Finite Group Databasebeta

← C5×#18298 #11941018

Subgroups — C5×#18298 #11941018

Order 1280.

1024 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3460C211yesmaximal, characteristic, complemented
2C5×#3188C212yesmaximal, complemented
3C5×#2635C211yesmaximal, characteristic, complemented
4C5×#1618C212yesmaximal, complemented
5C5×#1617C211yesmaximal, characteristic, complemented
6C5×#1616C211yesmaximal, characteristic, complemented
7C5×#1600C212yesmaximal, complemented
8C5×#1599C211yesmaximal, characteristic, complemented
9C5×#1598C211yesmaximal, characteristic, complemented
10C5×#1516C212yesmaximal, complemented
11C5×#1459C211yesmaximal, characteristic, complemented
12C5×#544C2211yescharacteristic
13C5×#542—22no—
14C5×#540—22no—
15C5×#538—21no—
16C5×#538C2212yes—
17C5×#537C2211yescharacteristic
18C5×#535—21no—
19C5×#532—22no—
20C5×#529—22no—
21C5×#525—21no—
22C5×#525C2212yes—
23C2×C5×#121C2211yescharacteristic
24C4×C5×#41—21no—
25C2×C4×C5×D4C2211yescharacteristic
26C5×#484C2212yes—
27C5×#482—22no—
28C5×#481C2212yes—
29C5×#466—22no—
30C5×#465—22no—
31C5×#450C2212yes—
32C5×#449—22no—
33C5×#447C2212yes—
34C2×C5×C22⋊C8C2212yes—
35C5×#400C2211yescharacteristic
36C5×#399C2211yescharacteristic
37C5×#394—21no—
38C5×#394C2211yescharacteristic
39C5×#392—21no—
40C5×#392C2211yescharacteristic
41C5×#388—21no—
42C5×#386—21no—
43C5×#381C2211yescharacteristic
44C5×#328C2212yes—
45C5×#328C2212yes—
46C5×#327C2212yes—
47C5×#327C2212yes—
48C5×#324C2211yescharacteristic
49C5×#324C2211yescharacteristic
50C5×#323C2212yes—
51#18298C511yesmaximal, characteristic, direct product factor, Sylow
52C2×C5×#41—21no—
53C2×C5×#41—21no—
54C2×C5×#41D412yescomplemented
55C22×C5×D4—21no—
56C22×C5×D4—21no—
57C22×C5×D4D411yescharacteristic
58C22×C5×D4C2311yescharacteristic
59C23×C4×C5D411yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C2×C5×SD16—22no—
62C2×C5×D8—22no—
63C22×C5×C8—22no—
64C5×C4⋊Q8—22no—
65C5×#127—22no—
66C5×#126—22no—
67C5×#126—22no—
68C5×#125—22no—
69C5×#124—22no—
70C5×#124—22no—
71C5×#124—22no—
72C5×#123—22no—
73C5×#123—22no—
74C5×#123—22no—
75C5×#123—22no—
76C5×C22⋊Q8—21no—
77C5×C22⋊Q8—21no—
78C5×C22⋊Q8—22no—
79C5×C22⋊Q8D412yescomplemented
80C5×C22⋊Q8C2312yes—
81C5×#121—21no—
82C5×#121—22no—
83C5×#121—22no—
84C5×#121—22no—
85C5×#121—22no—
86C5×#121—22no—
87C5×#121—21no—
88C5×#121—22no—
89C5×#121—22no—
90C5×#121D412yescomplemented
91C5×#121C2312yes—
92C5×#120—22no—
93C5×#120—22no—
94C4×C5×Q8—21no—
95C4×C5×Q8—21no—
96C4×C5×D4—21no—
97C4×C5×D4—21no—
98C4×C5×D4—22no—
99C4×C5×D4—22no—
100C4×C5×D4—22no—
101C4×C5×D4—22no—
102C4×C5×D4—22no—
103C4×C5×D4—22no—
104C5×#117—22no—
105C5×#117—21no—
106C5×#117—21no—
107C5×#117D412yescomplemented
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4D411yescharacteristic
118C2×C5×C22⋊C4C2311yescharacteristic
119C2×C42×C5—22no—
120C2×C42×C5D411yescharacteristic
121C5×#107—22no—
122C5×#106—22no—
123C5×#103—22no—
124C5×#102—22no—
125C5×#102—22no—
126C5×#102—22no—
127C5×C22⋊C8—22no—
128C5×C22⋊C8C2312yes—
129C5×C22⋊C8C2312yes—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C5×#95C2311yescharacteristic
