Finite Group Databasebeta

← C5×#71552 #14280989

Subgroups — C5×#71552 #14280989

Order 1920.

624 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C4⋊C4C211yesmaximal, characteristic
2C5×#5207C212yesmaximal
3C5×#4528C214yesmaximal, complemented
4C5×#1463—31nomaximal, Hall
5C23×C3×C4×C5C411yescharacteristic
6C23×C3×C4×C5C411yescharacteristic
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×C5×C4⋊C4—22no—
9C2×C3×C5×C4⋊C4—22no—
10C2×C3×C5×C4⋊C4C412yes—
11C2×C3×C5×C4⋊C4C2212yes—
12C2×C5×#208—22no—
13C5×#830—22no—
14C5×#830C2214yes—
15#71552C511yesmaximal, characteristic, direct product factor, Hall
16C22×C5×C4⋊C4D311yescharacteristic
17C5×#407—32no—
18C5×#324—34no—
19C24×C3×C5C2×C411yescharacteristic
20C22×C3×C4×C5—21no—
21C22×C3×C4×C5—21no—
22C22×C3×C4×C5—24no—
23C22×C3×C4×C5—21no—
24C22×C3×C4×C5—21no—
25C22×C3×C4×C5—42no—
26C22×C3×C4×C5—42no—
27C22×C3×C4×C5C2×C412yes—
28C22×C3×C4×C5C2×C412yes—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5D412yes—
32C22×C3×C4×C5C2311yescharacteristic
33C3×C5×C4⋊C4—24no—
34C3×C5×C4⋊C4—24no—
35C5×#208—44no—
36C2×C5×C3⋊C8—24no—
37C22×C3×C4⋊C4C2×C511yescharacteristic
38#5207C2×C512yes—
39#4528C2×C514yescomplemented
40C23×C4×C5Dic311yescharacteristic
41C23×C4×C5Dic311yescharacteristic
42C23×C4×C5C2×D311yescharacteristic
43C2×C5×M16—62no—
44C2×C5×C4⋊C4—22no—
45C2×C5×C4⋊C4—22no—
46C2×C5×C4⋊C4Dic312yes—
47C2×C5×C4⋊C4C2×D312yes—
48C5×C22⋊C8—34no—
49C5×C22⋊C8—62no—
50#1463—31noSylow
51C23×C3×C5—22no—
52C23×C3×C5—22no—
53C23×C3×C5—22no—
54C23×C3×C5C22⋊C411yescharacteristic
55C23×C3×C5C22⋊C411yescharacteristic
56C23×C3×C5C22×C411yescharacteristic
57C2×C3×C4×C5—24no—
58C2×C3×C4×C5—24no—
59C2×C3×C4×C5—24no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5—22no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5—42no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—42no—
67C2×C3×C4×C5—42no—
68C2×C3×C4×C5—42no—
69C2×C3×C4×C5C22⋊C412yes—
70C2×C3×C4×C5M1614yescomplemented
71C2×C3×C4×C5C2×D412yes—
72C5×C3⋊C8—44no—
73C23×C3×C4C4×C511yescharacteristic
74C23×C3×C4C4×C511yescharacteristic
75C23×C3×C4C22×C511yescharacteristic
76C2×C3×C4⋊C4—22no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4C4×C512yes—
79C2×C3×C4⋊C4C22×C512yes—
80C2×#208—22no—
81#830—22no—
82#830C22×C514yes—
83C24×C5C2×Dic311yescharacteristic
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—24no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—42no—
90C22×C4×C5—42no—
91C22×C4×C5C2×Dic312yes—
92C22×C4×C5C2×Dic312yes—
93C22×C4×C5C2×Dic311yescharacteristic
94C22×C4×C5#6712yes—
95C22×C4×C5#6712yes—
96C22×C4×C5C22×D311yescharacteristic
97C5×M16—124no—
98C2×C5×C8—64no—
99C5×C4⋊C4—24no—
100C5×C4⋊C4—24no—
101C22×C4⋊C4C5×D311yescharacteristic
102#407—32no—
103#324—34no—
104C22×C3×C5—28no—
105C22×C3×C5—21no—
106C22×C3×C5—21no—
107C22×C3×C5—21no—
108C22×C3×C5—21no—
109C22×C3×C5—21no—
110C22×C3×C5—21no—
111C22×C3×C5#9912yes—
112C22×C3×C5#10112yes—
113C22×C3×C5C2×C22⋊C411yescharacteristic
114C22×C3×C5C2×M1612yes—
115C3×C4×C5—24no—
116C3×C4×C5—22no—
117C3×C4×C5—22no—
118C3×C4×C5—42no—
119C24×C3C2×C4×C511yescharacteristic
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—24no—
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—42no—
126C22×C3×C4—42no—
127C22×C3×C4C2×C4×C512yes—
128C22×C3×C4C2×C4×C512yes—
129C22×C3×C4C2×C4×C511yescharacteristic
130C22×C3×C4C5×D412yes—
131C22×C3×C4C5×D412yes—
132C22×C3×C4C23×C511yescharacteristic
133C3×C4⋊C4—24no—
134C3×C4⋊C4—24no—
135#208—44no—
136C2×C3⋊C8—24no—
137C23×C5—22no—
138C23×C5—22no—
139C23×C5—22no—
140C23×C5#21711yescharacteristic
141C23×C5#21711yescharacteristic
142C23×C5C22×Dic311yescharacteristic
143C2×C4×C5—24no—
144C2×C4×C5—24no—
145C2×C4×C5—24no—
146C2×C4×C5—22no—
