Finite Group Databasebeta

← C5×#11085 #11933805

Subgroups — C5×#11085 #11933805

Order 1280.

938 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#421C211yesmaximal, characteristic
2C22×C5×#104C211yesmaximal, characteristic
3C2×C5×#410C211yesmaximal, characteristic
4C5×#2296C211yesmaximal, characteristic, complemented
5C2×C5×#344C211yesmaximal, characteristic, complemented
6C2×C5×#339C211yesmaximal, 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×C42×C5C2211yescharacteristic
15C5×#421—22no—
16C5×#421C414yescomplemented
17C2×C5×#104—22no—
18C2×C5×#104—22no—
19C2×C5×#104—22no—
20C2×C5×#104—22no—
21C5×#410—22no—
22C5×#410—22no—
23C2×C5×#99—22no—
24C5×#389—22no—
25C5×#385—22no—
26C4×C5×C4⋊C4—22no—
27C5×#344—22no—
28C5×#339—22no—
29C5×H(3,ℤ/4)—22no—
30#11085C511yesmaximal, characteristic, direct product factor, Sylow
31C2×C5×#41—21no—
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×#41C2×C412yes—
42C2×C5×#41D412yes—
43C22×C5×Q8Q811yescharacteristic
44C22×C5×D4—21no—
45C22×C5×D4Q811yescharacteristic
46C23×C4×C5—21no—
47C23×C4×C5—21no—
48C23×C4×C5C2311yescharacteristic
49C2×C5×M16—21no—
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×M16C2×C412yes—
60C2×C5×M16D412yes—
61C22×C5×C8—21no—
62C22×C5×C8—21no—
63C5×#117—21no—
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×#117C2×C412yes—
73C5×#117D412yes—
74C5×#117D412yes—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—24no—
78C2×C5×C4⋊C4—21no—
79C2×C5×C22⋊C4—21no—
80C2×C5×C22⋊C4—21no—
81C2×C5×C22⋊C4D412yes—
82C2×C42×C5—21no—
83C2×C42×C5—21no—
84C2×C42×C5—21no—
85C2×C42×C5—21no—
86C2×C42×C5—21no—
87C2×C42×C5—21no—
88C2×C42×C5—21no—
89C2×C42×C5D412yes—
90C2×C42×C5D412yes—
91C5×#104—28no—
92C5×#104—28no—
93C5×#99—28no—
94C5×#95—24no—
95C2×#421C2×C511yescharacteristic
96C22×#104C2×C511yescharacteristic
97C2×#410C2×C511yescharacteristic
98#2296C2×C511yescharacteristic, complemented
99C2×#344C2×C511yescharacteristic, complemented
100C2×#339C2×C511yescharacteristic, complemented
101C2×H(3,ℤ/4)C2×C511yescharacteristic, complemented
102C24×C5—21no—
103C24×C5C2×D411yescharacteristic
104C5×#41—22no—
105C5×#41—22no—
106C5×#41—22no—
107C5×#41—22no—
108C5×#41—22no—
109C5×#41—22no—
110C5×#41—22no—
111C5×#41—22no—
112C5×#41—41no—
113C5×#41—41no—
114C5×#41—41no—
115C5×#41—41no—
116C5×#41—41no—
117C5×#41—41no—
118C5×#41—41no—
119C5×#41—41no—
120C2×C5×Q8—21no—
121C2×C5×Q8—21no—
122C2×C5×Q8—21no—
123C2×C5×Q8—21no—
124C2×C5×Q8—21no—
125C2×C5×Q8C4⋊C412yescomplemented
126C2×C5×D4—22no—
127C2×C5×D4—22no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×C5×D4—21no—
133C2×C5×D4—41no—
134C2×C5×D4—41no—
135C2×C5×D4—41no—
136C2×C5×D4—41no—
137C2×C5×D4C4⋊C412yescomplemented
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—44no—
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×C5C22×C411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×Q811yescharacteristic
160C22×C4×C5#4111yescharacteristic
161C22×C4×C5#4111yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C22×C4×C5#4111yescharacteristic
