Finite Group Databasebeta

← C5×#18573 #11941293

Subgroups — C5×#18573 #11941293

Order 1280.

934 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3522C211yesmaximal, characteristic
2C5×#3218C211yesmaximal, characteristic, complemented
3C5×#3141C211yesmaximal, characteristic, complemented
4C2×C5×#475C211yesmaximal, characteristic, complemented
5C5×#1645C212yesmaximal, complemented
6C5×#1643C212yesmaximal, complemented
7C5×#1642C212yesmaximal, complemented
8C5×#1640C212yesmaximal, complemented
9C5×#1551C211yesmaximal, characteristic, complemented
10C5×#1491C211yesmaximal, characteristic, complemented
11C5×#1483C211yesmaximal, characteristic, complemented
12C5×#559—21no—
13C5×#559C2211yescharacteristic
14C5×Q82C2211yescharacteristic
15C5×#554—21no—
16C5×#554C2211yescharacteristic
17C5×#550C2211yescharacteristic
18C5×#548—21no—
19C5×#547—22no—
20C5×#547—21no—
21C5×#542—22no—
22C5×#542—21no—
23C5×#532—21no—
24C5×#532C2211yescharacteristic
25C2×C5×C4⋊Q8C2211yescharacteristic
26C5×#529—21no—
27C5×#529C2211yescharacteristic
28C5×#520—21no—
29C2×C4×C5×Q8C2211yescharacteristic
30C5×#497—21no—
31C5×#491—21no—
32C5×#489—22no—
33C5×#487C2212yes—
34C5×#486C2212yes—
35C5×#475—21no—
36C5×#475—21no—
37C5×#475C2212yes—
38C5×#475C2212yes—
39C5×#462C2212yes—
40C5×#461C2212yes—
41C5×#451—21no—
42C5×#448—21no—
43C5×#432C2211yescharacteristic
44C2×C5×#106—21no—
45C2×C5×C4⋊C8C2211yescharacteristic
46C5×#417—22no—
47C2×C5×#103—21no—
48C4×C5×M16C2211yescharacteristic
49C5×#333C2212yes—
50C5×#331C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×Q8⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18573C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—22no—
57C2×C5×#41—21no—
58C2×C5×#41D412yes—
59C22×C5×Q8—21no—
60C22×C5×Q8D411yescharacteristic
61C2×C5×Q16—22no—
62C2×C5×SD16—22no—
63C2×C5×M16—21no—
64C22×C5×C8—21no—
65C5×C4⋊Q8—22no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8C2312yes—
72C5×C4⋊Q8C2311yescharacteristic
73C5×#127—21no—
74C5×#127C2311yescharacteristic
75C5×#126—22no—
76C5×#126—21no—
77C5×#125—21no—
78C5×#125D411yescharacteristic
79C5×#124—22no—
80C5×#124—22no—
81C5×#124—21no—
82C5×#124—21no—
83C5×#124D412yes—
84C5×#124D411yescharacteristic
85C5×#123—22no—
86C5×#123—22no—
87C5×#123—22no—
88C5×#123—22no—
89C5×#123—21no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—22no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8D411yescharacteristic
96C5×#121—22no—
97C5×#121—22no—
98C5×#121—21no—
99C5×#121—21no—
100C5×#121—21no—
101C5×#121D411yescharacteristic
102C4×C5×Q8—21no—
103C4×C5×Q8—21no—
104C4×C5×Q8—21no—
105C4×C5×Q8—21no—
106C4×C5×Q8D411yescharacteristic
107C4×C5×Q8D411yescharacteristic
108C4×C5×Q8C2311yescharacteristic
109C4×C5×Q8C2311yescharacteristic
110C4×C5×Q8C2311yescharacteristic
111C4×C5×D4—22no—
112C4×C5×D4—22no—
113C4×C5×D4—22no—
114C4×C5×D4—21no—
115C4×C5×D4—21no—
116C4×C5×D4—21no—
117C4×C5×D4—21no—
118C4×C5×D4—21no—
119C4×C5×D4—21no—
120C4×C5×D4—21no—
121C4×C5×D4C2311yescharacteristic
122C5×#117—22no—
123C5×#117—21no—
124C2×C5×C4⋊C4—22no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4—21no—
