Finite Group Databasebeta

← C5×C4⋊(#120⋊C3) #14510939

Subgroups — C5×C4⋊(#120⋊C3) #14510939

Order 1920.

508 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C4×C5×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C5×#120⋊C3C212yesmaximal, complemented
3C5×#2847C311yesmaximal, characteristic, complemented, Hall
4C2×C5×C22⋊A4C2211yescharacteristic
5C5×D4×A4—41nomaximal
6C5×#120⋊C3—22no—
7C4⋊(#120⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
8C24×C4×C5C2×C311yescharacteristic, complemented
9C2×C5×#121—31no—
10C2×C5×#120C2×C312yescomplemented
11C5×#386—32no—
12C5×#380—31no—
13C5×C22⋊A4D411yescharacteristic, complemented
14C22×C5×A4—42no—
15C4×C5×A4—41no—
16C4×C5×A4—82no—
17C4×C22⋊A4C2×C511yescharacteristic, complemented
18C2×#120⋊C3C2×C512yescomplemented
19C25×C5C22×C311yescharacteristic
20C22×C5×D4—32no—
21C22×C5×D4A411yescharacteristic, complemented
22C23×C4×C5—31no—
23C23×C4×C5—31no—
24C23×C4×C5—62no—
25C23×C4×C5—62no—
26C5×#121—62no—
27C5×#121—62no—
28C5×#120—22no—
29C5×#120—62no—
30C2×C5×C4⋊C4—31no—
31C2×C5×C22⋊C4—32no—
32C2×C5×C22⋊C4—32no—
33C5×#95—32no—
34#2847C3×C511yescharacteristic, complemented, Sylow
35C2×C5×A4—41no—
36C2×C5×A4—82no—
37C2×C5×A4—82no—
38C3×C5×D4—161no—
39C2×C22⋊A4C22×C511yescharacteristic
40D4×A4—41no—
41#120⋊C3—22no—
42C24×C5—31no—
43C24×C5—31no—
44C24×C5—62no—
45C24×C5—62no—
46C24×C5C3×D411yescharacteristic, complemented
47C24×C5C2×A412yes—
48C2×C5×D4—61no—
49C2×C5×D4—61no—
50C2×C5×D4—62no—
51C2×C5×D4—62no—
52C2×C5×D4—64no—
53C2×C5×D4—64no—
54C22×C4×C5—22no—
55C22×C4×C5—32no—
56C22×C4×C5—32no—
57C22×C4×C5—31no—
58C22×C4×C5—32no—
59C22×C4×C5—62no—
60C22×C4×C5—62no—
61C22×C4×C5—64no—
62C22×C4×C5—62no—
63C22×C4×C5—62no—
64C22×C4×C5—64no—
65C22×C4×C5—62no—
66C22×C4×C5—62no—
67C22×C4×C5C2×A411yescharacteristic
68C5×C4⋊C4—61no—
69C5×C4⋊C4—61no—
70C5×C22⋊C4—64no—
71C5×C22⋊C4—62no—
72C5×C22⋊C4—62no—
73C24×C4C2×C3×C511yescharacteristic, complemented
74C2×#121—31no—
75C2×#120C2×C3×C512yescomplemented
76#386—32no—
77#380—31no—
78C22×C3×C5—162no—
79C5×A4—41no—
80C5×A4—82no—
81C3×C4×C5—161no—
82C22⋊A4C5×D411yescharacteristic, complemented
83C22×A4—42no—
84C4×A4—41no—
85C4×A4—82no—
86C23×C5—22no—
87C23×C5—22no—
88C23×C5—32no—
89C23×C5—32no—
90C23×C5—31no—
91C23×C5—31no—
92C23×C5—62no—
93C23×C5—62no—
94C23×C5—62no—
95C23×C5—62no—
96C23×C5—62no—
97C23×C5—62no—
98C23×C5—64no—
99C23×C5—62no—
100C23×C5—62no—
101C23×C5—62no—
102C23×C5—64no—
103C23×C5C22×A411yescharacteristic
104C5×D4—41no—
105C5×D4—121no—
106C5×D4—124no—
107C5×D4—124no—
108C2×C4×C5—31no—
109C2×C4×C5—31no—
110C2×C4×C5—32no—
111C2×C4×C5—62no—
112C2×C4×C5—64no—
113C2×C4×C5—62no—
114C2×C4×C5—64no—
115C2×C4×C5—62no—
116C2×C4×C5—62no—
117C2×C4×C5—62no—
118C2×C4×C5—62no—
119C2×C4×C5—62no—
120C2×C4×C5—62no—
121C25C22×C3×C511yescharacteristic
122C22×D4—32no—
123C22×D4C5×A411yescharacteristic, complemented
124C23×C4—31no—
125C23×C4—31no—
126C23×C4—62no—
127C23×C4—62no—
128#121—62no—
129#121—62no—
130#120—22no—
131#120—62no—
132C2×C4⋊C4—31no—
133C2×C22⋊C4—32no—
134C2×C22⋊C4—32no—
135#95—32no—
136C2×C3×C5—161no—
137C2×C3×C5—322no—
138C2×A4—41no—
139C2×A4—82no—
140C2×A4—82no—
