Finite Group Databasebeta

← C5×#11122 #11933842

Subgroups — C5×#11122 #11933842

Order 1280.

1038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#106C211yesmaximal, characteristic
2C22×C5×#103C211yesmaximal, characteristic
3C22×C5×#103C211yesmaximal, characteristic
4C2×C5×#391C211yesmaximal, characteristic
5C2×C5×#340C211yesmaximal, characteristic
6C2×C5×#336C211yesmaximal, characteristic
7C5×C4⋊#95C211yesmaximal, characteristic
8C23×C5×Q8C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C23×C5×C8C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C2×C5×#106—22no—
16C2×C5×#106—22no—
17C2×C5×#106—22no—
18C2×C5×#103—22no—
19C2×C5×#103—22no—
20C2×C5×#103—22no—
21C2×C5×#103—22no—
22C2×C5×#103—22no—
23C2×C5×#103C414yescomplemented
24C5×#391—22no—
25C5×#391—22no—
26C2×C5×#95—22no—
27C2×C5×#95—22no—
28C5×#340—22no—
29C5×#336—22no—
30#11122C511yesmaximal, characteristic, direct product factor, Sylow
31C22×C5×Q8—21no—
32C22×C5×Q8—21no—
33C22×C5×Q8—21no—
34C22×C5×Q8—21no—
35C22×C5×Q8—21no—
36C22×C5×Q8—21no—
37C22×C5×Q8—21no—
38C22×C5×Q8—21no—
39C22×C5×Q8—21no—
40C22×C5×Q8—21no—
41C22×C5×Q8—21no—
42C22×C5×Q8C2×C412yes—
43C22×C5×Q8D412yes—
44C22×C5×Q8Q812yes—
45C23×C4×C5—21no—
46C23×C4×C5—21no—
47C23×C4×C5—21no—
48C23×C4×C5—21no—
49C23×C4×C5D412yes—
50C23×C4×C5C2311yescharacteristic
51C22×C5×C8—21no—
52C22×C5×C8—21no—
53C22×C5×C8—21no—
54C22×C5×C8—21no—
55C22×C5×C8—21no—
56C22×C5×C8—21no—
57C22×C5×C8—21no—
58C22×C5×C8—21no—
59C22×C5×C8—21no—
60C22×C5×C8—21no—
61C22×C5×C8C2×C412yes—
62C22×C5×C8D412yes—
63C22×C5×C8D412yes—
64C22×C5×C8D412yes—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4C2×C412yes—
81C2×C5×C4⋊C4D412yes—
82C2×C5×C4⋊C4D412yes—
83C2×C42×C5—21no—
84C2×C42×C5—21no—
85C2×C42×C5—21no—
86C2×C42×C5—21no—
87C2×C42×C5—21no—
88C2×C42×C5—21no—
89C5×#106—28no—
90C5×#103—28no—
91C5×#103—28no—
92C5×#95—28no—
93C5×#95—44no—
94C22×#106C2×C511yescharacteristic
95C22×#103C2×C511yescharacteristic
96C22×#103C2×C511yescharacteristic
97C2×#391C2×C511yescharacteristic
98C2×#340C2×C511yescharacteristic
99C2×#336C2×C511yescharacteristic
100C4⋊#95C2×C511yescharacteristic
101C24×C5C2×D411yescharacteristic
102C2×C5×Q8—22no—
103C2×C5×Q8—22no—
104C2×C5×Q8—22no—
105C2×C5×Q8—22no—
106C2×C5×Q8—22no—
107C2×C5×Q8—22no—
108C2×C5×Q8—22no—
109C2×C5×Q8—22no—
110C2×C5×Q8—22no—
111C2×C5×Q8—22no—
112C2×C5×Q8—22no—
113C2×C5×Q8—22no—
114C2×C5×Q8—22no—
115C2×C5×Q8—22no—
116C2×C5×Q8—22no—
117C2×C5×Q8—41no—
118C2×C5×Q8—41no—
119C2×C5×Q8—41no—
120C2×C5×Q8—41no—
121C2×C5×Q8—41no—
122C2×C5×Q8—41no—
123C2×C5×Q8—41no—
124C2×C5×Q8—41no—
125C2×C5×Q8—41no—
126C2×C5×Q8—41no—
127C2×C5×Q8—41no—
128C2×C5×Q8—41no—
129C2×C5×Q8C4⋊C414yes—
130C22×C4×C5—22no—
131C22×C4×C5—22no—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—41no—
143C22×C4×C5—41no—
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×C5—41no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5—42no—
155C22×C4×C5—42no—
156C22×C4×C5—42no—
