Finite Group Databasebeta

← C5×#24082 #11946802

Subgroups — C5×#24082 #11946802

Order 1280.

1130 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3494C211yesmaximal, characteristic
2C5×#3092C211yesmaximal, characteristic, complemented
3C2×C5×#428C211yesmaximal, characteristic, complemented
4C5×#2501C211yesmaximal, characteristic, complemented
5C5×#2060C212yesmaximal, complemented
6C5×#2037C212yesmaximal, complemented
7C5×#1900C211yesmaximal, characteristic, complemented
8C5×#1871C211yesmaximal, characteristic, complemented
9C5×#1859C212yesmaximal, complemented
10C5×#1856C212yesmaximal, complemented
11C5×#1826C211yesmaximal, characteristic, complemented
12C22×C5×M16C2211yescharacteristic
13C5×#555—21no—
14C5×#553—21no—
15C5×#553—21no—
16C5×#551—22no—
17C5×#547—21no—
18C5×#546—22no—
19C5×#544C2211yescharacteristic
20C5×#542—21no—
21C5×#540—21no—
22C5×#535C2211yescharacteristic
23C5×#532—21no—
24C5×#529—21no—
25C5×#525C2211yescharacteristic
26C2×C5×#123—22no—
27C2×C5×#121C2211yescharacteristic
28C5×#520C2211yescharacteristic
29C5×#518C2211yescharacteristic
30C2×C5×#117C2211yescharacteristic
31C22×C5×C4⋊C4C2211yescharacteristic
32C5×#484—21no—
33C5×#483—21no—
34C5×#481—21no—
35C5×#480—21no—
36C5×#428—21no—
37C5×#428—21no—
38C5×#428C2212yes—
39C5×#428C2212yes—
40C5×#428C2212yes—
41C2×C5×#107—21no—
42C2×C5×#106—21no—
43C2×C5×#104C2212yes—
44C5×#417C2212yes—
45C2×C5×#100C2212yes—
46C5×#407C2211yescharacteristic
47C5×#399—22no—
48C5×#390C2212yes—
49C5×#384C2212yes—
50C4×C5×C22⋊C4C2211yescharacteristic
51C5×#343C2212yes—
52C5×#339C2212yes—
53C5×#339C2212yes—
54C5×#339C2212yes—
55#24082C511yesmaximal, characteristic, direct product factor, Sylow
56C2×C5×#41—22no—
57C2×C5×#41C2311yescharacteristic
58C22×C5×D4D412yes—
59C22×C5×D4C2311yescharacteristic
60C23×C4×C5—21no—
61C23×C4×C5C2311yescharacteristic
62C2×C5×M16—21no—
63C2×C5×M16—24no—
64C2×C5×M16C2312yes—
65C2×C5×M16C2312yes—
66C22×C5×C8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×#127—21no—
70C5×#126—22no—
71C5×#126—22no—
72C5×#125—21no—
73C5×#125—21no—
74C5×#124—22no—
75C5×#124—22no—
76C5×#124—21no—
77C5×#123—22no—
78C5×#123—22no—
79C5×#123—22no—
80C5×#123—22no—
81C5×#123—21no—
82C5×#123—48no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8D411yescharacteristic
86C5×C22⋊Q8D411yescharacteristic
87C5×#121—22no—
88C5×#121—22no—
89C5×#121—22no—
90C5×#121—21no—
91C5×#121—21no—
92C5×#121—21no—
93C5×#121—21no—
94C5×#121—21no—
95C5×#121—21no—
96C5×#121D411yescharacteristic
97C5×#121D411yescharacteristic
98C5×#120—21no—
99C5×#120—22no—
100C4×C5×Q8—21no—
101C4×C5×D4—22no—
102C4×C5×D4—22no—
103C4×C5×D4—21no—
104C4×C5×D4—22no—
105C4×C5×D4—21no—
106C4×C5×D4—21no—
107C4×C5×D4—21no—
108C4×C5×D4—21no—
109C4×C5×D4—21no—
110C4×C5×D4—21no—
111C5×#117—22no—
112C5×#117—21no—
113C5×#117—21no—
114C5×#117—21no—
115C5×#117D411yescharacteristic
116C5×#117D411yescharacteristic
117C5×#117C2311yescharacteristic
118C5×#117C2311yescharacteristic
119C5×#117C2311yescharacteristic
120C2×C5×C4⋊C4—21no—
121C2×C5×C4⋊C4—21no—
122C2×C5×C4⋊C4—21no—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—24no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4D411yescharacteristic
128C2×C5×C4⋊C4D411yescharacteristic
129C2×C5×C4⋊C4C2312yes—
130C2×C5×C4⋊C4C2311yescharacteristic
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4—22no—
134C2×C5×C22⋊C4—24no—
135C2×C5×C22⋊C4D412yes—
