Finite Group Databasebeta

← C5×#11057 #11933777

Subgroups — C5×#11057 #11933777

Order 1280.

910 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
1C2×C5×#421C211yesmaximal, characteristic
2C2×C5×#417C211yesmaximal, characteristic
3C2×C5×#410C211yesmaximal, characteristic
4C5×#2316C211yesmaximal, characteristic, complemented
5C2×C5×#344C211yesmaximal, characteristic, complemented
6C5×#1736C211yesmaximal, 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
14C22×C5×C4⋊C4C2211yescharacteristic
15C5×#421—22no—
16C5×#421—22no—
17C2×C5×#104—22no—
18C5×#417—22no—
19C5×#417—22no—
20C2×C5×#103C412yescomplemented
21C2×C5×#102C412yescomplemented
22C5×#410—22no—
23C5×#410—22no—
24C2×C5×#99—22no—
25C5×#389—22no—
26C5×#389—22no—
27C5×#380—22no—
28C5×#344—22no—
29C5×#340—22no—
30C5×H(3,ℤ/4)—22no—
31#11057C511yesmaximal, 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×C5—21no—
49C23×C4×C5C2311yescharacteristic
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×M16—21no—
59C2×C5×M16—21no—
60C2×C5×M16—21no—
61C2×C5×M16D412yes—
62C22×C5×C8—21no—
63C22×C5×C8C2×C412yes—
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×#117D412yes—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—24no—
83C2×C5×C4⋊C4C2×C412yes—
84C2×C5×C4⋊C4D412yes—
85C2×C5×C4⋊C4D412yes—
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—21no—
88C2×C5×C22⋊C4D412yes—
89C2×C42×C5—21no—
90C2×C42×C5—21no—
91C2×C42×C5D412yes—
92C5×#104—28no—
93C5×#103—24no—
94C5×#102—24no—
95C5×#99—28no—
96C5×#95—24no—
97C2×#421C2×C511yescharacteristic
98C2×#417C2×C511yescharacteristic
99C2×#410C2×C511yescharacteristic
100#2316C2×C511yescharacteristic, complemented
101C2×#344C2×C511yescharacteristic, complemented
102#1736C2×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⋊C412yescomplemented
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⋊C412yescomplemented
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—41no—
149C22×C4×C5—41no—
150C22×C4×C5—41no—
151C22×C4×C5—41no—
152C22×C4×C5—41no—
153C22×C4×C5—82no—
154C22×C4×C5C22×C411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×D411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×Q811yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C22×C4×C5#4111yescharacteristic
164C22×C4×C5#4111yescharacteristic
165C22×C4×C5#4111yescharacteristic
166C22×C4×C5#4111yescharacteristic
167C22×C4×C5#4111yescharacteristic
168C5×M16—22no—
169C5×M16—22no—
170C5×M16—41no—
171C5×M16—41no—
172C5×M16—41no—
173C5×M16—41no—
174C5×M16—41no—
175C5×M16—41no—
176C2×C5×C8—22no—
177C2×C5×C8—22no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8—41no—
181C2×C5×C8—41no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4—22no—
185C5×C4⋊C4—22no—
186C5×C4⋊C4—41no—
187C5×C4⋊C4—41no—
188C5×C4⋊C4—41no—
189C5×C4⋊C4—41no—
190C5×C4⋊C4—41no—
191C5×C4⋊C4—84no—
192C5×C4⋊C4C22⋊C414yes—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—22no—
196C5×C22⋊C4—41no—
197C5×C22⋊C4—41no—
198C5×C22⋊C4—41no—
199C42×C5—22no—
200C42×C5—22no—
201C42×C5—22no—
202C42×C5—41no—
203C42×C5—41no—
204C42×C5—41no—
205C22×#41C22×C511yescharacteristic
206C22×M16C22×C511yescharacteristic
207C22×M16C22×C511yescharacteristic
208C2×#117C22×C511yescharacteristic
209C2×#117C22×C511yescharacteristic
210C2×#117C22×C511yescharacteristic
211C22×C4⋊C4C22×C511yescharacteristic
212#421—22no—
213#421—22no—
214C2×#104—22no—
215#417—22no—
216#417—22no—
217C2×#103C4×C512yescomplemented
218C2×#102C4×C512yescomplemented
219#410—22no—
220#410—22no—
221C2×#99—22no—
222#389—22no—
223#389—22no—
224#380—22no—
225#344—22no—
226#340—22no—
227H(3,ℤ/4)—22no—
228C23×C5—22no—
229C23×C5—41no—
230C23×C5—41no—
231C23×C5—41no—
232C23×C5—41no—
233C23×C5—81no—
234C23×C5—81no—
235C23×C5C4×D411yescharacteristic
236C23×C5#12011yescharacteristic
237C23×C5#12011yescharacteristic
238C23×C5#12111yescharacteristic
239C23×C5#12111yescharacteristic