157C22×C4×C5—42no—
158C22×C4×C5SD1614yes—
159C22×C4×C5C22×C411yescharacteristic
160C22×C4×C5C2×D411yescharacteristic
161C22×C4×C5C2×D411yescharacteristic
162C22×C4×C5C2×D411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×Q811yescharacteristic
167C22×C4×C5#4111yescharacteristic
168C22×C4×C5#4111yescharacteristic
169C22×C4×C5#4111yescharacteristic
170C22×C4×C5#4111yescharacteristic
171C22×C4×C5#4111yescharacteristic
172C22×C4×C5#4111yescharacteristic
173C2×C5×C8—22no—
174C2×C5×C8—22no—
175C2×C5×C8—22no—
176C2×C5×C8—22no—
177C2×C5×C8—22no—
178C2×C5×C8—22no—
179C2×C5×C8—22no—
180C2×C5×C8—22no—
181C2×C5×C8—22no—
182C2×C5×C8—41no—
183C2×C5×C8—41no—
184C2×C5×C8—41no—
185C2×C5×C8—41no—
186C2×C5×C8C22⋊C414yes—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—41no—
194C5×C4⋊C4—41no—
195C5×C4⋊C4—41no—
196C5×C4⋊C4—41no—
197C5×C4⋊C4—41no—
198C5×C4⋊C4—41no—
199C42×C5—41no—
200C42×C5—41no—
201C42×C5—41no—
202C42×C5—41no—
203C23×Q8C22×C511yescharacteristic
204C23×C8C22×C511yescharacteristic
205C23×C8C22×C511yescharacteristic
206C22×C4⋊C4C22×C511yescharacteristic
207C22×C4⋊C4C22×C511yescharacteristic
208C22×C4⋊C4C22×C511yescharacteristic
209C22×C42C22×C511yescharacteristic
210C2×#106—22no—
211C2×#106—22no—
212C2×#106—22no—
213C2×#103—22no—
214C2×#103—22no—
215C2×#103—22no—
216C2×#103—22no—
217C2×#103—22no—
218C2×#103C4×C514yescomplemented
219#391—22no—
220#391—22no—
221C2×#95—22no—
222C2×#95—22no—
223#340—22no—
224#336—22no—
225C23×C5C4×D411yescharacteristic
226C23×C5#12011yescharacteristic
227C23×C5#12111yescharacteristic
228C23×C5#12111yescharacteristic
229C23×C5C22⋊Q811yescharacteristic
230C23×C5#12311yescharacteristic
231C23×C5#12711yescharacteristic
232C23×C5C2×SD1612yes—
233C23×C5#13512yes—
234C23×C5#13712yes—
235C23×C5#13712yes—
236C5×Q8—24no—
237C5×Q8—24no—
238C5×Q8—42no—
239C5×Q8—42no—
240C5×Q8—42no—
241C5×Q8—42no—
242C5×Q8—42no—
243C5×Q8—42no—
244C2×C4×C5—24no—
245C2×C4×C5—24no—
246C2×C4×C5—24no—
247C2×C4×C5—24no—
248C2×C4×C5—42no—
249C2×C4×C5—42no—
250C2×C4×C5—42no—
251C2×C4×C5—42no—
252C2×C4×C5—42no—
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—44no—
262C2×C4×C5—44no—
263C2×C4×C5—44no—
264C2×C4×C5—82no—
265C2×C4×C5—82no—
266C2×C4×C5—82no—
267C2×C4×C5—81no—
268C2×C4×C5—81no—
269C2×C4×C5—81no—
270C2×C4×C5—81no—
271C2×C4×C5—81no—
272C2×C4×C5—81no—
273C2×C4×C5C2×C22⋊C411yescharacteristic
274C2×C4×C5C2×C4⋊C411yescharacteristic
275C2×C4×C5#11711yescharacteristic
276C2×C4×C5C4×D411yescharacteristic
277C2×C4×C5C4×D411yescharacteristic
278C2×C4×C5C4×D411yescharacteristic
279C2×C4×C5#12011yescharacteristic
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#12411yescharacteristic
297C2×C4×C5#12411yescharacteristic
298C2×C4×C5#12411yescharacteristic
299C2×C4×C5#12611yescharacteristic
300C2×C4×C5#12611yescharacteristic
301C5×C8—24no—
302C5×C8—42no—
303C22×Q8—21no—
304C22×Q8—21no—
305C22×Q8—21no—
306C22×Q8—21no—
307C22×Q8—21no—
308C22×Q8—21no—
309C22×Q8—21no—
310C22×Q8—21no—
