Finite Group Databasebeta

← C5×#71539 #14280958

Subgroups — C5×#71539 #14280958

Order 1920.

880 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
2C5×#5207C212yesmaximal, complemented
3C5×#4525C214yesmaximal, complemented
4C5×#1462—31nomaximal, Hall
5C25×C3×C5C411yescharacteristic
6C23×C3×C4×C5C411yescharacteristic
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×C5×C22⋊C4—22no—
9C2×C3×C5×C22⋊C4—22no—
10C2×C3×C5×C22⋊C4C412yes—
11C2×C3×C5×C22⋊C4C2212yes—
12C2×C5×#208—22no—
13C5×#830—22no—
14C5×#830C2214yescomplemented
15#71539C511yesmaximal, characteristic, direct product factor, Hall
16C22×C5×C22⋊C4D311yescharacteristic
17C5×#407—32no—
18C5×#323—34no—
19C24×C3×C5—21no—
20C24×C3×C5—21no—
21C24×C3×C5—24no—
22C24×C3×C5—42no—
23C24×C3×C5—42no—
24C24×C3×C5C2×C411yescharacteristic
25C24×C3×C5C2×C412yes—
26C22×C3×C4×C5—21no—
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5—42no—
30C22×C3×C4×C5C2×C412yes—
31C22×C3×C4×C5C2×C411yescharacteristic
32C22×C3×C4×C5D412yes—
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C3×C5×C22⋊C4—24no—
36C3×C5×C22⋊C4—24no—
37C5×#208—44no—
38C2×C5×C3⋊C8—24no—
39C22×C3×C22⋊C4C2×C511yescharacteristic
40#5207C2×C512yescomplemented
41#4525C2×C514yescomplemented
42C25×C5Dic311yescharacteristic
43C23×C4×C5Dic311yescharacteristic
44C23×C4×C5C2×D311yescharacteristic
45C2×C5×M16—62no—
46C2×C5×C22⋊C4—22no—
47C2×C5×C22⋊C4—22no—
48C2×C5×C22⋊C4Dic312yes—
49C2×C5×C22⋊C4C2×D312yes—
50C5×C22⋊C8—34no—
51C5×C22⋊C8—62no—
52#1462—31noSylow
53C23×C3×C5—22no—
54C23×C3×C5—22no—
55C23×C3×C5—22no—
56C23×C3×C5—24no—
57C23×C3×C5—24no—
58C23×C3×C5—22no—
59C23×C3×C5—22no—
60C23×C3×C5—416no—
61C23×C3×C5—42no—
62C23×C3×C5—42no—
63C23×C3×C5—42no—
64C23×C3×C5—42no—
65C23×C3×C5—42no—
66C23×C3×C5—42no—
67C23×C3×C5C22⋊C411yescharacteristic
68C23×C3×C5C22⋊C411yescharacteristic
69C23×C3×C5M1614yescomplemented
70C23×C3×C5C22×C411yescharacteristic
71C2×C3×C4×C5—24no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5—42no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5—42no—
77C2×C3×C4×C5—42no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5C22⋊C412yes—
80C2×C3×C4×C5C2×D412yes—
81C5×C3⋊C8—44no—
82C25×C3C4×C511yescharacteristic
83C23×C3×C4C4×C511yescharacteristic
84C23×C3×C4C22×C511yescharacteristic
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—22no—
87C2×C3×C22⋊C4C4×C512yes—
88C2×C3×C22⋊C4C22×C512yes—
89C2×#208—22no—
90#830—22no—
91#830C22×C514yescomplemented
92C24×C5—24no—
93C24×C5—21no—
94C24×C5—21no—
95C24×C5—42no—
96C24×C5—42no—
97C24×C5C2×Dic311yescharacteristic
98C24×C5C2×Dic312yes—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—42no—
102C22×C4×C5—42no—
103C22×C4×C5C2×Dic312yes—
104C22×C4×C5C2×Dic311yescharacteristic
105C22×C4×C5#6712yes—
106C22×C4×C5#6712yes—
107C22×C4×C5C22×D311yescharacteristic
108C5×M16—124no—
109C2×C5×C8—64no—
110C5×C22⋊C4—24no—
111C5×C22⋊C4—24no—
112C22×C22⋊C4C5×D311yescharacteristic
