Finite Group Databasebeta

← C5×#11132 #11933852

Subgroups — C5×#11132 #11933852

Order 1280.

864 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2911C211yesmaximal, characteristic, complemented
2C2×C5×#421C211yesmaximal, characteristic
3C5×#2896C211yesmaximal, characteristic
4C2×C5×#410C211yesmaximal, characteristic
5C2×C5×#344C211yesmaximal, characteristic, complemented
6C5×#1740C211yesmaximal, characteristic, complemented
7C2×C5×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×M16C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C2×C5×#117C2211yescharacteristic
12C2×C5×#117C2211yescharacteristic
13C2×C5×#117C2211yescharacteristic
14C2×C5×#117C2211yescharacteristic
15C5×#428—22no—
16C5×#428—22no—
17C5×#427—22no—
18C5×#421—22no—
19C5×#421—22no—
20C2×C5×#104—22no—
21C5×#419C412yescomplemented
22C5×#418C412yescomplemented
23C5×#417—22no—
24C5×#416—22no—
25C5×#410—22no—
26C5×#410—22no—
27C2×C5×#99—22no—
28C5×#344—22no—
29C5×#342—22no—
30C5×H(3,ℤ/4)—22no—
31#11132C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C2×C5×#41—21no—
34C2×C5×#41—21no—
35C2×C5×#41—21no—
36C2×C5×#41—21no—
37C2×C5×#41—21no—
38C2×C5×#41—21no—
39C2×C5×#41—21no—
40C2×C5×#41—21no—
41C2×C5×#41—21no—
42C2×C5×#41D412yes—
43C2×C5×#41Q812yes—
44C22×C5×Q8C2×C411yescharacteristic
45C22×C5×D4—21no—
46C22×C5×D4C2×C411yescharacteristic
47C23×C4×C5—21no—
48C23×C4×C5C2311yescharacteristic
49C2×C5×M16—21no—
50C2×C5×M16—21no—
51C2×C5×M16—21no—
52C2×C5×M16—21no—
53C2×C5×M16—21no—
54C2×C5×M16—21no—
55C2×C5×M16—21no—
56C2×C5×M16—21no—
57C2×C5×M16—21no—
58C2×C5×M16C2×C412yes—
59C2×C5×M16D412yes—
60C2×C5×M16D412yes—
61C22×C5×C8—21no—
62C22×C5×C8D412yes—
63C5×#117—21no—
64C5×#117—21no—
65C5×#117—21no—
66C5×#117—21no—
67C5×#117—21no—
68C5×#117—21no—
69C5×#117—21no—
70C5×#117—21no—
71C5×#117—21no—
72C5×#117—21no—
73C5×#117—21no—
74C5×#117—21no—
75C5×#117—21no—
76C5×#117C2×C412yes—
77C5×#117D412yes—
78C5×#117D412yes—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C22⋊C4—21no—
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4D412yes—
87C2×C42×C5—21no—
88C2×C42×C5—21no—
89C2×C42×C5—21no—
90C2×C42×C5—21no—
91C5×#107—24no—
92C5×#106—24no—
93C5×#104—28no—
94C5×#103—24no—
95C5×#102—24no—
96C5×#99—28no—
97#2911C2×C511yescharacteristic, complemented
98C2×#421C2×C511yescharacteristic
99#2896C2×C511yescharacteristic
100C2×#410C2×C511yescharacteristic
101C2×#344C2×C511yescharacteristic, complemented
102#1740C2×C511yescharacteristic, complemented
103C2×H(3,ℤ/4)C2×C511yescharacteristic, complemented
104C24×C5—21no—
105C24×C5C2×D411yescharacteristic
106C5×#41—22no—
107C5×#41—22no—
108C5×#41—22no—
109C5×#41—22no—
110C5×#41—22no—
111C5×#41—22no—
112C5×#41—22no—
113C5×#41—22no—
114C5×#41—41no—
115C5×#41—41no—
116C5×#41—41no—
117C5×#41—41no—
118C5×#41—41no—
119C5×#41—41no—
120C5×#41—41no—
121C5×#41—41no—
122C2×C5×Q8—21no—
123C2×C5×Q8—21no—
124C2×C5×Q8—21no—
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127C2×C5×Q8C4⋊C412yes—
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—41no—
136C2×C5×D4—41no—
137C2×C5×D4—41no—
138C2×C5×D4—41no—