141C3×D4—161no—
142C22×C5—22no—
143C22×C5—31no—
144C22×C5—31no—
145C22×C5—32no—
146C22×C5—32no—
147C22×C5—42no—
148C22×C5—62no—
149C22×C5—62no—
150C22×C5—62no—
151C22×C5—64no—
152C22×C5—62no—
153C22×C5—62no—
154C22×C5—62no—
155C22×C5—64no—
156C22×C5—62no—
157C22×C5—122no—
158C22×C5—122no—
159C22×C5D4×A411yescharacteristic
160C4×C5—31no—
161C4×C5—62no—
162C4×C5—122no—
163C4×C5#120⋊C311yescharacteristic, complemented
164C24—31no—
165C24—31no—
166C24—62no—
167C24—62no—
168C24C3×C5×D411yescharacteristic, complemented
169C24C2×C5×A412yes—
170C2×D4—61no—
171C2×D4—61no—
172C2×D4—62no—
173C2×D4—62no—
174C2×D4—64no—
175C2×D4—64no—
176C22×C4—22no—
177C22×C4—32no—
178C22×C4—32no—
179C22×C4—31no—
180C22×C4—32no—
181C22×C4—62no—
182C22×C4—62no—
183C22×C4—64no—
184C22×C4—62no—
185C22×C4—62no—
186C22×C4—64no—
187C22×C4—62no—
188C22×C4—62no—
189C22×C4C2×C5×A411yescharacteristic
190C4⋊C4—61no—
191C4⋊C4—61no—
192C22⋊C4—64no—
193C22⋊C4—62no—
194C22⋊C4—62no—
195C3×C5—161noHall
196C22×C3—162no—
197A4—41no—
198A4—82no—
199C3×C4—161no—
200C2×C5—31no—
201C2×C5—31no—
202C2×C5—62no—
203C2×C5—62no—
204C2×C5—82no—
205C2×C5C2×#120⋊C311yescharacteristic
206C23—22no—
207C23—22no—
208C23—32no—
209C23—32no—
210C23—31no—
211C23—31no—
212C23—62no—
213C23—62no—
214C23—62no—
215C23—62no—
216C23—62no—
217C23—62no—
218C23—64no—
219C23—62no—
220C23—62no—
221C23—62no—
222C23—64no—
223C23C22×C5×A411yescharacteristic
224D4—41no—
225D4—121no—
226D4—124no—
227D4—124no—
228C2×C4—31no—
229C2×C4—31no—
230C2×C4—32no—
231C2×C4—62no—
232C2×C4—64no—
233C2×C4—62no—
234C2×C4—64no—
235C2×C4—62no—
236C2×C4—62no—
237C2×C4—62no—
238C2×C4—62no—
239C2×C4—62no—
240C2×C4—62no—
241C2×C3—161no—
242C2×C3—322no—
243C5C4⋊(#120⋊C3)11yescharacteristic, direct product factor, Sylow
244C22—22no—
245C22—31no—
246C22—31no—
247C22—32no—
248C22—32no—
249C22—42no—
250C22—62no—
251C22—62no—
252C22—62no—
253C22—64no—
254C22—62no—
255C22—62no—
256C22—62no—
257C22—64no—
258C22—62no—
259C22—122no—
260C22—122no—
261C22C5×D4×A411yescharacteristic
262C4—31no—
263C4—62no—
264C4—122no—
265C4C5×#120⋊C311yescharacteristic, complemented
266C3—161noSylow
267C2—31no—
268C2—31no—
269C2—62no—
270C2—62no—
271C2—82no—
272C2C2×C5×#120⋊C311yescharacteristic
subgroupG/H
centerC2×C5C2×#120⋊C3
commutator, cosocleC25C22×C3×C5
FrattiniC23C22×C5×A4
FittingC5×#2847C3
socleC23×C5C22×A4
hypercenterC4×C5#120⋊C3
hypocenterC24C3×C5×D4
LCSG ▷ C25 ▷ C24
UCSC1 ◁ C2×C5 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
1. C4×C5×C22⋊A4C2semidirect
2. C2×C5×#120⋊C3C2semidirect
3. C5×#2847C3semidirect
7. C4⋊(#120⋊C3)C5direct (N × H)
8. C24×C4×C5C2×C3semidirect
10. C2×C5×#120C2×C3semidirect
13. C5×C22⋊A4D4semidirect
17. C4×C22⋊A4C2×C5semidirect
18. C2×#120⋊C3C2×C5semidirect
21. C22×C5×D4A4semidirect
34. #2847C3×C5semidirect
46. C24×C5C3×D4semidirect
73. C24×C4C2×C3×C5semidirect
75. C2×#120C2×C3×C5semidirect
82. C22⋊A4C5×D4semidirect
123. C22×D4C5×A4semidirect
163. C4×C5#120⋊C3semidirect
168. C24C3×C5×D4semidirect
243. C5C4⋊(#120⋊C3)direct (N × H)
265. C4C5×#120⋊C3semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C22⋊A42
C2×C5×#120⋊C32
C5×#28473
C5×D4×A44
C4⋊(#120⋊C3)5