Finite Group Databasebeta

← C5×#11079 #11933799

Subgroups — C5×#11079 #11933799

Order 1280.

990 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#104C211yesmaximal, characteristic
2C2×C5×#417C211yesmaximal, characteristic
3C5×#2311C211yesmaximal, characteristic
4C2×C5×#382C211yesmaximal, characteristic, complemented
5C2×C5×#343C211yesmaximal, characteristic, complemented
6C5×#1736C211yesmaximal, characteristic, complemented
7C2×C5×#339C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×M16C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C2×C5×#117C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C42×C5C2211yescharacteristic
15C2×C5×#104—22no—
16C2×C5×#104—22no—
17C2×C5×#104C414yescomplemented
18C5×#417—22no—
19C5×#417—22no—
20C2×C5×#103—21no—
21C2×C5×#102—21no—
22C5×#391—21no—
23C5×#390—21no—
24C5×#386—22no—
25C5×#382—22no—
26C5×#382—22no—
27C5×#380—22no—
28C2×C5×#95—22no—
29C5×#343—22no—
30C5×#340—22no—
31C5×#339—22no—
32#11079C511yesmaximal, characteristic, direct product factor, Sylow
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×#41—21no—
43C2×C5×#41C2×C412yes—
44C2×C5×#41Q812yes—
45C22×C5×Q8D411yescharacteristic
46C22×C5×D4—21no—
47C22×C5×D4D411yescharacteristic
48C23×C4×C5—21no—
49C23×C4×C5—21no—
50C23×C4×C5—21no—
51C23×C4×C5D412yes—
52C23×C4×C5C2311yescharacteristic
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×M16—21no—
62C2×C5×M16—21no—
63C2×C5×M16C2×C412yes—
64C2×C5×M16D412yes—
65C22×C5×C8—21no—
66C22×C5×C8—21no—
67C5×#117—21no—
68C5×#117—21no—
69C5×#117—21no—
70C5×#117—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⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4D412yes—
83C2×C5×C4⋊C4D412yes—
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4—24no—
86C2×C42×C5—21no—
87C2×C42×C5—21no—
88C2×C42×C5—21no—
89C2×C42×C5—21no—
90C2×C42×C5C2×C412yes—
91C2×C42×C5D412yes—
92C2×C42×C5D412yes—
93C5×#104—28no—
94C5×#103—24no—
95C5×#102—24no—
96C5×#95—28no—
97C5×#95—24no—
98C22×#104C2×C511yescharacteristic
99C2×#417C2×C511yescharacteristic
100#2311C2×C511yescharacteristic
101C2×#382C2×C511yescharacteristic, complemented
102C2×#343C2×C511yescharacteristic, complemented
103#1736C2×C511yescharacteristic, complemented
104C2×#339C2×C511yescharacteristic, complemented
105C24×C5—21no—
106C24×C5C2×D411yescharacteristic
107C5×#41—22no—
108C5×#41—22no—
109C5×#41—22no—
110C5×#41—22no—
111C5×#41—22no—
112C5×#41—22no—
113C5×#41—22no—
114C5×#41—22no—
115C5×#41—41no—
116C5×#41—41no—
117C5×#41—41no—
118C5×#41—41no—
119C5×#41—41no—
120C5×#41—41no—
121C5×#41—41no—
122C5×#41—41no—
123C2×C5×Q8—21no—
124C2×C5×Q8—21no—
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127C2×C5×Q8—21no—
128C2×C5×Q8C4⋊C412yes—
129C2×C5×D4—22no—
130C2×C5×D4—22no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—41no—
137C2×C5×D4—41no—
138C2×C5×D4—41no—
139C2×C5×D4—41no—
140C2×C5×D4C4⋊C412yes—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—42no—
153C22×C4×C5—42no—
154C22×C4×C5—41no—
155C22×C4×C5—41no—
156C22×C4×C5—41no—
157C22×C4×C5—41no—
158C22×C4×C5—44no—
159C22×C4×C5—44no—
160C22×C4×C5—41no—
161C22×C4×C5—41no—
162C22×C4×C5C22×C411yescharacteristic