311C22×Q8—21no—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8C2×C4×C512yes—
315C22×Q8C5×D412yes—
316C22×Q8C5×Q812yes—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C5×D412yes—
322C23×C4C23×C511yescharacteristic
323C22×C8—21no—
324C22×C8—21no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—21no—
332C22×C8—21no—
333C22×C8C2×C4×C512yes—
334C22×C8C5×D412yes—
335C22×C8C5×D412yes—
336C22×C8C5×D412yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4C2×C4×C512yes—
353C2×C4⋊C4C5×D412yes—
354C2×C4⋊C4C5×D412yes—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361#106—28no—
362#103—28no—
363#103—28no—
364#95—28no—
365#95—44no—
366C22×C5#38511yescharacteristic
367C22×C5#38811yescharacteristic
368C22×C5#39011yescharacteristic
369C22×C5#39211yescharacteristic
370C22×C5#39411yescharacteristic
371C22×C5#39611yescharacteristic
372C22×C5#39911yescharacteristic
373C22×C5C4×SD1612yes—
374C22×C5#44112yes—
375C22×C5#44812yes—
376C22×C5#45212yes—
377C22×C5#46112yes—
378C22×C5#46412yes—
379C22×C5#46512yes—
380C22×C5#47012yes—
381C22×C5#47512yes—
382C22×C5#47912yes—
383C22×C5#48312yes—
384C22×C5#48512yes—
385C22×C5#49211yescharacteristic
386C22×C5#49511yescharacteristic
387C22×C5#49711yescharacteristic
388C22×C5#49711yescharacteristic
389C4×C5—44no—
390C4×C5—44no—
391C4×C5—82no—
392C4×C5—82no—
393C4×C5—82no—
394C4×C5#38011yescharacteristic
395C4×C5#38511yescharacteristic
396C4×C5#38611yescharacteristic
397C4×C5#38811yescharacteristic
398C4×C5#39311yescharacteristic
399C4×C5#39411yescharacteristic
400C4×C5#39611yescharacteristic
401C4×C5#39711yescharacteristic
402C24C2×C5×D411yescharacteristic
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8C5×C4⋊C414yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4C5×SD1614yes—
460C22×C4C22×C4×C511yescharacteristic
461C22×C4C2×C5×D411yescharacteristic
462C22×C4C2×C5×D411yescharacteristic
463C22×C4C2×C5×D411yescharacteristic
464C22×C4C2×C5×D411yescharacteristic
465C22×C4C2×C5×D411yescharacteristic
466C22×C4C2×C5×D411yescharacteristic
467C22×C4C2×C5×Q811yescharacteristic
468C22×C4C5×#4111yescharacteristic
469C22×C4C5×#4111yescharacteristic
470C22×C4C5×#4111yescharacteristic
471C22×C4C5×#4111yescharacteristic
472C22×C4C5×#4111yescharacteristic
473C22×C4C5×#4111yescharacteristic
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8C5×C22⋊C414yes—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C42—41no—
501C42—41no—
502C42—41no—
503C42—41no—
504C2×C5#143911yescharacteristic
505C2×C5#186512yes—
506C2×C5#192712yes—
507C2×C5#196811yescharacteristic
508C2×C5#197111yescharacteristic
509C2×C5#201311yescharacteristic
510C2×C5#201511yescharacteristic
511C2×C5#203512yes—
512C2×C5#206612yes—
513C2×C5#209611yescharacteristic
514C2×C5#209711yescharacteristic
515C23C4×C5×D411yescharacteristic
516C23C5×#12011yescharacteristic
517C23C5×#12111yescharacteristic
518C23C5×#12111yescharacteristic
519C23C5×C22⋊Q811yescharacteristic