134C5×#95C2311yescharacteristic
135#3460C2×C511yescharacteristic, complemented
136#3188C2×C512yescomplemented
137#2635C2×C511yescharacteristic, complemented
138#1618C2×C512yescomplemented
139#1617C2×C511yescharacteristic, complemented
140#1616C2×C511yescharacteristic, complemented
141#1600C2×C512yescomplemented
142#1599C2×C511yescharacteristic, complemented
143#1598C2×C511yescharacteristic, complemented
144#1516C2×C512yescomplemented
145#1459C2×C511yescharacteristic, complemented
146C24×C5—21no—
147C24×C5C2×D411yescharacteristic
148C24×C5C2×D411yescharacteristic
149C5×#41—42no—
150C5×#41—42no—
151C5×#41—82no—
152C5×#41—82no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8C2×D412yes—
156C2×C5×D4—21no—
157C2×C5×D4—22no—
158C2×C5×D4—22no—
159C2×C5×D4—22no—
160C2×C5×D4—22no—
161C2×C5×D4—21no—
162C2×C5×D4—22no—
163C2×C5×D4—22no—
164C2×C5×D4—22no—
165C2×C5×D4—22no—
166C2×C5×D4—41no—
167C2×C5×D4—42no—
168C2×C5×D4—42no—
169C2×C5×D4—81no—
170C2×C5×D4—81no—
171C2×C5×D4—81no—
172C2×C5×D4—81no—
173C2×C5×D4—81no—
174C2×C5×D4C2×D412yes—
175C22×C4×C5—22no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—81no—
184C22×C4×C5—81no—
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D412yes—
190C22×C4×C5C2×D412yes—
191C22×C4×C5C2411yescharacteristic
192C5×SD16—82no—
193C5×D8—82no—
194C2×C5×C8—22no—
195C2×C5×C8—22no—
196C2×C5×C8—82no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—81no—
208C5×C4⋊C4C2×D412yes—
209C5×C4⋊C4C2×D412yes—
210C5×C22⋊C4—22no—
211C5×C22⋊C4—22no—
212C5×C22⋊C4—22no—
213C5×C22⋊C4—22no—
214C5×C22⋊C4—22no—
215C5×C22⋊C4—22no—
216C5×C22⋊C4—22no—
217C5×C22⋊C4—22no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—41no—
222C5×C22⋊C4—41no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—81no—
225C5×C22⋊C4—81no—
226C5×C22⋊C4—81no—
227C5×C22⋊C4—81no—
228C42×C5—22no—
229C42×C5—22no—
230C42×C5—21no—
231C42×C5—22no—
232C42×C5—21no—
233#544C22×C511yescharacteristic
234#542—22no—
235#540—22no—
236#538—21no—
237#538C22×C512yes—
238#537C22×C511yescharacteristic
239#535—21no—
240#532—22no—
241#529—22no—
242#525—21no—
243#525C22×C512yes—
244C2×#121C22×C511yescharacteristic
245C4×#41—21no—
246C2×C4×D4C22×C511yescharacteristic
247#484C22×C512yes—
248#482—22no—
249#481C22×C512yes—
250#466—22no—
251#465—22no—
252#450C22×C512yes—
253#449—22no—
254#447C22×C512yes—
255C2×C22⋊C8C22×C512yes—
256#400C22×C511yescharacteristic
257#399C22×C511yescharacteristic
258#394—21no—
259#394C22×C511yescharacteristic
260#392—21no—
261#392C22×C511yescharacteristic
262#388—21no—
263#386—21no—
264#381C22×C511yescharacteristic
265#328C22×C512yes—
266#328C22×C512yes—
267#327C22×C512yes—
268#327C22×C512yes—
269#324C22×C511yescharacteristic
270#324C22×C511yescharacteristic
271#323C22×C512yes—
272C23×C5—21no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—22no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5—41no—
285C23×C5—41no—
286C23×C5—41no—
287C23×C5—41no—
288C23×C5—41no—
289C23×C5#12012yes—
290C23×C5C22×D411yescharacteristic
291C5×Q8—42no—
292C5×Q8—42no—
293C5×Q8—81no—