163C22×C4×C5C2×D411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×Q811yescharacteristic
170C22×C4×C5#4111yescharacteristic
171C22×C4×C5#4111yescharacteristic
172C22×C4×C5#4111yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C22×C4×C5#4111yescharacteristic
175C22×C4×C5#4111yescharacteristic
176C5×M16—22no—
177C5×M16—22no—
178C5×M16—22no—
179C5×M16—22no—
180C5×M16—41no—
181C5×M16—41no—
182C5×M16—41no—
183C5×M16—41no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—41no—
187C2×C5×C8—41no—
188C2×C5×C8—41no—
189C2×C5×C8—41no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—41no—
195C5×C4⋊C4—41no—
196C5×C4⋊C4—41no—
197C5×C4⋊C4—41no—
198C5×C4⋊C4—41no—
199C5×C4⋊C4—41no—
200C5×C22⋊C4—41no—
201C5×C22⋊C4—41no—
202C5×C22⋊C4—84no—
203C42×C5—22no—
204C42×C5—22no—
205C42×C5—22no—
206C42×C5—41no—
207C42×C5—41no—
208C42×C5C22⋊C414yescomplemented
209C22×#41C22×C511yescharacteristic
210C22×M16C22×C511yescharacteristic
211C22×M16C22×C511yescharacteristic
212C2×#117C22×C511yescharacteristic
213C22×C4⋊C4C22×C511yescharacteristic
214C22×C4⋊C4C22×C511yescharacteristic
215C22×C42C22×C511yescharacteristic
216C2×#104—22no—
217C2×#104—22no—
218C2×#104C4×C514yescomplemented
219#417—22no—
220#417—22no—
221C2×#103—21no—
222C2×#102—21no—
223#391—21no—
224#390—21no—
225#386—22no—
226#382—22no—
227#382—22no—
228#380—22no—
229C2×#95—22no—
230#343—22no—
231#340—22no—
232#339—22no—
233C23×C5—22no—
234C23×C5—22no—
235C23×C5—22no—
236C23×C5—41no—
237C23×C5—41no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5C4×D411yescharacteristic
241C23×C5#12011yescharacteristic
242C23×C5#12011yescharacteristic
243C23×C5#12111yescharacteristic
244C23×C5#12111yescharacteristic
245C23×C5C22⋊Q811yescharacteristic
246C23×C5#12411yescharacteristic
247C5×Q8—22no—
248C5×Q8—22no—
249C5×Q8—41no—
250C5×Q8—41no—
251C5×D4—22no—
252C5×D4—22no—
253C5×D4—42no—
254C5×D4—42no—
255C5×D4—42no—
256C5×D4—42no—
257C5×D4—41no—
258C5×D4—41no—
259C2×C4×C5—22no—
260C2×C4×C5—24no—
261C2×C4×C5—44no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—44no—
265C2×C4×C5—41no—
266C2×C4×C5—41no—
267C2×C4×C5—42no—
268C2×C4×C5—42no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—44no—
272C2×C4×C5—44no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—44no—
279C2×C4×C5—82no—
280C2×C4×C5—82no—
281C2×C4×C5—82no—
282C2×C4×C5C2×C22⋊C411yescharacteristic
283C2×C4×C5C2×C4⋊C411yescharacteristic
284C2×C4×C5#11711yescharacteristic
285C2×C4×C5C4×D411yescharacteristic
286C2×C4×C5C4×D411yescharacteristic
287C2×C4×C5C4×D411yescharacteristic
288C2×C4×C5#12011yescharacteristic
289C2×C4×C5#12111yescharacteristic
290C2×C4×C5#12111yescharacteristic
291C2×C4×C5#12111yescharacteristic
292C2×C4×C5#12111yescharacteristic
293C2×C4×C5#12111yescharacteristic
294C2×C4×C5#12111yescharacteristic
295C2×C4×C5C22⋊Q811yescharacteristic
296C2×C4×C5C22⋊Q811yescharacteristic
297C2×C4×C5C22⋊Q811yescharacteristic
298C2×C4×C5C22⋊Q811yescharacteristic
299C2×C4×C5C22⋊Q811yescharacteristic
300C2×C4×C5#12311yescharacteristic
301C2×C4×C5#12311yescharacteristic
302C2×C4×C5#12311yescharacteristic
303C2×C4×C5#12311yescharacteristic
