Finite Group Databasebeta

← C5×#18588 #11941308

Subgroups — C5×#18588 #11941308

Order 1280.

898 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3523C211yesmaximal, characteristic
2C5×#3239C211yesmaximal, characteristic
3C5×#3165C211yesmaximal, characteristic, complemented
4C2×C5×#462C211yesmaximal, characteristic, complemented
5C5×#1653C212yesmaximal, complemented
6C5×#1652C212yesmaximal, complemented
7C5×#1649C212yesmaximal, complemented
8C5×#1648C212yesmaximal, complemented
9C5×#1552C211yesmaximal, characteristic, complemented
10C5×#1491C211yesmaximal, characteristic, complemented
11C5×#1483C211yesmaximal, characteristic
12C22×C5×Q16—21no—
13C5×#557—21no—
14C5×#557C2211yescharacteristic
15C5×#557C2211yescharacteristic
16C5×#556—21no—
17C5×#556C2211yescharacteristic
18C5×#552—22no—
19C5×#552—21no—
20C5×D4×Q8—21no—
21C5×D4×Q8C2211yescharacteristic
22C5×#541—22no—
23C5×#541—21no—
24C5×#533—21no—
25C5×#533C2211yescharacteristic
26C2×C5×C4⋊Q8C2211yescharacteristic
27C5×#529—21no—
28C5×#529C2211yescharacteristic
29C5×#519—21no—
30C2×C4×C5×Q8C2211yescharacteristic
31C5×#501—21no—
32C5×#501—22no—
33C5×#500C2212yes—
34C5×#498C2212yes—
35C5×#489—21no—
36C5×#484—21no—
37C5×#481—21no—
38C5×#475C2212yes—
39C5×#474C2212yes—
40C5×#462—21no—
41C5×#462—21no—
42C5×#462C2212yes—
43C5×#462C2212yes—
44C5×#432C2211yescharacteristic
45C5×#428—22no—
46C2×C5×C4⋊C8C2211yescharacteristic
47C2×C5×#103—21no—
48C4×C5×M16C2211yescharacteristic
49C5×#332C2212yes—
50C5×#332C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×Q8⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18588C511yesmaximal, characteristic, direct product factor, Sylow
56C22×C5×Q8—21no—
57C22×C5×Q8—21no—
58C22×C5×Q8D411yescharacteristic
59C2×C5×Q16—22no—
60C2×C5×Q16—22no—
61C2×C5×Q16—44no—
62C2×C5×M16—21no—
63C22×C5×C8—21no—
64C5×C4⋊Q8—22no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8C2312yes—
72C5×C4⋊Q8C2311yescharacteristic
73C5×C4⋊Q8C2311yescharacteristic
74C5×#126—22no—
75C5×#126—22no—
76C5×#126—22no—
77C5×#126—22no—
78C5×#126—21no—
79C5×#125—22no—
80C5×#125—22no—
81C5×#125—22no—
82C5×#125—21no—
83C5×#125—22no—
84C5×#125—22no—
85C5×#125—21no—
86C5×#125D411yescharacteristic
87C5×#125D412yes—
88C5×#124—21no—
89C5×#124D411yescharacteristic
90C5×#123—22no—
91C5×#123—21no—
92C5×C22⋊Q8—22no—
93C5×C22⋊Q8—22no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8—21no—
96C5×C22⋊Q8—21no—
97C5×C22⋊Q8—21no—
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8D411yescharacteristic
100C5×#121D411yescharacteristic
101C4×C5×Q8—22no—
102C4×C5×Q8—22no—
103C4×C5×Q8—21no—
104C4×C5×Q8—21no—
105C4×C5×Q8—21no—
106C4×C5×Q8—21no—
107C4×C5×Q8—21no—
108C4×C5×Q8—21no—
109C4×C5×Q8—21no—
110C4×C5×Q8—21no—
111C4×C5×Q8—21no—
112C4×C5×Q8D411yescharacteristic
113C4×C5×Q8D411yescharacteristic
114C4×C5×Q8C2311yescharacteristic
115C4×C5×Q8C2311yescharacteristic
116C4×C5×Q8C2311yescharacteristic
117C4×C5×D4—22no—
118C4×C5×D4—21no—
119C4×C5×D4—21no—
120C4×C5×D4C2311yescharacteristic
121C5×#117—22no—
122C5×#117—22no—
123C5×#117—22no—
124C5×#117—21no—
125C5×#117—21no—
126C5×#117D412yes—
127C2×C5×C4⋊C4—21no—
128C2×C5×C4⋊C4—21no—
129C2×C5×C4⋊C4—21no—
130C2×C5×C4⋊C4D411yescharacteristic
131C2×C42×C5—21no—
132C2×C42×C5C2311yescharacteristic
133C5×#107—24no—
134C5×#107—22no—
135C5×#106—24no—
136C5×#106—22no—
137C5×C4⋊C8—21no—
138C5×C4⋊C8C2312yes—
139C5×C4⋊C8C2312yes—
140C5×#103—22no—
141C5×#103—22no—
142C5×#103—22no—
143C5×#102—22no—
144C5×C22⋊C8—21no—
145C5×#97—21no—
146C5×#97—21no—
147C4×C5×C8C2312yes—
148#3523C2×C511yescharacteristic
149#3239C2×C511yescharacteristic
150#3165C2×C511yescharacteristic, complemented
151C2×#462C2×C511yescharacteristic, complemented
152#1653C2×C512yescomplemented
153#1652C2×C512yescomplemented
154#1649C2×C512yescomplemented
155#1648C2×C512yescomplemented
156#1552C2×C511yescharacteristic, complemented
157#1491C2×C511yescharacteristic, complemented
158#1483C2×C511yescharacteristic
159C2×C5×Q8—22no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—21no—
163C2×C5×Q8—22no—
164C2×C5×Q8—22no—
165C2×C5×Q8—41no—
