Finite Group Databasebeta

← C5×#71750 #14281861

Subgroups — C5×#71750 #14281861

Order 1920.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 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×#4925C211yesmaximal, characteristic, complemented
4C5×#4535C212yesmaximal, complemented
5C5×D4⋊(C3⋊C8)C212yesmaximal, complemented
6C5×#1482—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
18C5×#830—21no—
19C5×#830—21no—
20C5×C4⋊(C3⋊C8)—21no—
21C5×C4⋊(C3⋊C8)C2212yes—
22C4×C5×C3⋊C8—21no—
23C4×C5×C3⋊C8C2212yes—
24#71750C511yesmaximal, characteristic, direct product factor, Hall
25C5×#529D311yescharacteristic
26C5×#431—31no—
27C5×#431—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
53C2×C5×C3⋊C8—22no—
54C2×C5×C3⋊C8—22no—
55C3×#529C2×C511yescharacteristic
56#4925C2×C511yescharacteristic, complemented
57#4925C2×C511yescharacteristic, complemented
58#4535C2×C512yescomplemented
59D4⋊(C3⋊C8)C2×C512yescomplemented
60C5×#126—21no—
61C5×#125Dic311yescharacteristic
62C5×#124Dic311yescharacteristic
63C5×#123—21no—
64C5×C22⋊Q8Dic311yescharacteristic
65C5×#121Dic311yescharacteristic
66C4×C5×Q8C2×D311yescharacteristic
67C4×C5×D4—21no—
68C4×C5×D4C2×D311yescharacteristic
69C5×#117—21no—
70C2×C42×C5C2×D311yescharacteristic
71C5×C4⋊C8—32no—
72C5×C4⋊C8—61no—
73C5×C22⋊C8—61no—
74C5×C22⋊C8—61no—
75C4×C5×C8—32no—
76C4×C5×C8—61no—
77#1482—31noSylow
78C23×C3×C5—21no—
79C23×C3×C5C22⋊C411yescharacteristic
80C3×C5×Q8—22no—
81C3×C5×D4—22no—
82C3×C5×D4—42no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5—42no—
90C2×C3×C4×C5C22⋊C411yescharacteristic
91C2×C3×C4×C5C22⋊C411yescharacteristic
92C2×C3×C4×C5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C5×C3⋊C8—42no—
97C5×C3⋊C8—42no—
98C3×#126—21no—
99C3×#125C4×C511yescharacteristic
100C3×#124C4×C511yescharacteristic
101C3×#123—21no—
102C3×C22⋊Q8C4×C511yescharacteristic
103C3×#121C4×C511yescharacteristic
104C3×C4×Q8C22×C511yescharacteristic
105C3×C4×D4—21no—
106C3×C4×D4C22×C511yescharacteristic
107C3×#117—21no—
108C2×C3×C42C22×C511yescharacteristic
109#830—21no—
110#830—21no—
111C4⋊(C3⋊C8)—21no—
112C4⋊(C3⋊C8)C22×C512yes—
113C4×C3⋊C8—21no—
114C4×C3⋊C8C22×C512yes—
115C2×C5×Q8C2×Dic311yescharacteristic
116C2×C5×D4—21no—
117C2×C5×D4C2×Dic311yescharacteristic
118C22×C4×C5—21no—
119C22×C4×C5C2×Dic311yescharacteristic
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5#6711yescharacteristic
122C2×C5×C8—62no—
123C2×C5×C8—62no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C2×Dic311yescharacteristic
129C5×C4⋊C4C2×Dic311yescharacteristic
130C5×C22⋊C4—21no—
131C5×C22⋊C4—21no—
132C5×C22⋊C4—21no—
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C42×C5—21no—
136C42×C5C2×Dic311yescharacteristic
137C42×C5#6711yescharacteristic
138C42×C5#6711yescharacteristic
139C42×C5C22×D311yescharacteristic
140#529C5×D311yescharacteristic
141#431—31no—
142#431—31no—
143Q8⋊C8—32no—
144D4⋊C8—32no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—41no—
149C22×C3×C5—41no—
150C22×C3×C5—41no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5—41no—
158C3×C4×C5—41no—
159C3×C4×C5#13112yes—
160C3×C4×C5#13512yes—
161C2×C3×Q8C2×C4×C511yescharacteristic
162C2×C3×D4—21no—
163C2×C3×D4C2×C4×C511yescharacteristic
164C22×C3×C4—21no—
165C22×C3×C4C2×C4×C511yescharacteristic
166C22×C3×C4C5×D411yescharacteristic
167C22×C3×C4C5×D411yescharacteristic
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4C2×C4×C511yescharacteristic
173C3×C4⋊C4C2×C4×C511yescharacteristic
174C3×C22⋊C4—21no—
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C22⋊C4—21no—
179C3×C42—21no—
180C3×C42C2×C4×C511yescharacteristic
181C3×C42C5×D411yescharacteristic
182C3×C42C5×D411yescharacteristic
183C3×C42C23×C511yescharacteristic
184C2×C3⋊C8—22no—
185C2×C3⋊C8—22no—
186C23×C5—21no—
187C23×C5#21711yescharacteristic
188C5×Q8—22no—
189C5×D4—22no—
190C5×D4—42no—
