Finite Group Databasebeta

← C5×#18579 #11941299

Subgroups — C5×#18579 #11941299

Order 1280.

932 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3520C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic, complemented
3C5×#3139C211yesmaximal, characteristic, complemented
4C2×C5×#476C211yesmaximal, characteristic, complemented
5C5×#1638C212yesmaximal, complemented
6C5×#1637C212yesmaximal, complemented
7C5×#1635C212yesmaximal, complemented
8C5×#1635C212yesmaximal, complemented
9C5×#1552C211yesmaximal, characteristic, complemented
10C5×#1490C211yesmaximal, characteristic, complemented
11C5×#1483C211yesmaximal, characteristic, complemented
12C5×#556C2211yescharacteristic
13C5×#554—21no—
14C5×#552—21no—
15C5×#551—22no—
16C5×D4×Q8C2211yescharacteristic
17C5×#548—21no—
18C5×#547C2211yescharacteristic
19C5×#547C2211yescharacteristic
20C5×#546—21no—
21C5×#542—21no—
22C5×#539—22no—
23C5×#533C2211yescharacteristic
24C2×C5×C4⋊Q8C2211yescharacteristic
25C5×#529C2211yescharacteristic
26C5×#525—21no—
27C2×C5×C22⋊Q8—21no—
28C5×#520—21no—
29C2×C4×C5×D4C2211yescharacteristic
30C5×#501—21no—
31C5×#491—22no—
32C5×#489—21no—
33C5×#487C2212yescomplemented
34C5×#487C2212yescomplemented
35C5×#483—21no—
36C5×#480—21no—
37C5×#477C2212yescomplemented
38C5×#476—21no—
39C5×#476—21no—
40C5×#476C2212yes—
41C5×#476C2212yes—
42C5×#476C2212yescomplemented
43C5×#432C2211yescharacteristic
44C2×C5×#106—21no—
45C2×C5×C4⋊C8C2211yescharacteristic
46C5×#419—22no—
47C2×C5×#102—21no—
48C4×C5×M16C2211yescharacteristic
49C5×#332C2212yescomplemented
50C5×#332C2212yescomplemented
51C5×Q8⋊C8C2212yescomplemented
52C5×D4⋊C8C2212yes—
53C5×D4⋊C8C2212yes—
54C5×D4⋊C8C2212yescomplemented
55#18579C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C2×C5×#41—21no—
58C22×C5×Q8—21no—
59C22×C5×Q8—21no—
60C22×C5×D4D411yescharacteristic
61C23×C4×C5—21no—
62C2×C5×M16—21no—
63C22×C5×C8—21no—
64C5×C4⋊Q8—21no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8C2312yes—
69C5×C4⋊Q8C2311yescharacteristic
70C5×C4⋊Q8C2311yescharacteristic
71C5×#126—22no—
72C5×#126—22no—
73C5×#126—21no—
74C5×#125—22no—
75C5×#125D412yes—
76C5×#125D411yescharacteristic
77C5×#124—22no—
78C5×#124—21no—
79C5×#124D411yescharacteristic
80C5×#123—22no—
81C5×#123—22no—
82C5×#123—21no—
83C5×#123—22no—
84C5×#123—22no—
85C5×C22⋊Q8—22no—
86C5×C22⋊Q8—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8—21no—
92C5×C22⋊Q8—21no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8D411yescharacteristic
96C5×#121—22no—
97C5×#121—21no—
98C5×#121—21no—
99C5×#121D411yescharacteristic
100C5×#120—22no—
101C4×C5×Q8—21no—
102C4×C5×Q8—21no—
103C4×C5×Q8—21no—
104C4×C5×Q8C2311yescharacteristic
105C4×C5×D4—22no—
106C4×C5×D4—22no—
107C4×C5×D4—22no—
108C4×C5×D4—21no—
109C4×C5×D4—21no—
110C4×C5×D4—21no—
111C4×C5×D4—21no—
112C4×C5×D4D411yescharacteristic
113C4×C5×D4D411yescharacteristic
114C4×C5×D4C2311yescharacteristic
115C4×C5×D4C2311yescharacteristic
116C4×C5×D4C2311yescharacteristic
117C5×#117—22no—
118C5×#117—21no—
119C5×#117—21no—
120C5×#117D412yes—
121C2×C5×C4⋊C4—22no—
122C2×C5×C4⋊C4—21no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4D411yescharacteristic
127C2×C5×C22⋊C4—22no—
