Finite Group Databasebeta

← C5×#71753 #14282520

Subgroups — C5×#71753 #14282520

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#529C211yesmaximal, characteristic
2C5×#4925C211yesmaximal, characteristic, complemented
3C5×#4924C211yesmaximal, characteristic, complemented
4C5×#4535C212yesmaximal, complemented
5C5×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C5×#1495—31nomaximal, Hall
7C3×C5×#126—21no—
8C3×C5×#125C411yescharacteristic
9C3×C5×#124C411yescharacteristic
10C3×C5×#123—21no—
11C3×C5×C22⋊Q8C411yescharacteristic
12C3×C5×#121C411yescharacteristic
13C3×C4×C5×Q8C2211yescharacteristic
14C3×C4×C5×D4—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C5×#208—21no—
19C5×#830—21no—
20C5×C4⋊(C3⋊C8)—21no—
21C5×C4⋊(C3⋊C8)—21no—
22C5×C4⋊(C3⋊C8)C2212yes—
23C4×C5×C3⋊C8C2212yes—
24#71753C511yesmaximal, characteristic, direct product factor, Hall
25C5×#529D311yescharacteristic
26C5×#431—31no—
27C5×#423—31no—
28C5×Q8⋊C8—32no—
29C5×D4⋊C8—32no—
30C2×C3×C5×Q8C2×C411yescharacteristic
31C2×C3×C5×D4—21no—
32C2×C3×C5×D4C2×C411yescharacteristic
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C3×C5×C4⋊C4—21no—
38C3×C5×C4⋊C4—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4C2×C411yescharacteristic
42C3×C5×C4⋊C4C2×C411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C5×C22⋊C4—21no—
46C3×C5×C22⋊C4—21no—
47C3×C5×C22⋊C4—21no—
48C3×C42×C5—21no—
49C3×C42×C5C2×C411yescharacteristic
50C3×C42×C5D411yescharacteristic
51C3×C42×C5D411yescharacteristic
52C3×C42×C5C2311yescharacteristic
53C5×#208—42no—
54C2×C5×C3⋊C8—22no—
55C2×C5×C3⋊C8—22no—
56C3×#529C2×C511yescharacteristic
57#4925C2×C511yescharacteristic, complemented
58#4924C2×C511yescharacteristic, complemented
59#4535C2×C512yescomplemented
60D4⋊(C3⋊C8)C2×C512yescomplemented
61C2×C5×M16—61no—
62C5×#126—21no—
63C5×#125Dic311yescharacteristic
64C5×#124Dic311yescharacteristic
65C5×#123—21no—
66C5×C22⋊Q8Dic311yescharacteristic
67C5×#121Dic311yescharacteristic
68C4×C5×Q8C2×D311yescharacteristic
69C4×C5×D4—21no—
70C4×C5×D4C2×D311yescharacteristic
71C5×#117—21no—
72C2×C42×C5C2×D311yescharacteristic
73C5×C4⋊C8—32no—
74C5×C4⋊C8—61no—
75C5×C4⋊C8—61no—
76C5×C22⋊C8—61no—
77C4×C5×C8—32no—
78#1495—31noSylow
79C23×C3×C5—21no—
80C23×C3×C5C22⋊C411yescharacteristic
81C3×C5×Q8—22no—
82C3×C5×D4—22no—
83C3×C5×D4—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5C22⋊C411yescharacteristic
94C2×C3×C4×C5C22⋊C411yescharacteristic
95C2×C3×C4×C5C22⋊C411yescharacteristic
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C5×C3⋊C8—42no—
100C5×C3⋊C8—42no—
101C3×#126—21no—
102C3×#125C4×C511yescharacteristic
103C3×#124C4×C511yescharacteristic
104C3×#123—21no—
105C3×C22⋊Q8C4×C511yescharacteristic
106C3×#121C4×C511yescharacteristic
107C3×C4×Q8C22×C511yescharacteristic
108C3×C4×D4—21no—
109C3×C4×D4C22×C511yescharacteristic
110C3×#117—21no—
111C2×C3×C42C22×C511yescharacteristic
112C2×#208—21no—
113#830—21no—
114C4⋊(C3⋊C8)—21no—
115C4⋊(C3⋊C8)—21no—
116C4⋊(C3⋊C8)C22×C512yes—
117C4×C3⋊C8C22×C512yes—
