Finite Group Databasebeta

← C5×#7582 #11930302

Subgroups — C5×#7582 #11930302

Order 1280.

606 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#121C211yesmaximal, characteristic
2C5×#1817C211yesmaximal, characteristic, complemented
3C4×C5×C22⋊C8C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal, complemented
6C2×C5×#121C411yescharacteristic
7C2×C4×C5×D4—21no—
8C2×C4×C5×D4C411yescharacteristic
9C22×C42×C5C2211yescharacteristic
10C2×C5×C22⋊C8—21no—
11C2×C5×C22⋊C8—21no—
12C2×C4×C5×C8—21no—
13C5×#390C2211yescharacteristic
14C5×#389C2211yescharacteristic
15C5×#388—21no—
16C5×#386—21no—
17C5×#380C411yescharacteristic
18C4×C5×C4⋊C4C411yescharacteristic
19C4×C5×C22⋊C4—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7582C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×D4—21no—
25C22×C5×D4C2×C411yescharacteristic
26C23×C4×C5—21no—
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C22×C5×C8—22no—
31C22×C5×C8—22no—
32C5×#121—22no—
33C5×#121C814yescomplemented
34C4×C5×D4—42no—
35C4×C5×D4—44no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C42×C5—21no—
46C2×C42×C5—42no—
47C2×C42×C5C2×C411yescharacteristic
48C2×C42×C5D411yescharacteristic
49C2×C42×C5D411yescharacteristic
50C2×C42×C5C2311yescharacteristic
51C5×C22⋊C8—24no—
52C5×C22⋊C8—42no—
53C4×C5×C8—42no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C4×#121C2×C511yescharacteristic
58#1817C2×C511yescharacteristic, complemented
59C4×C22⋊C8C2×C511yescharacteristic, complemented
60#1271C2×C512yescomplemented
61#1270C2×C512yescomplemented
62C24×C5—21no—
63C24×C5C22⋊C411yescharacteristic
64C2×C5×D4—24no—
65C2×C5×D4—21no—
66C2×C5×D4—41no—
67C2×C5×D4—41no—
68C2×C5×D4—42no—
69C2×C5×D4—42no—
70C2×C5×D4C2×C812yes—
71C22×C4×C5—21no—
72C22×C4×C5—22no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—42no—
83C22×C4×C5—42no—
84C22×C4×C5—42no—
85C22×C4×C5C22⋊C411yescharacteristic
86C22×C4×C5C22⋊C411yescharacteristic
87C22×C4×C5C22⋊C411yescharacteristic
88C22×C4×C5C2×C812yes—
89C22×C4×C5M1612yes—
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C2×C5×C8—24no—
94C2×C5×C8—42no—
95C2×C5×C8—42no—
96C2×C5×C8—42no—
97C2×C5×C8—42no—
98C2×C5×C8—42no—
99C5×C4⋊C4—21no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—41no—
102C5×C4⋊C4—42no—
103C5×C4⋊C4C2×C812yes—
104C5×C22⋊C4—24no—
105C5×C22⋊C4—42no—
106C5×C22⋊C4—42no—
107C5×C22⋊C4—42no—
108C5×C22⋊C4—42no—
109C42×C5—22no—
110C42×C5—22no—
111C42×C5—41no—
112C42×C5—41no—
113C42×C5—42no—
114C2×#121C4×C511yescharacteristic
115C2×C4×D4—21no—
116C2×C4×D4C4×C511yescharacteristic
117C22×C42C22×C511yescharacteristic
118C2×C22⋊C8—21no—
119C2×C22⋊C8—21no—
120C2×C4×C8—21no—
121#390C22×C511yescharacteristic
122#389C22×C511yescharacteristic
123#388—21no—
124#386—21no—
125#380C4×C511yescharacteristic
126C4×C4⋊C4C4×C511yescharacteristic
127C4×C22⋊C4—21no—
128#336—21no—
129#336C22×C512yes—
130#336C22×C512yes—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5—22no—
138C23×C5—41no—
139C23×C5—41no—
140C23×C5—41no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5C22⋊C812yes—
145C23×C5C2×C22⋊C411yescharacteristic
146C5×D4—42no—
147C5×D4—42no—
148C5×D4—48no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—22no—
162C2×C4×C5—42no—
163C2×C4×C5—42no—
164C2×C4×C5—44no—
165C2×C4×C5—44no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—41no—
172C2×C4×C5—41no—
173C2×C4×C5—41no—
174C2×C4×C5—84no—
175C2×C4×C5C22⋊C812yes—
176C2×C4×C5#9912yes—
177C2×C4×C5#10412yes—
178C2×C4×C5C22×C811yescharacteristic
179C2×C4×C5C2×M1611yescharacteristic
180C2×C4×C5#13512yes—
181C2×C4×C5AGL(1,ℤ/8)12yes—
182C5×C8—44no—
183C5×C8—82no—
184C22×D4—21no—
185C22×D4C2×C4×C511yescharacteristic
186C23×C4—21no—
187C23×C4C2×C4×C511yescharacteristic
188C23×C4C5×D411yescharacteristic
189C23×C4C5×D411yescharacteristic
190C22×C8—22no—
191C22×C8—22no—
192#121—22no—
193#121C5×C814yescomplemented
194C4×D4—42no—
