Finite Group Databasebeta

← C5×#18265 #11940985

Subgroups — C5×#18265 #11940985

Order 1280.

1124 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3537C211yesmaximal, characteristic
2C5×#3092C211yesmaximal, characteristic, complemented
3C2×C5×#481C211yesmaximal, characteristic, complemented
4C5×#2501C211yesmaximal, characteristic, complemented
5C5×#1618C214yesmaximal, complemented
6C5×#1613C214yesmaximal, complemented
7C5×#1507C211yesmaximal, characteristic, complemented
8C5×#1501C211yesmaximal, characteristic, complemented
9C5×#1471C211yesmaximal, characteristic, complemented
10C5×#560—22no—
11C5×#553—21no—
12C5×#553—21no—
13C5×D42—22no—
14C5×D42—21no—
15C5×D42—21no—
16C5×#540—21no—
17C5×#538—21no—
18C5×#538C2212yes—
19C5×#535—21no—
20C5×#534—21no—
21C5×#534C2212yes—
22C5×#525C2211yescharacteristic
23C2×C5×#123—22no—
24C2×C5×#121C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic, complemented
27C5×#484C2212yescomplemented
28C5×#483—21no—
29C5×#481—22no—
30C5×#481C2214yescomplemented
31C5×#481C2212yescomplemented
32C5×#480—21no—
33C5×#428—21no—
34C2×C5×#106—21no—
35C5×#417—21no—
36C2×C5×#102—21no—
37C5×#407C2211yescharacteristic, complemented
38C2×C5×C22⋊C8C2211yescharacteristic, complemented
39C5×#399C2214yescomplemented
40C5×#390—21no—
41C5×#384—21no—
42C4×C5×C22⋊C4C2211yescharacteristic, complemented
43C5×#328C2212yescomplemented
44C5×#327C2212yescomplemented
45C5×#327C2214yescomplemented
46C5×#323C2214yescomplemented
47#18265C511yesmaximal, characteristic, direct product factor, Sylow
48C2×C5×#41D411yescharacteristic
49C22×C5×D4—22no—
50C22×C5×D4—21no—
51C22×C5×D4—21no—
52C22×C5×D4—22no—
53C22×C5×D4D411yescharacteristic
54C22×C5×D4D412yes—
55C22×C5×D4D411yescharacteristic
56C23×C4×C5—21no—
57C23×C4×C5C2311yescharacteristic
58C2×C5×M16—21no—
59C22×C5×C8—21no—
60C5×#127—22no—
61C5×#127—21no—
62C5×#126—22no—
63C5×#126—22no—
64C5×#125—21no—
65C5×#124—22no—
66C5×#123—22no—
67C5×#123—21no—
68C5×#123—22no—
69C5×#123—22no—
70C5×#123—22no—
71C5×#123—48no—
72C5×C22⋊Q8D411yescharacteristic
73C5×C22⋊Q8C2311yescharacteristic
74C5×#121—22no—
75C5×#121—21no—
76C5×#121—21no—
77C5×#121—22no—
78C5×#121—22no—
79C5×#121—22no—
80C5×#121—22no—
81C5×#121—21no—
82C5×#121—21no—
83C5×#121—21no—
84C5×#121—21no—
85C5×#121—21no—
86C5×#121—21no—
87C5×#121—22no—
88C5×#121D411yescharacteristic
89C5×#121D412yes—
90C5×#121C2312yes—
91C5×#121C2311yescharacteristic
92C5×#120—22no—
93C5×#120—22no—
94C5×#120—22no—
95C5×#120—21no—
96C5×#120—22no—
97C5×#120—22no—
98C5×#120—22no—
99C4×C5×D4—22no—
100C4×C5×D4—21no—
101C4×C5×D4—21no—
102C4×C5×D4—21no—
103C4×C5×D4—21no—
104C4×C5×D4—22no—
105C5×#117—21no—
106C5×#117D411yescharacteristic
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—24no—
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4D411yescharacteristic
115C2×C5×C4⋊C4C2312yes—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—24no—
119C2×C5×C22⋊C4C2312yes—
120C2×C42×C5—21no—
121C5×#107—22no—
122C5×#106—24no—
123C5×#106—22no—
124C5×#103—22no—
125C5×#102—24no—
126C5×#102—22no—
127C5×C22⋊C8—21no—
128C5×C22⋊C8—21no—
129C5×C22⋊C8C2312yes—
130C5×C22⋊C8C2312yes—
131C5×#95C2312yes—
132#3537C2×C511yescharacteristic
133#3092C2×C511yescharacteristic, complemented
134C2×#481C2×C511yescharacteristic, complemented
