Finite Group Databasebeta

← C5×#18553 #11941273

Subgroups — C5×#18553 #11941273

Order 1280.

1008 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3483C211yesmaximal, characteristic
2C5×#3141C211yesmaximal, characteristic, complemented
3C5×#3079C211yesmaximal, characteristic, complemented
4C5×#3039C211yesmaximal, characteristic, complemented
5C5×#1646C212yesmaximal, complemented
6C5×#1645C212yesmaximal, complemented
7C5×#1642C212yesmaximal, complemented
8C5×#1641C212yesmaximal, complemented
9C5×#1560C211yesmaximal, characteristic, complemented
10C5×#1489C211yesmaximal, characteristic, complemented
11C5×#1489C211yesmaximal, characteristic, complemented
12C2×C5×#137—21no—
13C5×Q82C2211yescharacteristic
14C5×#555—22no—
15C5×#555—21no—
16C5×#555—21no—
17C5×#555C2211yescharacteristic
18C5×#550—21no—
19C5×#550—21no—
20C5×#550C2211yescharacteristic
21C5×#550C2211yescharacteristic
22C5×#532—22no—
23C5×#532—21no—
24C5×#532—21no—
25C5×#532C2211yescharacteristic
26C2×C5×C4⋊Q8C2211yescharacteristic
27C4×C5×#41—21no—
28C4×C5×#41—21no—
29C4×C5×#41C2211yescharacteristic
30C4×C5×#41C2211yescharacteristic
31C5×#489—22no—
32C5×#487C2212yes—
33C5×#486C2212yes—
34C5×#477—21no—
35C5×#476—21no—
36C5×#475C2212yes—
37C5×#474C2212yes—
38C5×#462—21no—
39C5×#462C2212yes—
40C5×#461—21no—
41C5×#461C2212yes—
42C5×#428—21no—
43C5×#423C2211yescharacteristic
44C5×#423C2211yescharacteristic
45C5×#419—21no—
46C5×#417—21no—
47C5×#417—22no—
48C4×C5×M16C2211yescharacteristic
49C5×#333C2212yes—
50C5×#331C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×D4⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18553C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—22no—
57C2×C5×#41—21no—
58C2×C5×#41—21no—
59C2×C5×#41D411yescharacteristic
60C2×C5×#41D411yescharacteristic
61C2×C5×#41D412yes—
62C22×C5×Q8—21no—
63C5×#137—44no—
64C2×C5×Q16—22no—
65C2×C5×SD16—22no—
66C2×C5×M16—21no—
67C2×C5×M16—21no—
68C2×C5×M16—21no—
69C5×C4⋊Q8—22no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8—21no—
72C5×C4⋊Q8—21no—
73C5×C4⋊Q8—21no—
74C5×C4⋊Q8—21no—
75C5×C4⋊Q8C2312yes—
76C5×C4⋊Q8C2311yescharacteristic
77C5×#127—22no—
78C5×#127—21no—
79C5×#127—21no—
80C5×#127C2311yescharacteristic
81C5×#124—22no—
82C5×#124—22no—
83C5×#124—22no—
84C5×#124—22no—
85C5×#124D412yes—
86C5×#121—22no—
87C5×#121—22no—
88C5×#121—22no—
89C5×#121—22no—
90C5×#121—21no—
91C5×#121—21no—
92C5×#121—22no—
93C5×#121—22no—
94C5×#121—21no—
95C5×#121—21no—
96C5×#121—21no—
97C5×#121—21no—
98C4×C5×Q8—21no—
99C4×C5×Q8—21no—
100C4×C5×Q8D411yescharacteristic
101C4×C5×Q8D411yescharacteristic
102C4×C5×Q8C2311yescharacteristic
103C4×C5×Q8C2311yescharacteristic
104C4×C5×D4—22no—
105C4×C5×D4—22no—
106C4×C5×D4—22no—
107C4×C5×D4—22no—
108C4×C5×D4—21no—
109C4×C5×D4—21no—
110C4×C5×D4—21no—
111C4×C5×D4—21no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4—21no—
115C4×C5×D4—21no—
116C4×C5×D4D411yescharacteristic
117C4×C5×D4D411yescharacteristic
118C4×C5×D4C2311yescharacteristic
119C4×C5×D4C2311yescharacteristic
120C5×#117—22no—
121C5×#117—22no—
122C5×#117—21no—
123C5×#117—21no—
124C5×#117—21no—
125C5×#117—21no—
126C5×#117D411yescharacteristic
127C5×#117D411yescharacteristic
128C2×C5×C4⋊C4—21no—
129C2×C5×C4⋊C4—21no—
130C2×C42×C5—22no—
131C2×C42×C5—21no—
132C2×C42×C5—21no—
133C2×C42×C5C2311yescharacteristic