139C2×C5×D4C4⋊C412yes—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—41no—
145C22×C4×C5—41no—
146C22×C4×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5—41no—
149C22×C4×C5—41no—
150C22×C4×C5—41no—
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×Q811yescharacteristic
159C22×C4×C5#4111yescharacteristic
160C22×C4×C5#4111yescharacteristic
161C22×C4×C5#4111yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C22×C4×C5#4111yescharacteristic
164C22×C4×C5#4111yescharacteristic
165C5×M16—22no—
166C5×M16—22no—
167C5×M16—22no—
168C5×M16—22no—
169C5×M16—22no—
170C5×M16—22no—
171C5×M16—41no—
172C5×M16—41no—
173C2×C5×C8—22no—
174C2×C5×C8—22no—
175C2×C5×C8—22no—
176C2×C5×C8—41no—
177C2×C5×C8—41no—
178C2×C5×C8C22⋊C414yes—
179C5×C4⋊C4—22no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—41no—
183C5×C4⋊C4—41no—
184C5×C4⋊C4—41no—
185C5×C4⋊C4—41no—
186C5×C4⋊C4—41no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C5×C22⋊C4—41no—
193C5×C22⋊C4—41no—
194C5×C22⋊C4—41no—
195C42×C5—22no—
196C42×C5—22no—
197C42×C5—22no—
198C42×C5—41no—
199C42×C5—41no—
200C42×C5—41no—
201C42×C5—41no—
202C42×C5—41no—
203C22×#41C22×C511yescharacteristic
204C22×M16C22×C511yescharacteristic
205C22×M16C22×C511yescharacteristic
206C2×#117C22×C511yescharacteristic
207C2×#117C22×C511yescharacteristic
208C2×#117C22×C511yescharacteristic
209C2×#117C22×C511yescharacteristic
210#428—22no—
211#428—22no—
212#427—22no—
213#421—22no—
214#421—22no—
215C2×#104—22no—
216#419C4×C512yescomplemented
217#418C4×C512yescomplemented
218#417—22no—
219#416—22no—
220#410—22no—
221#410—22no—
222C2×#99—22no—
223#344—22no—
224#342—22no—
225H(3,ℤ/4)—22no—
226C23×C5—22no—
227C23×C5—41no—
228C23×C5—41no—
229C23×C5—81no—
230C23×C5—82no—
231C23×C5C4×D411yescharacteristic
232C23×C5#12011yescharacteristic
233C23×C5#12111yescharacteristic
234C23×C5#12111yescharacteristic
235C23×C5C22⋊Q811yescharacteristic
236C23×C5#12311yescharacteristic
237C23×C5#12711yescharacteristic
238C5×Q8—22no—
239C5×Q8—22no—
240C5×Q8—41no—
241C5×Q8—41no—
242C5×D4—22no—
243C5×D4—22no—
244C5×D4—42no—
245C5×D4—42no—
246C5×D4—42no—
247C5×D4—42no—
248C5×D4—41no—
249C5×D4—41no—
250C2×C4×C5—22no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—42no—
254C2×C4×C5—42no—
255C2×C4×C5—42no—
256C2×C4×C5—42no—
257C2×C4×C5—42no—
258C2×C4×C5—42no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—82no—
262C2×C4×C5—82no—
263C2×C4×C5—82no—
264C2×C4×C5—82no—
265C2×C4×C5C2×C22⋊C411yescharacteristic
266C2×C4×C5C2×C4⋊C411yescharacteristic
267C2×C4×C5#11711yescharacteristic
268C2×C4×C5C4×D411yescharacteristic
269C2×C4×C5C4×D411yescharacteristic
270C2×C4×C5C4×D411yescharacteristic
271C2×C4×C5#12011yescharacteristic
272C2×C4×C5#12011yescharacteristic
273C2×C4×C5#12111yescharacteristic
274C2×C4×C5#12111yescharacteristic
275C2×C4×C5#12111yescharacteristic
276C2×C4×C5#12111yescharacteristic
277C2×C4×C5#12111yescharacteristic
278C2×C4×C5#12111yescharacteristic
279C2×C4×C5C22⋊Q811yescharacteristic
280C2×C4×C5C22⋊Q811yescharacteristic
281C2×C4×C5C22⋊Q811yescharacteristic
282C2×C4×C5C22⋊Q811yescharacteristic
283C2×C4×C5C22⋊Q811yescharacteristic
284C2×C4×C5#12311yescharacteristic