135#2501C2×C511yescharacteristic, complemented
136#1618C2×C514yescomplemented
137#1613C2×C514yescomplemented
138#1507C2×C511yescharacteristic, complemented
139#1501C2×C511yescharacteristic, complemented
140#1471C2×C511yescharacteristic, complemented
141C24×C5—22no—
142C24×C5—21no—
143C24×C5C2×D411yescharacteristic
144C24×C5C2×D412yes—
145C5×#41—42no—
146C2×C5×Q8C2×D411yescharacteristic
147C2×C5×D4—22no—
148C2×C5×D4—21no—
149C2×C5×D4—21no—
150C2×C5×D4—22no—
151C2×C5×D4—22no—
152C2×C5×D4—22no—
153C2×C5×D4—22no—
154C2×C5×D4—22no—
155C2×C5×D4—22no—
156C2×C5×D4—21no—
157C2×C5×D4—22no—
158C2×C5×D4—22no—
159C2×C5×D4—21no—
160C2×C5×D4—21no—
161C2×C5×D4—21no—
162C2×C5×D4—42no—
163C2×C5×D4—42no—
164C2×C5×D4—44no—
165C2×C5×D4—82no—
166C2×C5×D4—82no—
167C2×C5×D4—84no—
168C2×C5×D4—84no—
169C2×C5×D4C2×D411yescharacteristic
170C2×C5×D4C2×D412yes—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—22no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—22no—
177C22×C4×C5—42no—
178C22×C4×C5—44no—
179C22×C4×C5—41no—
180C22×C4×C5—41no—
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2×D411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2411yescharacteristic
188C5×M16—42no—
189C2×C5×C8—22no—
190C2×C5×C8—22no—
191C2×C5×C8—42no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—22no—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—48no—
202C5×C4⋊C4—41no—
203C5×C4⋊C4—41no—
204C5×C4⋊C4C2×D412yes—
205C5×C4⋊C4C2×D411yescharacteristic
206C5×C4⋊C4C2×D411yescharacteristic
207C5×C22⋊C4—24no—
208C5×C22⋊C4—22no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4—22no—
211C5×C22⋊C4—22no—
212C5×C22⋊C4—22no—
213C5×C22⋊C4—21no—
214C5×C22⋊C4—21no—
215C5×C22⋊C4—21no—
216C5×C22⋊C4—22no—
217C5×C22⋊C4—21no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—21no—
222C5×C22⋊C4—48no—
223C42×C5—22no—
224C42×C5—21no—
225C42×C5—42no—
226#560—22no—
227#553—21no—
228#553—21no—
229D42—22no—
230D42—21no—
231D42—21no—
232#540—21no—
233#538—21no—
234#538C22×C512yes—
235#535—21no—
236#534—21no—
237#534C22×C512yes—
238#525C22×C511yescharacteristic
239C2×#123—22no—
240C2×#121C22×C511yescharacteristic
241C2×#121C22×C511yescharacteristic
242C22×C4⋊C4C22×C511yescharacteristic, complemented
243#484C22×C512yescomplemented
244#483—21no—
245#481—22no—
246#481C22×C514yescomplemented
247#481C22×C512yescomplemented
248#480—21no—
249#428—21no—
250C2×#106—21no—
251#417—21no—
252C2×#102—21no—
253#407C22×C511yescharacteristic, complemented
254C2×C22⋊C8C22×C511yescharacteristic, complemented
255#399C22×C514yescomplemented
256#390—21no—
257#384—21no—
258C4×C22⋊C4C22×C511yescharacteristic, complemented
259#328C22×C512yescomplemented
260#327C22×C512yescomplemented
261#327C22×C514yescomplemented
262#323C22×C514yescomplemented
263C23×C5—22no—
264C23×C5—22no—
265C23×C5—22no—
266C23×C5—22no—
267C23×C5—21no—
268C23×C5—24no—
269C23×C5—41no—
270C23×C5—42no—
271C23×C5—42no—
272C23×C5—42no—
273C23×C5—81no—
274C23×C5—81no—
275C23×C5—82no—
276C23×C5—82no—
277C23×C5—82no—
278C23×C5#12011yescharacteristic
279C23×C5#12011yescharacteristic
280C23×C5C22×D411yescharacteristic
281C5×Q8—41no—
282C5×D4—42no—
283C5×D4—41no—
284C5×D4—44no—
285C5×D4—42no—
286C5×D4—44no—
287C5×D4—42no—
288C5×D4—42no—
289C5×D4—42no—
290C5×D4—81no—
291C5×D4—82no—
292C5×D4—82no—
293C5×D4—81no—
294C5×D4—82no—