240C23×C5C22⋊Q811yescharacteristic
241C23×C5#12411yescharacteristic
242C5×Q8—22no—
243C5×Q8—22no—
244C5×Q8—41no—
245C5×Q8—41no—
246C5×D4—22no—
247C5×D4—22no—
248C5×D4—42no—
249C5×D4—42no—
250C5×D4—42no—
251C5×D4—42no—
252C5×D4—41no—
253C5×D4—41no—
254C2×C4×C5—22no—
255C2×C4×C5—24no—
256C2×C4×C5—44no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—42no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—82no—
271C2×C4×C5—82no—
272C2×C4×C5—81no—
273C2×C4×C5—81no—
274C2×C4×C5C2×C22⋊C411yescharacteristic
275C2×C4×C5C2×C4⋊C411yescharacteristic
276C2×C4×C5#11711yescharacteristic
277C2×C4×C5C4×D411yescharacteristic
278C2×C4×C5C4×D411yescharacteristic
279C2×C4×C5C4×D411yescharacteristic
280C2×C4×C5#12011yescharacteristic
281C2×C4×C5#12111yescharacteristic
282C2×C4×C5#12111yescharacteristic
283C2×C4×C5#12111yescharacteristic
284C2×C4×C5#12111yescharacteristic
285C2×C4×C5#12111yescharacteristic
286C2×C4×C5#12111yescharacteristic
287C2×C4×C5C22⋊Q811yescharacteristic
288C2×C4×C5C22⋊Q811yescharacteristic
289C2×C4×C5C22⋊Q811yescharacteristic
290C2×C4×C5C22⋊Q811yescharacteristic
291C2×C4×C5C22⋊Q811yescharacteristic
292C2×C4×C5#12311yescharacteristic
293C2×C4×C5#12311yescharacteristic
294C2×C4×C5#12311yescharacteristic
295C2×C4×C5#12311yescharacteristic
296C2×C4×C5#12311yescharacteristic
297C2×C4×C5#12411yescharacteristic
298C2×C4×C5#12411yescharacteristic
299C2×C4×C5#12611yescharacteristic
300C2×C4×C5#12611yescharacteristic
301C2×C4×C5#12711yescharacteristic
302C5×C8—42no—
303C5×C8—42no—
304C2×#41—21no—
305C2×#41—21no—
306C2×#41—21no—
307C2×#41—21no—
308C2×#41—21no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41C5×D412yes—
315C2×#41C5×Q812yes—
316C22×Q8C2×C4×C511yescharacteristic
317C22×D4—21no—
318C22×D4C2×C4×C511yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C511yescharacteristic
322C2×M16—21no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16C5×D412yes—
334C22×C8—21no—
335C22×C8C2×C4×C512yes—
336#117—21no—
337#117—21no—
338#117—21no—
339#117—21no—
340#117—21no—
341#117—21no—
342#117—21no—
343#117—21no—
344#117—21no—
345#117—21no—
346#117—21no—
347#117C5×D412yes—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4C2×C4×C512yes—
356C2×C4⋊C4C5×D412yes—
357C2×C4⋊C4C5×D412yes—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4C5×D412yes—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42C5×D412yes—
364#104—28no—
365#103—24no—
366#102—24no—
367#99—28no—
368#95—24no—
369C22×C5—21no—
370C22×C5—21no—
371C22×C5—21no—
372C22×C5—21no—
373C22×C5—21no—
374C22×C5—21no—
375C22×C5—41no—
376C22×C5—41no—
377C22×C5—41no—
378C22×C5—41no—
379C22×C5—42no—
380C22×C5—82no—
381C22×C5—82no—
382C22×C5—81no—
383C22×C5—81no—
384C22×C5#38511yescharacteristic
385C22×C5#38611yescharacteristic
386C22×C5#38811yescharacteristic
387C22×C5#39211yescharacteristic
388C22×C5#39311yescharacteristic
389C22×C5#39411yescharacteristic
390C22×C5#39611yescharacteristic
391C4×C5—44no—
392C4×C5—42no—
393C4×C5—82no—
394C4×C5—82no—
395C4×C5—82no—
396C4×C5#38011yescharacteristic
397C4×C5#38511yescharacteristic
398C4×C5#38811yescharacteristic
399C4×C5#39011yescharacteristic
400C4×C5#39411yescharacteristic
401C4×C5#39611yescharacteristic
402C4×C5#39711yescharacteristic
403C4×C5#39911yescharacteristic
404C24—21no—
405C24C2×C5×D411yescharacteristic
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C5×C4⋊C412yescomplemented
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4C5×C4⋊C412yescomplemented
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—82no—
454C22×C4C22×C4×C511yescharacteristic
455C22×C4C2×C5×D411yescharacteristic
456C22×C4C2×C5×D411yescharacteristic
457C22×C4C2×C5×D411yescharacteristic
458C22×C4C2×C5×D411yescharacteristic
459C22×C4C2×C5×D411yescharacteristic
460C22×C4C2×C5×D411yescharacteristic
461C22×C4C2×C5×Q811yescharacteristic
462C22×C4C5×#4111yescharacteristic
463C22×C4C5×#4111yescharacteristic