134C5×#107—22no—
135C5×#106—22no—
136C5×C4⋊C8—21no—
137C5×C4⋊C8—21no—
138C5×C4⋊C8C2312yes—
139C5×C4⋊C8C2312yes—
140C5×#103—22no—
141C5×#103—24no—
142C5×#103—22no—
143C5×#103—22no—
144C5×#102—22no—
145C5×#102—24no—
146C5×#97—21no—
147C4×C5×C8C2312yes—
148#3483C2×C511yescharacteristic
149#3141C2×C511yescharacteristic, complemented
150#3079C2×C511yescharacteristic, complemented
151#3039C2×C511yescharacteristic, complemented
152#1646C2×C512yescomplemented
153#1645C2×C512yescomplemented
154#1642C2×C512yescomplemented
155#1641C2×C512yescomplemented
156#1560C2×C511yescharacteristic, complemented
157#1489C2×C511yescharacteristic, complemented
158#1489C2×C511yescharacteristic, complemented
159C5×#41—22no—
160C5×#41—22no—
161C5×#41—41no—
162C5×#41—41no—
163C5×#41—44no—
164C5×#41—42no—
165C5×#41—42no—
166C5×#41—42no—
167C5×#41—42no—
168C5×#41—84no—
169C2×C5×Q8—22no—
170C2×C5×Q8—22no—
171C2×C5×Q8—42no—
172C2×C5×Q8—42no—
173C2×C5×Q8—41no—
174C2×C5×Q8C2×D411yescharacteristic
175C2×C5×Q8C2×D411yescharacteristic
176C2×C5×Q8C2×D412yes—
177C2×C5×D4—22no—
178C2×C5×D4—22no—
179C2×C5×D4—21no—
180C2×C5×D4—21no—
181C2×C5×D4—22no—
182C2×C5×D4—22no—
183C2×C5×D4—22no—
184C2×C5×D4—22no—
185C2×C5×D4—21no—
186C2×C5×D4—21no—
187C2×C5×D4C2×D411yescharacteristic
188C2×C5×D4C2×D411yescharacteristic
189C2×C5×D4C2×D412yes—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—22no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—41no—
200C22×C4×C5C2×D411yescharacteristic
201C22×C4×C5C2×D411yescharacteristic
202C22×C4×C5C2×D411yescharacteristic
203C5×Q16—44no—
204C5×SD16—44no—
205C5×M16—42no—
206C5×M16—42no—
207C5×M16—42no—
208C2×C5×C8—22no—
209C2×C5×C8—22no—
210C2×C5×C8—22no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—22no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—41no—
222C5×C4⋊C4—41no—
223C5×C4⋊C4C2×D411yescharacteristic
224C5×C4⋊C4C2×D411yescharacteristic
225C5×C4⋊C4C2×D411yescharacteristic
226C5×C4⋊C4C2×D411yescharacteristic
227C5×C22⋊C4—22no—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—22no—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—21no—
232C5×C22⋊C4—21no—
233C5×C22⋊C4—22no—
234C5×C22⋊C4—22no—
235C5×C22⋊C4—21no—
236C5×C22⋊C4—21no—
237C5×C22⋊C4—21no—
238C5×C22⋊C4—21no—
239C42×C5—22no—
240C42×C5—22no—
241C42×C5—21no—
242C42×C5—21no—
243C42×C5—21no—
244C42×C5—21no—
245C42×C5—21no—
246C42×C5—21no—
247C42×C5C2×D411yescharacteristic
248C42×C5C2×D411yescharacteristic
249C42×C5C2×D411yescharacteristic
250C42×C5C2411yescharacteristic
251C2×#137—21no—
252Q82C22×C511yescharacteristic
253#555—22no—
254#555—21no—
255#555—21no—
256#555C22×C511yescharacteristic
257#550—21no—
258#550—21no—
259#550C22×C511yescharacteristic
260#550C22×C511yescharacteristic
261#532—22no—
262#532—21no—
263#532—21no—
264#532C22×C511yescharacteristic
265C2×C4⋊Q8C22×C511yescharacteristic
266C4×#41—21no—
267C4×#41—21no—
268C4×#41C22×C511yescharacteristic
269C4×#41C22×C511yescharacteristic
270#489—22no—
271#487C22×C512yes—
272#486C22×C512yes—
273#477—21no—
274#476—21no—
275#475C22×C512yes—
276#474C22×C512yes—
277#462—21no—
278#462C22×C512yes—
279#461—21no—
280#461C22×C512yes—
281#428—21no—
282#423C22×C511yescharacteristic
283#423C22×C511yescharacteristic
284#419—21no—
285#417—21no—
286#417—22no—
287C4×M16C22×C511yescharacteristic
288#333C22×C512yes—
289#331C22×C512yes—
