Finite Group Databasebeta

← C5×#24083 #11946803

Subgroups — C5×#24083 #11946803

Order 1280.

1074 conjugacy classes of subgroups.

The subgroup lattice has 694 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×#2504C211yesmaximal, characteristic, complemented
5C5×#2061C212yesmaximal, complemented
6C5×#2037C212yesmaximal, complemented
7C5×#1900C211yesmaximal, characteristic, complemented
8C5×#1871C211yesmaximal, characteristic, complemented
9C5×#1860C212yesmaximal, 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×#121C2211yescharacteristic
27C5×#520C2211yescharacteristic
28C5×#518C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31C5×#484—21no—
32C5×#483—21no—
33C5×#481—21no—
34C5×#480—21no—
35C5×#428—21no—
36C5×#428—21no—
37C5×#428C2212yes—
38C5×#428C2212yes—
39C5×#428C2212yes—
40C2×C5×#107—21no—
41C2×C5×#106—21no—
42C2×C5×#104C2212yes—
43C5×#417C2212yes—
44C2×C5×#100C2212yes—
45C5×#407C2211yescharacteristic
46C5×#397—22no—
47C5×#390C2212yes—
48C5×#386—22no—
49C5×#382C2212yes—
50C4×C5×C22⋊C4C2211yescharacteristic
51C5×#343C2212yes—
52C5×#339C2212yes—
53C5×#339C2212yes—
54C5×#339C2212yes—
55#24083C511yesmaximal, 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×C22⋊Q8—22no—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8D411yescharacteristic
85C5×C22⋊Q8D411yescharacteristic
86C5×#121—22no—
87C5×#121—22no—
88C5×#121—22no—
89C5×#121—21no—
90C5×#121—21no—
91C5×#121—21no—
92C5×#121—21no—
93C5×#121—21no—
94C5×#121—21no—
95C5×#121D411yescharacteristic
96C5×#121D411yescharacteristic
97C5×#120—21no—
98C5×#120—22no—
99C4×C5×Q8—21no—
100C4×C5×D4—22no—
101C4×C5×D4—22no—
102C4×C5×D4—21no—
103C4×C5×D4—22no—
104C4×C5×D4—21no—
105C4×C5×D4—21no—
106C4×C5×D4—21no—
107C4×C5×D4—21no—
108C4×C5×D4—21no—
109C4×C5×D4—21no—
110C5×#117—22no—
111C5×#117—21no—
112C5×#117—21no—
113C5×#117—21no—
114C5×#117D411yescharacteristic
115C5×#117D411yescharacteristic
116C5×#117C2311yescharacteristic
117C5×#117C2311yescharacteristic
118C5×#117C2311yescharacteristic
119C2×C5×C4⋊C4—21no—
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⋊C4D411yescharacteristic
126C2×C5×C4⋊C4D411yescharacteristic
127C2×C5×C4⋊C4C2312yes—
128C2×C5×C4⋊C4C2311yescharacteristic
129C2×C5×C22⋊C4—21no—
130C2×C5×C22⋊C4—22no—
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—24no—
133C2×C5×C22⋊C4D412yes—
134C2×C42×C5—21no—
135C2×C42×C5C2312yes—
136C5×#107—22no—
137C5×#107—22no—
138C5×#107—22no—
139C5×#106—22no—
140C5×#106—22no—
141C5×#106—22no—
142C5×#104—24no—
143C5×#103—22no—
144C5×#102—22no—
145C5×#100—24no—
146C5×C22⋊C8—21no—
147C5×C22⋊C8—21no—
148C5×#95—21no—
149C5×#95—24no—
150#3494C2×C511yescharacteristic
151#3092C2×C511yescharacteristic, complemented
152C2×#428C2×C511yescharacteristic, complemented
153#2504C2×C511yescharacteristic, complemented
154#2061C2×C512yescomplemented
155#2037C2×C512yescomplemented
156#1900C2×C511yescharacteristic, complemented
157#1871C2×C511yescharacteristic, complemented
158#1860C2×C512yescomplemented
159#1856C2×C512yescomplemented
160#1826C2×C511yescharacteristic, complemented