464C22×C4C5×#4111yescharacteristic
465C22×C4C5×#4111yescharacteristic
466C22×C4C5×#4111yescharacteristic
467C22×C4C5×#4111yescharacteristic
468M16—22no—
469M16—22no—
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474M16—41no—
475M16—41no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—41no—
481C2×C8—41no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—84no—
492C4⋊C4C5×C22⋊C414yes—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—22no—
500C42—22no—
501C42—22no—
502C42—41no—
503C42—41no—
504C42—41no—
505C2×C5—21no—
506C2×C5—21no—
507C2×C5—21no—
508C2×C5—21no—
509C2×C5—21no—
510C2×C5—21no—
511C2×C5—82no—
512C2×C5#143911yescharacteristic
513C2×C5#190411yescharacteristic
514C2×C5#190511yescharacteristic
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—81no—
521C23—81no—
522C23C4×C5×D411yescharacteristic
523C23C5×#12011yescharacteristic
524C23C5×#12011yescharacteristic
525C23C5×#12111yescharacteristic
526C23C5×#12111yescharacteristic
527C23C5×C22⋊Q811yescharacteristic
528C23C5×#12411yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—41no—
532Q8—41no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—41no—
540D4—41no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—44no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4C2×C5×C22⋊C411yescharacteristic
562C2×C4C2×C5×C4⋊C411yescharacteristic
563C2×C4C5×#11711yescharacteristic
564C2×C4C4×C5×D411yescharacteristic
565C2×C4C4×C5×D411yescharacteristic
566C2×C4C4×C5×D411yescharacteristic
567C2×C4C5×#12011yescharacteristic
568C2×C4C5×#12111yescharacteristic
569C2×C4C5×#12111yescharacteristic
570C2×C4C5×#12111yescharacteristic
571C2×C4C5×#12111yescharacteristic
572C2×C4C5×#12111yescharacteristic
573C2×C4C5×#12111yescharacteristic
574C2×C4C5×C22⋊Q811yescharacteristic
575C2×C4C5×C22⋊Q811yescharacteristic
576C2×C4C5×C22⋊Q811yescharacteristic
577C2×C4C5×C22⋊Q811yescharacteristic
578C2×C4C5×C22⋊Q811yescharacteristic
579C2×C4C5×#12311yescharacteristic
580C2×C4C5×#12311yescharacteristic
581C2×C4C5×#12311yescharacteristic
582C2×C4C5×#12311yescharacteristic
583C2×C4C5×#12311yescharacteristic
584C2×C4C5×#12411yescharacteristic
585C2×C4C5×#12411yescharacteristic
586C2×C4C5×#12611yescharacteristic
587C2×C4C5×#12611yescharacteristic
588C2×C4C5×#12711yescharacteristic
589C8—42no—
590C8—42no—
591C5#1105711yescharacteristic, direct product factor, Sylow
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—42no—
603C22—82no—
604C22—82no—
605C22—81no—
606C22—81no—
607C22C5×#38511yescharacteristic
608C22C5×#38611yescharacteristic
609C22C5×#38811yescharacteristic
610C22C5×#39211yescharacteristic
611C22C5×#39311yescharacteristic
612C22C5×#39411yescharacteristic
613C22C5×#39611yescharacteristic
614C4—44no—
615C4—42no—
616C4—82no—
617C4—82no—
618C4—82no—
619C4C5×#38011yescharacteristic
620C4C5×#38511yescharacteristic
621C4C5×#38811yescharacteristic
622C4C5×#39011yescharacteristic
623C4C5×#39411yescharacteristic
624C4C5×#39611yescharacteristic
625C4C5×#39711yescharacteristic
626C4C5×#39911yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—82no—
634C2C5×#143911yescharacteristic
635C2C5×#190411yescharacteristic
636C2C5×#190511yescharacteristic
subgroupG/H
center, socleC22×C5#386
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#2316C2semidirect
5. C2×C5×#344C2semidirect
6. C5×#1736C2semidirect
7. C2×C5×H(3,ℤ/4)C2semidirect
20. C2×C5×#103C4semidirect
21. C2×C5×#102C4semidirect
31. #11057C5direct (N × H)
100. #2316C2×C5semidirect
101. C2×#344C2×C5semidirect
102. #1736C2×C5semidirect
103. C2×H(3,ℤ/4)C2×C5semidirect
127. C2×C5×Q8C4⋊C4semidirect
139. C2×C5×D4C4⋊C4semidirect
217. C2×#103C4×C5semidirect
218. C2×#102C4×C5semidirect
427. C2×Q8C5×C4⋊C4semidirect
439. C2×D4C5×C4⋊C4semidirect
591. C5#11057direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4212
C2×C5×#4172
C2×C5×#4102
C5×#23162
C2×C5×#3442
C5×#17362
C2×C5×H(3,ℤ/4)2
#110575