136C2×C42×C5—21no—
137C2×C42×C5C2312yes—
138C5×#107—22no—
139C5×#107—22no—
140C5×#107—22no—
141C5×#106—22no—
142C5×#106—22no—
143C5×#106—22no—
144C5×#104—24no—
145C5×#103—22no—
146C5×#102—22no—
147C5×#100—24no—
148C5×C22⋊C8—21no—
149C5×C22⋊C8—21no—
150C5×#95—21no—
151#3494C2×C511yescharacteristic
152#3092C2×C511yescharacteristic, complemented
153C2×#428C2×C511yescharacteristic, complemented
154#2501C2×C511yescharacteristic, complemented
155#2060C2×C512yescomplemented
156#2037C2×C512yescomplemented
157#1900C2×C511yescharacteristic, complemented
158#1871C2×C511yescharacteristic, complemented
159#1859C2×C512yescomplemented
160#1856C2×C512yescomplemented
161#1826C2×C511yescharacteristic, complemented
162C24×C5C2×D411yescharacteristic
163C24×C5C2×D412yes—
164C5×#41—22no—
165C5×#41—22no—
166C5×#41—84no—
167C2×C5×Q8—22no—
168C2×C5×Q8C2×D411yescharacteristic
169C2×C5×D4—21no—
170C2×C5×D4—22no—
171C2×C5×D4—21no—
172C2×C5×D4—22no—
173C2×C5×D4—22no—
174C2×C5×D4—21no—
175C2×C5×D4—22no—
176C2×C5×D4—21no—
177C2×C5×D4—21no—
178C2×C5×D4—22no—
179C2×C5×D4—22no—
180C2×C5×D4—44no—
181C2×C5×D4C2×D411yescharacteristic
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—21no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—22no—
192C22×C4×C5—44no—
193C22×C4×C5—41no—
194C22×C4×C5—41no—
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D411yescharacteristic
200C22×C4×C5C2×D412yes—
201C22×C4×C5C2411yescharacteristic
202C5×M16—24no—
203C5×M16—22no—
204C5×M16—22no—
205C5×M16—22no—
206C5×M16#4114yescomplemented
207C2×C5×C8—24no—
208C2×C5×C8—22no—
209C2×C5×C8—22no—
210C5×C4⋊C4—22no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—22no—
214C5×C4⋊C4—21no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—21no—
217C5×C4⋊C4—21no—
218C5×C4⋊C4—21no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—48no—
223C5×C4⋊C4—41no—
224C5×C4⋊C4—41no—
225C5×C4⋊C4C2×D411yescharacteristic
226C5×C4⋊C4C2×D411yescharacteristic
227C5×C4⋊C4C2×D411yescharacteristic
228C5×C4⋊C4C2×D411yescharacteristic
229C5×C4⋊C4C2×D411yescharacteristic
230C5×C4⋊C4C2×D411yescharacteristic
231C5×C22⋊C4—22no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—24no—
234C5×C22⋊C4—22no—
235C5×C22⋊C4—22no—
236C5×C22⋊C4—22no—
237C5×C22⋊C4—21no—
238C5×C22⋊C4—21no—
239C5×C22⋊C4—21no—
240C5×C22⋊C4—21no—
241C5×C22⋊C4—21no—
242C5×C22⋊C4—21no—
243C5×C22⋊C4—21no—
244C5×C22⋊C4—22no—
245C5×C22⋊C4—22no—
246C5×C22⋊C4—21no—
247C5×C22⋊C4—21no—
248C5×C22⋊C4—48no—
249C42×C5—22no—
250C42×C5—21no—
251C42×C5—21no—
252C42×C5—21no—
253C42×C5—21no—
254C42×C5—21no—
255C42×C5—22no—
256C42×C5—22no—
257C22×M16C22×C511yescharacteristic
258#555—21no—
259#553—21no—
260#553—21no—
261#551—22no—
262#547—21no—
263#546—22no—
264#544C22×C511yescharacteristic
265#542—21no—
266#540—21no—
267#535C22×C511yescharacteristic
268#532—21no—
269#529—21no—
270#525C22×C511yescharacteristic
271C2×#123—22no—
272C2×#121C22×C511yescharacteristic
273#520C22×C511yescharacteristic
274#518C22×C511yescharacteristic
275C2×#117C22×C511yescharacteristic
276C22×C4⋊C4C22×C511yescharacteristic
277#484—21no—
278#483—21no—
279#481—21no—
280#480—21no—
281#428—21no—
282#428—21no—
283#428C22×C512yes—
284#428C22×C512yes—
285#428C22×C512yes—
286C2×#107—21no—
287C2×#106—21no—
288C2×#104C22×C512yes—
289#417C22×C512yes—
290C2×#100C22×C512yes—
291#407C22×C511yescharacteristic
292#399—22no—
293#390C22×C512yes—
294#384C22×C512yes—
295C4×C22⋊C4C22×C511yescharacteristic
