Finite Group Databasebeta

← C5×#18543 #11941263

Subgroups — C5×#18543 #11941263

Order 1280.

954 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3482C211yesmaximal, characteristic
2C5×#3165C211yesmaximal, characteristic, complemented
3C5×#3079C211yesmaximal, characteristic, complemented
4C5×#3039C211yesmaximal, characteristic, complemented
5C5×#1652C212yesmaximal, complemented
6C5×#1651C212yesmaximal, complemented
7C5×#1648C212yesmaximal, complemented
8C5×#1647C212yesmaximal, complemented
9C5×#1561C211yesmaximal, characteristic, complemented
10C5×#1489C211yesmaximal, characteristic, complemented
11C5×#1489C211yesmaximal, characteristic, complemented
12C2×C5×#137—21no—
13C5×#557C2211yescharacteristic
14C5×#556—21no—
15C5×#556C2211yescharacteristic
16C5×#552—22no—
17C5×#552—21no—
18C5×D4×Q8C2211yescharacteristic
19C5×#548—21no—
20C5×#547—21no—
21C5×#547C2211yescharacteristic
22C5×#533—21no—
23C5×#533C2211yescharacteristic
24C2×C5×C4⋊Q8C2211yescharacteristic
25C5×#529—21no—
26C5×#529—22no—
27C4×C5×#41—21no—
28C4×C5×#41C2211yescharacteristic
29C4×C5×#41C2211yescharacteristic
30C2×C4×C5×Q8—21no—
31C5×#501—22no—
32C5×#500C2212yes—
33C5×#498C2212yes—
34C5×#477—21no—
35C5×#476—21no—
36C5×#475C2212yes—
37C5×#474C2212yes—
38C5×#462—21no—
39C5×#462C2212yes—
40C5×#461—21no—
41C5×#461C2212yes—
42C5×#428—21no—
43C5×#428—22no—
44C5×#423C2211yescharacteristic
45C5×#423C2211yescharacteristic
46C5×#419—21no—
47C5×#417—21no—
48C4×C5×M16C2211yescharacteristic
49C5×#332C2212yes—
50C5×#332C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×D4⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18543C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—21no—
57C2×C5×#41D411yescharacteristic
58C2×C5×#41D411yescharacteristic
59C22×C5×Q8—21no—
60C22×C5×Q8—21no—
61C5×#137—44no—
62C2×C5×Q16—22no—
63C2×C5×SD16—22no—
64C2×C5×M16—21no—
65C2×C5×M16—21no—
66C2×C5×M16—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8—21no—
72C5×C4⋊Q8C2312yes—
73C5×C4⋊Q8C2311yescharacteristic
74C5×C4⋊Q8C2311yescharacteristic
75C5×#126—22no—
76C5×#126—22no—
77C5×#126—22no—
78C5×#125—22no—
79C5×#125—22no—
80C5×#125—21no—
81C5×#125D412yes—
82C5×#124—22no—
83C5×#124—21no—
84C5×#123—22no—
85C5×#123—22no—
86C5×#123—22no—
87C5×C22⋊Q8—22no—
88C5×C22⋊Q8—21no—
89C5×C22⋊Q8—21no—
90C5×C22⋊Q8—21no—
91C5×C22⋊Q8—21no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—21no—
94C5×#121—22no—
95C5×#121—21no—
96C4×C5×Q8—22no—
97C4×C5×Q8—22no—
98C4×C5×Q8—21no—
99C4×C5×Q8—21no—
100C4×C5×Q8—21no—
101C4×C5×Q8—21no—
102C4×C5×Q8—21no—
103C4×C5×Q8D411yescharacteristic
104C4×C5×Q8D411yescharacteristic
105C4×C5×Q8C2311yescharacteristic
106C4×C5×Q8C2311yescharacteristic
107C4×C5×D4—22no—
108C4×C5×D4—22no—
109C4×C5×D4—21no—
110C4×C5×D4—21no—
111C4×C5×D4—21no—
112C4×C5×D4—21no—
113C4×C5×D4—21no—
114C4×C5×D4D411yescharacteristic
115C4×C5×D4D411yescharacteristic
116C4×C5×D4C2311yescharacteristic
117C4×C5×D4C2311yescharacteristic
118C5×#117—22no—
119C5×#117—22no—
120C5×#117—21no—
121C5×#117—21no—
122C5×#117—21no—
123C5×#117D411yescharacteristic
124C5×#117D411yescharacteristic
125C5×#117D412yes—
126C2×C5×C4⋊C4—22no—
127C2×C5×C4⋊C4—21no—
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×#107—24no—