113#407—32no—
114#323—34no—
115C22×C3×C5—28no—
116C22×C3×C5—21no—
117C22×C3×C5—21no—
118C22×C3×C5—21no—
119C22×C3×C5—21no—
120C22×C3×C5—21no—
121C22×C3×C5—21no—
122C22×C3×C5—24no—
123C22×C3×C5—44no—
124C22×C3×C5—48no—
125C22×C3×C5—48no—
126C22×C3×C5—44no—
127C22×C3×C5—42no—
128C22×C3×C5—42no—
129C22×C3×C5#9912yes—
130C22×C3×C5#10012yes—
131C22×C3×C5C2×C22⋊C411yescharacteristic
132C22×C3×C5C2×M1612yes—
133C3×C4×C5—22no—
134C3×C4×C5—22no—
135C3×C4×C5—42no—
136C24×C3—21no—
137C24×C3—21no—
138C24×C3—24no—
139C24×C3—42no—
140C24×C3—42no—
141C24×C3C2×C4×C511yescharacteristic
142C24×C3C2×C4×C512yes—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—42no—
146C22×C3×C4—42no—
147C22×C3×C4C2×C4×C512yes—
148C22×C3×C4C2×C4×C511yescharacteristic
149C22×C3×C4C5×D412yes—
150C22×C3×C4C5×D412yes—
151C22×C3×C4C23×C511yescharacteristic
152C3×C22⋊C4—24no—
153C3×C22⋊C4—24no—
154#208—44no—
155C2×C3⋊C8—24no—
156C23×C5—22no—
157C23×C5—22no—
158C23×C5—22no—
159C23×C5—24no—
160C23×C5—24no—
161C23×C5—22no—
162C23×C5—22no—
163C23×C5—42no—
164C23×C5—42no—
165C23×C5—416no—
166C23×C5—42no—
167C23×C5—42no—
168C23×C5—42no—
169C23×C5—42no—
170C23×C5#20814yescomplemented
171C23×C5#21711yescharacteristic
172C23×C5#21711yescharacteristic
173C23×C5C22×Dic311yescharacteristic
174C2×C4×C5—24no—
175C2×C4×C5—22no—
176C2×C4×C5—41no—
177C2×C4×C5—42no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—42no—
181C2×C4×C5—42no—
182C2×C4×C5#21712yes—
183C2×C4×C5C2×#6712yes—
184C5×C8—124no—
185C25C5×Dic311yescharacteristic
186C23×C4C5×Dic311yescharacteristic
187C23×C4C2×C5×D311yescharacteristic
188C2×M16—62no—
189C2×C22⋊C4—22no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4C5×Dic312yes—
192C2×C22⋊C4C2×C5×D312yes—
193C22⋊C8—34no—
194C22⋊C8—62no—
195C2×C3×C5—22no—
196C2×C3×C5—22no—
197C2×C3×C5—22no—
198C2×C3×C5—44no—
199C2×C3×C5#40711yescharacteristic
200C2×C3×C5C2×#9911yescharacteristic
201C2×C3×C5C2×#10011yescharacteristic
202C23×C3—22no—
203C23×C3—22no—
204C23×C3—22no—
205C23×C3—24no—
206C23×C3—24no—
207C23×C3—22no—
208C23×C3—22no—
209C23×C3—42no—
210C23×C3—42no—
211C23×C3—416no—
212C23×C3—42no—
213C23×C3—42no—
214C23×C3—42no—
215C23×C3—42no—
216C23×C3C5×C22⋊C411yescharacteristic
217C23×C3C5×C22⋊C411yescharacteristic
218C23×C3C5×M1614yescomplemented
219C23×C3C22×C4×C511yescharacteristic
220C2×C3×C4—24no—
221C2×C3×C4—22no—
222C2×C3×C4—41no—
223C2×C3×C4—42no—
224C2×C3×C4—41no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4C5×C22⋊C412yes—
229C2×C3×C4C2×C5×D412yes—
230C3⋊C8—44no—
231C22×C5—28no—
232C22×C5—21no—
233C22×C5—21no—
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—21no—
238C22×C5—24no—
239C22×C5—44no—
240C22×C5—48no—
241C22×C5—48no—
242C22×C5—44no—
243C22×C5—42no—
244C22×C5—42no—
245C22×C5#83312yes—
246C22×C5#83412yes—
247C22×C5C2×#20812yes—
248C22×C5C2×#21711yescharacteristic
249C4×C5—22no—
250C4×C5—22no—
251C4×C5—42no—