161C24×C5C2×D411yescharacteristic
162C24×C5C2×D412yes—
163C5×#41—22no—
164C5×#41—22no—
165C5×#41—84no—
166C2×C5×Q8—22no—
167C2×C5×Q8C2×D411yescharacteristic
168C2×C5×D4—21no—
169C2×C5×D4—22no—
170C2×C5×D4—21no—
171C2×C5×D4—22no—
172C2×C5×D4—22no—
173C2×C5×D4—21no—
174C2×C5×D4—22no—
175C2×C5×D4—21no—
176C2×C5×D4—21no—
177C2×C5×D4—22no—
178C2×C5×D4—22no—
179C2×C5×D4—44no—
180C2×C5×D4C2×D411yescharacteristic
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—21no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—41no—
192C22×C4×C5—41no—
193C22×C4×C5—82no—
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2×D411yescharacteristic
199C22×C4×C5C2×D412yes—
200C22×C4×C5C2411yescharacteristic
201C5×M16—24no—
202C5×M16—22no—
203C5×M16—22no—
204C5×M16—22no—
205C5×M16#4114yescomplemented
206C2×C5×C8—24no—
207C2×C5×C8—22no—
208C2×C5×C8—22no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—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×C4⋊C4C2×D411yescharacteristic
228C5×C4⋊C4C2×D411yescharacteristic
229C5×C22⋊C4—22no—
230C5×C22⋊C4—22no—
231C5×C22⋊C4—22no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—22no—
234C5×C22⋊C4—21no—
235C5×C22⋊C4—21no—
236C5×C22⋊C4—21no—
237C5×C22⋊C4—21no—
238C5×C22⋊C4—21no—
239C5×C22⋊C4—21no—
240C5×C22⋊C4—21no—
241C5×C22⋊C4—22no—
242C5×C22⋊C4—22no—
243C5×C22⋊C4—21no—
244C5×C22⋊C4—21no—
245C5×C22⋊C4—42no—
246C5×C22⋊C4—84no—
247C42×C5—22no—
248C42×C5—21no—
249C42×C5—21no—
250C42×C5—21no—
251C42×C5—21no—
252C42×C5—21no—
253C42×C5—22no—
254C42×C5—22no—
255C22×M16C22×C511yescharacteristic
256#555—21no—
257#553—21no—
258#553—21no—
259#551—22no—
260#547—21no—
261#546—22no—
262#544C22×C511yescharacteristic
263#542—21no—
264#540—21no—
265#535C22×C511yescharacteristic
266#532—21no—
267#529—21no—
268#525C22×C511yescharacteristic
269C2×#121C22×C511yescharacteristic
270#520C22×C511yescharacteristic
271#518C22×C511yescharacteristic
272C2×#117C22×C511yescharacteristic
273C22×C4⋊C4C22×C511yescharacteristic
274#484—21no—
275#483—21no—
276#481—21no—
277#480—21no—
278#428—21no—
279#428—21no—
280#428C22×C512yes—
281#428C22×C512yes—
282#428C22×C512yes—
283C2×#107—21no—
284C2×#106—21no—
285C2×#104C22×C512yes—
286#417C22×C512yes—
287C2×#100C22×C512yes—
288#407C22×C511yescharacteristic
289#397—22no—
290#390C22×C512yes—
291#386—22no—
292#382C22×C512yes—
293C4×C22⋊C4C22×C511yescharacteristic
294#343C22×C512yes—
295#339C22×C512yes—
296#339C22×C512yes—
297#339C22×C512yes—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5—22no—
301C23×C5—21no—
302C23×C5—24no—
303C23×C5—41no—
304C23×C5—42no—
305C23×C5—42no—
306C23×C5#12011yescharacteristic
307C23×C5#12011yescharacteristic
308C23×C5C22×D411yescharacteristic
309C5×Q8—22no—
310C5×Q8—82no—
311C5×D4—22no—
312C5×D4—42no—
313C5×D4—44no—
314C5×D4—42no—
315C5×D4—41no—
316C5×D4—41no—
317C5×D4—42no—
318C5×D4—81no—
319C5×D4—82no—
320C5×D4—82no—
321C5×D4—82no—
322C2×C4×C5—22no—
323C2×C4×C5—21no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—22no—
337C2×C4×C5—42no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—44no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5—81no—
