Finite Group Databasebeta

← C5×#11117 #11933837

Subgroups — C5×#11117 #11933837

Order 1280.

910 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#428C211yesmaximal, characteristic, complemented
2C2×C5×#421C211yesmaximal, characteristic
3C5×#2896C211yesmaximal, characteristic
4C5×#2311C211yesmaximal, characteristic
5C2×C5×#344C211yesmaximal, characteristic, complemented
6C5×#1740C211yesmaximal, characteristic, complemented
7C5×#1736C211yesmaximal, 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×#428—22no—
16C5×#428—22no—
17C2×C5×#107—21no—
18C2×C5×#106—21no—
19C5×#421—22no—
20C5×#421C414yescomplemented
21C2×C5×#104—22no—
22C5×#419—21no—
23C5×#418—21no—
24C5×#417—21no—
25C5×#417—21no—
26C5×#416—22no—
27C5×#391—21no—
28C5×#390—21no—
29C5×#386—22no—
30C5×#380—22no—
31C5×#344—22no—
32C5×#342—22no—
33C5×#340—22no—
34#11117C511yesmaximal, characteristic, direct product factor, Sylow
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×#41—21no—
44C2×C5×#41—21no—
45C2×C5×#41C2×C412yes—
46C2×C5×#41Q812yes—
47C22×C5×Q8D411yescharacteristic
48C22×C5×D4—21no—
49C22×C5×D4D411yescharacteristic
50C23×C4×C5—21no—
51C23×C4×C5—21no—
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×M16C2×C412yes—
63C2×C5×M16D412yes—
64C2×C5×M16D412yes—
65C22×C5×C8—21no—
66C22×C5×C8D412yes—
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×#117—21no—
77C5×#117—21no—
78C5×#117C2×C412yes—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4—21no—
81C2×C5×C4⋊C4—21no—
82C2×C5×C4⋊C4—21no—
83C2×C5×C4⋊C4—21no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4D412yes—
87C2×C5×C4⋊C4D411yescharacteristic
88C2×C5×C4⋊C4D411yescharacteristic
89C2×C5×C22⋊C4—21no—
90C2×C5×C22⋊C4—21no—
91C2×C5×C22⋊C4—24no—
92C2×C5×C22⋊C4D412yes—
93C2×C42×C5—21no—
94C2×C42×C5—21no—
95C2×C42×C5—21no—
96C5×#107—24no—
97C5×#106—24no—
98C5×#104—28no—
99C5×#103—22no—
100C5×#103—22no—
101C5×#102—22no—
102C5×#102—22no—
103C5×#95—24no—
104C2×#428C2×C511yescharacteristic, complemented
105C2×#421C2×C511yescharacteristic
106#2896C2×C511yescharacteristic
107#2311C2×C511yescharacteristic
108C2×#344C2×C511yescharacteristic, complemented
109#1740C2×C511yescharacteristic, complemented
110#1736C2×C511yescharacteristic, complemented
111C24×C5—21no—
112C24×C5C2×D411yescharacteristic
113C5×#41—22no—
114C5×#41—22no—
115C5×#41—22no—
116C5×#41—22no—
117C5×#41—22no—
118C5×#41—22no—
119C5×#41—22no—
120C5×#41—22no—
121C5×#41—41no—
122C5×#41—41no—
123C5×#41—41no—
124C5×#41—41no—
125C5×#41—41no—
126C5×#41—41no—
127C5×#41—41no—
128C5×#41—41no—
129C2×C5×Q8—21no—
130C2×C5×Q8—21no—
131C2×C5×Q8—21no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8C4⋊C412yes—
135C2×C5×D4—22no—
136C2×C5×D4—22no—
137C2×C5×D4—21no—
138C2×C5×D4—21no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—41no—
143C2×C5×D4—41no—
144C2×C5×D4—41no—
145C2×C5×D4—41no—
146C2×C5×D4C4⋊C412yes—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—41no—
155C22×C4×C5—41no—
156C22×C4×C5—41no—
157C22×C4×C5—41no—
158C22×C4×C5—41no—
159C22×C4×C5—41no—
160C22×C4×C5—41no—
