Finite Group Databasebeta

← C5×#13091 #11935811

Subgroups — C5×#13091 #11935811

Order 1280.

724 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#410C211yesmaximal, characteristic
2C5×#2432C211yesmaximal, characteristic
3C2×C5×#354C212yesmaximal, complemented
4C5×#1782C211yesmaximal, characteristic
5C5×#1393C212yesmaximal, complemented
6C22×C5×#41C2211yescharacteristic
7C2×C5×C4⋊Q8C411yescharacteristic, complemented
8C2×C5×#124C2211yescharacteristic
9C2×C5×C22⋊Q8C411yescharacteristic, complemented
10C2×C5×#117—21no—
11C5×#410—24no—
12C2×C5×#99—21no—
13C2×C5×#99—21no—
14C2×C5×#99C2212yes—
15C2×C5×#99C2212yes—
16C5×#394—21no—
17C5×#394—21no—
18C5×#391C411yescharacteristic, complemented
19C5×#390C2211yescharacteristic
20C5×#385—21no—
21C5×#385—21no—
22C5×#381—21no—
23C4×C5×C22⋊C4C411yescharacteristic, complemented
24C5×#354—24no—
25#13091C511yesmaximal, characteristic, direct product factor, Sylow
26C2×C5×#41—22no—
27C2×C5×#41—22no—
28C2×C5×#41—41no—
29C2×C5×#41—41no—
30C2×C5×#41—42no—
31C22×C5×Q8C2×C411yescharacteristic
32C22×C5×Q8C2×C411yescharacteristic
33C22×C5×D4D411yescharacteristic
34C22×C5×D4D411yescharacteristic
35C22×C5×D4C2311yescharacteristic
36C23×C4×C5C2×C411yescharacteristic
37C23×C4×C5D411yescharacteristic
38C23×C4×C5D411yescharacteristic
39C5×C4⋊Q8—42no—
40C5×#124—22no—
41C5×#124—22no—
42C5×C22⋊Q8—41no—
43C5×C22⋊Q8—41no—
44C5×#117—24no—
45C5×#117—42no—
46C2×C5×C4⋊C4—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—41no—
50C2×C5×C4⋊C4C2×C411yescharacteristic
51C2×C5×C22⋊C4—22no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—21no—
55C2×C5×C22⋊C4—21no—
56C2×C5×C22⋊C4—21no—
57C2×C5×C22⋊C4—21no—
58C2×C5×C22⋊C4—22no—
59C2×C42×C5—41no—
60C2×C42×C5C2×C411yescharacteristic
61C2×C42×C5C2×C411yescharacteristic
62C5×#99—24no—
63C5×#99—22no—
64C5×#99—22no—
65C5×#99—22no—
66C5×#99—42no—
67C5×#99D414yes—
68C5×#95—21no—
69C5×#95—21no—
70C5×#95—21no—
71C5×#95—41no—
72C5×#95—41no—
73C2×#410C2×C511yescharacteristic
74#2432C2×C511yescharacteristic
75C2×#354C2×C512yescomplemented
76#1782C2×C511yescharacteristic
77#1393C2×C512yescomplemented
78C24×C5C22⋊C411yescharacteristic
79C24×C5C2×D411yescharacteristic
80C24×C5C2×D411yescharacteristic
81C5×#41—44no—
82C5×#41—44no—
83C5×#41—44no—
84C5×#41—44no—
85C2×C5×Q8—22no—
86C2×C5×Q8—22no—
87C2×C5×Q8—22no—
88C2×C5×Q8—41no—
89C2×C5×Q8—41no—
90C2×C5×Q8—41no—
91C2×C5×D4—21no—
92C2×C5×D4—22no—
93C2×C5×D4—21no—
94C2×C5×D4—22no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4C2×D412yes—
101C2×C5×D4#4112yes—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—22no—
107C22×C4×C5—21no—
108C22×C4×C5—22no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—21no—
113C22×C4×C5—22no—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5—21no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5—42no—
120C22×C4×C5—42no—
121C22×C4×C5C22⋊C411yescharacteristic
122C22×C4×C5C22⋊C411yescharacteristic
123C22×C4×C5C22⋊C411yescharacteristic
124C22×C4×C5C22×C411yescharacteristic
125C5×C4⋊C4—41no—
126C5×C4⋊C4—42no—
127C5×C4⋊C4—44no—
128C5×C4⋊C4—41no—