147C2×C4×C5—22no—
148C2×C4×C5—22no—
149C2×C4×C5—41no—
150C2×C4×C5—42no—
151C2×C4×C5—41no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5#20814yescomplemented
156C2×C4×C5#21712yes—
157C2×C4×C5C2×#6712yes—
158C5×C8—124no—
159C23×C4C5×Dic311yescharacteristic
160C23×C4C5×Dic311yescharacteristic
161C23×C4C2×C5×D311yescharacteristic
162C2×M16—62no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4C5×Dic312yes—
166C2×C4⋊C4C2×C5×D312yes—
167C22⋊C8—34no—
168C22⋊C8—62no—
169C2×C3×C5—22no—
170C2×C3×C5—22no—
171C2×C3×C5—22no—
172C2×C3×C5#40711yescharacteristic
173C2×C3×C5C2×#9911yescharacteristic
174C2×C3×C5C2×#10111yescharacteristic
175C23×C3—22no—
176C23×C3—22no—
177C23×C3—22no—
178C23×C3C5×C22⋊C411yescharacteristic
179C23×C3C5×C22⋊C411yescharacteristic
180C23×C3C22×C4×C511yescharacteristic
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—24no—
186C2×C3×C4—22no—
187C2×C3×C4—41no—
188C2×C3×C4—42no—
189C2×C3×C4—41no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—42no—
193C2×C3×C4C5×C22⋊C412yes—
194C2×C3×C4C5×M1614yescomplemented
195C2×C3×C4C2×C5×D412yes—
196C3⋊C8—44no—
197C22×C5—28no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#83412yes—
205C22×C5#83612yes—
206C22×C5C2×#20812yes—
207C22×C5C2×#21711yescharacteristic
208C4×C5—24no—
209C4×C5—22no—
210C4×C5—22no—
211C4×C5—42no—
212C24C2×C5×Dic311yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—24no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4C2×C5×Dic312yes—
221C22×C4C2×C5×Dic312yes—
222C22×C4C2×C5×Dic311yescharacteristic
223C22×C4C5×#6712yes—
224C22×C4C5×#6712yes—
225C22×C4C22×C5×D311yescharacteristic
226M16—124no—
227C2×C8—64no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C3×C5#146311yescharacteristic, complemented, Hall
231C22×C3—28no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3C5×#9912yes—
239C22×C3C5×#10112yes—
240C22×C3C2×C5×C22⋊C411yescharacteristic
241C22×C3C2×C5×M1612yes—
242C3×C4—24no—
243C3×C4—22no—
244C3×C4—22no—
245C3×C4—42no—
246C2×C5—22no—
247C2×C5—22no—
248C2×C5—22no—
249C2×C5#520711yescharacteristic
250C2×C5C2×#83411yescharacteristic
251C2×C5C2×#83611yescharacteristic
252C23—22no—
253C23—22no—
254C23—22no—
255C23C5×#21711yescharacteristic
256C23C5×#21711yescharacteristic
257C23C22×C5×Dic311yescharacteristic
258C2×C4—24no—
259C2×C4—24no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4C5×#20814yescomplemented
271C2×C4C5×#21712yes—
272C2×C4C2×C5×#6712yes—
273C8—124no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3C5×#40711yescharacteristic
278C2×C3C2×C5×#9911yescharacteristic
279C2×C3C2×C5×#10111yescharacteristic
280C5#7155211yescharacteristic, direct product factor, Sylow
281C22—28no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22C5×#83412yes—
289C22C5×#83612yes—
290C22C2×C5×#20812yes—
291C22C2×C5×#21711yescharacteristic
292C4—24no—
293C4—22no—
294C4—22no—
295C4—42no—
296C3C5×#146311yescharacteristic, complemented, Sylow
297C2—22no—
298C2—22no—
299C2—22no—
300C2C5×#520711yescharacteristic
301C2C2×C5×#83411yescharacteristic
302C2C2×C5×#83611yescharacteristic
subgroupG/H
centerC22×C5C2×#217
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC22×C3×C5×C4⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC22×C5×C4⋊C4D3
hypocenterC3C5×#1463
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C22×C5×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×#4528C2semidirect
15. #71552C5direct (N × H)
39. #4528C2×C5semidirect
70. C2×C3×C4×C5M16semidirect
155. C2×C4×C5#208semidirect
194. C2×C3×C4C5×M16semidirect
230. C3×C5#1463semidirect
270. C2×C4C5×#208semidirect
280. C5#71552direct (N × H)
296. C3C5×#1463semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×C4⋊C42
C5×#52072
C5×#45282
C5×#14633
#715525