161C22×C4×C5—82no—
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—41no—
180C5×M16—41no—
181C5×M16—41no—
182C5×M16—41no—
183C5×M16C22⋊C414yescomplemented
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—22no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C2×C5×C8—22no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—41no—
198C5×C4⋊C4—41no—
199C5×C4⋊C4—41no—
200C5×C4⋊C4—41no—
201C5×C4⋊C4—41no—
202C5×C22⋊C4—22no—
203C5×C22⋊C4—22no—
204C5×C22⋊C4—22no—
205C5×C22⋊C4—41no—
206C5×C22⋊C4—41no—
207C5×C22⋊C4—41no—
208C5×C22⋊C4—84no—
209C42×C5—22no—
210C42×C5—41no—
211C42×C5—41no—
212C42×C5—41no—
213C42×C5—41no—
214C42×C5—41no—
215C22×#41C22×C511yescharacteristic
216C22×M16C22×C511yescharacteristic
217C22×M16C22×C511yescharacteristic
218C2×#117C22×C511yescharacteristic
219C2×#117C22×C511yescharacteristic
220C2×#117C22×C511yescharacteristic
221C22×C4⋊C4C22×C511yescharacteristic
222#428—22no—
223#428—22no—
224C2×#107—21no—
225C2×#106—21no—
226#421—22no—
227#421C4×C514yescomplemented
228C2×#104—22no—
229#419—21no—
230#418—21no—
231#417—21no—
232#417—21no—
233#416—22no—
234#391—21no—
235#390—21no—
236#386—22no—
237#380—22no—
238#344—22no—
239#342—22no—
240#340—22no—
241C23×C5—22no—
242C23×C5—41no—
243C23×C5—41no—
244C23×C5—42no—
245C23×C5—42no—
246C23×C5—41no—
247C23×C5—41no—
248C23×C5C4×D411yescharacteristic
249C23×C5#12011yescharacteristic
250C23×C5#12111yescharacteristic
251C23×C5#12111yescharacteristic
252C23×C5C22⋊Q811yescharacteristic
253C23×C5#12311yescharacteristic
254C23×C5#12711yescharacteristic
255C5×Q8—22no—
256C5×Q8—22no—
257C5×Q8—41no—
258C5×Q8—41no—
259C5×D4—22no—
260C5×D4—22no—
261C5×D4—42no—
262C5×D4—42no—
263C5×D4—42no—
264C5×D4—42no—
265C5×D4—41no—
266C5×D4—41no—
267C2×C4×C5—22no—
268C2×C4×C5—41no—
269C2×C4×C5—41no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—42no—
273C2×C4×C5—42no—
274C2×C4×C5—42no—
275C2×C4×C5—44no—
276C2×C4×C5—42no—
277C2×C4×C5—42no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—42no—
281C2×C4×C5—42no—
282C2×C4×C5—81no—
283C2×C4×C5—81no—
284C2×C4×C5—82no—
285C2×C4×C5—82no—
286C2×C4×C5—81no—
287C2×C4×C5—81no—
288C2×C4×C5C2×C22⋊C411yescharacteristic
289C2×C4×C5C2×C4⋊C411yescharacteristic
290C2×C4×C5#11711yescharacteristic
291C2×C4×C5C4×D411yescharacteristic
292C2×C4×C5C4×D411yescharacteristic
293C2×C4×C5C4×D411yescharacteristic
294C2×C4×C5#12011yescharacteristic
295C2×C4×C5#12011yescharacteristic
296C2×C4×C5#12111yescharacteristic
297C2×C4×C5#12111yescharacteristic
298C2×C4×C5#12111yescharacteristic
299C2×C4×C5#12111yescharacteristic
300C2×C4×C5#12111yescharacteristic
301C2×C4×C5#12111yescharacteristic
302C2×C4×C5C22⋊Q811yescharacteristic
303C2×C4×C5C22⋊Q811yescharacteristic
304C2×C4×C5C22⋊Q811yescharacteristic
305C2×C4×C5C22⋊Q811yescharacteristic
306C2×C4×C5C22⋊Q811yescharacteristic
307C2×C4×C5#12311yescharacteristic
308C2×C4×C5#12311yescharacteristic
309C2×C4×C5#12311yescharacteristic
310C2×C4×C5#12311yescharacteristic
311C2×C4×C5#12411yescharacteristic
312C2×C4×C5#12411yescharacteristic
313C2×C4×C5#12411yescharacteristic