347C2×C4×C5—82no—
348C2×C4×C5—82no—
349C2×C4×C5—82no—
350C2×C4×C5—82no—
351C2×C4×C5—82no—
352C2×C4×C5#12011yescharacteristic
353C2×C4×C5#12011yescharacteristic
354C2×C4×C5C22×D411yescharacteristic
355C2×C4×C5C22×D411yescharacteristic
356C2×C4×C5C2×#4112yes—
357C2×C4×C52−1+412yes—
358C5×C8—24no—
359C5×C8—42no—
360C2×#41—22no—
361C2×#41C23×C511yescharacteristic
362C22×D4C5×D412yes—
363C22×D4C23×C511yescharacteristic
364C23×C4—21no—
365C23×C4C23×C511yescharacteristic
366C2×M16—21no—
367C2×M16—24no—
368C2×M16C23×C512yes—
369C2×M16C23×C512yes—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373#127—21no—
374#126—22no—
375#126—22no—
376#125—21no—
377#125—21no—
378#124—22no—
379#124—22no—
380#124—21no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—21no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8C5×D411yescharacteristic
389C22⋊Q8C5×D411yescharacteristic
390#121—22no—
391#121—22no—
392#121—22no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121C5×D411yescharacteristic
400#121C5×D411yescharacteristic
401#120—21no—
402#120—22no—
403C4×Q8—21no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—21no—
407C4×D4—22no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414#117—22no—
415#117—21no—
416#117—21no—
417#117—21no—
418#117C5×D411yescharacteristic
419#117C5×D411yescharacteristic
420#117C23×C511yescharacteristic
421#117C23×C511yescharacteristic
422#117C23×C511yescharacteristic
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4C5×D411yescharacteristic
430C2×C4⋊C4C5×D411yescharacteristic
431C2×C4⋊C4C23×C512yes—
432C2×C4⋊C4C23×C511yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4C5×D412yes—
438C2×C42—21no—
439C2×C42C23×C512yes—
440#107—22no—
441#107—22no—
442#107—22no—
443#106—22no—
444#106—22no—
445#106—22no—
446#104—24no—
447#103—22no—
448#102—22no—
449#100—24no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452#95—21no—
453#95—24no—
454C22×C5—21no—
455C22×C5—21no—
456C22×C5—21no—
457C22×C5—21no—
458C22×C5—21no—
459C22×C5—21no—
460C22×C5—21no—
461C22×C5—44no—
462C22×C5—41no—
463C22×C5—42no—
464C22×C5—41no—
465C22×C5—42no—
466C22×C5—42no—
467C22×C5—41no—
468C22×C5—84no—
469C22×C5#45512yes—
470C22×C5C2×#12011yescharacteristic
471C22×C5#54712yes—
472C4×C5—21no—
473C4×C5—21no—
474C4×C5—41no—
475C4×C5—41no—
476C4×C5—41no—
477C4×C5—42no—
478C4×C5—41no—
479C4×C5—41no—
480C4×C5—41no—
481C4×C5—41no—
482C4×C5—82no—
483C4×C5—82no—
484C4×C5#52511yescharacteristic
485C4×C5#53611yescharacteristic
486C4×C5#54712yes—
487C24C2×C5×D411yescharacteristic
488C24C2×C5×D412yes—
489#41—22no—
490#41—22no—
491#41—84no—
492C2×Q8—22no—
493C2×Q8C2×C5×D411yescharacteristic
494C2×D4—21no—
495C2×D4—22no—
496C2×D4—21no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—21no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—44no—
506C2×D4C2×C5×D411yescharacteristic
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—82no—
520C22×C4C2×C5×D411yescharacteristic
521C22×C4C2×C5×D411yescharacteristic
522C22×C4C2×C5×D411yescharacteristic