129C5×C4⋊C4—41no—
130C5×C4⋊C4—42no—
131C5×C22⋊C4—24no—
132C5×C22⋊C4—42no—
133C5×C22⋊C4—42no—
134C5×C22⋊C4—42no—
135C5×C22⋊C4—42no—
136C5×C22⋊C4—42no—
137C5×C22⋊C4—41no—
138C5×C22⋊C4—42no—
139C5×C22⋊C4—41no—
140C5×C22⋊C4—42no—
141C5×C22⋊C4—42no—
142C42×C5—22no—
143C42×C5—41no—
144C42×C5—44no—
145C22×#41C22×C511yescharacteristic
146C2×C4⋊Q8C4×C511yescharacteristic, complemented
147C2×#124C22×C511yescharacteristic
148C2×C22⋊Q8C4×C511yescharacteristic, complemented
149C2×#117—21no—
150#410—24no—
151C2×#99—21no—
152C2×#99—21no—
153C2×#99C22×C512yes—
154C2×#99C22×C512yes—
155#394—21no—
156#394—21no—
157#391C4×C511yescharacteristic, complemented
158#390C22×C511yescharacteristic
159#385—21no—
160#385—21no—
161#381—21no—
162C4×C22⋊C4C4×C511yescharacteristic, complemented
163#354—24no—
164C23×C5—21no—
165C23×C5—21no—
166C23×C5—21no—
167C23×C5—21no—
168C23×C5—21no—
169C23×C5—21no—
170C23×C5—21no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5—41no—
174C23×C5—41no—
175C23×C5—41no—
176C23×C5—41no—
177C23×C5C2×C22⋊C411yescharacteristic
178C23×C5#12011yescharacteristic
179C23×C5#12112yes—
180C23×C5#12311yescharacteristic
181C5×Q8—44no—
182C5×Q8—82no—
183C5×D4—42no—
184C5×D4—42no—
185C5×D4—44no—
186C5×D4—42no—
187C5×D4—42no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—22no—
191C2×C4×C5—22no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—22no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—21no—
202C2×C4×C5—42no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—44no—
209C2×C4×C5—41no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—41no—
215C2×C4×C5—41no—
216C2×C4×C5—41no—
217C2×C4×C5—41no—
218C2×C4×C5—82no—
219C2×C4×C5—82no—
220C2×C4×C5—82no—
221C2×C4×C5—82no—
222C2×C4×C5—82no—
223C2×C4×C5#9912yes—
224C2×C4×C5#9911yescharacteristic
225C2×C4×C5#9911yescharacteristic
226C2×C4×C5C4×D412yes—
227C2×#41—22no—
228C2×#41—22no—
229C2×#41—41no—
230C2×#41—41no—
231C2×#41—42no—
232C22×Q8C2×C4×C511yescharacteristic
233C22×Q8C2×C4×C511yescharacteristic
234C22×D4C5×D411yescharacteristic
235C22×D4C5×D411yescharacteristic
236C22×D4C23×C511yescharacteristic
237C23×C4C2×C4×C511yescharacteristic
238C23×C4C5×D411yescharacteristic
239C23×C4C5×D411yescharacteristic
240C4⋊Q8—42no—
241#124—22no—
242#124—22no—
243C22⋊Q8—41no—
244C22⋊Q8—41no—
245#117—24no—
246#117—42no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—41no—
251C2×C4⋊C4C2×C4×C511yescharacteristic
252C2×C22⋊C4—22no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—22no—
260C2×C42—41no—
261C2×C42C2×C4×C511yescharacteristic
262C2×C42C2×C4×C511yescharacteristic
263#99—24no—
264#99—22no—
265#99—22no—
266#99—22no—
267#99—42no—
268#99C5×D414yes—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—41no—
273#95—41no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—22no—
279C22×C5—41no—
280C22×C5—42no—
281C22×C5—41no—
282C22×C5—41no—
283C22×C5—41no—
284C22×C5—41no—
285C22×C5—41no—
286C22×C5—41no—
287C22×C5—41no—
288C22×C5—41no—
289C22×C5—81no—
290C22×C5—81no—
291C22×C5—81no—
292C22×C5—81no—
293C22×C5#38611yescharacteristic