314C2×C4×C5#12611yescharacteristic
315C2×C4×C5#12611yescharacteristic
316C5×C8—24no—
317C5×C8—42no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41C2×C4×C512yes—
329C2×#41C5×Q812yes—
330C22×Q8C5×D411yescharacteristic
331C22×D4—21no—
332C22×D4C5×D411yescharacteristic
333C23×C4—21no—
334C23×C4—21no—
335C23×C4C23×C511yescharacteristic
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×M16—21no—
345C2×M16C2×C4×C512yes—
346C2×M16C5×D412yes—
347C2×M16C5×D412yes—
348C22×C8—21no—
349C22×C8C5×D412yes—
350#117—21no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—21no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117C2×C4×C512yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4C5×D412yes—
370C2×C4⋊C4C5×D411yescharacteristic
371C2×C4⋊C4C5×D411yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4C5×D412yes—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379#107—24no—
380#106—24no—
381#104—28no—
382#103—22no—
383#103—22no—
384#102—22no—
385#102—22no—
386#95—24no—
387C22×C5—21no—
388C22×C5—21no—
389C22×C5—21no—
390C22×C5—21no—
391C22×C5—21no—
392C22×C5—21no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—44no—
398C22×C5—42no—
399C22×C5—82no—
400C22×C5—81no—
401C22×C5—81no—
402C22×C5#38511yescharacteristic
403C22×C5#38811yescharacteristic
404C22×C5#39011yescharacteristic
405C22×C5#39211yescharacteristic
406C22×C5#39411yescharacteristic
407C22×C5#39611yescharacteristic
408C22×C5#39911yescharacteristic
409C4×C5—42no—
410C4×C5—82no—
411C4×C5—82no—
412C4×C5—82no—
413C4×C5—81no—
414C4×C5—81no—
415C4×C5#38011yescharacteristic
416C4×C5#38511yescharacteristic
417C4×C5#38611yescharacteristic
418C4×C5#38811yescharacteristic
419C4×C5#39311yescharacteristic
420C4×C5#39411yescharacteristic
421C4×C5#39611yescharacteristic
422C4×C5#39711yescharacteristic
423C24—21no—
424C24C2×C5×D411yescharacteristic
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C5×C4⋊C412yes—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4C5×C4⋊C412yes—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—82no—
474C22×C4C22×C4×C511yescharacteristic
475C22×C4C2×C5×D411yescharacteristic
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D411yescharacteristic
478C22×C4C2×C5×D411yescharacteristic
479C22×C4C2×C5×D411yescharacteristic
480C22×C4C2×C5×D411yescharacteristic
481C22×C4C2×C5×Q811yescharacteristic
482C22×C4C5×#4111yescharacteristic
483C22×C4C5×#4111yescharacteristic
484C22×C4C5×#4111yescharacteristic
485C22×C4C5×#4111yescharacteristic
486C22×C4C5×#4111yescharacteristic
487C22×C4C5×#4111yescharacteristic
488M16—22no—
489M16—22no—
490M16—22no—
491M16—41no—
492M16—41no—
493M16—41no—
494M16—41no—
495M16C5×C22⋊C414yescomplemented
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—84no—
521C42—22no—
522C42—41no—
523C42—41no—
524C42—41no—
525C42—41no—
526C42—41no—
527C2×C5—21no—
528C2×C5—21no—
529C2×C5—21no—
530C2×C5—21no—
531C2×C5—21no—
532C2×C5—21no—
533C2×C5—82no—
534C2×C5#143911yescharacteristic
535C2×C5#200811yescharacteristic
536C2×C5#200911yescharacteristic
537C23—22no—
