Finite Group Databasebeta

← C5×#18690 #11941410

Subgroups — C5×#18690 #11941410

Order 1280.

878 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3544C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic, complemented
3C5×#3218C211yesmaximal, characteristic, complemented
4C2×C5×#487C211yesmaximal, characteristic, complemented
5C5×#1646C212yesmaximal, complemented
6C5×#1645C212yesmaximal, complemented
7C5×#1644C212yesmaximal, complemented
8C5×#1643C212yesmaximal, complemented
9C5×#1558C211yesmaximal, characteristic, complemented
10C5×#1494C211yesmaximal, characteristic, complemented
11C5×#1494C211yesmaximal, characteristic, complemented
12C5×#563—22no—
13C5×Q82C2211yescharacteristic
14C5×#555C2211yescharacteristic
15C5×#554C2211yescharacteristic
16C5×#554C2211yescharacteristic
17C5×#552—21no—
18C5×#552—21no—
19C5×#547—21no—
20C5×#547—21no—
21C5×#544—21no—
22C5×#544—21no—
23C5×#542—21no—
24C5×#542—21no—
25C5×#536—22no—
26C2×C5×C4⋊Q8C2211yescharacteristic
27C2×C5×C4⋊Q8C2211yescharacteristic
28C5×#529C2211yescharacteristic
29C5×#529C2211yescharacteristic
30C5×#501—21no—
31C5×#497—21no—
32C5×#491—21no—
33C5×#489—21no—
34C5×#487—22no—
35C5×#487C2212yes—
36C5×#487C2212yes—
37C5×#484—21no—
38C5×#481—21no—
39C5×#475C2212yes—
40C5×#474C2212yes—
41C5×#462C2212yes—
42C5×#461C2212yes—
43C5×#451—21no—
44C5×#448—21no—
45C5×#432C2211yescharacteristic
46C5×#432C2211yescharacteristic
47C2×C5×#103—22no—
48C2×C4×C5×C8C2211yescharacteristic
49C5×#333C2212yes—
50C5×#333C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×D4⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18690C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—22no—
57C22×C5×Q8—21no—
58C22×C5×Q8D412yes—
59C2×C5×Q16—22no—
60C2×C5×SD16—22no—
61C22×C5×C8—21no—
62C5×C4⋊Q8—22no—
63C5×C4⋊Q8—22no—
64C5×C4⋊Q8—21no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8D412yes—
72C5×C4⋊Q8C2312yes—
73C5×C4⋊Q8C2311yescharacteristic
74C5×C4⋊Q8C2311yescharacteristic
75C5×#126—22no—
76C5×#126—22no—
77C5×#126—21no—
78C5×#126—21no—
79C5×#125—22no—
80C5×#125—22no—
81C5×#125—21no—
82C5×#125—21no—
83C5×#125D411yescharacteristic
84C5×#125D411yescharacteristic
85C5×#124—22no—
86C5×#124—22no—
87C5×#124D411yescharacteristic
88C5×#124D411yescharacteristic
89C5×#123—22no—
90C5×#123—22no—
91C5×#123—22no—
92C5×#123—22no—
93C5×#123—21no—
94C5×#123—21no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8—22no—
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8—21no—
102C5×C22⋊Q8—21no—
103C5×C22⋊Q8D411yescharacteristic
104C5×C22⋊Q8D411yescharacteristic
105C5×#121—21no—
106C5×#121—21no—
107C5×#121D411yescharacteristic
108C5×#121D411yescharacteristic
109C4×C5×Q8—21no—
110C4×C5×Q8—21no—
111C4×C5×Q8C2311yescharacteristic
112C4×C5×Q8C2311yescharacteristic
113C4×C5×D4—21no—
114C4×C5×D4—21no—
115C4×C5×D4—21no—
116C4×C5×D4—21no—
117C4×C5×D4C2311yescharacteristic
118C4×C5×D4C2311yescharacteristic
119C5×#117—22no—
120C5×#117—21no—
121C5×#117—21no—
122C5×#117—21no—
123C5×#117—21no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4—21no—
128C2×C5×C4⋊C4—21no—
129C2×C5×C4⋊C4—21no—
130C2×C42×C5C2311yescharacteristic
131C5×#107—22no—
132C5×#106—22no—
133C5×C4⋊C8C2312yes—
134C5×C4⋊C8C2312yes—
135C5×#103—24no—
136C5×#103—24no—
137C5×#103—22no—
138C5×#103—22no—
139C5×#103—22no—
140C5×#102—22no—
141C5×C22⋊C8—21no—
142C5×C22⋊C8—21no—
143C5×#97—21no—
144C5×#97—21no—
145C4×C5×C8—21no—
146C4×C5×C8C2312yes—
147#3544C2×C511yescharacteristic
148#3239C2×C511yescharacteristic, complemented
149#3218C2×C511yescharacteristic, complemented
150C2×#487C2×C511yescharacteristic, complemented
151#1646C2×C512yescomplemented
152#1645C2×C512yescomplemented
153#1644C2×C512yescomplemented
154#1643C2×C512yescomplemented
155#1558C2×C511yescharacteristic, complemented
156#1494C2×C511yescharacteristic, complemented
157#1494C2×C511yescharacteristic, complemented
158C5×#41—84no—