164C22×C4×C5#4111yescharacteristic
165C22×C4×C5#4111yescharacteristic
166C5×M16—22no—
167C5×M16—22no—
168C5×M16—22no—
169C5×M16—22no—
170C5×M16—41no—
171C5×M16—41no—
172C5×M16—41no—
173C5×M16—41no—
174C2×C5×C8—22no—
175C2×C5×C8—22no—
176C2×C5×C8—41no—
177C2×C5×C8—41no—
178C2×C5×C8—41no—
179C2×C5×C8—41no—
180C5×C4⋊C4—22no—
181C5×C4⋊C4—22no—
182C5×C4⋊C4—22no—
183C5×C4⋊C4—48no—
184C5×C4⋊C4—41no—
185C5×C4⋊C4—41no—
186C5×C4⋊C4—41no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C5×C22⋊C4—41no—
193C42×C5—22no—
194C42×C5—22no—
195C42×C5—22no—
196C42×C5—22no—
197C42×C5—41no—
198C42×C5—41no—
199C42×C5—41no—
200C42×C5—41no—
201C42×C5—41no—
202C42×C5C22⋊C414yes—
203C22×#41C22×C511yescharacteristic
204C22×M16C22×C511yescharacteristic
205C22×M16C22×C511yescharacteristic
206C2×#117C22×C511yescharacteristic
207C2×#117C22×C511yescharacteristic
208C2×#117C22×C511yescharacteristic
209C22×C42C22×C511yescharacteristic
210#421—22no—
211#421C4×C514yescomplemented
212C2×#104—22no—
213C2×#104—22no—
214C2×#104—22no—
215C2×#104—22no—
216#410—22no—
217#410—22no—
218C2×#99—22no—
219#389—22no—
220#385—22no—
221C4×C4⋊C4—22no—
222#344—22no—
223#339—22no—
224H(3,ℤ/4)—22no—
225C23×C5—22no—
226C23×C5—42no—
227C23×C5—41no—
228C23×C5—41no—
229C23×C5—82no—
230C23×C5C4×D411yescharacteristic
231C23×C5#12011yescharacteristic
232C23×C5#12011yescharacteristic
233C23×C5#12111yescharacteristic
234C23×C5#12111yescharacteristic
235C23×C5C22⋊Q811yescharacteristic
236C23×C5#12411yescharacteristic
237C5×Q8—22no—
238C5×Q8—22no—
239C5×Q8—41no—
240C5×Q8—41no—
241C5×D4—22no—
242C5×D4—22no—
243C5×D4—42no—
244C5×D4—42no—
245C5×D4—42no—
246C5×D4—42no—
247C5×D4—41no—
248C5×D4—41no—
249C2×C4×C5—24no—
250C2×C4×C5—22no—
251C2×C4×C5—24no—
252C2×C4×C5—44no—
253C2×C4×C5—42no—
254C2×C4×C5—44no—
255C2×C4×C5—44no—
256C2×C4×C5—42no—
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—44no—
264C2×C4×C5—42no—
265C2×C4×C5—42no—
266C2×C4×C5—82no—
267C2×C4×C5C2×C22⋊C411yescharacteristic
268C2×C4×C5C2×C4⋊C411yescharacteristic
269C2×C4×C5#11711yescharacteristic
270C2×C4×C5C4×D411yescharacteristic
271C2×C4×C5C4×D411yescharacteristic
272C2×C4×C5C4×D411yescharacteristic
273C2×C4×C5#12011yescharacteristic
274C2×C4×C5#12111yescharacteristic
275C2×C4×C5#12111yescharacteristic
276C2×C4×C5#12111yescharacteristic
277C2×C4×C5#12111yescharacteristic
278C2×C4×C5#12111yescharacteristic
279C2×C4×C5#12111yescharacteristic
280C2×C4×C5C22⋊Q811yescharacteristic
281C2×C4×C5C22⋊Q811yescharacteristic
282C2×C4×C5C22⋊Q811yescharacteristic
283C2×C4×C5C22⋊Q811yescharacteristic
284C2×C4×C5C22⋊Q811yescharacteristic
285C2×C4×C5#12311yescharacteristic
286C2×C4×C5#12311yescharacteristic
287C2×C4×C5#12311yescharacteristic
288C2×C4×C5#12311yescharacteristic
289C2×C4×C5#12311yescharacteristic
290C2×C4×C5#12411yescharacteristic
291C2×C4×C5#12411yescharacteristic
292C2×C4×C5#12611yescharacteristic
293C2×C4×C5#12611yescharacteristic
294C2×C4×C5#12711yescharacteristic
295C5×C8—42no—
296C5×C8—42no—
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—21no—