538C23—41no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—41no—
543C23—41no—
544C23C4×C5×D411yescharacteristic
545C23C5×#12011yescharacteristic
546C23C5×#12111yescharacteristic
547C23C5×#12111yescharacteristic
548C23C5×C22⋊Q811yescharacteristic
549C23C5×#12311yescharacteristic
550C23C5×#12711yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—41no—
554Q8—41no—
555D4—22no—
556D4—22no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—41no—
562D4—41no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4C2×C5×C22⋊C411yescharacteristic
585C2×C4C2×C5×C4⋊C411yescharacteristic
586C2×C4C5×#11711yescharacteristic
587C2×C4C4×C5×D411yescharacteristic
588C2×C4C4×C5×D411yescharacteristic
589C2×C4C4×C5×D411yescharacteristic
590C2×C4C5×#12011yescharacteristic
591C2×C4C5×#12011yescharacteristic
592C2×C4C5×#12111yescharacteristic
593C2×C4C5×#12111yescharacteristic
594C2×C4C5×#12111yescharacteristic
595C2×C4C5×#12111yescharacteristic
596C2×C4C5×#12111yescharacteristic
597C2×C4C5×#12111yescharacteristic
598C2×C4C5×C22⋊Q811yescharacteristic
599C2×C4C5×C22⋊Q811yescharacteristic
600C2×C4C5×C22⋊Q811yescharacteristic
601C2×C4C5×C22⋊Q811yescharacteristic
602C2×C4C5×C22⋊Q811yescharacteristic
603C2×C4C5×#12311yescharacteristic
604C2×C4C5×#12311yescharacteristic
605C2×C4C5×#12311yescharacteristic
606C2×C4C5×#12311yescharacteristic
607C2×C4C5×#12411yescharacteristic
608C2×C4C5×#12411yescharacteristic
609C2×C4C5×#12411yescharacteristic
610C2×C4C5×#12611yescharacteristic
611C2×C4C5×#12611yescharacteristic
612C8—24no—
613C8—42no—
614C5#1111711yescharacteristic, direct product factor, Sylow
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—44no—
626C22—42no—
627C22—82no—
628C22—81no—
629C22—81no—
630C22C5×#38511yescharacteristic
631C22C5×#38811yescharacteristic
632C22C5×#39011yescharacteristic
633C22C5×#39211yescharacteristic
634C22C5×#39411yescharacteristic
635C22C5×#39611yescharacteristic
636C22C5×#39911yescharacteristic
637C4—42no—
638C4—82no—
639C4—82no—
640C4—82no—
641C4—81no—
642C4—81no—
643C4C5×#38011yescharacteristic
644C4C5×#38511yescharacteristic
645C4C5×#38611yescharacteristic
646C4C5×#38811yescharacteristic
647C4C5×#39311yescharacteristic
648C4C5×#39411yescharacteristic
649C4C5×#39611yescharacteristic
650C4C5×#39711yescharacteristic
651C2—21no—
652C2—21no—
653C2—21no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—82no—
658C2C5×#143911yescharacteristic
659C2C5×#200811yescharacteristic
660C2C5×#200911yescharacteristic
subgroupG/H
center, socleC22×C5#392
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
1. C2×C5×#428C2semidirect
5. C2×C5×#344C2semidirect
6. C5×#1740C2semidirect
7. C5×#1736C2semidirect
20. C5×#421C4semidirect
34. #11117C5direct (N × H)
104. C2×#428C2×C5semidirect
108. C2×#344C2×C5semidirect
109. #1740C2×C5semidirect
110. #1736C2×C5semidirect
183. C5×M16C22⋊C4semidirect
227. #421C4×C5semidirect
495. M16C5×C22⋊C4semidirect
614. C5#11117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4282
C2×C5×#4212
C5×#28962
C5×#23112
C2×C5×#3442
C5×#17402
C5×#17362
#111175