136C5×#106—22no—
137C5×#106—24no—
138C5×C4⋊C8—21no—
139C5×C4⋊C8—21no—
140C5×C4⋊C8C2312yes—
141C5×C4⋊C8C2312yes—
142C5×#103—22no—
143C5×#103—22no—
144C5×#103—22no—
145C5×#102—22no—
146C5×#97—21no—
147C4×C5×C8C2312yes—
148#3482C2×C511yescharacteristic
149#3165C2×C511yescharacteristic, complemented
150#3079C2×C511yescharacteristic, complemented
151#3039C2×C511yescharacteristic, complemented
152#1652C2×C512yescomplemented
153#1651C2×C512yescomplemented
154#1648C2×C512yescomplemented
155#1647C2×C512yescomplemented
156#1561C2×C511yescharacteristic, complemented
157#1489C2×C511yescharacteristic, complemented
158#1489C2×C511yescharacteristic, complemented
159C5×#41—22no—
160C5×#41—22no—
161C5×#41—41no—
162C5×#41—41no—
163C5×#41—42no—
164C5×#41—42no—
165C2×C5×Q8—22no—
166C2×C5×Q8—21no—
167C2×C5×Q8—21no—
168C2×C5×Q8—22no—
169C2×C5×Q8—42no—
170C2×C5×Q8—42no—
171C2×C5×Q8—42no—
172C2×C5×Q8—42no—
173C2×C5×Q8—41no—
174C2×C5×Q8C2×D411yescharacteristic
175C2×C5×Q8C2×D411yescharacteristic
176C2×C5×D4—22no—
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4C2×D411yescharacteristic
180C2×C5×D4C2×D411yescharacteristic
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—41no—
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C5×Q16—44no—
194C5×SD16—44no—
195C5×M16—24no—
196C5×M16—42no—
197C5×M16—42no—
198C2×C5×C8—22no—
199C2×C5×C8—22no—
200C2×C5×C8—22no—
201C5×C4⋊C4—22no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—22no—
205C5×C4⋊C4—22no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—22no—
216C5×C4⋊C4—22no—
217C5×C4⋊C4—41no—
218C5×C4⋊C4—41no—
219C5×C4⋊C4C2×D411yescharacteristic
220C5×C4⋊C4C2×D411yescharacteristic
221C5×C4⋊C4C2×D411yescharacteristic
222C5×C4⋊C4C2×D411yescharacteristic
223C5×C4⋊C4C2×D412yes—
224C5×C4⋊C4C2×D412yes—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—22no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—21no—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—21no—
235C5×C22⋊C4—21no—
236C42×C5—22no—
237C42×C5—22no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5—21no—
241C42×C5—22no—
242C42×C5—21no—
243C42×C5—21no—
244C42×C5—21no—
245C42×C5C2×D411yescharacteristic
246C42×C5C2×D411yescharacteristic
247C42×C5C2×D411yescharacteristic
248C42×C5C2411yescharacteristic
249C2×#137—21no—
250#557C22×C511yescharacteristic
251#556—21no—
252#556C22×C511yescharacteristic
253#552—22no—
254#552—21no—
255D4×Q8C22×C511yescharacteristic
256#548—21no—
257#547—21no—
258#547C22×C511yescharacteristic
259#533—21no—
260#533C22×C511yescharacteristic
261C2×C4⋊Q8C22×C511yescharacteristic
262#529—21no—
263#529—22no—
264C4×#41—21no—
265C4×#41C22×C511yescharacteristic
266C4×#41C22×C511yescharacteristic
267C2×C4×Q8—21no—
268#501—22no—
269#500C22×C512yes—
270#498C22×C512yes—
271#477—21no—
272#476—21no—
273#475C22×C512yes—
274#474C22×C512yes—
275#462—21no—
276#462C22×C512yes—
277#461—21no—
278#461C22×C512yes—
279#428—21no—
280#428—22no—
281#423C22×C511yescharacteristic
282#423C22×C511yescharacteristic
283#419—21no—
284#417—21no—
285C4×M16C22×C511yescharacteristic
286#332C22×C512yes—
287#332C22×C512yes—
288Q8⋊C8C22×C512yes—
289Q8⋊C8C22×C512yes—
290D4⋊C8C22×C512yes—