294C5×D4—44no—
295C5×D4—42no—
296C5×D4—42no—
297C5×D4—42no—
298C5×D4—42no—
299C5×D4—42no—
300C5×D4—42no—
301C5×D4—82no—
302C5×D4—82no—
303C5×D4—82no—
304C5×D4—81no—
305C5×D4—82no—
306C5×D4—84no—
307C5×D4—84no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—21no—
315C2×C4×C5—42no—
316C2×C4×C5—41no—
317C2×C4×C5—42no—
318C2×C4×C5—41no—
319C2×C4×C5—42no—
320C2×C4×C5—44no—
321C2×C4×C5—44no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—81no—
334C2×C4×C5—82no—
335C2×C4×C5#12011yescharacteristic
336C2×C4×C5#12011yescharacteristic
337C2×C4×C5#13512yes—
338C2×C4×C5C22×D412yes—
339C5×C8—42no—
340C5×C8—42no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41C5×D412yescomplemented
344C22×D4—21no—
345C22×D4—21no—
346C22×D4C5×D411yescharacteristic
347C22×D4C23×C511yescharacteristic
348C23×C4C5×D411yescharacteristic
349C23×C4C23×C511yescharacteristic
350C2×SD16—22no—
351C2×D8—22no—
352C22×C8—22no—
353C4⋊Q8—22no—
354#127—22no—
355#126—22no—
356#126—22no—
357#125—22no—
358#124—22no—
359#124—22no—
360#124—22no—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—22no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8C5×D412yescomplemented
369C22⋊Q8C23×C512yes—
370#121—21no—
371#121—22no—
372#121—22no—
373#121—22no—
374#121—22no—
375#121—22no—
376#121—21no—
377#121—22no—
378#121—22no—
379#121C5×D412yescomplemented
380#121C23×C512yes—
381#120—22no—
382#120—22no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393#117—22no—
394#117—21no—
395#117—21no—
396#117C5×D412yescomplemented
397C2×C4⋊C4—21no—
398C2×C4⋊C4C23×C511yescharacteristic
399C2×C4⋊C4C23×C511yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4C5×D411yescharacteristic
407C2×C22⋊C4C23×C511yescharacteristic
408C2×C42—22no—
409C2×C42C5×D411yescharacteristic
410#107—22no—
411#106—22no—
412#103—22no—
413#102—22no—
414#102—22no—
415#102—22no—
416C22⋊C8—22no—
417C22⋊C8C23×C512yes—
418C22⋊C8C23×C512yes—
419#95—21no—
420#95—21no—
421#95—21no—
422#95C23×C511yescharacteristic
423#95C23×C511yescharacteristic
424C22×C5—21no—
425C22×C5—21no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—42no—
430C22×C5—42no—
431C22×C5—41no—
432C22×C5—42no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—42no—
436C22×C5—81no—
437C22×C5—81no—
438C22×C5—81no—
439C22×C5—81no—
440C22×C5—81no—
441C22×C5—81no—
442C22×C5—81no—
443C22×C5—81no—
444C22×C5—81no—
445C22×C5—81no—
446C22×C5C2×#12011yescharacteristic
447C22×C5C2×#13511yescharacteristic
448C22×C5#57511yescharacteristic
449C4×C5—22no—
450C4×C5—22no—
451C4×C5—21no—
452C4×C5—21no—
453C4×C5—42no—
454C4×C5—41no—
455C4×C5—42no—
456C4×C5—41no—
457C4×C5—42no—
458C4×C5—81no—
459C4×C5—81no—
460C4×C5—81no—
461C24—21no—
462C24C2×C5×D411yescharacteristic
463C24C2×C5×D411yescharacteristic
464#41—42no—
465#41—42no—
466#41—82no—
467#41—82no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8C2×C5×D412yes—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—41no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4—81no—
489C2×D4C2×C5×D412yes—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4C2×C5×D411yescharacteristic