523C22×C4C2×C5×D411yescharacteristic
524C22×C4C2×C5×D411yescharacteristic
525C22×C4C2×C5×D412yes—
526C22×C4C24×C511yescharacteristic
527M16—24no—
528M16—22no—
529M16—22no—
530M16—22no—
531M16C5×#4114yescomplemented
532C2×C8—24no—
533C2×C8—22no—
534C2×C8—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4C2×C5×D411yescharacteristic
550C4⋊C4C2×C5×D411yescharacteristic
551C4⋊C4C2×C5×D411yescharacteristic
552C4⋊C4C2×C5×D411yescharacteristic
553C4⋊C4C2×C5×D411yescharacteristic
554C4⋊C4C2×C5×D411yescharacteristic
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—42no—
572C22⋊C4—84no—
573C42—22no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—22no—
580C42—22no—
581C2×C5—22no—
582C2×C5—22no—
583C2×C5—41no—
584C2×C5—81no—
585C2×C5—82no—
586C2×C5#240611yescharacteristic
587C2×C5C2×#45511yescharacteristic
588C2×C5#302111yescharacteristic
589C23—22no—
590C23—22no—
591C23—22no—
592C23—21no—
593C23—24no—
594C23—41no—
595C23—42no—
596C23—42no—
597C23C5×#12011yescharacteristic
598C23C5×#12011yescharacteristic
599C23C22×C5×D411yescharacteristic
600Q8—22no—
601Q8—82no—
602D4—22no—
603D4—44no—
604D4—42no—
605D4—42no—
606D4—41no—
607D4—41no—
608D4—42no—
609D4—82no—
610D4—81no—
611D4—82no—
612D4—82no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—44no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—81no—
638C2×C4—82no—
639C2×C4—82no—
640C2×C4—82no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4C5×#12011yescharacteristic
644C2×C4C5×#12011yescharacteristic
645C2×C4C22×C5×D411yescharacteristic
646C2×C4C22×C5×D411yescharacteristic
647C2×C4C2×C5×#4112yes—
648C2×C4C5×2−1+412yes—
649C8—24no—
650C8—42no—
651C5#2408311yescharacteristic, direct product factor, Sylow
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—44no—
660C22—41no—
661C22—42no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—84no—
667C22C5×#45512yes—
668C22C2×C5×#12011yescharacteristic
669C22C5×#54712yes—
670C4—21no—
671C4—21no—
672C4—41no—
673C4—41no—
674C4—42no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—82no—
681C4—82no—
682C4C5×#52511yescharacteristic
683C4C5×#53611yescharacteristic
684C4C5×#54712yes—
685C2—22no—
686C2—22no—
687C2—41no—
688C2—82no—
689C2—81no—
690C2C5×#240611yescharacteristic
691C2C2×C5×#45511yescharacteristic
692C2C5×#302111yescharacteristic
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×#2504C2semidirect
5. C5×#2061C2semidirect
6. C5×#2037C2semidirect
7. C5×#1900C2semidirect
8. C5×#1871C2semidirect
9. C5×#1860C2semidirect
10. C5×#1856C2semidirect
11. C5×#1826C2semidirect
55. #24083C5direct (N × H)
151. #3092C2×C5semidirect
152. C2×#428C2×C5semidirect
153. #2504C2×C5semidirect
154. #2061C2×C5semidirect
155. #2037C2×C5semidirect
156. #1900C2×C5semidirect
157. #1871C2×C5semidirect
158. #1860C2×C5semidirect
159. #1856C2×C5semidirect
160. #1826C2×C5semidirect
205. C5×M16#41semidirect
531. M16C5×#41semidirect
651. C5#24083direct (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×#25042
C5×#20612
C5×#20372
C5×#19002
C5×#18712
C5×#18602
C5×#18562
C5×#18262
#240835