304C2×C4×C5#12311yescharacteristic
305C2×C4×C5#12411yescharacteristic
306C2×C4×C5#12411yescharacteristic
307C2×C4×C5#12611yescharacteristic
308C2×C4×C5#12611yescharacteristic
309C2×C4×C5#12711yescharacteristic
310C5×C8—42no—
311C5×C8—42no—
312C2×#41—21no—
313C2×#41—21no—
314C2×#41—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41C2×C4×C512yes—
323C2×#41C5×Q812yes—
324C22×Q8C5×D411yescharacteristic
325C22×D4—21no—
326C22×D4C5×D411yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4C5×D412yes—
331C23×C4C23×C511yescharacteristic
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16C2×C4×C512yes—
343C2×M16C5×D412yes—
344C22×C8—21no—
345C22×C8—21no—
346#117—21no—
347#117—21no—
348#117—21no—
349#117—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4C5×D412yes—
362C2×C4⋊C4C5×D412yes—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—24no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42C2×C4×C512yes—
370C2×C42C5×D412yes—
371C2×C42C5×D412yes—
372#104—28no—
373#103—24no—
374#102—24no—
375#95—28no—
376#95—24no—
377C22×C5—22no—
378C22×C5—22no—
379C22×C5—21no—
380C22×C5—21no—
381C22×C5—21no—
382C22×C5—21no—
383C22×C5—22no—
384C22×C5—22no—
385C22×C5—44no—
386C22×C5—42no—
387C22×C5—81no—
388C22×C5—81no—
389C22×C5—82no—
390C22×C5#38511yescharacteristic
391C22×C5#38611yescharacteristic
392C22×C5#38811yescharacteristic
393C22×C5#39211yescharacteristic
394C22×C5#39311yescharacteristic
395C22×C5#39411yescharacteristic
396C22×C5#39611yescharacteristic
397C22×C5#45412yes—
398C22×C5#45512yes—
399C4×C5—44no—
400C4×C5—42no—
401C4×C5—82no—
402C4×C5—82no—
403C4×C5—82no—
404C4×C5#38011yescharacteristic
405C4×C5#38511yescharacteristic
406C4×C5#38811yescharacteristic
407C4×C5#39011yescharacteristic
408C4×C5#39411yescharacteristic
409C4×C5#39611yescharacteristic
410C4×C5#39711yescharacteristic
411C4×C5#39911yescharacteristic
412C24—21no—
413C24C2×C5×D411yescharacteristic
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—41no—
423#41—41no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C5×C4⋊C412yes—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—41no—
447C2×D4C5×C4⋊C412yes—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4C22×C4×C511yescharacteristic
470C22×C4C2×C5×D411yescharacteristic
471C22×C4C2×C5×D411yescharacteristic
472C22×C4C2×C5×D411yescharacteristic
473C22×C4C2×C5×D411yescharacteristic
474C22×C4C2×C5×D411yescharacteristic
475C22×C4C2×C5×D411yescharacteristic
476C22×C4C2×C5×Q811yescharacteristic
477C22×C4C5×#4111yescharacteristic
478C22×C4C5×#4111yescharacteristic
479C22×C4C5×#4111yescharacteristic
480C22×C4C5×#4111yescharacteristic
481C22×C4C5×#4111yescharacteristic
482C22×C4C5×#4111yescharacteristic
483M16—22no—
484M16—22no—
485M16—22no—
486M16—22no—
487M16—41no—
488M16—41no—
489M16—41no—
490M16—41no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—84no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—41no—
514C42—41no—
515C42C5×C22⋊C414yescomplemented
516C2×C5—21no—
517C2×C5—21no—
518C2×C5—21no—
519C2×C5—21no—
520C2×C5—82no—
521C2×C5#143911yescharacteristic
522C2×C5#186012yes—
523C2×C5#200311yescharacteristic
524C2×C5#200411yescharacteristic