128C2×C5×C4⋊C4—21no—
129C2×C5×C4⋊C4D411yescharacteristic
130C2×C42×C5—21no—
131C2×C42×C5C2311yescharacteristic
132C5×#106—22no—
133C5×#106—22no—
134C5×C4⋊C8—21no—
135C5×C4⋊C8C2312yes—
136C5×C4⋊C8C2312yes—
137C5×#103—22no—
138C5×#103—22no—
139C5×#103—24no—
140C5×#103—22no—
141C5×#103—22no—
142C5×#102—24no—
143C5×C22⋊C8—21no—
144C5×#97—21no—
145C5×#97—21no—
146C4×C5×C8C2312yes—
147#3522C2×C511yescharacteristic
148#3218C2×C511yescharacteristic, complemented
149#3141C2×C511yescharacteristic, complemented
150C2×#475C2×C511yescharacteristic, complemented
151#1645C2×C512yescomplemented
152#1643C2×C512yescomplemented
153#1642C2×C512yescomplemented
154#1640C2×C512yescomplemented
155#1551C2×C511yescharacteristic, complemented
156#1491C2×C511yescharacteristic, complemented
157#1483C2×C511yescharacteristic, complemented
158C5×#41—44no—
159C5×#41—42no—
160C5×#41—42no—
161C5×#41—84no—
162C2×C5×Q8—22no—
163C2×C5×Q8—21no—
164C2×C5×Q8—22no—
165C2×C5×Q8—22no—
166C2×C5×Q8—41no—
167C2×C5×Q8—41no—
168C2×C5×Q8—82no—
169C2×C5×Q8C2×D411yescharacteristic
170C2×C5×Q8C2×D411yescharacteristic
171C2×C5×Q8C2×D411yescharacteristic
172C2×C5×Q8C2×D412yes—
173C2×C5×D4—22no—
174C2×C5×D4—22no—
175C2×C5×D4—21no—
176C2×C5×D4—22no—
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4C2×D411yescharacteristic
180C2×C5×D4C2×D412yes—
181C22×C4×C5—22no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—21no—
187C22×C4×C5—22no—
188C22×C4×C5—41no—
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C5×Q16—82no—
193C5×SD16—82no—
194C5×M16—42no—
195C2×C5×C8—22no—
196C2×C5×C8—22no—
197C2×C5×C8—22no—
198C2×C5×C8—42no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
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—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—22no—
215C5×C4⋊C4—22no—
216C5×C4⋊C4—41no—
217C5×C4⋊C4—41no—
218C5×C4⋊C4C2×D411yescharacteristic
219C5×C4⋊C4C2×D411yescharacteristic
220C5×C4⋊C4C2×D411yescharacteristic
221C5×C4⋊C4C2×D411yescharacteristic
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—21no—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—21no—
233C5×C22⋊C4—21no—
234C42×C5—22no—
235C42×C5—21no—
236C42×C5—21no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5C2×D411yescharacteristic
241C42×C5C2×D411yescharacteristic
242C42×C5C2×D411yescharacteristic
243C42×C5C2411yescharacteristic
244#559—21no—
245#559C22×C511yescharacteristic
246Q82C22×C511yescharacteristic
247#554—21no—
248#554C22×C511yescharacteristic
249#550C22×C511yescharacteristic
250#548—21no—
251#547—22no—
252#547—21no—
253#542—22no—
254#542—21no—
255#532—21no—
256#532C22×C511yescharacteristic
257C2×C4⋊Q8C22×C511yescharacteristic
258#529—21no—
259#529C22×C511yescharacteristic
260#520—21no—
261C2×C4×Q8C22×C511yescharacteristic
262#497—21no—
263#491—21no—
264#489—22no—
265#487C22×C512yes—
266#486C22×C512yes—
267#475—21no—
268#475—21no—
269#475C22×C512yes—
270#475C22×C512yes—
271#462C22×C512yes—
272#461C22×C512yes—
273#451—21no—
274#448—21no—
275#432C22×C511yescharacteristic
276C2×#106—21no—