128C2×C5×C22⋊C4—21no—
129C2×C42×C5C2311yescharacteristic
130C5×#107—22no—
131C5×#106—22no—
132C5×#106—22no—
133C5×#106—22no—
134C5×C4⋊C8—21no—
135C5×C4⋊C8C2312yes—
136C5×C4⋊C8C2312yes—
137C5×#103—22no—
138C5×#103—24no—
139C5×#103—24no—
140C5×#102—22no—
141C5×#102—22no—
142C5×#102—22no—
143C5×C22⋊C8—21no—
144C5×#97—21no—
145C5×#97—21no—
146C4×C5×C8C2312yes—
147#3520C2×C511yescharacteristic
148#3238C2×C511yescharacteristic, complemented
149#3139C2×C511yescharacteristic, complemented
150C2×#476C2×C511yescharacteristic, complemented
151#1638C2×C512yescomplemented
152#1637C2×C512yescomplemented
153#1635C2×C512yescomplemented
154#1635C2×C512yescomplemented
155#1552C2×C511yescharacteristic, complemented
156#1490C2×C511yescharacteristic, complemented
157#1483C2×C511yescharacteristic, complemented
158C24×C5—21no—
159C5×#41—42no—
160C5×#41—42no—
161C5×#41—82no—
162C2×C5×Q8—22no—
163C2×C5×Q8—21no—
164C2×C5×Q8—21no—
165C2×C5×Q8—22no—
166C2×C5×Q8—44no—
167C2×C5×Q8—41no—
168C2×C5×Q8—82no—
169C2×C5×Q8C2×D411yescharacteristic
170C2×C5×D4—22no—
171C2×C5×D4—22no—
172C2×C5×D4—21no—
173C2×C5×D4—22no—
174C2×C5×D4—21no—
175C2×C5×D4—41no—
176C2×C5×D4C2×D411yescharacteristic
177C2×C5×D4C2×D411yescharacteristic
178C2×C5×D4C2×D411yescharacteristic
179C22×C4×C5—22no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—41no—
189C22×C4×C5—82no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C5×M16—42no—
194C2×C5×C8—22no—
195C2×C5×C8—22no—
196C2×C5×C8—22no—
197C2×C5×C8—42no—
198C5×C4⋊C4—22no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—22no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—41no—
214C5×C4⋊C4—41no—
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C4⋊C4C2×D411yescharacteristic
219C5×C4⋊C4C2×D412yes—
220C5×C4⋊C4C2×D412yes—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—21no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—21no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—21no—
232C5×C22⋊C4—21no—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—21no—
235C5×C22⋊C4—21no—
236C42×C5—22no—
237C42×C5—22no—
238C42×C5—21no—
239C42×C5C2×D411yescharacteristic
240C42×C5C2×D411yescharacteristic
241C42×C5C2×D411yescharacteristic
242C42×C5C2411yescharacteristic
243#556C22×C511yescharacteristic
244#554—21no—
245#552—21no—
246#551—22no—
247D4×Q8C22×C511yescharacteristic
248#548—21no—
249#547C22×C511yescharacteristic
250#547C22×C511yescharacteristic
251#546—21no—
252#542—21no—
253#539—22no—
254#533C22×C511yescharacteristic
255C2×C4⋊Q8C22×C511yescharacteristic
256#529C22×C511yescharacteristic
257#525—21no—
258C2×C22⋊Q8—21no—
259#520—21no—
260C2×C4×D4C22×C511yescharacteristic
261#501—21no—
262#491—22no—
263#489—21no—
264#487C22×C512yescomplemented
265#487C22×C512yescomplemented
266#483—21no—
267#480—21no—
268#477C22×C512yescomplemented
269#476—21no—
270#476—21no—
271#476C22×C512yes—
272#476C22×C512yes—
273#476C22×C512yescomplemented
274#432C22×C511yescharacteristic
275C2×#106—21no—
276C2×C4⋊C8C22×C511yescharacteristic
277#419—22no—
278C2×#102—21no—
279C4×M16C22×C511yescharacteristic
280#332C22×C512yescomplemented
281#332C22×C512yescomplemented
282Q8⋊C8C22×C512yescomplemented