195C4×D4—44no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×C4×C511yescharacteristic
198C2×C4⋊C4C2×C4×C511yescharacteristic
199C2×C4⋊C4C2×C4×C511yescharacteristic
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C42—21no—
206C2×C42—42no—
207C2×C42C2×C4×C511yescharacteristic
208C2×C42C5×D411yescharacteristic
209C2×C42C5×D411yescharacteristic
210C2×C42C23×C511yescharacteristic
211C22⋊C8—24no—
212C22⋊C8—42no—
213C4×C8—42no—
214#95—21no—
215#95—21no—
216#95—21no—
217C22×C5—22no—
218C22×C5—22no—
219C22×C5—22no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5—41no—
224C22×C5—42no—
225C22×C5—42no—
226C22×C5—42no—
227C22×C5—81no—
228C22×C5—81no—
229C22×C5—81no—
230C22×C5—81no—
231C22×C5C2×C22⋊C811yescharacteristic
232C22×C5C2×#9911yescharacteristic
233C22×C5#41311yescharacteristic
234C22×C5#41611yescharacteristic
235C22×C5#41811yescharacteristic
236C22×C5C2×#10411yescharacteristic
237C22×C5#42111yescharacteristic
238C4×C5—22no—
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—22no—
242C4×C5—22no—
243C4×C5—22no—
244C4×C5—22no—
245C4×C5—42no—
246C4×C5—81no—
247C4×C5—81no—
248C24—21no—
249C24C5×C22⋊C411yescharacteristic
250C2×D4—24no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—42no—
255C2×D4—42no—
256C2×D4C2×C5×C812yes—
257C22×C4—21no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4C5×C22⋊C411yescharacteristic
272C22×C4C5×C22⋊C411yescharacteristic
273C22×C4C5×C22⋊C411yescharacteristic
274C22×C4C2×C5×C812yes—
275C22×C4C5×M1612yes—
276C22×C4C22×C4×C511yescharacteristic
277C22×C4C2×C5×D411yescharacteristic
278C22×C4C2×C5×D411yescharacteristic
279C2×C8—24no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4C2×C5×C812yes—
290C22⋊C4—24no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C42—22no—
296C42—22no—
297C42—41no—
298C42—41no—
299C42—42no—
300C2×C5—42no—
301C2×C5—82no—
302C2×C5#145911yescharacteristic
303C2×C5#147611yescharacteristic
304C2×C5#147811yescharacteristic
305C2×C5#150711yescharacteristic
306C2×C5#151611yescharacteristic
307C2×C5#152911yescharacteristic
308C2×C5#155311yescharacteristic
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—22no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23C5×C22⋊C812yes—
323C23C2×C5×C22⋊C411yescharacteristic
324D4—42no—
325D4—42no—
326D4—48no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—84no—
353C2×C4C5×C22⋊C812yes—
354C2×C4C5×#9912yes—
355C2×C4C5×#10412yes—
356C2×C4C22×C5×C811yescharacteristic
357C2×C4C2×C5×M1611yescharacteristic
358C2×C4C5×#13512yes—
359C2×C4C5×AGL(1,ℤ/8)12yes—
360C8—44no—
361C8—82no—
362C5#758211yescharacteristic, direct product factor, Sylow
363C22—22no—
364C22—22no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22C2×C5×C22⋊C811yescharacteristic
378C22C2×C5×#9911yescharacteristic
379C22C5×#41311yescharacteristic
380C22C5×#41611yescharacteristic
381C22C5×#41811yescharacteristic
382C22C2×C5×#10411yescharacteristic
383C22C5×#42111yescharacteristic
384C4—22no—
385C4—22no—
386C4—22no—
387C4—22no—
388C4—21no—
389C4—21no—
390C4—22no—
391C4—42no—
392C4—81no—
393C4—81no—
394C2—42no—
395C2—82no—
396C2C5×#145911yescharacteristic
397C2C5×#147611yescharacteristic
398C2C5×#147811yescharacteristic
399C2C5×#150711yescharacteristic
400C2C5×#151611yescharacteristic
401C2C5×#152911yescharacteristic
402C2C5×#155311yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC2×C4C22×C5×C8
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#121C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1817C2semidirect
3. C4×C5×C22⋊C8C2semidirect
4. C5×#1271C2semidirect
5. C5×#1270C2semidirect
23. #7582C5direct (N × H)
33. C5×#121C8semidirect
58. #1817C2×C5semidirect
59. C4×C22⋊C8C2×C5semidirect
60. #1271C2×C5semidirect
61. #1270C2×C5semidirect
193. #121C5×C8semidirect
362. C5#7582direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#1212
C5×#18172
C4×C5×C22⋊C82
C5×#12712
C5×#12702
#75825