520C23C5×#12311yescharacteristic
521C23C5×#12711yescharacteristic
522C23C2×C5×SD1612yes—
523C23C5×#13512yes—
524C23C5×#13712yes—
525C23C5×#13712yes—
526Q8—24no—
527Q8—24no—
528Q8—42no—
529Q8—42no—
530Q8—42no—
531Q8—42no—
532Q8—42no—
533Q8—42no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4C2×C5×C22⋊C411yescharacteristic
564C2×C4C2×C5×C4⋊C411yescharacteristic
565C2×C4C5×#11711yescharacteristic
566C2×C4C4×C5×D411yescharacteristic
567C2×C4C4×C5×D411yescharacteristic
568C2×C4C4×C5×D411yescharacteristic
569C2×C4C5×#12011yescharacteristic
570C2×C4C5×#12011yescharacteristic
571C2×C4C5×#12111yescharacteristic
572C2×C4C5×#12111yescharacteristic
573C2×C4C5×#12111yescharacteristic
574C2×C4C5×#12111yescharacteristic
575C2×C4C5×#12111yescharacteristic
576C2×C4C5×#12111yescharacteristic
577C2×C4C5×C22⋊Q811yescharacteristic
578C2×C4C5×C22⋊Q811yescharacteristic
579C2×C4C5×C22⋊Q811yescharacteristic
580C2×C4C5×C22⋊Q811yescharacteristic
581C2×C4C5×C22⋊Q811yescharacteristic
582C2×C4C5×#12311yescharacteristic
583C2×C4C5×#12311yescharacteristic
584C2×C4C5×#12311yescharacteristic
585C2×C4C5×#12311yescharacteristic
586C2×C4C5×#12411yescharacteristic
587C2×C4C5×#12411yescharacteristic
588C2×C4C5×#12411yescharacteristic
589C2×C4C5×#12611yescharacteristic
590C2×C4C5×#12611yescharacteristic
591C8—24no—
592C8—42no—
593C5#1112211yescharacteristic, direct product factor, Sylow
594C22C5×#38511yescharacteristic
595C22C5×#38811yescharacteristic
596C22C5×#39011yescharacteristic
597C22C5×#39211yescharacteristic
598C22C5×#39411yescharacteristic
599C22C5×#39611yescharacteristic
600C22C5×#39911yescharacteristic
601C22C4×C5×SD1612yes—
602C22C5×#44112yes—
603C22C5×#44812yes—
604C22C5×#45212yes—
605C22C5×#46112yes—
606C22C5×#46412yes—
607C22C5×#46512yes—
608C22C5×#47012yes—
609C22C5×#47512yes—
610C22C5×#47912yes—
611C22C5×#48312yes—
612C22C5×#48512yes—
613C22C5×#49211yescharacteristic
614C22C5×#49511yescharacteristic
615C22C5×#49711yescharacteristic
616C22C5×#49711yescharacteristic
617C4—44no—
618C4—44no—
619C4—82no—
620C4—82no—
621C4—82no—
622C4C5×#38011yescharacteristic
623C4C5×#38511yescharacteristic
624C4C5×#38611yescharacteristic
625C4C5×#38811yescharacteristic
626C4C5×#39311yescharacteristic
627C4C5×#39411yescharacteristic
628C4C5×#39611yescharacteristic
629C4C5×#39711yescharacteristic
630C2C5×#143911yescharacteristic
631C2C5×#186512yes—
632C2C5×#192712yes—
633C2C5×#196811yescharacteristic
634C2C5×#197111yescharacteristic
635C2C5×#201311yescharacteristic
636C2C5×#201511yescharacteristic
637C2C5×#203512yes—
638C2C5×#206612yes—
639C2C5×#209611yescharacteristic
640C2C5×#209711yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C5C2×D4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
23. C2×C5×#103C4semidirect
30. #11122C5direct (N × H)
218. C2×#103C4×C5semidirect
593. C5#11122direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1062
C22×C5×#1032
C2×C5×#3912
C2×C5×#3402
C2×C5×#3362
C5×C4⋊#952
#111225