Finite Group Databasebeta

← C5×#11078 #11933798

Subgroups — C5×#11078 #11933798

Order 1280.

1078 conjugacy classes of subgroups.

The subgroup lattice has 656 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×#384C211yesmaximal, 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⋊C4—22no—
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C2×C5×#104—22no—
17C2×C5×#104—22no—
18C2×C5×#104C414yescomplemented
19C5×#417—22no—
20C5×#417—22no—
21C2×C5×#103—21no—
22C2×C5×#102—21no—
23C5×#391—21no—
24C5×#390—21no—
25C5×#386—22no—
26C5×#384—22no—
27C5×#384—22no—
28C5×#380—22no—
29C5×#343—22no—
30C5×#340—22no—
31C5×#339—22no—
32#11078C511yesmaximal, 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—28no—
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—21no—
83C2×C5×C4⋊C4—48no—
84C2×C5×C4⋊C4D412yes—
85C2×C5×C4⋊C4D412yes—
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—24no—
88C2×C42×C5—21no—
89C2×C42×C5—21no—
90C2×C42×C5—21no—
91C2×C42×C5—21no—
92C2×C42×C5C2×C412yes—
93C2×C42×C5D412yes—
94C2×C42×C5D412yes—
95C5×#104—28no—
96C5×#103—24no—
97C5×#102—24no—
98C5×#95—24no—
99C22×#104C2×C511yescharacteristic
100C2×#417C2×C511yescharacteristic
101#2311C2×C511yescharacteristic
102C2×#384C2×C511yescharacteristic, complemented
103C2×#343C2×C511yescharacteristic, complemented
104#1736C2×C511yescharacteristic, complemented
105C2×#339C2×C511yescharacteristic, complemented
106C24×C5—21no—
107C24×C5C2×D411yescharacteristic
108C5×#41—22no—
109C5×#41—22no—
110C5×#41—22no—
111C5×#41—22no—
112C5×#41—22no—
113C5×#41—22no—
114C5×#41—22no—
115C5×#41—22no—
116C5×#41—41no—
117C5×#41—41no—
118C5×#41—41no—
119C5×#41—41no—
120C5×#41—41no—
121C5×#41—41no—
122C5×#41—41no—
123C5×#41—41no—
124C2×C5×Q8—21no—
125C2×C5×Q8—21no—
126C2×C5×Q8—21no—
127C2×C5×Q8—21no—
128C2×C5×Q8—21no—
129C2×C5×Q8C4⋊C412yescomplemented
130C2×C5×D4—22no—
131C2×C5×D4—22no—
132C2×C5×D4—21no—
133C2×C5×D4—21no—
134C2×C5×D4—21no—
135C2×C5×D4—21no—
136C2×C5×D4—21no—
137C2×C5×D4—41no—
138C2×C5×D4—41no—
139C2×C5×D4—41no—
140C2×C5×D4—41no—
141C2×C5×D4C4⋊C412yescomplemented
142C22×C4×C5—24no—
143C22×C4×C5—24no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—41no—
156C22×C4×C5—41no—
157C22×C4×C5—41no—
158C22×C4×C5—41no—
159C22×C4×C5—44no—
160C22×C4×C5—44no—
161C22×C4×C5—41no—
162C22×C4×C5—41no—
163C22×C4×C5C22×C411yescharacteristic
164C22×C4×C5C2×D411yescharacteristic
165C22×C4×C5C2×D411yescharacteristic
166C22×C4×C5C2×D411yescharacteristic
167C22×C4×C5C2×D411yescharacteristic
168C22×C4×C5C2×D411yescharacteristic
169C22×C4×C5C2×D411yescharacteristic
170C22×C4×C5C2×Q811yescharacteristic
171C22×C4×C5#4111yescharacteristic
172C22×C4×C5#4111yescharacteristic
173C22×C4×C5#4111yescharacteristic
174C22×C4×C5#4111yescharacteristic
175C22×C4×C5#4111yescharacteristic
176C22×C4×C5#4111yescharacteristic
177C5×M16—22no—
178C5×M16—22no—
179C5×M16—22no—
180C5×M16—22no—
181C5×M16—41no—
182C5×M16—41no—
183C5×M16—41no—
184C5×M16—41no—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C2×C5×C8—41no—
188C2×C5×C8—41no—