303C2×#41—21no—
304C2×#41—21no—
305C2×#41—21no—
306C2×#41—21no—
307C2×#41C2×C4×C512yes—
308C2×#41C5×D412yes—
309C22×Q8C5×Q811yescharacteristic
310C22×D4—21no—
311C22×D4C5×Q811yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4C23×C511yescharacteristic
315C2×M16—21no—
316C2×M16—21no—
317C2×M16—21no—
318C2×M16—21no—
319C2×M16—21no—
320C2×M16—21no—
321C2×M16—21no—
322C2×M16—21no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16C2×C4×C512yes—
326C2×M16C5×D412yes—
327C22×C8—21no—
328C22×C8—21no—
329#117—21no—
330#117—21no—
331#117—21no—
332#117—21no—
333#117—21no—
334#117—21no—
335#117—21no—
336#117—21no—
337#117—21no—
338#117C2×C4×C512yes—
339#117C5×D412yes—
340#117C5×D412yes—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4C5×D412yes—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42C5×D412yes—
356C2×C42C5×D412yes—
357#104—28no—
358#104—28no—
359#99—28no—
360#95—24no—
361C22×C5—22no—
362C22×C5—22no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—41no—
367C22×C5—41no—
368C22×C5—42no—
369C22×C5—82no—
370C22×C5—82no—
371C22×C5—82no—
372C22×C5#38511yescharacteristic
373C22×C5#38611yescharacteristic
374C22×C5#38811yescharacteristic
375C22×C5#39211yescharacteristic
376C22×C5#39311yescharacteristic
377C22×C5#39411yescharacteristic
378C22×C5#39611yescharacteristic
379C4×C5—44no—
380C4×C5—44no—
381C4×C5—42no—
382C4×C5—82no—
383C4×C5—82no—
384C4×C5#38011yescharacteristic
385C4×C5#38511yescharacteristic
386C4×C5#38811yescharacteristic
387C4×C5#39011yescharacteristic
388C4×C5#39411yescharacteristic
389C4×C5#39611yescharacteristic
390C4×C5#39711yescharacteristic
391C4×C5#39911yescharacteristic
392C24—21no—
393C24C2×C5×D411yescharacteristic
394#41—22no—
395#41—22no—
396#41—22no—
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—41no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8C5×C4⋊C412yescomplemented
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4C5×C4⋊C412yescomplemented
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4C22×C4×C511yescharacteristic
443C22×C4C2×C5×D411yescharacteristic
444C22×C4C2×C5×D411yescharacteristic
445C22×C4C2×C5×D411yescharacteristic
446C22×C4C2×C5×D411yescharacteristic
447C22×C4C2×C5×D411yescharacteristic
448C22×C4C2×C5×D411yescharacteristic
449C22×C4C2×C5×Q811yescharacteristic
450C22×C4C5×#4111yescharacteristic
451C22×C4C5×#4111yescharacteristic
452C22×C4C5×#4111yescharacteristic
453C22×C4C5×#4111yescharacteristic
454C22×C4C5×#4111yescharacteristic
455C22×C4C5×#4111yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—41no—
461M16—41no—
462M16—41no—
463M16—41no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—48no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—41no—
483C42—22no—
484C42—22no—
485C42—22no—
486C42—22no—
487C42—41no—
488C42—41no—
489C42—41no—
490C42—41no—
491C42—41no—
492C42C5×C22⋊C414yes—
493C2×C5—21no—
494C2×C5—21no—
495C2×C5—21no—
496C2×C5—21no—
497C2×C5—21no—
498C2×C5—21no—
499C2×C5—82no—
500C2×C5#143911yescharacteristic
501C2×C5#203112yes—
502C23—22no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—82no—