118C2×C5×Q8C2×Dic311yescharacteristic
119C2×C5×D4—21no—
120C2×C5×D4C2×Dic311yescharacteristic
121C22×C4×C5—21no—
122C22×C4×C5C2×Dic311yescharacteristic
123C22×C4×C5#6711yescharacteristic
124C22×C4×C5#6711yescharacteristic
125C5×M16—122no—
126C2×C5×C8—62no—
127C2×C5×C8—62no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4C2×Dic311yescharacteristic
133C5×C4⋊C4C2×Dic311yescharacteristic
134C5×C22⋊C4—21no—
135C5×C22⋊C4—21no—
136C5×C22⋊C4—21no—
137C5×C22⋊C4—21no—
138C5×C22⋊C4—21no—
139C42×C5—21no—
140C42×C5C2×Dic311yescharacteristic
141C42×C5#6711yescharacteristic
142C42×C5#6711yescharacteristic
143C42×C5C22×D311yescharacteristic
144#529C5×D311yescharacteristic
145#431—31no—
146#423—31no—
147Q8⋊C8—32no—
148D4⋊C8—32no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5—41no—
162C3×C4×C5—41no—
163C3×C4×C5#13112yes—
164C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
165C3×C4×C5#13711yescharacteristic
166C2×C3×Q8C2×C4×C511yescharacteristic
167C2×C3×D4—21no—
168C2×C3×D4C2×C4×C511yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4C2×C4×C511yescharacteristic
171C22×C3×C4C5×D411yescharacteristic
172C22×C3×C4C5×D411yescharacteristic
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4C2×C4×C511yescharacteristic
178C3×C4⋊C4C2×C4×C511yescharacteristic
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C42—21no—
185C3×C42C2×C4×C511yescharacteristic
186C3×C42C5×D411yescharacteristic
187C3×C42C5×D411yescharacteristic
188C3×C42C23×C511yescharacteristic
189#208—42no—
190C2×C3⋊C8—22no—
191C2×C3⋊C8—22no—
192C23×C5—21no—
193C23×C5#21711yescharacteristic
194C5×Q8—22no—
195C5×D4—22no—
196C5×D4—42no—
197C2×C4×C5—22no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5#21711yescharacteristic
207C2×C4×C5#21711yescharacteristic
208C2×C4×C5#21711yescharacteristic
209C2×C4×C5C22×Dic311yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C5×C8—122no—
213C5×C8—122no—
214C2×M16—61no—
215#126—21no—
216#125C5×Dic311yescharacteristic
217#124C5×Dic311yescharacteristic
218#123—21no—
219C22⋊Q8C5×Dic311yescharacteristic
220#121C5×Dic311yescharacteristic
221C4×Q8C2×C5×D311yescharacteristic
222C4×D4—21no—
223C4×D4C2×C5×D311yescharacteristic
224#117—21no—
225C2×C42C2×C5×D311yescharacteristic
226C4⋊C8—32no—
227C4⋊C8—61no—
228C4⋊C8—61no—
229C22⋊C8—61no—
230C4×C8—32no—
231C2×C3×C5—41no—
232C2×C3×C5—81no—
233C2×C3×C5#40811yescharacteristic
234C2×C3×C5#41711yescharacteristic
235C2×C3×C5#42111yescharacteristic
236C23×C3—21no—
237C23×C3C5×C22⋊C411yescharacteristic
238C3×Q8—22no—
239C3×D4—22no—
240C3×D4—42no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4C5×C22⋊C411yescharacteristic
251C2×C3×C4C5×C22⋊C411yescharacteristic
252C2×C3×C4C5×C22⋊C411yescharacteristic
253C2×C3×C4C22×C4×C511yescharacteristic
254C2×C3×C4C2×C5×D411yescharacteristic
255C2×C3×C4C2×C5×D411yescharacteristic
256C3⋊C8—42no—
257C3⋊C8—42no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—41no—
262C22×C5—41no—
263C22×C5—41no—
264C22×C5C2×#21711yescharacteristic
