Finite Group Databasebeta

← C5×#18700 #11941420

Subgroups — C5×#18700 #11941420

Order 1280.

878 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3552C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic, complemented
3C5×#3218C211yesmaximal, characteristic, complemented
4C2×C5×#498C211yesmaximal, characteristic, complemented
5C5×#1654C212yesmaximal, complemented
6C5×#1653C212yesmaximal, complemented
7C5×#1652C212yesmaximal, complemented
8C5×#1651C212yesmaximal, complemented
9C5×#1556C211yesmaximal, characteristic, complemented
10C5×#1494C211yesmaximal, characteristic, complemented
11C5×#1494C211yesmaximal, characteristic, complemented
12C5×#563—22no—
13C5×#557C2211yescharacteristic
14C5×#556C2211yescharacteristic
15C5×#554—21no—
16C5×#553—21no—
17C5×D4×Q8—21no—
18C5×D4×Q8C2211yescharacteristic
19C5×#548—21no—
20C5×#547C2211yescharacteristic
21C5×#544—21no—
22C5×#542—21no—
23C5×#541—21no—
24C5×#539—22no—
25C5×#536—21no—
26C2×C5×C4⋊Q8C2211yescharacteristic
27C2×C5×C4⋊Q8C2211yescharacteristic
28C5×#529C2211yescharacteristic
29C5×#529C2211yescharacteristic
30C5×#501—21no—
31C5×#498—22no—
32C5×#498C2212yes—
33C5×#498C2212yes—
34C5×#497—21no—
35C5×#491—21no—
36C5×#489—21no—
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×#106—22no—
48C2×C4×C5×C8C2211yescharacteristic
49C5×#332C2212yes—
50C5×#332C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×D4⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18700C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C22×C5×Q8—21no—
58C22×C5×Q8—21no—
59C22×C5×Q8—21no—
60C2×C5×Q16—22no—
61C2×C5×SD16—22no—
62C22×C5×C8—21no—
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—22no—
78C5×#126—21no—
79C5×#126—21no—
80C5×#125—22no—
81C5×#125—22no—
82C5×#125—22no—
83C5×#125—21no—
84C5×#125D411yescharacteristic
85C5×#125D411yescharacteristic
86C5×#124—22no—
87C5×#124—21no—
88C5×#124D411yescharacteristic
89C5×#124D411yescharacteristic
90C5×#123—22no—
91C5×#123—22no—
92C5×#123—21no—
93C5×#123—21no—
94C5×#123—22no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8—22no—
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8—22no—
100C5×C22⋊Q8—21no—
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8—21no—
103C5×C22⋊Q8—21no—
104C5×C22⋊Q8D411yescharacteristic
105C5×C22⋊Q8D411yescharacteristic
106C5×#121—22no—
107C5×#121—21no—
108C5×#121D411yescharacteristic
109C5×#121D411yescharacteristic
110C4×C5×Q8—21no—
111C4×C5×Q8—21no—
112C4×C5×Q8—21no—
113C4×C5×Q8C2311yescharacteristic
114C4×C5×Q8C2311yescharacteristic
115C4×C5×D4—22no—
116C4×C5×D4—22no—
117C4×C5×D4—21no—
118C4×C5×D4—21no—
119C4×C5×D4—21no—
120C4×C5×D4C2311yescharacteristic
121C4×C5×D4C2311yescharacteristic
122C5×#117—21no—
123C5×#117—21no—
124C5×#117—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4—21no—
128C2×C5×C4⋊C4—21no—
129C2×C5×C4⋊C4D412yes—
130C2×C42×C5C2311yescharacteristic
131C5×#107—22no—
132C5×#106—24no—
133C5×#106—24no—
134C5×#106—22no—
135C5×C4⋊C8C2312yes—
136C5×C4⋊C8C2312yes—
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#3552C2×C511yescharacteristic
148#3239C2×C511yescharacteristic, complemented
149#3218C2×C511yescharacteristic, complemented
150C2×#498C2×C511yescharacteristic, complemented
151#1654C2×C512yescomplemented
152#1653C2×C512yescomplemented
153#1652C2×C512yescomplemented
154#1651C2×C512yescomplemented
155#1556C2×C511yescharacteristic, complemented
156#1494C2×C511yescharacteristic, complemented
157#1494C2×C511yescharacteristic, complemented
158C5×#41—82no—
159C2×C5×Q8—22no—
160C2×C5×Q8—22no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—22no—
164C2×C5×Q8—41no—
165C2×C5×Q8—82no—
166C2×C5×Q8—82no—
167C2×C5×Q8—82no—