189C2×C5×C8—41no—
190C2×C5×C8—41no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4—416no—
196C5×C4⋊C4—41no—
197C5×C4⋊C4—41no—
198C5×C4⋊C4—41no—
199C5×C4⋊C4—41no—
200C5×C4⋊C4—41no—
201C5×C4⋊C4—41no—
202C5×C22⋊C4—41no—
203C5×C22⋊C4—41no—
204C5×C22⋊C4—84no—
205C42×C5—22no—
206C42×C5—22no—
207C42×C5—22no—
208C42×C5—41no—
209C42×C5—41no—
210C42×C5C22⋊C414yescomplemented
211C22×#41C22×C511yescharacteristic
212C22×M16C22×C511yescharacteristic
213C22×M16C22×C511yescharacteristic
214C2×#117C22×C511yescharacteristic
215C22×C4⋊C4—22no—
216C22×C4⋊C4C22×C511yescharacteristic
217C22×C4⋊C4C22×C511yescharacteristic
218C22×C42C22×C511yescharacteristic
219C2×#104—22no—
220C2×#104—22no—
221C2×#104C4×C514yescomplemented
222#417—22no—
223#417—22no—
224C2×#103—21no—
225C2×#102—21no—
226#391—21no—
227#390—21no—
228#386—22no—
229#384—22no—
230#384—22no—
231#380—22no—
232#343—22no—
233#340—22no—
234#339—22no—
235C23×C5—22no—
236C23×C5—22no—
237C23×C5—22no—
238C23×C5—41no—
239C23×C5—41no—
240C23×C5—42no—
241C23×C5—42no—
242C23×C5C4×D411yescharacteristic
243C23×C5#12011yescharacteristic
244C23×C5#12011yescharacteristic
245C23×C5#12111yescharacteristic
246C23×C5#12111yescharacteristic
247C23×C5C22⋊Q811yescharacteristic
248C23×C5#12411yescharacteristic
249C5×Q8—22no—
250C5×Q8—22no—
251C5×Q8—41no—
252C5×Q8—41no—
253C5×D4—22no—
254C5×D4—22no—
255C5×D4—42no—
256C5×D4—42no—
257C5×D4—42no—
258C5×D4—42no—
259C5×D4—41no—
260C5×D4—41no—
261C2×C4×C5—24no—
262C2×C4×C5—28no—
263C2×C4×C5—24no—
264C2×C4×C5—28no—
265C2×C4×C5—24no—
266C2×C4×C5—22no—
267C2×C4×C5—41no—
268C2×C4×C5—41no—
269C2×C4×C5—42no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—44no—
274C2×C4×C5—44no—
275C2×C4×C5—42no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—42no—
279C2×C4×C5—44no—
280C2×C4×C5—42no—
281C2×C4×C5—82no—
282C2×C4×C5—82no—
283C2×C4×C5—82no—
284C2×C4×C5C2×C22⋊C411yescharacteristic
285C2×C4×C5C2×C4⋊C411yescharacteristic
286C2×C4×C5#11711yescharacteristic
287C2×C4×C5C4×D411yescharacteristic
288C2×C4×C5C4×D411yescharacteristic
289C2×C4×C5C4×D411yescharacteristic
290C2×C4×C5#12011yescharacteristic
291C2×C4×C5#12111yescharacteristic
292C2×C4×C5#12111yescharacteristic
293C2×C4×C5#12111yescharacteristic
294C2×C4×C5#12111yescharacteristic
295C2×C4×C5#12111yescharacteristic
296C2×C4×C5#12111yescharacteristic
297C2×C4×C5C22⋊Q811yescharacteristic
298C2×C4×C5C22⋊Q811yescharacteristic
299C2×C4×C5C22⋊Q811yescharacteristic
300C2×C4×C5C22⋊Q811yescharacteristic
301C2×C4×C5C22⋊Q811yescharacteristic
302C2×C4×C5#12311yescharacteristic
303C2×C4×C5#12311yescharacteristic
304C2×C4×C5#12311yescharacteristic
305C2×C4×C5#12311yescharacteristic
306C2×C4×C5#12311yescharacteristic
307C2×C4×C5#12411yescharacteristic
308C2×C4×C5#12411yescharacteristic
309C2×C4×C5#12611yescharacteristic
310C2×C4×C5#12611yescharacteristic
311C2×C4×C5#12711yescharacteristic
312C5×C8—42no—
313C5×C8—42no—
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×#41—21no—
323C2×#41—21no—
324C2×#41C2×C4×C512yes—
325C2×#41C5×Q812yes—
326C22×Q8C5×D411yescharacteristic