525C2×C5#204012yes—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23C4×C5×D411yescharacteristic
534C23C5×#12011yescharacteristic
535C23C5×#12011yescharacteristic
536C23C5×#12111yescharacteristic
537C23C5×#12111yescharacteristic
538C23C5×C22⋊Q811yescharacteristic
539C23C5×#12411yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—41no—
543Q8—41no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—42no—
549D4—42no—
550D4—41no—
551D4—41no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—44no—
565C2×C4—44no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4C2×C5×C22⋊C411yescharacteristic
576C2×C4C2×C5×C4⋊C411yescharacteristic
577C2×C4C5×#11711yescharacteristic
578C2×C4C4×C5×D411yescharacteristic
579C2×C4C4×C5×D411yescharacteristic
580C2×C4C4×C5×D411yescharacteristic
581C2×C4C5×#12011yescharacteristic
582C2×C4C5×#12111yescharacteristic
583C2×C4C5×#12111yescharacteristic
584C2×C4C5×#12111yescharacteristic
585C2×C4C5×#12111yescharacteristic
586C2×C4C5×#12111yescharacteristic
587C2×C4C5×#12111yescharacteristic
588C2×C4C5×C22⋊Q811yescharacteristic
589C2×C4C5×C22⋊Q811yescharacteristic
590C2×C4C5×C22⋊Q811yescharacteristic
591C2×C4C5×C22⋊Q811yescharacteristic
592C2×C4C5×C22⋊Q811yescharacteristic
593C2×C4C5×#12311yescharacteristic
594C2×C4C5×#12311yescharacteristic
595C2×C4C5×#12311yescharacteristic
596C2×C4C5×#12311yescharacteristic
597C2×C4C5×#12311yescharacteristic
598C2×C4C5×#12411yescharacteristic
599C2×C4C5×#12411yescharacteristic
600C2×C4C5×#12611yescharacteristic
601C2×C4C5×#12611yescharacteristic
602C2×C4C5×#12711yescharacteristic
603C8—42no—
604C8—42no—
605C5#1107911yescharacteristic, direct product factor, Sylow
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—44no—
615C22—42no—
616C22—82no—
617C22—81no—
618C22—81no—
619C22C5×#38511yescharacteristic
620C22C5×#38611yescharacteristic
621C22C5×#38811yescharacteristic
622C22C5×#39211yescharacteristic
623C22C5×#39311yescharacteristic
624C22C5×#39411yescharacteristic
625C22C5×#39611yescharacteristic
626C22C5×#45412yes—
627C22C5×#45512yes—
628C4—44no—
629C4—42no—
630C4—82no—
631C4—82no—
632C4—82no—
633C4C5×#38011yescharacteristic
634C4C5×#38511yescharacteristic
635C4C5×#38811yescharacteristic
636C4C5×#39011yescharacteristic
637C4C5×#39411yescharacteristic
638C4C5×#39611yescharacteristic
639C4C5×#39711yescharacteristic
640C4C5×#39911yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—82no—
646C2C5×#143911yescharacteristic
647C2C5×#186012yes—
648C2C5×#200311yescharacteristic
649C2C5×#200411yescharacteristic
650C2C5×#204012yes—
subgroupG/H
center, socleC23×C5#120
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C5×#382C2semidirect
5. C2×C5×#343C2semidirect
6. C5×#1736C2semidirect
7. C2×C5×#339C2semidirect
17. C2×C5×#104C4semidirect
32. #11079C5direct (N × H)
101. C2×#382C2×C5semidirect
102. C2×#343C2×C5semidirect
103. #1736C2×C5semidirect
104. C2×#339C2×C5semidirect
208. C42×C5C22⋊C4semidirect
218. C2×#104C4×C5semidirect
515. C42C5×C22⋊C4semidirect
605. C5#11079direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1042
C2×C5×#4172
C5×#23112
C2×C5×#3822
C2×C5×#3432
C5×#17362
C2×C5×#3392
#110795