294C22×C5C2×#9911yescharacteristic
295C22×C5C2×#9911yescharacteristic
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—22no—
299C4×C5—22no—
300C4×C5—42no—
301C4×C5—41no—
302C4×C5—81no—
303C4×C5—84no—
304C4×C5—81no—
305C4×C5—81no—
306C4×C5—162no—
307C24C5×C22⋊C411yescharacteristic
308C24C2×C5×D411yescharacteristic
309C24C2×C5×D411yescharacteristic
310#41—44no—
311#41—44no—
312#41—44no—
313#41—44no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8—41no—
318C2×Q8—41no—
319C2×Q8—41no—
320C2×D4—21no—
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—22no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4C2×C5×D412yes—
330C2×D4C5×#4112yes—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4C5×C22⋊C411yescharacteristic
351C22×C4C5×C22⋊C411yescharacteristic
352C22×C4C5×C22⋊C411yescharacteristic
353C22×C4C22×C4×C511yescharacteristic
354C4⋊C4—41no—
355C4⋊C4—42no—
356C4⋊C4—44no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—42no—
360C22⋊C4—24no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—42no—
366C22⋊C4—41no—
367C22⋊C4—42no—
368C22⋊C4—41no—
369C22⋊C4—42no—
370C22⋊C4—42no—
371C42—22no—
372C42—41no—
373C42—44no—
374C2×C5—21no—
375C2×C5—21no—
376C2×C5—41no—
377C2×C5—42no—
378C2×C5—41no—
379C2×C5—81no—
380C2×C5#189811yescharacteristic
381C2×C5#212611yescharacteristic
382C2×C5#212911yescharacteristic
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23C2×C5×C22⋊C411yescharacteristic
397C23C5×#12011yescharacteristic
398C23C5×#12112yes—
399C23C5×#12311yescharacteristic
400Q8—44no—
401Q8—82no—
402D4—42no—
403D4—42no—
404D4—44no—
405D4—42no—
406D4—42no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—44no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4C5×#9911yescharacteristic
443C2×C4C5×#9911yescharacteristic
444C2×C4C5×#9912yes—
445C2×C4C4×C5×D412yes—
446C5#1309111yescharacteristic, direct product factor, Sylow
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—22no—
452C22—41no—
453C22—42no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22C5×#38611yescharacteristic
467C22C2×C5×#9911yescharacteristic
468C22C2×C5×#9911yescharacteristic
469C4—21no—
470C4—21no—
471C4—22no—
472C4—22no—
473C4—42no—
474C4—41no—
475C4—81no—
476C4—84no—
477C4—81no—
478C4—81no—
479C4—162no—
480C2—21no—
481C2—21no—
482C2—41no—
483C2—42no—
484C2—41no—
485C2—81no—
486C2C5×#189811yescharacteristic
487C2C5×#212611yescharacteristic
488C2C5×#212911yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC22×D4C23×C5
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C22×C5×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#354C2semidirect
5. C5×#1393C2semidirect
7. C2×C5×C4⋊Q8C4semidirect
9. C2×C5×C22⋊Q8C4semidirect
18. C5×#391C4semidirect
23. C4×C5×C22⋊C4C4semidirect
25. #13091C5direct (N × H)
75. C2×#354C2×C5semidirect
77. #1393C2×C5semidirect
146. C2×C4⋊Q8C4×C5semidirect
148. C2×C22⋊Q8C4×C5semidirect
157. #391C4×C5semidirect
162. C4×C22⋊C4C4×C5semidirect
446. C5#13091direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4102
C5×#24322
C2×C5×#3542
C5×#17822
C5×#13932
#130915