168C2×C5×Q8C2×D411yescharacteristic
169C2×C5×Q8C2×D411yescharacteristic
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—22no—
173C2×C5×D4C2×D411yescharacteristic
174C2×C5×D4C2×D411yescharacteristic
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—41no—
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C5×Q16—82no—
185C5×SD16—82no—
186C2×C5×C8—24no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C2×C5×C8—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—22no—
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—22no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4C2×D411yescharacteristic
213C5×C4⋊C4C2×D412yes—
214C5×C4⋊C4C2×D412yes—
215C5×C4⋊C4C2×D411yescharacteristic
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—22no—
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—
231C5×C22⋊C4—21no—
232C42×C5—22no—
233C42×C5—22no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5C2×D411yescharacteristic
237C42×C5C2×D411yescharacteristic
238C42×C5C2×D411yescharacteristic
239C42×C5C2411yescharacteristic
240#563—22no—
241#557C22×C511yescharacteristic
242#556C22×C511yescharacteristic
243#554—21no—
244#553—21no—
245D4×Q8—21no—
246D4×Q8C22×C511yescharacteristic
247#548—21no—
248#547C22×C511yescharacteristic
249#544—21no—
250#542—21no—
251#541—21no—
252#539—22no—
253#536—21no—
254C2×C4⋊Q8C22×C511yescharacteristic
255C2×C4⋊Q8C22×C511yescharacteristic
256#529C22×C511yescharacteristic
257#529C22×C511yescharacteristic
258#501—21no—
259#498—22no—
260#498C22×C512yes—
261#498C22×C512yes—
262#497—21no—
263#491—21no—
264#489—21no—
265#484—21no—
266#481—21no—
267#475C22×C512yes—
268#474C22×C512yes—
269#462C22×C512yes—
270#461C22×C512yes—
271#451—21no—
272#448—21no—
273#432C22×C511yescharacteristic
274#432C22×C511yescharacteristic
275C2×#106—22no—
276C2×C4×C8C22×C511yescharacteristic
277#332C22×C512yes—
278#332C22×C512yes—
279Q8⋊C8C22×C512yes—
280Q8⋊C8C22×C512yes—
281D4⋊C8C22×C512yes—
282D4⋊C8C22×C512yes—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5#12011yescharacteristic
286C5×Q8—22no—
287C5×Q8—22no—
288C5×Q8—42no—
289C5×Q8—42no—
290C5×Q8—42no—
291C5×Q8—42no—
292C5×Q8—82no—
293C5×Q8—82no—
294C5×Q8—82no—
295C5×D4—22no—
296C5×D4—22no—
297C5×D4—42no—
298C5×D4—42no—
299C5×D4—82no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—21no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—21no—
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—82no—
318C2×C4×C5#12011yescharacteristic
319C2×C4×C5#12011yescharacteristic
320C2×C4×C5#12011yescharacteristic
321C2×C4×C5C22×D411yescharacteristic
322C2×C4×C5C22×D411yescharacteristic
323C2×C4×C5C22×D411yescharacteristic
324C5×C8—24no—
325C5×C8—42no—
326C5×C8—42no—
327C2×#41—21no—
328C22×Q8—21no—
329C22×Q8—21no—
330C22×Q8—21no—
331C2×Q16—22no—
332C2×SD16—22no—
333C22×C8—21no—
334C4⋊Q8—22no—
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8C5×D412yes—
343C4⋊Q8C23×C512yes—
344C4⋊Q8C23×C511yescharacteristic
345C4⋊Q8C23×C511yescharacteristic
346#126—22no—
347#126—22no—
348#126—22no—
349#126—21no—
350#126—21no—
351#125—22no—
352#125—22no—
353#125—22no—
354#125—21no—
355#125C5×D411yescharacteristic
356#125C5×D411yescharacteristic
357#124—22no—
358#124—21no—
359#124C5×D411yescharacteristic
360#124C5×D411yescharacteristic
361#123—22no—
362#123—22no—
363#123—21no—
364#123—21no—
365#123—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8C5×D411yescharacteristic
376C22⋊Q8C5×D411yescharacteristic
377#121—22no—
378#121—21no—
379#121C5×D411yescharacteristic
380#121C5×D411yescharacteristic
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8C23×C511yescharacteristic
385C4×Q8C23×C511yescharacteristic