327C22×D4—21no—
328C22×D4C5×D411yescharacteristic
329C23×C4—21no—
330C23×C4—21no—
331C23×C4—21no—
332C23×C4C5×D412yes—
333C23×C4C23×C511yescharacteristic
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×M16—21no—
343C2×M16—21no—
344C2×M16C2×C4×C512yes—
345C2×M16C5×D412yes—
346C22×C8—21no—
347C22×C8—21no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—48no—
365C2×C4⋊C4C5×D412yes—
366C2×C4⋊C4C5×D412yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—24no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42C2×C4×C512yes—
374C2×C42C5×D412yes—
375C2×C42C5×D412yes—
376#104—28no—
377#103—24no—
378#102—24no—
379#95—24no—
380C22×C5—22no—
381C22×C5—22no—
382C22×C5—21no—
383C22×C5—21no—
384C22×C5—21no—
385C22×C5—21no—
386C22×C5—22no—
387C22×C5—22no—
388C22×C5—44no—
389C22×C5—42no—
390C22×C5—81no—
391C22×C5—81no—
392C22×C5—82no—
393C22×C5#38511yescharacteristic
394C22×C5#38611yescharacteristic
395C22×C5#38811yescharacteristic
396C22×C5#39211yescharacteristic
397C22×C5#39311yescharacteristic
398C22×C5#39411yescharacteristic
399C22×C5#39611yescharacteristic
400C22×C5#45312yes—
401C22×C5#45612yes—
402C4×C5—28no—
403C4×C5—42no—
404C4×C5—82no—
405C4×C5—82no—
406C4×C5—82no—
407C4×C5#38011yescharacteristic
408C4×C5#38511yescharacteristic
409C4×C5#38811yescharacteristic
410C4×C5#39011yescharacteristic
411C4×C5#39411yescharacteristic
412C4×C5#39611yescharacteristic
413C4×C5#39711yescharacteristic
414C4×C5#39911yescharacteristic
415C24—21no—
416C24C2×C5×D411yescharacteristic
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—22no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432#41—41no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C5×C4⋊C412yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C5×C4⋊C412yescomplemented
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4C22×C4×C511yescharacteristic
473C22×C4C2×C5×D411yescharacteristic
474C22×C4C2×C5×D411yescharacteristic
475C22×C4C2×C5×D411yescharacteristic
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D411yescharacteristic
478C22×C4C2×C5×D411yescharacteristic
479C22×C4C2×C5×Q811yescharacteristic
480C22×C4C5×#4111yescharacteristic
481C22×C4C5×#4111yescharacteristic
482C22×C4C5×#4111yescharacteristic
483C22×C4C5×#4111yescharacteristic
484C22×C4C5×#4111yescharacteristic
485C22×C4C5×#4111yescharacteristic
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—41no—
491M16—41no—
492M16—41no—
493M16—41no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—416no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—84no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—41no—
518C42—41no—
519C42C5×C22⋊C414yescomplemented
520C2×C5—21no—
521C2×C5—21no—
522C2×C5—21no—
523C2×C5—21no—
524C2×C5—82no—
525C2×C5#143911yescharacteristic
526C2×C5#185912yes—
527C2×C5#200211yescharacteristic
528C2×C5#200511yescharacteristic
529C2×C5#203912yes—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—41no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23C4×C5×D411yescharacteristic