507C23C4×C5×D411yescharacteristic
508C23C5×#12011yescharacteristic
509C23C5×#12011yescharacteristic
510C23C5×#12111yescharacteristic
511C23C5×#12111yescharacteristic
512C23C5×C22⋊Q811yescharacteristic
513C23C5×#12411yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—41no—
517Q8—41no—
518D4—22no—
519D4—22no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—41no—
525D4—41no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—82no—
544C2×C4C2×C5×C22⋊C411yescharacteristic
545C2×C4C2×C5×C4⋊C411yescharacteristic
546C2×C4C5×#11711yescharacteristic
547C2×C4C4×C5×D411yescharacteristic
548C2×C4C4×C5×D411yescharacteristic
549C2×C4C4×C5×D411yescharacteristic
550C2×C4C5×#12011yescharacteristic
551C2×C4C5×#12111yescharacteristic
552C2×C4C5×#12111yescharacteristic
553C2×C4C5×#12111yescharacteristic
554C2×C4C5×#12111yescharacteristic
555C2×C4C5×#12111yescharacteristic
556C2×C4C5×#12111yescharacteristic
557C2×C4C5×C22⋊Q811yescharacteristic
558C2×C4C5×C22⋊Q811yescharacteristic
559C2×C4C5×C22⋊Q811yescharacteristic
560C2×C4C5×C22⋊Q811yescharacteristic
561C2×C4C5×C22⋊Q811yescharacteristic
562C2×C4C5×#12311yescharacteristic
563C2×C4C5×#12311yescharacteristic
564C2×C4C5×#12311yescharacteristic
565C2×C4C5×#12311yescharacteristic
566C2×C4C5×#12311yescharacteristic
567C2×C4C5×#12411yescharacteristic
568C2×C4C5×#12411yescharacteristic
569C2×C4C5×#12611yescharacteristic
570C2×C4C5×#12611yescharacteristic
571C2×C4C5×#12711yescharacteristic
572C8—42no—
573C8—42no—
574C5#1108511yescharacteristic, direct product factor, Sylow
575C22—22no—
576C22—22no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22C5×#38511yescharacteristic
587C22C5×#38611yescharacteristic
588C22C5×#38811yescharacteristic
589C22C5×#39211yescharacteristic
590C22C5×#39311yescharacteristic
591C22C5×#39411yescharacteristic
592C22C5×#39611yescharacteristic
593C4—44no—
594C4—44no—
595C4—42no—
596C4—82no—
597C4—82no—
598C4C5×#38011yescharacteristic
599C4C5×#38511yescharacteristic
600C4C5×#38811yescharacteristic
601C4C5×#39011yescharacteristic
602C4C5×#39411yescharacteristic
603C4C5×#39611yescharacteristic
604C4C5×#39711yescharacteristic
605C4C5×#39911yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—82no—
613C2C5×#143911yescharacteristic
614C2C5×#203112yes—
subgroupG/H
centerC2×C4×C5#124
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
socleC22×C5#393
prime radicalC22×C5×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#2296C2semidirect
5. C2×C5×#344C2semidirect
6. C2×C5×#339C2semidirect
7. C2×C5×H(3,ℤ/4)C2semidirect
16. C5×#421C4semidirect
30. #11085C5direct (N × H)
98. #2296C2×C5semidirect
99. C2×#344C2×C5semidirect
100. C2×#339C2×C5semidirect
101. C2×H(3,ℤ/4)C2×C5semidirect
125. C2×C5×Q8C4⋊C4semidirect
137. C2×C5×D4C4⋊C4semidirect
211. #421C4×C5semidirect
415. C2×Q8C5×C4⋊C4semidirect
427. C2×D4C5×C4⋊C4semidirect
574. C5#11085direct (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
C22×C5×#1042
C2×C5×#4102
C5×#22962
C2×C5×#3442
C2×C5×#3392
C2×C5×H(3,ℤ/4)2
#110855