285C2×C4×C5#12311yescharacteristic
286C2×C4×C5#12311yescharacteristic
287C2×C4×C5#12311yescharacteristic
288C2×C4×C5#12411yescharacteristic
289C2×C4×C5#12411yescharacteristic
290C2×C4×C5#12411yescharacteristic
291C2×C4×C5#12611yescharacteristic
292C2×C4×C5#12611yescharacteristic
293C5×C8—24no—
294C5×C8—42no—
295C2×#41—21no—
296C2×#41—21no—
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—21no—
303C2×#41—21no—
304C2×#41—21no—
305C2×#41C5×D412yes—
306C2×#41C5×Q812yes—
307C22×Q8C2×C4×C511yescharacteristic
308C22×D4—21no—
309C22×D4C2×C4×C511yescharacteristic
310C23×C4—21no—
311C23×C4C23×C511yescharacteristic
312C2×M16—21no—
313C2×M16—21no—
314C2×M16—21no—
315C2×M16—21no—
316C2×M16—21no—
317C2×M16—21no—
318C2×M16—21no—
319C2×M16—21no—
320C2×M16—21no—
321C2×M16C2×C4×C512yes—
322C2×M16C5×D412yes—
323C2×M16C5×D412yes—
324C22×C8—21no—
325C22×C8C5×D412yes—
326#117—21no—
327#117—21no—
328#117—21no—
329#117—21no—
330#117—21no—
331#117—21no—
332#117—21no—
333#117—21no—
334#117—21no—
335#117—21no—
336#117—21no—
337#117—21no—
338#117—21no—
339#117C2×C4×C512yes—
340#117C5×D412yes—
341#117C5×D412yes—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4C5×D412yes—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354#107—24no—
355#106—24no—
356#104—28no—
357#103—24no—
358#102—24no—
359#99—28no—
360C22×C5—41no—
361C22×C5—41no—
362C22×C5—41no—
363C22×C5—41no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—41no—
367C22×C5—42no—
368C22×C5—82no—
369C22×C5—82no—
370C22×C5—82no—
371C22×C5#38511yescharacteristic
372C22×C5#38811yescharacteristic
373C22×C5#39011yescharacteristic
374C22×C5#39211yescharacteristic
375C22×C5#39411yescharacteristic
376C22×C5#39611yescharacteristic
377C22×C5#39911yescharacteristic
378C4×C5—42no—
379C4×C5—82no—
380C4×C5—82no—
381C4×C5—82no—
382C4×C5—82no—
383C4×C5#38011yescharacteristic
384C4×C5#38511yescharacteristic
385C4×C5#38611yescharacteristic
386C4×C5#38811yescharacteristic
387C4×C5#39311yescharacteristic
388C4×C5#39411yescharacteristic
389C4×C5#39611yescharacteristic
390C4×C5#39711yescharacteristic
391C24—21no—
392C24C2×C5×D411yescharacteristic
393#41—22no—
394#41—22no—
395#41—22no—
396#41—22no—
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8C5×C4⋊C412yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4C5×C4⋊C412yes—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4C22×C4×C511yescharacteristic
439C22×C4C2×C5×D411yescharacteristic
440C22×C4C2×C5×D411yescharacteristic
441C22×C4C2×C5×D411yescharacteristic
442C22×C4C2×C5×D411yescharacteristic
443C22×C4C2×C5×D411yescharacteristic
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×Q811yescharacteristic
446C22×C4C5×#4111yescharacteristic
447C22×C4C5×#4111yescharacteristic
448C22×C4C5×#4111yescharacteristic
449C22×C4C5×#4111yescharacteristic
450C22×C4C5×#4111yescharacteristic
451C22×C4C5×#4111yescharacteristic
452M16—22no—
453M16—22no—
454M16—22no—
455M16—22no—
456M16—22no—
457M16—22no—
458M16—41no—
459M16—41no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8C5×C22⋊C414yes—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—22no—
483C42—22no—
484C42—22no—
