Finite Group Databasebeta

← C5×#8576 #11931296

Subgroups — C5×#8576 #11931296

Order 1280.

614 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×C22⋊Q8C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic
3C2×C5×#328C212yesmaximal
4C5×#1434C211yesmaximal, characteristic
5C5×#1294C212yesmaximal
6C2×C5×C22⋊Q8C2211yescharacteristic
7C2×C4×C5×Q8C411yescharacteristic, complemented
8C22×C42×C5C2211yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×C22⋊C8C2212yes—
11C5×#391C411yescharacteristic, complemented
12C5×#389C411yescharacteristic, complemented
13C5×#387—21no—
14C5×#385—21no—
15C5×#380C2211yescharacteristic
16C4×C5×C4⋊C4—21no—
17C4×C5×C4⋊C4C411yescharacteristic, complemented
18C4×C5×C22⋊C4—21no—
19C2×C5×#95—21no—
20C2×C5×#95—21no—
21C2×C5×#95C2212yes—
22C5×#336—21no—
23C5×#328—24no—
24#8576C511yesmaximal, characteristic, direct product factor, Sylow
25C22×C5×Q8C2×C411yescharacteristic
26C23×C4×C5—22no—
27C23×C4×C5D411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C23×C4×C5C2311yescharacteristic
30C22×C5×C8—22no—
31C5×C22⋊Q8—21no—
32C5×C22⋊Q8—21no—
33C5×C22⋊Q8D412yes—
34C5×C22⋊Q8Q812yes—
35C4×C5×Q8—42no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C4⋊C4C2×C411yescharacteristic
41C2×C5×C4⋊C4C2×C411yescharacteristic
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C42×C5—21no—
45C2×C42×C5—21no—
46C2×C42×C5—42no—
47C2×C42×C5C2×C411yescharacteristic
48C2×C42×C5C2×C411yescharacteristic
49C2×C42×C5D411yescharacteristic
50C2×C42×C5D411yescharacteristic
51C5×C4⋊C8—42no—
52C5×C22⋊C8—22no—
53C5×C22⋊C8—22no—
54C5×#95—24no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95—21no—
60C5×#95—22no—
61C5×#95—22no—
62C5×#95—42no—
63C4×C22⋊Q8C2×C511yescharacteristic
64#1797C2×C511yescharacteristic
65C2×#328C2×C512yes—
66#1434C2×C511yescharacteristic
67#1294C2×C512yes—
68C24×C5C2×D411yescharacteristic
69C2×C5×Q8—21no—
70C2×C5×Q8—41no—
71C2×C5×Q8—41no—
72C2×C5×Q8C4⋊C412yes—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—22no—
78C22×C4×C5—22no—
79C22×C4×C5—24no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—42no—
87C22×C4×C5—42no—
88C22×C4×C5—42no—
89C22×C4×C5—42no—
90C22×C4×C5—42no—
91C22×C4×C5—42no—
92C22×C4×C5C22⋊C411yescharacteristic
93C22×C4×C5C22⋊C411yescharacteristic
94C22×C4×C5C22⋊C411yescharacteristic
95C22×C4×C5C22⋊C411yescharacteristic
96C22×C4×C5C22×C411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5C2×D411yescharacteristic
99C22×C4×C5C2×Q811yescharacteristic
100C22×C4×C5#4111yescharacteristic
101C22×C4×C5#4111yescharacteristic
102C2×C5×C8—42no—
103C2×C5×C8—42no—
104C2×C5×C8—42no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—22no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—42no—
111C5×C4⋊C4—42no—
112C5×C4⋊C4C4⋊C412yes—
113C5×C22⋊C4—22no—
114C5×C22⋊C4—22no—
115C5×C22⋊C4—42no—
116C42×C5—22no—
117C42×C5—22no—
118C42×C5—41no—
119C42×C5—41no—
120C42×C5—42no—
121C42×C5—42no—
122C2×C22⋊Q8C22×C511yescharacteristic
123C2×C4×Q8C4×C511yescharacteristic, complemented
124C22×C42C22×C511yescharacteristic
125C2×C4⋊C8—21no—
126C2×C22⋊C8C22×C512yes—
127#391C4×C511yescharacteristic, complemented
128#389C4×C511yescharacteristic, complemented
129#387—21no—
130#385—21no—
131#380C22×C511yescharacteristic
132C4×C4⋊C4—21no—
133C4×C4⋊C4C4×C511yescharacteristic, complemented
134C4×C22⋊C4—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95C22×C512yes—
138#336—21no—
139#328—24no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5C2×C22⋊C411yescharacteristic
145C23×C5#12111yescharacteristic
146C23×C5C22⋊Q811yescharacteristic
147C23×C5#13512yes—
148C23×C5#13712yes—
149C5×Q8—42no—
150C5×Q8—42no—
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—22no—
160C2×C4×C5—22no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—44no—
172C2×C4×C5—44no—
173C2×C4×C5—41no—
174C2×C4×C5—41no—
175C2×C4×C5—41no—
176C2×C4×C5—41no—
177C2×C4×C5—44no—
178C2×C4×C5—44no—
179C2×C4×C5—44no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—82no—
187C2×C4×C5—82no—
188C2×C4×C5—82no—
189C2×C4×C5—82no—
190C2×C4×C5#9912yes—
191C2×C4×C5#10412yes—
192C2×C4×C5C2×C4⋊C411yescharacteristic
193C2×C4×C5#11711yescharacteristic
194C2×C4×C5#12111yescharacteristic
195C2×C4×C5C22⋊Q811yescharacteristic