159C2×C5×Q8—22no—
160C2×C5×Q8—22no—
161C2×C5×Q8—22no—
162C2×C5×Q8—44no—
163C2×C5×Q8—41no—
164C2×C5×Q8—82no—
165C2×C5×Q8C2×D411yescharacteristic
166C2×C5×Q8C2×D411yescharacteristic
167C2×C5×Q8C2×D412yes—
168C2×C5×Q8C2×D412yes—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—22no—
172C2×C5×D4C2×D411yescharacteristic
173C2×C5×D4C2×D411yescharacteristic
174C22×C4×C5—22no—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—41no—
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C5×Q16—82no—
184C5×SD16—82no—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C2×C5×C8—22no—
188C2×C5×C8—42no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—22no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4—41no—
213C5×C4⋊C4C2×D411yescharacteristic
214C5×C4⋊C4C2×D411yescharacteristic
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C22⋊C4—22no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—21no—
222C5×C22⋊C4—21no—
223C5×C22⋊C4—21no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—21no—
227C5×C22⋊C4—21no—
228C5×C22⋊C4—21no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C42×C5—22no—
232C42×C5—22no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5C2×D411yescharacteristic
236C42×C5C2×D411yescharacteristic
237C42×C5C2×D411yescharacteristic
238C42×C5C2411yescharacteristic
239#563—22no—
240Q82C22×C511yescharacteristic
241#555C22×C511yescharacteristic
242#554C22×C511yescharacteristic
243#554C22×C511yescharacteristic
244#552—21no—
245#552—21no—
246#547—21no—
247#547—21no—
248#544—21no—
249#544—21no—
250#542—21no—
251#542—21no—
252#536—22no—
253C2×C4⋊Q8C22×C511yescharacteristic
254C2×C4⋊Q8C22×C511yescharacteristic
255#529C22×C511yescharacteristic
256#529C22×C511yescharacteristic
257#501—21no—
258#497—21no—
259#491—21no—
260#489—21no—
261#487—22no—
262#487C22×C512yes—
263#487C22×C512yes—
264#484—21no—
265#481—21no—
266#475C22×C512yes—
267#474C22×C512yes—
268#462C22×C512yes—
269#461C22×C512yes—
270#451—21no—
271#448—21no—
272#432C22×C511yescharacteristic
273#432C22×C511yescharacteristic
274C2×#103—22no—
275C2×C4×C8C22×C511yescharacteristic
276#333C22×C512yes—
277#333C22×C512yes—
278Q8⋊C8C22×C512yes—
279Q8⋊C8C22×C512yes—
280D4⋊C8C22×C512yes—
281D4⋊C8C22×C512yes—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5#12011yescharacteristic
285C5×Q8—22no—
286C5×Q8—22no—
287C5×Q8—42no—
288C5×Q8—42no—
289C5×Q8—42no—
290C5×Q8—42no—
291C5×Q8—82no—
292C5×Q8—82no—
293C5×Q8—82no—
294C5×D4—22no—
295C5×D4—22no—
296C5×D4—42no—
297C5×D4—42no—
298C5×D4—82no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—22no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—22no—
310C2×C4×C5—44no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—82no—
315C2×C4×C5—82no—
316C2×C4×C5—82no—
317C2×C4×C5#12011yescharacteristic
318C2×C4×C5#12011yescharacteristic
319C2×C4×C5#12011yescharacteristic
320C2×C4×C5C22×D411yescharacteristic
321C2×C4×C5C22×D411yescharacteristic
322C2×C4×C5C22×D411yescharacteristic
323C5×C8—42no—
324C5×C8—42no—
325C5×C8—42no—
326C2×#41—22no—
327C22×Q8—21no—
328C22×Q8C5×D412yes—
329C2×Q16—22no—
330C2×SD16—22no—
331C22×C8—21no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8C5×D412yes—
342C4⋊Q8C23×C512yes—
343C4⋊Q8C23×C511yescharacteristic
344C4⋊Q8C23×C511yescharacteristic
345#126—22no—
346#126—22no—
347#126—21no—
348#126—21no—
349#125—22no—
350#125—22no—
351#125—21no—
352#125—21no—
353#125C5×D411yescharacteristic
354#125C5×D411yescharacteristic
355#124—22no—
356#124—22no—
357#124C5×D411yescharacteristic
358#124C5×D411yescharacteristic
359#123—22no—
360#123—22no—
361#123—22no—
362#123—22no—
363#123—21no—
364#123—21no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8C5×D411yescharacteristic
374C22⋊Q8C5×D411yescharacteristic
375#121—21no—
376#121—21no—
377#121C5×D411yescharacteristic
378#121C5×D411yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C511yescharacteristic