485C42—41no—
486C42—41no—
487C42—41no—
488C42—41no—
489C42—41no—
490C2×C5—21no—
491C2×C5—21no—
492C2×C5—21no—
493C2×C5—21no—
494C2×C5—21no—
495C2×C5—21no—
496C2×C5—21no—
497C2×C5—82no—
498C2×C5#143911yescharacteristic
499C23—22no—
500C23—41no—
501C23—41no—
502C23—81no—
503C23—82no—
504C23C4×C5×D411yescharacteristic
505C23C5×#12011yescharacteristic
506C23C5×#12111yescharacteristic
507C23C5×#12111yescharacteristic
508C23C5×C22⋊Q811yescharacteristic
509C23C5×#12311yescharacteristic
510C23C5×#12711yescharacteristic
511Q8—22no—
512Q8—22no—
513Q8—41no—
514Q8—41no—
515D4—22no—
516D4—22no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—41no—
522D4—41no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4C2×C5×C22⋊C411yescharacteristic
539C2×C4C2×C5×C4⋊C411yescharacteristic
540C2×C4C5×#11711yescharacteristic
541C2×C4C4×C5×D411yescharacteristic
542C2×C4C4×C5×D411yescharacteristic
543C2×C4C4×C5×D411yescharacteristic
544C2×C4C5×#12011yescharacteristic
545C2×C4C5×#12011yescharacteristic
546C2×C4C5×#12111yescharacteristic
547C2×C4C5×#12111yescharacteristic
548C2×C4C5×#12111yescharacteristic
549C2×C4C5×#12111yescharacteristic
550C2×C4C5×#12111yescharacteristic
551C2×C4C5×#12111yescharacteristic
552C2×C4C5×C22⋊Q811yescharacteristic
553C2×C4C5×C22⋊Q811yescharacteristic
554C2×C4C5×C22⋊Q811yescharacteristic
555C2×C4C5×C22⋊Q811yescharacteristic
556C2×C4C5×C22⋊Q811yescharacteristic
557C2×C4C5×#12311yescharacteristic
558C2×C4C5×#12311yescharacteristic
559C2×C4C5×#12311yescharacteristic
560C2×C4C5×#12311yescharacteristic
561C2×C4C5×#12411yescharacteristic
562C2×C4C5×#12411yescharacteristic
563C2×C4C5×#12411yescharacteristic
564C2×C4C5×#12611yescharacteristic
565C2×C4C5×#12611yescharacteristic
566C8—24no—
567C8—42no—
568C5#1113211yescharacteristic, direct product factor, Sylow
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22C5×#38511yescharacteristic
581C22C5×#38811yescharacteristic
582C22C5×#39011yescharacteristic
583C22C5×#39211yescharacteristic
584C22C5×#39411yescharacteristic
585C22C5×#39611yescharacteristic
586C22C5×#39911yescharacteristic
587C4—42no—
588C4—82no—
589C4—82no—
590C4—82no—
591C4—82no—
592C4C5×#38011yescharacteristic
593C4C5×#38511yescharacteristic
594C4C5×#38611yescharacteristic
595C4C5×#38811yescharacteristic
596C4C5×#39311yescharacteristic
597C4C5×#39411yescharacteristic
598C4C5×#39611yescharacteristic
599C4C5×#39711yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—82no—
608C2C5×#143911yescharacteristic
subgroupG/H
centerC4×C5#397
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
socleC2×C5#1439
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#2911C2semidirect
5. C2×C5×#344C2semidirect
6. C5×#1740C2semidirect
7. C2×C5×H(3,ℤ/4)C2semidirect
21. C5×#419C4semidirect
22. C5×#418C4semidirect
31. #11132C5direct (N × H)
97. #2911C2×C5semidirect
101. C2×#344C2×C5semidirect
102. #1740C2×C5semidirect
103. C2×H(3,ℤ/4)C2×C5semidirect
216. #419C4×C5semidirect
217. #418C4×C5semidirect
568. C5#11132direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29112
C2×C5×#4212
C5×#28962
C2×C5×#4102
C2×C5×#3442
C5×#17402
C2×C5×H(3,ℤ/4)2
#111325