252C24—24no—
253C24—21no—
254C24—21no—
255C24—42no—
256C24—42no—
257C24C2×C5×Dic311yescharacteristic
258C24C2×C5×Dic312yes—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4C2×C5×Dic312yes—
264C22×C4C2×C5×Dic311yescharacteristic
265C22×C4C5×#6712yes—
266C22×C4C5×#6712yes—
267C22×C4C22×C5×D311yescharacteristic
268M16—124no—
269C2×C8—64no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C3×C5#146211yescharacteristic, complemented, Hall
273C22×C3—28no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—24no—
281C22×C3—44no—
282C22×C3—44no—
283C22×C3—48no—
284C22×C3—48no—
285C22×C3—42no—
286C22×C3—42no—
287C22×C3C5×#9912yes—
288C22×C3C5×#10012yes—
289C22×C3C2×C5×C22⋊C411yescharacteristic
290C22×C3C2×C5×M1612yes—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—42no—
294C2×C5—22no—
295C2×C5—22no—
296C2×C5—22no—
297C2×C5—44no—
298C2×C5#520711yescharacteristic
299C2×C5C2×#83311yescharacteristic
300C2×C5C2×#83411yescharacteristic
301C23—22no—
302C23—22no—
303C23—22no—
304C23—24no—
305C23—24no—
306C23—22no—
307C23—22no—
308C23—42no—
309C23—42no—
310C23—416no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23C5×#20814yescomplemented
316C23C5×#21711yescharacteristic
317C23C5×#21711yescharacteristic
318C23C22×C5×Dic311yescharacteristic
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4C5×#21712yes—
328C2×C4C2×C5×#6712yes—
329C8—124no—
330C2×C3—22no—
331C2×C3—22no—
332C2×C3—22no—
333C2×C3—44no—
334C2×C3C5×#40711yescharacteristic
335C2×C3C2×C5×#9911yescharacteristic
336C2×C3C2×C5×#10011yescharacteristic
337C5#7153911yescharacteristic, direct product factor, Sylow
338C22—28no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—24no—
346C22—44no—
347C22—44no—
348C22—48no—
349C22—48no—
350C22—42no—
351C22—42no—
352C22C5×#83312yes—
353C22C5×#83412yes—
354C22C2×C5×#20812yes—
355C22C2×C5×#21711yescharacteristic
356C4—22no—
357C4—22no—
358C4—42no—
359C3C5×#146211yescharacteristic, complemented, Sylow
360C2—22no—
361C2—22no—
362C2—22no—
363C2—44no—
364C2C5×#520711yescharacteristic
365C2C2×C5×#83311yescharacteristic
366C2C2×C5×#83411yescharacteristic
subgroupG/H
centerC22×C5C2×#217
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC22×C3×C5×C22⋊C4C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC25×C3×C5C4
cosocleC22×C3×C4C23×C5
hypercenterC22×C5×C22⋊C4D3
hypocenterC3C5×#1462
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C22×C5×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#5207C2semidirect
3. C5×#4525C2semidirect
14. C5×#830C22semidirect
15. #71539C5direct (N × H)
40. #5207C2×C5semidirect
41. #4525C2×C5semidirect
69. C23×C3×C5M16semidirect
91. #830C22×C5semidirect
170. C23×C5#208semidirect
218. C23×C3C5×M16semidirect
272. C3×C5#1462semidirect
315. C23C5×#208semidirect
337. C5#71539direct (N × H)
359. C3C5×#1462semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×C22⋊C42
C5×#52072
C5×#45252
C5×#14623
#715395