296#343C22×C512yes—
297#339C22×C512yes—
298#339C22×C512yes—
299#339C22×C512yes—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5—22no—
303C23×C5—21no—
304C23×C5—24no—
305C23×C5—41no—
306C23×C5—42no—
307C23×C5—42no—
308C23×C5#12011yescharacteristic
309C23×C5#12011yescharacteristic
310C23×C5C22×D411yescharacteristic
311C5×Q8—22no—
312C5×Q8—82no—
313C5×D4—22no—
314C5×D4—42no—
315C5×D4—44no—
316C5×D4—42no—
317C5×D4—41no—
318C5×D4—41no—
319C5×D4—42no—
320C5×D4—81no—
321C5×D4—82no—
322C5×D4—82no—
323C5×D4—82no—
324C2×C4×C5—22no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—24no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—22no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—42no—
346C2×C4×C5—44no—
347C2×C4×C5—42no—
348C2×C4×C5—81no—
349C2×C4×C5—82no—
350C2×C4×C5—82no—
351C2×C4×C5—82no—
352C2×C4×C5—82no—
353C2×C4×C5—82no—
354C2×C4×C5#12011yescharacteristic
355C2×C4×C5#12011yescharacteristic
356C2×C4×C5C22×D411yescharacteristic
357C2×C4×C5C22×D411yescharacteristic
358C2×C4×C5C2×#4112yes—
359C2×C4×C52−1+412yes—
360C5×C8—24no—
361C5×C8—42no—
362C2×#41—22no—
363C2×#41C23×C511yescharacteristic
364C22×D4C5×D412yes—
365C22×D4C23×C511yescharacteristic
366C23×C4—21no—
367C23×C4C23×C511yescharacteristic
368C2×M16—21no—
369C2×M16—24no—
370C2×M16C23×C512yes—
371C2×M16C23×C512yes—
372C22×C8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375#127—21no—
376#126—22no—
377#126—22no—
378#125—21no—
379#125—21no—
380#124—22no—
381#124—22no—
382#124—21no—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—22no—
387#123—21no—
388#123—48no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8C5×D411yescharacteristic
392C22⋊Q8C5×D411yescharacteristic
393#121—22no—
394#121—22no—
395#121—22no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121C5×D411yescharacteristic
403#121C5×D411yescharacteristic
404#120—21no—
405#120—22no—
406C4×Q8—21no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—22no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417#117—22no—
418#117—21no—
419#117—21no—
420#117—21no—
421#117C5×D411yescharacteristic
422#117C5×D411yescharacteristic
423#117C23×C511yescharacteristic
424#117C23×C511yescharacteristic
425#117C23×C511yescharacteristic
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4C5×D411yescharacteristic
434C2×C4⋊C4C5×D411yescharacteristic
435C2×C4⋊C4C23×C512yes—
436C2×C4⋊C4C23×C511yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4C5×D412yes—
442C2×C42—21no—
443C2×C42C23×C512yes—
444#107—22no—
445#107—22no—
446#107—22no—
447#106—22no—
448#106—22no—
449#106—22no—
450#104—24no—
451#103—22no—
452#102—22no—
453#100—24no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456#95—21no—
457C22×C5—21no—
458C22×C5—21no—
459C22×C5—21no—
460C22×C5—21no—
461C22×C5—21no—
462C22×C5—21no—
463C22×C5—21no—
464C22×C5—44no—
465C22×C5—41no—
466C22×C5—42no—
467C22×C5—41no—
468C22×C5—42no—
469C22×C5—42no—
470C22×C5—41no—
471C22×C5—84no—
472C22×C5#45312yes—
473C22×C5C2×#12011yescharacteristic
474C22×C5#54712yes—
475C4×C5—21no—
476C4×C5—21no—
477C4×C5—44no—
478C4×C5—41no—
479C4×C5—41no—
480C4×C5—41no—
481C4×C5—42no—
482C4×C5—41no—
483C4×C5—41no—
484C4×C5—41no—
485C4×C5—41no—
486C4×C5—82no—
487C4×C5#52511yescharacteristic
488C4×C5#53611yescharacteristic
489C4×C5#54712yes—
490C24C2×C5×D411yescharacteristic
491C24C2×C5×D412yes—
492#41—22no—
493#41—22no—
494#41—84no—
495C2×Q8—22no—