283D4⋊C8C22×C512yes—
284D4⋊C8C22×C512yes—
285D4⋊C8C22×C512yescomplemented
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—42no—
290C23×C5—42no—
291C23×C5—81no—
292C23×C5#12011yescharacteristic
293C5×Q8—22no—
294C5×Q8—44no—
295C5×Q8—41no—
296C5×Q8—41no—
297C5×Q8—42no—
298C5×Q8—82no—
299C5×Q8—82no—
300C5×D4—21no—
301C5×D4—21no—
302C5×D4—21no—
303C5×D4—22no—
304C5×D4—42no—
305C5×D4—44no—
306C5×D4—42no—
307C5×D4—82no—
308C5×D4#13712yes—
309C2×C4×C5—22no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—22no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—22no—
318C2×C4×C5—21no—
319C2×C4×C5—21no—
320C2×C4×C5—44no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—81no—
327C2×C4×C5—81no—
328C2×C4×C5—81no—
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—21no—
342C2×#41—21no—
343C22×Q8—21no—
344C22×Q8—21no—
345C22×D4C5×D411yescharacteristic
346C23×C4—21no—
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8C23×C512yes—
354C4⋊Q8C23×C511yescharacteristic
355C4⋊Q8C23×C511yescharacteristic
356#126—22no—
357#126—22no—
358#126—21no—
359#125—22no—
360#125C5×D411yescharacteristic
361#125C5×D412yes—
362#124—22no—
363#124—21no—
364#124C5×D411yescharacteristic
365#123—22no—
366#123—22no—
367#123—21no—
368#123—22no—
369#123—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—22no—
379C22⋊Q8—21no—
380C22⋊Q8C5×D411yescharacteristic
381#121—22no—
382#121—21no—
383#121—21no—
384#121C5×D411yescharacteristic
385#120—22no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C23×C511yescharacteristic
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4C5×D411yescharacteristic
398C4×D4C5×D411yescharacteristic
399C4×D4C23×C511yescharacteristic
400C4×D4C23×C511yescharacteristic
401C4×D4C23×C511yescharacteristic
402#117—22no—
403#117—21no—
404#117—21no—
405#117C5×D412yes—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4C5×D411yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—21no—
414C2×C42C23×C511yescharacteristic
415#107—22no—
416#106—22no—
417#106—22no—
418#106—22no—
419C4⋊C8—21no—
420C4⋊C8C23×C512yes—
421C4⋊C8C23×C512yes—
422#103—22no—
423#103—24no—
424#103—24no—
425#102—22no—
426#102—22no—
427#102—22no—
428C22⋊C8—21no—
429#97—21no—
430#97—21no—
431C4×C8C23×C512yes—
432C22×C5—21no—
433C22×C5—21no—
434C22×C5—22no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—84no—
444C22×C5#45412yes—
445C22×C5C2×#12011yescharacteristic
446C4×C5—21no—
447C4×C5—21no—
448C4×C5—21no—
449C4×C5—21no—
450C4×C5—41no—
451C4×C5—42no—
452C4×C5—41no—
453C4×C5—41no—
454C4×C5—42no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5—82no—
458C4×C5C2×#13711yescharacteristic
459C4×C5#57511yescharacteristic
460C4×C5#57712yes—
461C24—21no—
462#41—42no—
463#41—42no—
464#41—82no—
465C2×Q8—22no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—22no—
469C2×Q8—44no—
470C2×Q8—41no—
471C2×Q8—82no—
472C2×Q8C2×C5×D411yescharacteristic
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4C2×C5×D411yescharacteristic
480C2×D4C2×C5×D411yescharacteristic
481C2×D4C2×C5×D411yescharacteristic
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—41no—
492C22×C4—82no—
493C22×C4C2×C5×D411yescharacteristic