196C5×C8—82no—
197C22×Q8C2×C4×C511yescharacteristic
198C23×C4—22no—
199C23×C4C5×D411yescharacteristic
200C23×C4C5×D411yescharacteristic
201C23×C4C23×C511yescharacteristic
202C22×C8—22no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C22⋊Q8C5×D412yes—
206C22⋊Q8C5×Q812yes—
207C4×Q8—42no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C2×C4×C511yescharacteristic
212C2×C4⋊C4C2×C4×C511yescharacteristic
213C2×C4⋊C4C2×C4×C511yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42—21no—
217C2×C42—21no—
218C2×C42—42no—
219C2×C42C2×C4×C511yescharacteristic
220C2×C42C2×C4×C511yescharacteristic
221C2×C42C5×D411yescharacteristic
222C2×C42C5×D411yescharacteristic
223C4⋊C8—42no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226#95—24no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—22no—
233#95—22no—
234#95—42no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—22no—
240C22×C5—22no—
241C22×C5—22no—
242C22×C5—22no—
243C22×C5#38011yescharacteristic
244C22×C5C2×#9911yescharacteristic
245C22×C5#41011yescharacteristic
246C22×C5#41611yescharacteristic
247C22×C5#41911yescharacteristic
248C22×C5C2×#10411yescharacteristic
249C22×C5#42111yescharacteristic
250C22×C5#46412yes—
251C22×C5#47912yes—
252C4×C5—21no—
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—21no—
256C4×C5—22no—
257C4×C5—22no—
258C4×C5—42no—
259C4×C5—42no—
260C4×C5—41no—
261C4×C5—41no—
262C4×C5—84no—
263C4×C5—81no—
264C4×C5—81no—
265C24C2×C5×D411yescharacteristic
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8C5×C4⋊C412yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C5×C22⋊C411yescharacteristic
290C22×C4C5×C22⋊C411yescharacteristic
291C22×C4C5×C22⋊C411yescharacteristic
292C22×C4C5×C22⋊C411yescharacteristic
293C22×C4C22×C4×C511yescharacteristic
294C22×C4C2×C5×D411yescharacteristic
295C22×C4C2×C5×D411yescharacteristic
296C22×C4C2×C5×Q811yescharacteristic
297C22×C4C5×#4111yescharacteristic
298C22×C4C5×#4111yescharacteristic
299C2×C8—42no—
300C2×C8—42no—
301C2×C8—42no—
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—42no—
308C4⋊C4—42no—
309C4⋊C4C5×C4⋊C412yes—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—42no—
313C42—22no—
314C42—22no—
315C42—41no—
316C42—41no—
317C42—42no—
318C42—42no—
319C2×C5—22no—
320C2×C5—22no—
321C2×C5#150111yescharacteristic
322C2×C5#150611yescharacteristic
323C2×C5#151111yescharacteristic
324C2×C5#152111yescharacteristic
325C2×C5#179911yescharacteristic
326C2×C5#180511yescharacteristic
327C2×C5#180611yescharacteristic
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23C2×C5×C22⋊C411yescharacteristic
333C23C5×#12111yescharacteristic
334C23C5×C22⋊Q811yescharacteristic
335C23C5×#13512yes—
336C23C5×#13712yes—
337Q8—42no—
338Q8—42no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4C5×#9912yes—
379C2×C4C5×#10412yes—
380C2×C4C2×C5×C4⋊C411yescharacteristic
381C2×C4C5×#11711yescharacteristic
382C2×C4C5×#12111yescharacteristic
383C2×C4C5×C22⋊Q811yescharacteristic
384C8—82no—
385C5#857611yescharacteristic, direct product factor, Sylow
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22C5×#38011yescharacteristic
395C22C2×C5×#9911yescharacteristic
396C22C5×#41011yescharacteristic
397C22C5×#41611yescharacteristic
398C22C5×#41911yescharacteristic
399C22C2×C5×#10411yescharacteristic
400C22C5×#42111yescharacteristic
401C22C5×#46412yes—
402C22C5×#47912yes—
403C4—22no—
404C4—22no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—41no—
410C4—41no—
411C4—42no—
412C4—42no—
413C4—84no—
414C4—81no—
415C4—81no—
416C2—22no—
417C2—22no—
418C2C5×#150111yescharacteristic
419C2C5×#150611yescharacteristic
420C2C5×#151111yescharacteristic
421C2C5×#152111yescharacteristic
422C2C5×#179911yescharacteristic
423C2C5×#180511yescharacteristic
424C2C5×#180611yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC24×C5C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C4×C5×Q8C4semidirect
11. C5×#391C4semidirect
12. C5×#389C4semidirect
17. C4×C5×C4⋊C4C4semidirect
24. #8576C5direct (N × H)
123. C2×C4×Q8C4×C5semidirect
127. #391C4×C5semidirect
128. #389C4×C5semidirect
133. C4×C4⋊C4C4×C5semidirect
385. C5#8576direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×C22⋊Q82
C5×#17972
C2×C5×#3282
C5×#14342
C5×#12942
#85765