291D4⋊C8C22×C512yes—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5#12011yescharacteristic
295C5×Q8—21no—
296C5×Q8—21no—
297C5×Q8—21no—
298C5×Q8—44no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×Q8—41no—
302C5×Q8—41no—
303C5×Q8—42no—
304C5×Q8—42no—
305C5×Q8—82no—
306C5×Q8#13712yescomplemented
307C5×D4—21no—
308C5×D4—21no—
309C5×D4—21no—
310C5×D4—42no—
311C5×D4—42no—
312C5×D4—44no—
313C5×D4AGL(1,ℤ/8)12yes—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5—21no—
319C2×C4×C5—22no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—22no—
327C2×C4×C5—42no—
328C2×C4×C5—42no—
329C2×C4×C5—44no—
330C2×C4×C5—44no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—82no—
339C2×C4×C5#12011yescharacteristic
340C2×C4×C5#12011yescharacteristic
341C2×C4×C5#12011yescharacteristic
342C2×C4×C5C22×D411yescharacteristic
343C2×C4×C5C22×D411yescharacteristic
344C2×C4×C5C22×D411yescharacteristic
345C5×C8—24no—
346C5×C8—42no—
347C5×C8—42no—
348C2×#41—21no—
349C2×#41C5×D411yescharacteristic
350C2×#41C5×D411yescharacteristic
351C22×Q8—21no—
352C22×Q8—21no—
353#137—44no—
354C2×Q16—22no—
355C2×SD16—22no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8C23×C512yes—
365C4⋊Q8C23×C511yescharacteristic
366C4⋊Q8C23×C511yescharacteristic
367#126—22no—
368#126—22no—
369#126—22no—
370#125—22no—
371#125—22no—
372#125—21no—
373#125C5×D412yes—
374#124—22no—
375#124—21no—
376#123—22no—
377#123—22no—
378#123—22no—
379C22⋊Q8—22no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—22no—
385C22⋊Q8—21no—
386#121—22no—
387#121—21no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C5×D411yescharacteristic
396C4×Q8C5×D411yescharacteristic
397C4×Q8C23×C511yescharacteristic
398C4×Q8C23×C511yescharacteristic
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C5×D411yescharacteristic
407C4×D4C5×D411yescharacteristic
408C4×D4C23×C511yescharacteristic
409C4×D4C23×C511yescharacteristic
410#117—22no—
411#117—22no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117C5×D411yescharacteristic
416#117C5×D411yescharacteristic
417#117C5×D412yes—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C42—22no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42C23×C511yescharacteristic
426#107—22no—
427#107—24no—
428#106—22no—
429#106—24no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8C23×C512yes—
433C4⋊C8C23×C512yes—
434#103—22no—
435#103—22no—
436#103—22no—
437#102—22no—
438#97—21no—
439C4×C8C23×C512yes—
440C22×C5—21no—
441C22×C5—22no—
442C22×C5—21no—
443C22×C5—21no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—41no—
448C22×C5—41no—
449C22×C5C2×#12011yescharacteristic
450C4×C5—21no—
451C4×C5—21no—
452C4×C5—22no—
453C4×C5—21no—
454C4×C5—41no—
455C4×C5—41no—
456C4×C5—42no—
457C4×C5—42no—
458C4×C5—41no—
459C4×C5—41no—
460C4×C5—41no—
461C4×C5—82no—
462C4×C5#45612yes—
463C4×C5C2×AGL(1,ℤ/8)11yescharacteristic
464C4×C5C2×#13711yescharacteristic
465C4×C5#57511yescharacteristic
466C4×C5#57511yescharacteristic
467#41—22no—
468#41—22no—
469#41—41no—
470#41—41no—
471#41—42no—
472#41—42no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—22no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—41no—
482C2×Q8C2×C5×D411yescharacteristic
483C2×Q8C2×C5×D411yescharacteristic