191C2×C4×C5—22no—
192C2×C4×C5—22no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—41no—
197C2×C4×C5—42no—
198C2×C4×C5#21711yescharacteristic
199C2×C4×C5#21711yescharacteristic
200C2×C4×C5#21711yescharacteristic
201C2×C4×C5C22×Dic311yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C5×C8—122no—
205C5×C8—122no—
206#126—21no—
207#125C5×Dic311yescharacteristic
208#124C5×Dic311yescharacteristic
209#123—21no—
210C22⋊Q8C5×Dic311yescharacteristic
211#121C5×Dic311yescharacteristic
212C4×Q8C2×C5×D311yescharacteristic
213C4×D4—21no—
214C4×D4C2×C5×D311yescharacteristic
215#117—21no—
216C2×C42C2×C5×D311yescharacteristic
217C4⋊C8—32no—
218C4⋊C8—61no—
219C22⋊C8—61no—
220C22⋊C8—61no—
221C4×C8—32no—
222C4×C8—61no—
223C2×C3×C5—41no—
224C2×C3×C5—81no—
225C2×C3×C5#40811yescharacteristic
226C2×C3×C5#41611yescharacteristic
227C2×C3×C5#42111yescharacteristic
228C23×C3—21no—
229C23×C3C5×C22⋊C411yescharacteristic
230C3×Q8—22no—
231C3×D4—22no—
232C3×D4—42no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—41no—
239C2×C3×C4—42no—
240C2×C3×C4C5×C22⋊C411yescharacteristic
241C2×C3×C4C5×C22⋊C411yescharacteristic
242C2×C3×C4C5×C22⋊C411yescharacteristic
243C2×C3×C4C22×C4×C511yescharacteristic
244C2×C3×C4C2×C5×D411yescharacteristic
245C2×C3×C4C2×C5×D411yescharacteristic
246C3⋊C8—42no—
247C3⋊C8—42no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5—41no—
254C22×C5C2×#21711yescharacteristic
255C4×C5—21no—
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—41no—
260C4×C5—41no—
261C4×C5—41no—
262C4×C5#94812yes—
263C4×C5#95012yes—
264C2×Q8C2×C5×Dic311yescharacteristic
265C2×D4—21no—
266C2×D4C2×C5×Dic311yescharacteristic
267C22×C4—21no—
268C22×C4C2×C5×Dic311yescharacteristic
269C22×C4C5×#6711yescharacteristic
270C22×C4C5×#6711yescharacteristic
271C2×C8—62no—
272C2×C8—62no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4C2×C5×Dic311yescharacteristic
278C4⋊C4C2×C5×Dic311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42C2×C5×Dic311yescharacteristic
286C42C5×#6711yescharacteristic
287C42C5×#6711yescharacteristic
288C42C22×C5×D311yescharacteristic
289C3×C5#148211yescharacteristic, complemented, Hall
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3C2×C5×C22⋊C411yescharacteristic
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4C5×#13112yes—
305C3×C4C5×#13512yes—
306C2×C5—41no—
307C2×C5—81no—
308C2×C5#523311yescharacteristic
309C2×C5#523411yescharacteristic
310C2×C5#523611yescharacteristic
311C23—21no—
312C23C5×#21711yescharacteristic
313Q8—22no—
314D4—22no—
315D4—42no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4C5×#21711yescharacteristic
324C2×C4C5×#21711yescharacteristic
325C2×C4C5×#21711yescharacteristic
326C2×C4C22×C5×Dic311yescharacteristic
327C2×C4C2×C5×#6711yescharacteristic
328C2×C4C2×C5×#6711yescharacteristic
329C8—122no—
330C8—122no—
331C2×C3—41no—
332C2×C3—81no—
333C2×C3C5×#40811yescharacteristic
334C2×C3C5×#41611yescharacteristic
335C2×C3C5×#42111yescharacteristic
336C5#7175011yescharacteristic, direct product factor, Sylow
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22C2×C5×#21711yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4C5×#94812yes—
352C4C5×#95012yes—
353C3C5×#148211yescharacteristic, complemented, Sylow
354C2—41no—
355C2—81no—
356C2C5×#523311yescharacteristic
357C2C5×#523411yescharacteristic
358C2C5×#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×#1482
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×#4925C2semidirect
4. C5×#4535C2semidirect
5. C5×D4⋊(C3⋊C8)C2semidirect
24. #71750C5direct (N × H)
56. #4925C2×C5semidirect
57. #4925C2×C5semidirect
58. #4535C2×C5semidirect
59. D4⋊(C3⋊C8)C2×C5semidirect
289. C3×C5#1482semidirect
336. C5#71750direct (N × H)
353. C3C5×#1482semidirect

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×#45352
C5×D4⋊(C3⋊C8)2
C5×#14823
#717505