295C5×D4—82no—
296C5×D4—82no—
297C5×D4—82no—
298C5×D4—82no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—24no—
303C2×C4×C5—21no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—42no—
312C2×C4×C5—42no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—44no—
316C2×C4×C5—42no—
317C2×C4×C5—81no—
318C2×C4×C5—82no—
319C2×C4×C5—82no—
320C2×C4×C5—82no—
321C2×C4×C5—82no—
322C2×C4×C5#12011yescharacteristic
323C2×C4×C5#12011yescharacteristic
324C2×C4×C5C22×D411yescharacteristic
325C2×C4×C5C22×D411yescharacteristic
326C5×C8—42no—
327C5×C8—42no—
328C2×#41C5×D411yescharacteristic
329C22×D4—22no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—22no—
333C22×D4C5×D412yes—
334C22×D4C5×D411yescharacteristic
335C22×D4C5×D411yescharacteristic
336C23×C4—21no—
337C23×C4C23×C511yescharacteristic
338C2×M16—21no—
339C22×C8—21no—
340#127—22no—
341#127—21no—
342#126—22no—
343#126—22no—
344#125—21no—
345#124—22no—
346#123—22no—
347#123—21no—
348#123—22no—
349#123—22no—
350#123—22no—
351#123—48no—
352C22⋊Q8C5×D411yescharacteristic
353C22⋊Q8C23×C511yescharacteristic
354#121—22no—
355#121—21no—
356#121—21no—
357#121—22no—
358#121—22no—
359#121—22no—
360#121—22no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—22no—
368#121C5×D412yes—
369#121C5×D411yescharacteristic
370#121C23×C512yes—
371#121C23×C511yescharacteristic
372#120—22no—
373#120—22no—
374#120—22no—
375#120—21no—
376#120—22no—
377#120—22no—
378#120—22no—
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—22no—
385#117—21no—
386#117C5×D411yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4C5×D411yescharacteristic
394C2×C4⋊C4C5×D411yescharacteristic
395C2×C4⋊C4C23×C512yes—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4C23×C512yes—
400C2×C42—21no—
401#107—22no—
402#106—24no—
403#106—22no—
404#103—22no—
405#102—24no—
406#102—22no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C23×C512yes—
410C22⋊C8C23×C512yes—
411#95C23×C512yes—
412C22×C5—21no—
413C22×C5—21no—
414C22×C5—21no—
415C22×C5—21no—
416C22×C5—21no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—44no—
420C22×C5—42no—
421C22×C5—42no—
422C22×C5—41no—
423C22×C5—42no—
424C22×C5—42no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—42no—
428C22×C5—42no—
429C22×C5—84no—
430C22×C5—162no—
431C22×C5—164no—
432C22×C5#45312yes—
433C22×C5C2×#12011yescharacteristic
434C22×C5#57712yes—
435C4×C5—21no—
436C4×C5—21no—
437C4×C5—21no—
438C4×C5—44no—
439C4×C5—42no—
440C4×C5—41no—
441C4×C5—42no—
442C4×C5—41no—
443C4×C5—41no—
444C4×C5—82no—
445C4×C5#45812yes—
446C24—22no—
447C24—21no—
448C24C2×C5×D411yescharacteristic
449C24C2×C5×D412yes—
450#41—42no—
451C2×Q8C2×C5×D411yescharacteristic
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4—82no—
471C2×D4—82no—
472C2×D4—84no—
473C2×D4—84no—
474C2×D4C2×C5×D411yescharacteristic
475C2×D4C2×C5×D412yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—42no—
483C22×C4—44no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4C2×C5×D411yescharacteristic
487C22×C4C2×C5×D411yescharacteristic
488C22×C4C2×C5×D411yescharacteristic
489C22×C4C2×C5×D412yes—
490C22×C4C2×C5×D411yescharacteristic
491C22×C4C2×C5×D411yescharacteristic
492C22×C4C24×C511yescharacteristic