290Q8⋊C8C22×C512yes—
291Q8⋊C8C22×C512yes—
292D4⋊C8C22×C512yes—
293D4⋊C8C22×C512yes—
294C23×C5—21no—
295C23×C5—21no—
296C23×C5—22no—
297C23×C5#12011yescharacteristic
298C5×Q8—21no—
299C5×Q8—21no—
300C5×Q8—42no—
301C5×Q8—42no—
302C5×Q8—42no—
303C5×Q8—82no—
304C5×Q8—82no—
305C5×Q8AGL(1,ℤ/8)12yes—
306C5×Q8#13712yescomplemented
307C5×D4—21no—
308C5×D4—21no—
309C5×D4—21no—
310C5×D4—21no—
311C5×D4—42no—
312C5×D4—42no—
313C5×D4—42no—
314C5×D4—44no—
315C5×D4—44no—
316C5×D4—41no—
317C5×D4—41no—
318C5×D4—41no—
319C5×D4—41no—
320C5×D4—82no—
321C5×D4—82no—
322C5×D4—82no—
323C5×D4—82no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—44no—
339C2×C4×C5—44no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—44no—
345C2×C4×C5—42no—
346C2×C4×C5—42no—
347C2×C4×C5—42no—
348C2×C4×C5—82no—
349C2×C4×C5#12011yescharacteristic
350C2×C4×C5#12011yescharacteristic
351C2×C4×C5#12011yescharacteristic
352C2×C4×C5C22×D411yescharacteristic
353C2×C4×C5C22×D411yescharacteristic
354C2×C4×C5C22×D411yescharacteristic
355C5×C8—42no—
356C5×C8—42no—
357C5×C8—42no—
358C2×#41—22no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41C5×D411yescharacteristic
362C2×#41C5×D411yescharacteristic
363C2×#41C5×D412yes—
364C22×Q8—21no—
365#137—44no—
366C2×Q16—22no—
367C2×SD16—22no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C4⋊Q8—22no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C512yes—
378C4⋊Q8C23×C511yescharacteristic
379#127—22no—
380#127—21no—
381#127—21no—
382#127C23×C511yescharacteristic
383#124—22no—
384#124—22no—
385#124—22no—
386#124—22no—
387#124C5×D412yes—
388#121—22no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—21no—
394#121—22no—
395#121—22no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8C5×D411yescharacteristic
403C4×Q8C5×D411yescharacteristic
404C4×Q8C23×C511yescharacteristic
405C4×Q8C23×C511yescharacteristic
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4C5×D411yescharacteristic
419C4×D4C5×D411yescharacteristic
420C4×D4C23×C511yescharacteristic
421C4×D4C23×C511yescharacteristic
422#117—22no—
423#117—22no—
424#117—21no—
425#117—21no—
426#117—21no—
427#117—21no—
428#117C5×D411yescharacteristic
429#117C5×D411yescharacteristic
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C42—22no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42C23×C511yescharacteristic
436#107—22no—
437#106—22no—
438C4⋊C8—21no—
439C4⋊C8—21no—
440C4⋊C8C23×C512yes—
441C4⋊C8C23×C512yes—
442#103—22no—
443#103—24no—
444#103—22no—
445#103—22no—
446#102—22no—
447#102—24no—
448#97—21no—
449C4×C8C23×C512yes—
450C22×C5—21no—
451C22×C5—21no—
452C22×C5—21no—
453C22×C5—41no—
454C22×C5—42no—
455C22×C5—41no—
456C22×C5—41no—
457C22×C5—42no—
458C22×C5—41no—
459C22×C5—42no—
460C22×C5—41no—
461C22×C5—41no—
462C22×C5C2×#12011yescharacteristic
463C4×C5—21no—
464C4×C5—22no—
465C4×C5—21no—
466C4×C5—22no—
467C4×C5—21no—
468C4×C5—41no—
469C4×C5—41no—
470C4×C5—42no—
471C4×C5—41no—
472C4×C5—41no—
473C4×C5—82no—
474C4×C5#45512yes—
475C4×C5C2×AGL(1,ℤ/8)11yescharacteristic
476C4×C5C2×#13711yescharacteristic
477C4×C5#57511yescharacteristic
478C4×C5#57511yescharacteristic
479#41—22no—
480#41—22no—
481#41—41no—
482#41—41no—
483#41—44no—
484#41—42no—
485#41—42no—
486#41—42no—
487#41—42no—
488#41—84no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—41no—