277C2×C4⋊C8C22×C511yescharacteristic
278#417—22no—
279C2×#103—21no—
280C4×M16C22×C511yescharacteristic
281#333C22×C512yes—
282#331C22×C512yes—
283Q8⋊C8C22×C512yes—
284Q8⋊C8C22×C512yes—
285Q8⋊C8C22×C512yes—
286D4⋊C8C22×C512yes—
287C23×C5—21no—
288C23×C5—22no—
289C23×C5#12011yescharacteristic
290C5×Q8—21no—
291C5×Q8—21no—
292C5×Q8—21no—
293C5×Q8—22no—
294C5×Q8—42no—
295C5×Q8—42no—
296C5×Q8—42no—
297C5×Q8—42no—
298C5×Q8—82no—
299C5×Q8—82no—
300C5×Q8#13712yes—
301C5×D4—22no—
302C5×D4—42no—
303C5×D4—44no—
304C5×D4—44no—
305C5×D4—42no—
306C5×D4—41no—
307C5×D4—41no—
308C5×D4—42no—
309C5×D4—82no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—42no—
323C2×C4×C5—44no—
324C2×C4×C5—42no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—42no—
328C2×C4×C5—82no—
329C2×C4×C5—82no—
330C2×C4×C5—82no—
331C2×C4×C5—82no—
332C2×C4×C5#12011yescharacteristic
333C2×C4×C5#12011yescharacteristic
334C2×C4×C5#12011yescharacteristic
335C2×C4×C5C22×D411yescharacteristic
336C2×C4×C5C22×D411yescharacteristic
337C2×C4×C5C22×D411yescharacteristic
338C5×C8—42no—
339C5×C8—42no—
340C5×C8—42no—
341C2×#41—22no—
342C2×#41—21no—
343C2×#41C5×D412yes—
344C22×Q8—21no—
345C22×Q8C5×D411yescharacteristic
346C2×Q16—22no—
347C2×SD16—22no—
348C2×M16—21no—
349C22×C8—21no—
350C4⋊Q8—22no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8C23×C512yes—
357C4⋊Q8C23×C511yescharacteristic
358#127—21no—
359#127C23×C511yescharacteristic
360#126—22no—
361#126—21no—
362#125—21no—
363#125C5×D411yescharacteristic
364#124—22no—
365#124—22no—
366#124—21no—
367#124—21no—
368#124C5×D411yescharacteristic
369#124C5×D412yes—
370#123—22no—
371#123—22no—
372#123—22no—
373#123—22no—
374#123—21no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8C5×D411yescharacteristic
381#121—22no—
382#121—22no—
383#121—21no—
384#121—21no—
385#121—21no—
386#121C5×D411yescharacteristic
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C5×D411yescharacteristic
392C4×Q8C5×D411yescharacteristic
393C4×Q8C23×C511yescharacteristic
394C4×Q8C23×C511yescharacteristic
395C4×Q8C23×C511yescharacteristic
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C23×C511yescharacteristic
407#117—22no—
408#117—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4C5×D411yescharacteristic
415C2×C42—21no—
416C2×C42C23×C511yescharacteristic
417#106—22no—
418#106—22no—
419C4⋊C8—21no—
420C4⋊C8C23×C512yes—
421C4⋊C8C23×C512yes—
422#103—22no—
423#103—22no—
424#103—24no—
425#103—22no—
426#103—22no—
427#102—24no—
428C22⋊C8—21no—
429#97—21no—
430#97—21no—
431C4×C8C23×C512yes—
432C22×C5—21no—
433C22×C5—21no—
434C22×C5—42no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—42no—
438C22×C5—42no—
439C22×C5—41no—
440C22×C5#45512yes—
441C22×C5C2×#12011yescharacteristic
442C4×C5—21no—
443C4×C5—22no—
444C4×C5—21no—
445C4×C5—21no—
446C4×C5—21no—
447C4×C5—41no—
448C4×C5—41no—
449C4×C5—41no—
450C4×C5—41no—
451C4×C5—41no—
452C4×C5—42no—
453C4×C5—41no—
454C4×C5—82no—
455C4×C5C2×#13711yescharacteristic
456C4×C5#57511yescharacteristic
457C4×C5#57712yes—
458#41—44no—
459#41—42no—
460#41—42no—
461#41—84no—