382C4×Q8C23×C511yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C511yescharacteristic
388C4×D4C23×C511yescharacteristic
389#117—22no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C42C23×C511yescharacteristic
401#107—22no—
402#106—22no—
403C4⋊C8C23×C512yes—
404C4⋊C8C23×C512yes—
405#103—24no—
406#103—24no—
407#103—22no—
408#103—22no—
409#103—22no—
410#102—22no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413#97—21no—
414#97—21no—
415C4×C8—21no—
416C4×C8C23×C512yes—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5#45512yes—
426C22×C5C2×#12011yescharacteristic
427C4×C5—21no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—21no—
431C4×C5—41no—
432C4×C5—41no—
433C4×C5—41no—
434C4×C5—41no—
435C4×C5—42no—
436C4×C5—42no—
437C4×C5—41no—
438C4×C5—41no—
439C4×C5—82no—
440C4×C5#57712yes—
441C4×C5#57812yes—
442#41—84no—
443C2×Q8—22no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—44no—
447C2×Q8—41no—
448C2×Q8—82no—
449C2×Q8C2×C5×D411yescharacteristic
450C2×Q8C2×C5×D411yescharacteristic
451C2×Q8C2×C5×D412yes—
452C2×Q8C2×C5×D412yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4C2×C5×D411yescharacteristic
457C2×D4C2×C5×D411yescharacteristic
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4C2×C5×D411yescharacteristic
465C22×C4C2×C5×D411yescharacteristic
466C22×C4C2×C5×D411yescharacteristic
467Q16—82no—
468SD16—82no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—42no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4C2×C5×D411yescharacteristic
498C4⋊C4C2×C5×D411yescharacteristic
499C4⋊C4C2×C5×D411yescharacteristic
500C4⋊C4C2×C5×D411yescharacteristic
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C42—22no—
516C42—22no—
517C42—21no—
518C42—21no—
519C42C2×C5×D411yescharacteristic
520C42C2×C5×D411yescharacteristic
521C42C2×C5×D411yescharacteristic
522C42C24×C511yescharacteristic
523C2×C5—22no—
524C2×C5—81no—
525C2×C5—81no—
526C2×C5#301011yescharacteristic
527C2×C5#301111yescharacteristic
528C2×C5C2×#45511yescharacteristic
529C23—21no—
530C23—21no—
531C23C5×#12011yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—42no—
535Q8—42no—
536Q8—42no—
537Q8—42no—
538Q8—82no—
539Q8—82no—
540Q8—82no—
541D4—22no—
542D4—22no—
543D4—42no—
544D4—42no—
545D4—82no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—44no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—82no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4C5×#12011yescharacteristic
565C2×C4C5×#12011yescharacteristic
566C2×C4C5×#12011yescharacteristic
567C2×C4C22×C5×D411yescharacteristic
568C2×C4C22×C5×D411yescharacteristic
569C2×C4C22×C5×D411yescharacteristic
570C8—42no—
571C8—42no—
572C8—42no—
573C5#1869011yescharacteristic, direct product factor, Sylow
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C5×#45512yes—
583C22C2×C5×#12011yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—82no—
597C4C5×#57712yes—
598C4C5×#57812yes—
599C2—22no—
600C2—81no—
601C2—81no—
602C2C5×#301011yescharacteristic
603C2C5×#301111yescharacteristic
604C2C2×C5×#45511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3544C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3239C2semidirect
3. C5×#3218C2semidirect
4. C2×C5×#487C2semidirect
5. C5×#1646C2semidirect
6. C5×#1645C2semidirect
7. C5×#1644C2semidirect
8. C5×#1643C2semidirect
9. C5×#1558C2semidirect
10. C5×#1494C2semidirect
11. C5×#1494C2semidirect
55. #18690C5direct (N × H)
148. #3239C2×C5semidirect
149. #3218C2×C5semidirect
150. C2×#487C2×C5semidirect
151. #1646C2×C5semidirect
152. #1645C2×C5semidirect
153. #1644C2×C5semidirect
154. #1643C2×C5semidirect
155. #1558C2×C5semidirect
156. #1494C2×C5semidirect
157. #1494C2×C5semidirect
573. C5#18690direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35442
C5×#32392
C5×#32182
C2×C5×#4872
C5×#16462
C5×#16452
C5×#16442
C5×#16432
C5×#15582
C5×#14942
#186905