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C23×C511yescharacteristic
392C4×D4C23×C511yescharacteristic
393#117—21no—
394#117—21no—
395#117—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4C5×D412yes—
401C2×C42C23×C511yescharacteristic
402#107—22no—
403#106—24no—
404#106—24no—
405#106—22no—
406C4⋊C8C23×C512yes—
407C4⋊C8C23×C512yes—
408#103—22no—
409#103—22no—
410#103—22no—
411#102—22no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414#97—21no—
415#97—21no—
416C4×C8—21no—
417C4×C8C23×C512yes—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5#45612yes—
427C22×C5C2×#12011yescharacteristic
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—21no—
431C4×C5—21no—
432C4×C5—41no—
433C4×C5—42no—
434C4×C5—41no—
435C4×C5—42no—
436C4×C5—41no—
437C4×C5—41no—
438C4×C5—41no—
439C4×C5—41no—
440C4×C5—82no—
441C4×C5#57712yes—
442C4×C5#57712yes—
443#41—82no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—22no—
449C2×Q8—41no—
450C2×Q8—82no—
451C2×Q8—82no—
452C2×Q8—82no—
453C2×Q8C2×C5×D411yescharacteristic
454C2×Q8C2×C5×D411yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4C2×C5×D411yescharacteristic
459C2×D4C2×C5×D411yescharacteristic
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×C5×D411yescharacteristic
467C22×C4C2×C5×D411yescharacteristic
468C22×C4C2×C5×D411yescharacteristic
469Q16—82no—
470SD16—82no—
471C2×C8—24no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
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×D412yes—
500C4⋊C4C2×C5×D412yes—
501C4⋊C4C2×C5×D411yescharacteristic
502C4⋊C4C2×C5×D411yescharacteristic
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C42—22no—
518C42—22no—
519C42—21no—
520C42—21no—
521C42C2×C5×D411yescharacteristic
522C42C2×C5×D411yescharacteristic
523C42C2×C5×D411yescharacteristic
524C42C24×C511yescharacteristic
525C2×C5—22no—
526C2×C5—81no—
527C2×C5—81no—
528C2×C5#300911yescharacteristic
529C2×C5#301011yescharacteristic
530C2×C5C2×#45611yescharacteristic
531C23—21no—
532C23—21no—
533C23C5×#12011yescharacteristic
534Q8—22no—
535Q8—22no—
536Q8—42no—
537Q8—42no—
538Q8—42no—
539Q8—42no—
540Q8—82no—
541Q8—82no—
542Q8—82no—
543D4—22no—
544D4—22no—
545D4—42no—
546D4—42no—
547D4—82no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4C5×#12011yescharacteristic
567C2×C4C5×#12011yescharacteristic
568C2×C4C5×#12011yescharacteristic
569C2×C4C22×C5×D411yescharacteristic
570C2×C4C22×C5×D411yescharacteristic
571C2×C4C22×C5×D411yescharacteristic
572C8—24no—
573C8—42no—
574C8—42no—
575C5#1870011yescharacteristic, direct product factor, Sylow
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22C5×#45612yes—
585C22C2×C5×#12011yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—82no—
599C4C5×#57712yes—
600C4C5×#57712yes—
601C2—22no—
602C2—81no—
603C2—81no—
604C2C5×#300911yescharacteristic
605C2C5×#301011yescharacteristic
606C2C2×C5×#45611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3552C2
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×#498C2semidirect
5. C5×#1654C2semidirect
6. C5×#1653C2semidirect
7. C5×#1652C2semidirect
8. C5×#1651C2semidirect
9. C5×#1556C2semidirect
10. C5×#1494C2semidirect
11. C5×#1494C2semidirect
55. #18700C5direct (N × H)
148. #3239C2×C5semidirect
149. #3218C2×C5semidirect
150. C2×#498C2×C5semidirect
151. #1654C2×C5semidirect
152. #1653C2×C5semidirect
153. #1652C2×C5semidirect
154. #1651C2×C5semidirect
155. #1556C2×C5semidirect
156. #1494C2×C5semidirect
157. #1494C2×C5semidirect
575. C5#18700direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35522
C5×#32392
C5×#32182
C2×C5×#4982
C5×#16542
C5×#16532
C5×#16522
C5×#16512
C5×#15562
C5×#14942
#187005