462C2×Q8—22no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—82no—
469C2×Q8C2×C5×D411yescharacteristic
470C2×Q8C2×C5×D411yescharacteristic
471C2×Q8C2×C5×D411yescharacteristic
472C2×Q8C2×C5×D412yes—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4C2×C5×D411yescharacteristic
480C2×D4C2×C5×D412yes—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4C2×C5×D411yescharacteristic
490C22×C4C2×C5×D411yescharacteristic
491C22×C4C2×C5×D411yescharacteristic
492Q16—82no—
493SD16—82no—
494M16—42no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—42no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4C2×C5×D411yescharacteristic
519C4⋊C4C2×C5×D411yescharacteristic
520C4⋊C4C2×C5×D411yescharacteristic
521C4⋊C4C2×C5×D411yescharacteristic
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C42—22no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42C2×C5×D411yescharacteristic
541C42C2×C5×D411yescharacteristic
542C42C2×C5×D411yescharacteristic
543C42C24×C511yescharacteristic
544C2×C5—22no—
545C2×C5—81no—
546C2×C5—82no—
547C2×C5#300711yescharacteristic
548C2×C5#301011yescharacteristic
549C2×C5C2×#45511yescharacteristic
550C23—21no—
551C23—22no—
552C23C5×#12011yescharacteristic
553Q8—21no—
554Q8—21no—
555Q8—21no—
556Q8—22no—
557Q8—42no—
558Q8—42no—
559Q8—42no—
560Q8—42no—
561Q8—82no—
562Q8—82no—
563Q8C5×#13712yes—
564D4—22no—
565D4—42no—
566D4—44no—
567D4—44no—
568D4—42no—
569D4—41no—
570D4—41no—
571D4—42no—
572D4—82no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4C5×#12011yescharacteristic
596C2×C4C5×#12011yescharacteristic
597C2×C4C5×#12011yescharacteristic
598C2×C4C22×C5×D411yescharacteristic
599C2×C4C22×C5×D411yescharacteristic
600C2×C4C22×C5×D411yescharacteristic
601C8—42no—
602C8—42no—
603C8—42no—
604C5#1857311yescharacteristic, direct product factor, Sylow
605C22—21no—
606C22—21no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—41no—
613C22C5×#45512yes—
614C22C2×C5×#12011yescharacteristic
615C4—21no—
616C4—22no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—82no—
628C4C2×C5×#13711yescharacteristic
629C4C5×#57511yescharacteristic
630C4C5×#57712yes—
631C2—22no—
632C2—81no—
633C2—82no—
634C2C5×#300711yescharacteristic
635C2C5×#301011yescharacteristic
636C2C2×C5×#45511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3522C2
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×#3218C2semidirect
3. C5×#3141C2semidirect
4. C2×C5×#475C2semidirect
5. C5×#1645C2semidirect
6. C5×#1643C2semidirect
7. C5×#1642C2semidirect
8. C5×#1640C2semidirect
9. C5×#1551C2semidirect
10. C5×#1491C2semidirect
11. C5×#1483C2semidirect
55. #18573C5direct (N × H)
148. #3218C2×C5semidirect
149. #3141C2×C5semidirect
150. C2×#475C2×C5semidirect
151. #1645C2×C5semidirect
152. #1643C2×C5semidirect
153. #1642C2×C5semidirect
154. #1640C2×C5semidirect
155. #1551C2×C5semidirect
156. #1491C2×C5semidirect
157. #1483C2×C5semidirect
604. C5#18573direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35222
C5×#32182
C5×#31412
C2×C5×#4752
C5×#16452
C5×#16432
C5×#16422
C5×#16402
C5×#15512
C5×#14912
C5×#14832
#185735