538C23C5×#12011yescharacteristic
539C23C5×#12011yescharacteristic
540C23C5×#12111yescharacteristic
541C23C5×#12111yescharacteristic
542C23C5×C22⋊Q811yescharacteristic
543C23C5×#12411yescharacteristic
544Q8—22no—
545Q8—22no—
546Q8—41no—
547Q8—41no—
548D4—22no—
549D4—22no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—41no—
555D4—41no—
556C2×C4—24no—
557C2×C4—28no—
558C2×C4—28no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4C2×C5×C22⋊C411yescharacteristic
580C2×C4C2×C5×C4⋊C411yescharacteristic
581C2×C4C5×#11711yescharacteristic
582C2×C4C4×C5×D411yescharacteristic
583C2×C4C4×C5×D411yescharacteristic
584C2×C4C4×C5×D411yescharacteristic
585C2×C4C5×#12011yescharacteristic
586C2×C4C5×#12111yescharacteristic
587C2×C4C5×#12111yescharacteristic
588C2×C4C5×#12111yescharacteristic
589C2×C4C5×#12111yescharacteristic
590C2×C4C5×#12111yescharacteristic
591C2×C4C5×#12111yescharacteristic
592C2×C4C5×C22⋊Q811yescharacteristic
593C2×C4C5×C22⋊Q811yescharacteristic
594C2×C4C5×C22⋊Q811yescharacteristic
595C2×C4C5×C22⋊Q811yescharacteristic
596C2×C4C5×C22⋊Q811yescharacteristic
597C2×C4C5×#12311yescharacteristic
598C2×C4C5×#12311yescharacteristic
599C2×C4C5×#12311yescharacteristic
600C2×C4C5×#12311yescharacteristic
601C2×C4C5×#12311yescharacteristic
602C2×C4C5×#12411yescharacteristic
603C2×C4C5×#12411yescharacteristic
604C2×C4C5×#12611yescharacteristic
605C2×C4C5×#12611yescharacteristic
606C2×C4C5×#12711yescharacteristic
607C8—42no—
608C8—42no—
609C5#1107811yescharacteristic, direct product factor, Sylow
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—42no—
620C22—82no—
621C22—81no—
622C22—81no—
623C22C5×#38511yescharacteristic
624C22C5×#38611yescharacteristic
625C22C5×#38811yescharacteristic
626C22C5×#39211yescharacteristic
627C22C5×#39311yescharacteristic
628C22C5×#39411yescharacteristic
629C22C5×#39611yescharacteristic
630C22C5×#45312yes—
631C22C5×#45612yes—
632C4—28no—
633C4—42no—
634C4—82no—
635C4—82no—
636C4—82no—
637C4C5×#38011yescharacteristic
638C4C5×#38511yescharacteristic
639C4C5×#38811yescharacteristic
640C4C5×#39011yescharacteristic
641C4C5×#39411yescharacteristic
642C4C5×#39611yescharacteristic
643C4C5×#39711yescharacteristic
644C4C5×#39911yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—82no—
650C2C5×#143911yescharacteristic
651C2C5×#185912yes—
652C2C5×#200211yescharacteristic
653C2C5×#200511yescharacteristic
654C2C5×#203912yes—
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×#384C2semidirect
5. C2×C5×#343C2semidirect
6. C5×#1736C2semidirect
7. C2×C5×#339C2semidirect
18. C2×C5×#104C4semidirect
32. #11078C5direct (N × H)
102. C2×#384C2×C5semidirect
103. C2×#343C2×C5semidirect
104. #1736C2×C5semidirect
105. C2×#339C2×C5semidirect
129. C2×C5×Q8C4⋊C4semidirect
141. C2×C5×D4C4⋊C4semidirect
210. C42×C5C22⋊C4semidirect
221. C2×#104C4×C5semidirect
438. C2×Q8C5×C4⋊C4semidirect
450. C2×D4C5×C4⋊C4semidirect
519. C42C5×C22⋊C4semidirect
609. C5#11078direct (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×#3842
C2×C5×#3432
C5×#17362
C2×C5×#3392
#110785