494C22×C4C2×C5×D411yescharacteristic
495C22×C4C2×C5×D411yescharacteristic
496M16—42no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—42no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4C2×C5×D412yes—
519C4⋊C4C2×C5×D412yes—
520C4⋊C4C2×C5×D411yescharacteristic
521C4⋊C4C2×C5×D411yescharacteristic
522C4⋊C4C2×C5×D411yescharacteristic
523C4⋊C4C2×C5×D411yescharacteristic
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C42—22no—
540C42—22no—
541C42—21no—
542C42C2×C5×D411yescharacteristic
543C42C2×C5×D411yescharacteristic
544C42C2×C5×D411yescharacteristic
545C42C24×C511yescharacteristic
546C2×C5—22no—
547C2×C5—42no—
548C2×C5—81no—
549C2×C5—81no—
550C2×C5#300711yescharacteristic
551C2×C5#300911yescharacteristic
552C2×C5C2×#45411yescharacteristic
553C23—21no—
554C23—21no—
555C23—21no—
556C23—42no—
557C23—42no—
558C23—81no—
559C23C5×#12011yescharacteristic
560Q8—22no—
561Q8—44no—
562Q8—41no—
563Q8—41no—
564Q8—42no—
565Q8—82no—
566Q8—82no—
567D4—21no—
568D4—21no—
569D4—21no—
570D4—22no—
571D4—42no—
572D4—44no—
573D4—42no—
574D4—82no—
575D4C5×#13712yes—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—44no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4C5×#12011yescharacteristic
600C2×C4C5×#12011yescharacteristic
601C2×C4C5×#12011yescharacteristic
602C2×C4C22×C5×D411yescharacteristic
603C2×C4C22×C5×D411yescharacteristic
604C2×C4C22×C5×D411yescharacteristic
605C8—42no—
606C8—42no—
607C8—42no—
608C5#1857911yescharacteristic, direct product factor, Sylow
609C22—21no—
610C22—21no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—84no—
621C22C5×#45412yes—
622C22C2×C5×#12011yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—41no—
633C4—41no—
634C4—82no—
635C4C2×C5×#13711yescharacteristic
636C4C5×#57511yescharacteristic
637C4C5×#57712yes—
638C2—22no—
639C2—42no—
640C2—81no—
641C2—81no—
642C2C5×#300711yescharacteristic
643C2C5×#300911yescharacteristic
644C2C2×C5×#45411yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3520C2
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×#3238C2semidirect
3. C5×#3139C2semidirect
4. C2×C5×#476C2semidirect
5. C5×#1638C2semidirect
6. C5×#1637C2semidirect
7. C5×#1635C2semidirect
8. C5×#1635C2semidirect
9. C5×#1552C2semidirect
10. C5×#1490C2semidirect
11. C5×#1483C2semidirect
33. C5×#487C22semidirect
34. C5×#487C22semidirect
37. C5×#477C22semidirect
42. C5×#476C22semidirect
49. C5×#332C22semidirect
50. C5×#332C22semidirect
51. C5×Q8⋊C8C22semidirect
54. C5×D4⋊C8C22semidirect
55. #18579C5direct (N × H)
148. #3238C2×C5semidirect
149. #3139C2×C5semidirect
150. C2×#476C2×C5semidirect
151. #1638C2×C5semidirect
152. #1637C2×C5semidirect
153. #1635C2×C5semidirect
154. #1635C2×C5semidirect
155. #1552C2×C5semidirect
156. #1490C2×C5semidirect
157. #1483C2×C5semidirect
264. #487C22×C5semidirect
265. #487C22×C5semidirect
268. #477C22×C5semidirect
273. #476C22×C5semidirect
280. #332C22×C5semidirect
281. #332C22×C5semidirect
282. Q8⋊C8C22×C5semidirect
285. D4⋊C8C22×C5semidirect
608. C5#18579direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35202
C5×#32382
C5×#31392
C2×C5×#4762
C5×#16382
C5×#16372
C5×#16352
C5×#15522
C5×#14902
C5×#14832
#185795