493M16—42no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—42no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—48no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4C2×C5×D412yes—
510C4⋊C4C2×C5×D411yescharacteristic
511C4⋊C4C2×C5×D411yescharacteristic
512C22⋊C4—24no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—48no—
528C42—22no—
529C42—21no—
530C42—42no—
531C2×C5—22no—
532C2×C5—22no—
533C2×C5—41no—
534C2×C5—82no—
535C2×C5—82no—
536C2×C5—81no—
537C2×C5#300911yescharacteristic
538C2×C5C2×#45311yescharacteristic
539C2×C5C2×#45811yescharacteristic
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—21no—
545C23—24no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—81no—
551C23—81no—
552C23—82no—
553C23—82no—
554C23—82no—
555C23C5×#12011yescharacteristic
556C23C5×#12011yescharacteristic
557C23C22×C5×D411yescharacteristic
558Q8—41no—
559D4—42no—
560D4—41no—
561D4—44no—
562D4—42no—
563D4—44no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—81no—
568D4—82no—
569D4—82no—
570D4—81no—
571D4—82no—
572D4—82no—
573D4—82no—
574D4—82no—
575D4—82no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—81no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4C5×#12011yescharacteristic
600C2×C4C5×#12011yescharacteristic
601C2×C4C22×C5×D411yescharacteristic
602C2×C4C22×C5×D411yescharacteristic
603C8—42no—
604C8—42no—
605C5#1826511yescharacteristic, direct product factor, Sylow
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—44no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—42no—
618C22—42no—
619C22—41no—
620C22—41no—
621C22—42no—
622C22—42no—
623C22—84no—
624C22—162no—
625C22—164no—
626C22C5×#45312yes—
627C22C2×C5×#12011yescharacteristic
628C22C5×#57712yes—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—42no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—82no—
639C4C5×#45812yes—
640C2—22no—
641C2—22no—
642C2—41no—
643C2—82no—
644C2—82no—
645C2—81no—
646C2C5×#300911yescharacteristic
647C2C2×C5×#45311yescharacteristic
648C2C2×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3537C2
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
2. C5×#3092C2semidirect
3. C2×C5×#481C2semidirect
4. C5×#2501C2semidirect
5. C5×#1618C2semidirect
6. C5×#1613C2semidirect
7. C5×#1507C2semidirect
8. C5×#1501C2semidirect
9. C5×#1471C2semidirect
26. C22×C5×C4⋊C4C22semidirect
27. C5×#484C22semidirect
30. C5×#481C22semidirect
31. C5×#481C22semidirect
37. C5×#407C22semidirect
38. C2×C5×C22⋊C8C22semidirect
39. C5×#399C22semidirect
42. C4×C5×C22⋊C4C22semidirect
43. C5×#328C22semidirect
44. C5×#327C22semidirect
45. C5×#327C22semidirect
46. C5×#323C22semidirect
47. #18265C5direct (N × H)
133. #3092C2×C5semidirect
134. C2×#481C2×C5semidirect
135. #2501C2×C5semidirect
136. #1618C2×C5semidirect
137. #1613C2×C5semidirect
138. #1507C2×C5semidirect
139. #1501C2×C5semidirect
140. #1471C2×C5semidirect
242. C22×C4⋊C4C22×C5semidirect
243. #484C22×C5semidirect
246. #481C22×C5semidirect
247. #481C22×C5semidirect
253. #407C22×C5semidirect
254. C2×C22⋊C8C22×C5semidirect
255. #399C22×C5semidirect
258. C4×C22⋊C4C22×C5semidirect
259. #328C22×C5semidirect
260. #327C22×C5semidirect
261. #327C22×C5semidirect
262. #323C22×C5semidirect
605. C5#18265direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35372
C5×#30922
C2×C5×#4812
C5×#25012
C5×#16182
C5×#16132
C5×#15072
C5×#15012
C5×#14712
#182655