496C2×Q8C2×C5×D411yescharacteristic
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—44no—
509C2×D4C2×C5×D411yescharacteristic
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—44no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D411yescharacteristic
526C22×C4C2×C5×D411yescharacteristic
527C22×C4C2×C5×D411yescharacteristic
528C22×C4C2×C5×D412yes—
529C22×C4C24×C511yescharacteristic
530M16—24no—
531M16—22no—
532M16—22no—
533M16—22no—
534M16C5×#4114yescomplemented
535C2×C8—24no—
536C2×C8—22no—
537C2×C8—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—48no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4C2×C5×D411yescharacteristic
554C4⋊C4C2×C5×D411yescharacteristic
555C4⋊C4C2×C5×D411yescharacteristic
556C4⋊C4C2×C5×D411yescharacteristic
557C4⋊C4C2×C5×D411yescharacteristic
558C4⋊C4C2×C5×D411yescharacteristic
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—48no—
577C42—22no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—22no—
584C42—22no—
585C2×C5—22no—
586C2×C5—22no—
587C2×C5—41no—
588C2×C5—81no—
589C2×C5—82no—
590C2×C5#240611yescharacteristic
591C2×C5C2×#45311yescharacteristic
592C2×C5#302211yescharacteristic
593C23—22no—
594C23—22no—
595C23—22no—
596C23—21no—
597C23—24no—
598C23—41no—
599C23—42no—
600C23—42no—
601C23C5×#12011yescharacteristic
602C23C5×#12011yescharacteristic
603C23C22×C5×D411yescharacteristic
604Q8—22no—
605Q8—82no—
606D4—22no—
607D4—44no—
608D4—42no—
609D4—42no—
610D4—41no—
611D4—41no—
612D4—42no—
613D4—82no—
614D4—81no—
615D4—82no—
616D4—82no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—81no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4—82no—
645C2×C4—82no—
646C2×C4—82no—
647C2×C4C5×#12011yescharacteristic
648C2×C4C5×#12011yescharacteristic
649C2×C4C22×C5×D411yescharacteristic
650C2×C4C22×C5×D411yescharacteristic
651C2×C4C2×C5×#4112yes—
652C2×C4C5×2−1+412yes—
653C8—24no—
654C8—42no—
655C5#2408211yescharacteristic, direct product factor, Sylow
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—41no—
665C22—42no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—84no—
671C22C5×#45312yes—
672C22C2×C5×#12011yescharacteristic
673C22C5×#54712yes—
674C4—21no—
675C4—21no—
676C4—44no—
677C4—41no—
678C4—41no—
679C4—42no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—82no—
686C4C5×#52511yescharacteristic
687C4C5×#53611yescharacteristic
688C4C5×#54712yes—
689C2—22no—
690C2—22no—
691C2—41no—
692C2—82no—
693C2—81no—
694C2C5×#240611yescharacteristic
695C2C2×C5×#45311yescharacteristic
696C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3494C2
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
2. C5×#3092C2semidirect
3. C2×C5×#428C2semidirect
4. C5×#2501C2semidirect
5. C5×#2060C2semidirect
6. C5×#2037C2semidirect
7. C5×#1900C2semidirect
8. C5×#1871C2semidirect
9. C5×#1859C2semidirect
10. C5×#1856C2semidirect
11. C5×#1826C2semidirect
55. #24082C5direct (N × H)
152. #3092C2×C5semidirect
153. C2×#428C2×C5semidirect
154. #2501C2×C5semidirect
155. #2060C2×C5semidirect
156. #2037C2×C5semidirect
157. #1900C2×C5semidirect
158. #1871C2×C5semidirect
159. #1859C2×C5semidirect
160. #1856C2×C5semidirect
161. #1826C2×C5semidirect
206. C5×M16#41semidirect
534. M16C5×#41semidirect
655. C5#24082direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34942
C5×#30922
C2×C5×#4282
C5×#25012
C5×#20602
C5×#20372
C5×#19002
C5×#18712
C5×#18592
C5×#18562
C5×#18262
#240825