501C22×C4C2×C5×D411yescharacteristic
502C22×C4C2×C5×D411yescharacteristic
503C22×C4C2×C5×D411yescharacteristic
504C22×C4C2×C5×D412yes—
505C22×C4C2×C5×D412yes—
506C22×C4C24×C511yescharacteristic
507SD16—82no—
508D8—82no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—82no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—81no—
523C4⋊C4C2×C5×D412yes—
524C4⋊C4C2×C5×D412yes—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C22⋊C4—81no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42—22no—
547C42—21no—
548C2×C5—21no—
549C2×C5—21no—
550C2×C5—42no—
551C2×C5—82no—
552C2×C5—81no—
553C2×C5—161no—
554C2×C5#300211yescharacteristic
555C2×C5#302111yescharacteristic
556C2×C5#302611yescharacteristic
557C23—21no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—21no—
562C23—21no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23C5×#12012yes—
575C23C22×C5×D411yescharacteristic
576Q8—42no—
577Q8—42no—
578Q8—81no—
579D4—44no—
580D4—42no—
581D4—42no—
582D4—42no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—82no—
587D4—82no—
588D4—81no—
589D4—82no—
590D4—82no—
591D4—84no—
592D4—84no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—42no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—81no—
619C2×C4—82no—
620C2×C4C5×#12011yescharacteristic
621C2×C4C5×#12011yescharacteristic
622C2×C4C5×#13512yes—
623C2×C4C22×C5×D412yes—
624C8—42no—
625C8—42no—
626C5#1829811yescharacteristic, direct product factor, Sylow
627C22—21no—
628C22—21no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—42no—
633C22—42no—
634C22—41no—
635C22—42no—
636C22—41no—
637C22—41no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×C5×#12011yescharacteristic
650C22C2×C5×#13511yescharacteristic
651C22C5×#57511yescharacteristic
652C4—22no—
653C4—22no—
654C4—21no—
655C4—21no—
656C4—42no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—81no—
664C2—21no—
665C2—21no—
666C2—42no—
667C2—81no—
668C2—82no—
669C2—161no—
670C2C5×#300211yescharacteristic
671C2C5×#302111yescharacteristic
672C2C5×#302611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C5×#3460C2semidirect
2. C5×#3188C2semidirect
3. C5×#2635C2semidirect
4. C5×#1618C2semidirect
5. C5×#1617C2semidirect
6. C5×#1616C2semidirect
7. C5×#1600C2semidirect
8. C5×#1599C2semidirect
9. C5×#1598C2semidirect
10. C5×#1516C2semidirect
11. C5×#1459C2semidirect
51. #18298C5direct (N × H)
54. C2×C5×#41D4semidirect
79. C5×C22⋊Q8D4semidirect
90. C5×#121D4semidirect
107. C5×#117D4semidirect
135. #3460C2×C5semidirect
136. #3188C2×C5semidirect
137. #2635C2×C5semidirect
138. #1618C2×C5semidirect
139. #1617C2×C5semidirect
140. #1616C2×C5semidirect
141. #1600C2×C5semidirect
142. #1599C2×C5semidirect
143. #1598C2×C5semidirect
144. #1516C2×C5semidirect
145. #1459C2×C5semidirect
343. C2×#41C5×D4semidirect
368. C22⋊Q8C5×D4semidirect
379. #121C5×D4semidirect
396. #117C5×D4semidirect
626. C5#18298direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34602
C5×#31882
C5×#26352
C5×#16182
C5×#16172
C5×#16162
C5×#16002
C5×#15992
C5×#15982
C5×#15162
C5×#14592
#182985