265C4×C5—21no—
266C4×C5—21no—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—41no—
270C4×C5—41no—
271C4×C5—41no—
272C4×C5#94812yes—
273C4×C5#94911yescharacteristic
274C4×C5#95111yescharacteristic
275C2×Q8C2×C5×Dic311yescharacteristic
276C2×D4—21no—
277C2×D4C2×C5×Dic311yescharacteristic
278C22×C4—21no—
279C22×C4C2×C5×Dic311yescharacteristic
280C22×C4C5×#6711yescharacteristic
281C22×C4C5×#6711yescharacteristic
282M16—122no—
283C2×C8—62no—
284C2×C8—62no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4C2×C5×Dic311yescharacteristic
290C4⋊C4C2×C5×Dic311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C42—21no—
297C42C2×C5×Dic311yescharacteristic
298C42C5×#6711yescharacteristic
299C42C5×#6711yescharacteristic
300C42C22×C5×D311yescharacteristic
301C3×C5#149511yescharacteristic, complemented, Hall
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—41no—
306C22×C3—41no—
307C22×C3—41no—
308C22×C3C2×C5×C22⋊C411yescharacteristic
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4C5×#13112yes—
317C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
318C3×C4C5×#13711yescharacteristic
319C2×C5—41no—
320C2×C5—81no—
321C2×C5#523211yescharacteristic
322C2×C5#523411yescharacteristic
323C2×C5#523611yescharacteristic
324C23—21no—
325C23C5×#21711yescharacteristic
326Q8—22no—
327D4—22no—
328D4—42no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4C5×#21711yescharacteristic
339C2×C4C5×#21711yescharacteristic
340C2×C4C5×#21711yescharacteristic
341C2×C4C22×C5×Dic311yescharacteristic
342C2×C4C2×C5×#6711yescharacteristic
343C2×C4C2×C5×#6711yescharacteristic
344C8—122no—
345C8—122no—
346C2×C3—41no—
347C2×C3—81no—
348C2×C3C5×#40811yescharacteristic
349C2×C3C5×#41711yescharacteristic
350C2×C3C5×#42111yescharacteristic
351C5#7175311yescharacteristic, direct product factor, Sylow
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22C2×C5×#21711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4C5×#94812yes—
367C4C5×#94911yescharacteristic
368C4C5×#95111yescharacteristic
369C3C5×#149511yescharacteristic, complemented, Sylow
370C2—41no—
371C2—81no—
372C2C5×#523211yescharacteristic
373C2C5×#523411yescharacteristic
374C2C5×#523611yescharacteristic
subgroupG/H
centerC2×C4×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#529C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×C5×#121C4
cosocleC3×C42C23×C5
hypercenterC5×#529D3
hypocenterC3C5×#1495
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C5×#529

Complements

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

NH ≅ G/Ntype
2. C5×#4925C2semidirect
3. C5×#4924C2semidirect
4. C5×#4535C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
24. #71753C5direct (N × H)
57. #4925C2×C5semidirect
58. #4924C2×C5semidirect
59. #4535C2×C5semidirect
60. D4⋊(C3⋊C8)C2×C5semidirect
301. C3×C5#1495semidirect
351. C5#71753direct (N × H)
369. C3C5×#1495semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5292
C5×#49252
C5×#49242
C5×#45352
C5×D4⋊(C3⋊C8)2
C5×#14953
#717535