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×C5×D411yescharacteristic
488C2×D4C2×C5×D411yescharacteristic
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—41no—
498C22×C4C2×C5×D411yescharacteristic
499C22×C4C2×C5×D411yescharacteristic
500C22×C4C2×C5×D411yescharacteristic
501Q16—44no—
502SD16—44no—
503M16—24no—
504M16—42no—
505M16—42no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4C2×C5×D411yescharacteristic
528C4⋊C4C2×C5×D411yescharacteristic
529C4⋊C4C2×C5×D411yescharacteristic
530C4⋊C4C2×C5×D412yes—
531C4⋊C4C2×C5×D411yescharacteristic
532C4⋊C4C2×C5×D412yes—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C42—22no—
545C42—22no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—22no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42C2×C5×D411yescharacteristic
554C42C2×C5×D411yescharacteristic
555C42C2×C5×D411yescharacteristic
556C42C24×C511yescharacteristic
557C2×C5—41no—
558C2×C5—42no—
559C2×C5—81no—
560C2×C5#300611yescharacteristic
561C2×C5#300711yescharacteristic
562C2×C5C2×#45611yescharacteristic
563C23—21no—
564C23—21no—
565C23C5×#12011yescharacteristic
566Q8—21no—
567Q8—21no—
568Q8—21no—
569Q8—44no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—42no—
575Q8—42no—
576Q8—82no—
577Q8C5×#13712yescomplemented
578D4—21no—
579D4—21no—
580D4—21no—
581D4—42no—
582D4—42no—
583D4—44no—
584D4C5×AGL(1,ℤ/8)12yes—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—82no—
610C2×C4C5×#12011yescharacteristic
611C2×C4C5×#12011yescharacteristic
612C2×C4C5×#12011yescharacteristic
613C2×C4C22×C5×D411yescharacteristic
614C2×C4C22×C5×D411yescharacteristic
615C2×C4C22×C5×D411yescharacteristic
616C8—24no—
617C8—42no—
618C8—42no—
619C5#1854311yescharacteristic, direct product factor, Sylow
620C22—21no—
621C22—22no—
622C22—21no—
623C22—21no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22C2×C5×#12011yescharacteristic
630C4—21no—
631C4—21no—
632C4—22no—
633C4—21no—
634C4—41no—
635C4—41no—
636C4—42no—
637C4—42no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—82no—
642C4C5×#45612yes—
643C4C2×C5×AGL(1,ℤ/8)11yescharacteristic
644C4C2×C5×#13711yescharacteristic
645C4C5×#57511yescharacteristic
646C4C5×#57511yescharacteristic
647C2—41no—
648C2—42no—
649C2—81no—
650C2C5×#300611yescharacteristic
651C2C5×#300711yescharacteristic
652C2C2×C5×#45611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3482C2
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×#3165C2semidirect
3. C5×#3079C2semidirect
4. C5×#3039C2semidirect
5. C5×#1652C2semidirect
6. C5×#1651C2semidirect
7. C5×#1648C2semidirect
8. C5×#1647C2semidirect
9. C5×#1561C2semidirect
10. C5×#1489C2semidirect
11. C5×#1489C2semidirect
55. #18543C5direct (N × H)
149. #3165C2×C5semidirect
150. #3079C2×C5semidirect
151. #3039C2×C5semidirect
152. #1652C2×C5semidirect
153. #1651C2×C5semidirect
154. #1648C2×C5semidirect
155. #1647C2×C5semidirect
156. #1561C2×C5semidirect
157. #1489C2×C5semidirect
158. #1489C2×C5semidirect
306. C5×Q8#137semidirect
577. Q8C5×#137semidirect
619. C5#18543direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34822
C5×#31652
C5×#30792
C5×#30392
C5×#16522
C5×#16512
C5×#16482
C5×#16472
C5×#15612
C5×#14892
#185435