
40C2×D52—91no—
41C2×D52—92no—
42C2×D52—91no—
43C3×C5×A4—22no—
44C3×C5×A4C2×D512yescomplemented
45C3×D3×D5—202no—
46C2×C3×C52—31no—
47C5×D15—32no—
48C5×D15C2×A412yescomplemented
49C3×C5⋊D5—31no—
50C3×C5⋊D5—41no—
51C3×C5⋊D5—81no—
52C3×C5⋊D5C2×A411yescharacteristic, complemented
53C3×C5×D5—122no—
54C2×D3×A4—251noHall
55C22×D15C3×D512yescomplemented
56C22×C5×D3—52no—
57C22×C3×D5—52no—
58C22×C3×D5—102no—
59C2×C5×A4—152no—
60C2×D3×D5—152no—
61C2×D3×D5—152no—
62C2×D3×D5—152no—
63C2×D3×D5—152no—
64D5×A4—32no—
65D5×A4—52no—
66D5×A4—102no—
67D5×A4—102no—
68D5×A4—104no—
69C22×C52C2×C3×D311yescharacteristic, complemented
70C2×C5⋊D5—31no—
71C2×C5⋊D5—31no—
72C2×C5×D5—92no—
73C2×C5×D5—92no—
74D52—31no—
75D52—92no—
76D52—92no—
77D52—91no—
78C3×D15—42no—
79C3×C5×D3—202no—
80C32×D5—202no—
81C32×D5—402no—
82C23×D5—152no—
83C3×C52—41no—
84C3×C52—81no—
85C3×C52C22×A411yescharacteristic, complemented
86C2×C3×A4—251no—
87D3×A4—52no—
88C22×C3×C5—22no—
89C22×C3×C5C2×C3×D512yescomplemented
90C2×D15—32no—
91C2×D15—32no—
92C2×C5×D3—152no—
93C2×C5×D3—152no—
94C2×C3×D5—152no—
95C2×C3×D5—152no—
96C2×C3×D5—302no—
97C2×C3×D5—302no—
98C2×C3×D5—602no—
99C5×A4—24no—
100C5×A4—22no—
101C5×A4—22no—
102C5×A4D3×D512yescomplemented
103D3×D5—52no—
104D3×D5—152no—
105D3×D5—152no—
106D3×D5—154no—
107D3×D5—152no—
108C2×C52—31no—
109C5⋊D5—31no—
110C5⋊D5D3×A411yescharacteristic, complemented
111C5×D5—32no—
112C5×D5—92no—
113C23×D3—251no—
114C22×A4—751no—
115C32×C5—42no—
116C32×C5—82no—
117C23×C5—152no—
118C22×D5—32no—
119C22×D5—52no—
120C22×D5—102no—
121C22×D5—452no—
122C22×D5—452no—
123C22×D5—452no—
124C22×D5—452no—
125C2×C3×D3—1001no—
126C3×A4D5211yescharacteristic, complemented
127C2×C3×C5—32no—
128C2×C3×C5—62no—
129C2×C3×C5—602no—
130D15—32no—
131D15D5×A412yescomplemented
132C3×D5—52no—
133C3×D5—102no—
134C3×D5—122no—
135C3×D5—152no—
136C3×D5—202no—
137C3×D5—302no—
138C3×D5—402no—
139C3×D5—402no—
140C3×D5—404no—
141C5×D3—52no—
142C5×D3—152no—
143C52C2×D3×A411yescharacteristic, complemented, Sylow
144C23×C3—251no—
145C22×D3—52no—
146C22×D3—751no—
147C22×D3—752no—
148C22×D3—751no—
149C2×A4—152no—
150C2×A4—251no—
151C2×A4—501no—
152C22×C5—22no—
153C22×C5—452no—
154C22×C5—452no—
155C22×C5C3×D3×D512yescomplemented
156C2×D5—92no—
157C2×D5—92no—
158C2×D5—152no—
159C2×D5—152no—
160C2×D5—152no—
161C2×D5—302no—
162C2×D5—302no—
163C2×D5—452no—
164C2×D5—452no—
165C2×D5—452no—
166C2×D5—454no—
167C2×C32—1001no—
168C3×D3—202no—
169C24—751noSylow
170C3×C5—22no—
171C3×C5—42no—
172C3×C5—82no—
173C3×C5—84no—
174C3×C5—82no—
175C3×C5C2×D5×A412yescomplemented
176C22×C3—3001no—
177C22×C3—751no—
178C22×C3—751no—
179C22×C3C3×D5211yescharacteristic, complemented
180C2×D3—152no—
181C2×D3—152no—
182C2×D3—251no—
183C2×D3—752no—
184C2×D3—751no—
185C2×D3—752no—
186A4—21no—
187A4D15⋊D511yescharacteristic, direct product factor
188C2×C5—32no—
189C2×C5—62no—
190C2×C5—152no—
191C2×C5—452no—
192D5—32no—
193D5—52no—
194D5—92no—
195D5—102no—
196D5—152no—
197D5—302no—
198C32—41noSylow
199C23—152no—
200C23—251no—
201C23—2251no—
202C23—2252no—
203C23—2251no—
204C2×C3—31no—
205C2×C3—251no—
206C2×C3—602no—
207C2×C3—751no—
208C2×C3—1001no—
209C2×C3—2001no—
210D3—52no—
211D3—152no—
212C5—22no—
213C5D3×D5×A412yescomplemented
214C22—452no—
215C22—452no—
216C22—751no—
217C22—751no—
218C22—751no—
219C22—2252no—
220C22—2251no—
221C22—2252no—
222C22C3×D15⋊D511yescharacteristic, complemented
223C3—41no—
224C3—81no—
225C3D52×A411yescharacteristic, complemented
226C2—31no—
227C2—152no—
228C2—251no—
229C2—452no—
230C2—751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C3×C52C22×C3
LCSG ▷ C22×C3×C52
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×A4×D15C2semidirect
2. C3×A4×C5⋊D5C2semidirect
3. C22×D15⋊D5C3semidirect
5. C3×C52×A4C22semidirect
8. C22×C5×D15C2×C3semidirect
9. C22×C3×C5⋊D5C2×C3semidirect
14. A4×C5⋊D5D3semidirect
19. A4×D15D5semidirect
23. C22×C3×C52C22×C3semidirect
29. C52×A4C2×D3semidirect
33. D15⋊D5A4direct (N × H)
38. C22×C5⋊D5C3×D3semidirect
44. C3×C5×A4C2×D5semidirect
48. C5×D15C2×A4semidirect
52. C3×C5⋊D5C2×A4semidirect
55. C22×D15C3×D5semidirect
69. C22×C52C2×C3×D3semidirect
85. C3×C52C22×A4semidirect
89. C22×C3×C5C2×C3×D5semidirect
102. C5×A4D3×D5semidirect
110. C5⋊D5D3×A4semidirect
126. C3×A4D52semidirect
131. D15D5×A4semidirect
143. C52C2×D3×A4semidirect
155. C22×C5C3×D3×D5semidirect
175. C3×C5C2×D5×A4semidirect
179. C22×C3C3×D52semidirect
187. A4D15⋊D5direct (N × H)
213. C5D3×D5×A4semidirect
222. C22C3×D15⋊D5semidirect
225. C3D52×A4semidirect

Maximal subgroups

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

subgroupindex
C5×A4×D152
C3×A4×C5⋊D52
C22×D15⋊D53
D52×A43
C3×D15⋊D54
D3×D5×A45