494C2×Q8C2×C5×D411yescharacteristic
495C2×Q8C2×C5×D411yescharacteristic
496C2×Q8C2×C5×D412yes—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4C2×C5×D411yescharacteristic
508C2×D4C2×C5×D411yescharacteristic
509C2×D4C2×C5×D412yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—41no—
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523Q16—44no—
524SD16—44no—
525M16—42no—
526M16—42no—
527M16—42no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4C2×C5×D411yescharacteristic
544C4⋊C4C2×C5×D411yescharacteristic
545C4⋊C4C2×C5×D411yescharacteristic
546C4⋊C4C2×C5×D411yescharacteristic
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C42—22no—
560C42—22no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42C2×C5×D411yescharacteristic
568C42C2×C5×D411yescharacteristic
569C42C2×C5×D411yescharacteristic
570C42C24×C511yescharacteristic
571C2×C5—41no—
572C2×C5—81no—
573C2×C5—81no—
574C2×C5—82no—
575C2×C5#300611yescharacteristic
576C2×C5#300711yescharacteristic
577C2×C5C2×#45511yescharacteristic
578C23—21no—
579C23—21no—
580C23—22no—
581C23C5×#12011yescharacteristic
582Q8—21no—
583Q8—21no—
584Q8—42no—
585Q8—42no—
586Q8—42no—
587Q8—82no—
588Q8—82no—
589Q8C5×AGL(1,ℤ/8)12yes—
590Q8C5×#13712yescomplemented
591D4—21no—
592D4—21no—
593D4—21no—
594D4—21no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—44no—
599D4—44no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—82no—
605D4—82no—
606D4—82no—
607D4—82no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—82no—
633C2×C4C5×#12011yescharacteristic
634C2×C4C5×#12011yescharacteristic
635C2×C4C5×#12011yescharacteristic
636C2×C4C22×C5×D411yescharacteristic
637C2×C4C22×C5×D411yescharacteristic
638C2×C4C22×C5×D411yescharacteristic
639C8—42no—
640C8—42no—
641C8—42no—
642C5#1855311yescharacteristic, direct product factor, Sylow
643C22—21no—
644C22—21no—
645C22—21no—
646C22—41no—
647C22—42no—
648C22—41no—
649C22—41no—
650C22—42no—
651C22—41no—
652C22—42no—
653C22—41no—
654C22—41no—
655C22C2×C5×#12011yescharacteristic
656C4—21no—
657C4—22no—
658C4—21no—
659C4—22no—
660C4—21no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—41no—
665C4—41no—
666C4—82no—
667C4C5×#45512yes—
668C4C2×C5×AGL(1,ℤ/8)11yescharacteristic
669C4C2×C5×#13711yescharacteristic
670C4C5×#57511yescharacteristic
671C4C5×#57511yescharacteristic
672C2—41no—
673C2—81no—
674C2—81no—
675C2—82no—
676C2C5×#300611yescharacteristic
677C2C5×#300711yescharacteristic
678C2C2×C5×#45511yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3483C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3141C2semidirect
3. C5×#3079C2semidirect
4. C5×#3039C2semidirect
5. C5×#1646C2semidirect
6. C5×#1645C2semidirect
7. C5×#1642C2semidirect
8. C5×#1641C2semidirect
9. C5×#1560C2semidirect
10. C5×#1489C2semidirect
11. C5×#1489C2semidirect
55. #18553C5direct (N × H)
149. #3141C2×C5semidirect
150. #3079C2×C5semidirect
151. #3039C2×C5semidirect
152. #1646C2×C5semidirect
153. #1645C2×C5semidirect
154. #1642C2×C5semidirect
155. #1641C2×C5semidirect
156. #1560C2×C5semidirect
157. #1489C2×C5semidirect
158. #1489C2×C5semidirect
306. C5×Q8#137semidirect
590. Q8C5×#137semidirect
642. C5#18553direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34832
C5×#31412
C5×#30792
C5×#30392
C5×#16462
C5×#16452
C5×#16422
C5×#16412
C5×#15602
C5×#14892
#185535