166C2×C5×Q8—42no—
167C2×C5×Q8—42no—
168C2×C5×Q8—42no—
169C2×C5×Q8—42no—
170C2×C5×Q8—41no—
171C2×C5×Q8C2×D411yescharacteristic
172C2×C5×Q8C2×D411yescharacteristic
173C2×C5×Q8C2×D411yescharacteristic
174C2×C5×D4—21no—
175C2×C5×D4C2×D411yescharacteristic
176C22×C4×C5—22no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—41no—
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C5×Q16—44no—
185C5×Q16—44no—
186C5×M16—24no—
187C2×C5×C8—22no—
188C2×C5×C8—22no—
189C2×C5×C8—22no—
190C2×C5×C8—42no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4—22no—
196C5×C4⋊C4—22no—
197C5×C4⋊C4—22no—
198C5×C4⋊C4—22no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—22no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—22no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—22no—
213C5×C4⋊C4—22no—
214C5×C4⋊C4—41no—
215C5×C4⋊C4—41no—
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C4⋊C4C2×D412yes—
219C5×C4⋊C4C2×D412yes—
220C5×C4⋊C4C2×D411yescharacteristic
221C5×C4⋊C4C2×D411yescharacteristic
222C5×C22⋊C4—22no—
223C5×C22⋊C4—22no—
224C5×C22⋊C4—22no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—21no—
228C5×C22⋊C4—21no—
229C5×C22⋊C4—21no—
230C5×C22⋊C4—21no—
231C42×C5—22no—
232C42×C5—22no—
233C42×C5—22no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5—22no—
237C42×C5—21no—
238C42×C5—21no—
239C42×C5—21no—
240C42×C5C2×D411yescharacteristic
241C42×C5C2×D411yescharacteristic
242C42×C5C2×D411yescharacteristic
243C42×C5C2411yescharacteristic
244C22×Q16—21no—
245#557—21no—
246#557C22×C511yescharacteristic
247#557C22×C511yescharacteristic
248#556—21no—
249#556C22×C511yescharacteristic
250#552—22no—
251#552—21no—
252D4×Q8—21no—
253D4×Q8C22×C511yescharacteristic
254#541—22no—
255#541—21no—
256#533—21no—
257#533C22×C511yescharacteristic
258C2×C4⋊Q8C22×C511yescharacteristic
259#529—21no—
260#529C22×C511yescharacteristic
261#519—21no—
262C2×C4×Q8C22×C511yescharacteristic
263#501—22no—
264#501—21no—
265#500C22×C512yes—
266#498C22×C512yes—
267#489—21no—
268#484—21no—
269#481—21no—
270#475C22×C512yes—
271#474C22×C512yes—
272#462—21no—
273#462—21no—
274#462C22×C512yes—
275#462C22×C512yes—
276#432C22×C511yescharacteristic
277#428—22no—
278C2×C4⋊C8C22×C511yescharacteristic
279C2×#103—21no—
280C4×M16C22×C511yescharacteristic
281#332C22×C512yes—
282#332C22×C512yes—
283Q8⋊C8C22×C512yes—
284Q8⋊C8C22×C512yes—
285Q8⋊C8C22×C512yes—
286D4⋊C8C22×C512yes—
287C23×C5—21no—
288C23×C5#12011yescharacteristic
289C5×Q8—21no—
290C5×Q8—21no—
291C5×Q8—21no—
292C5×Q8—22no—
293C5×Q8—42no—
294C5×Q8—44no—
295C5×Q8—41no—
296C5×Q8—41no—
297C5×Q8—42no—
298C5×Q8—42no—
299C5×Q8—42no—
300C5×Q8—82no—
301C5×Q8AGL(1,ℤ/8)12yes—
302C5×D4—22no—
303C5×D4—42no—
304C2×C4×C5—21no—
305C2×C4×C5—22no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—22no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—22no—
317C2×C4×C5—42no—
318C2×C4×C5—44no—
319C2×C4×C5—42no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—42no—
323C2×C4×C5—82no—
324C2×C4×C5#12011yescharacteristic
325C2×C4×C5#12011yescharacteristic
326C2×C4×C5#12011yescharacteristic
327C2×C4×C5C22×D411yescharacteristic
328C2×C4×C5C22×D411yescharacteristic
329C2×C4×C5C22×D411yescharacteristic
330C5×C8—24no—
331C5×C8—42no—
332C5×C8—42no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8C5×D411yescharacteristic
336C2×Q16—22no—
337C2×Q16—22no—
338C2×Q16—44no—
339C2×M16—21no—
340C22×C8—21no—
341C4⋊Q8—22no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8C23×C512yes—
349C4⋊Q8C23×C511yescharacteristic
350C4⋊Q8C23×C511yescharacteristic
351#126—22no—
352#126—22no—
353#126—22no—
354#126—22no—
355#126—21no—
356#125—22no—
357#125—22no—
358#125—22no—
359#125—21no—
360#125—22no—
361#125—22no—
362#125—21no—
363#125C5×D411yescharacteristic
364#125C5×D412yes—
365#124—21no—
366#124C5×D411yescharacteristic
367#123—22no—
368#123—21no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8C5×D411yescharacteristic
377#121C5×D411yescharacteristic
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8C5×D411yescharacteristic
390C4×Q8C5×D411yescharacteristic
391C4×Q8C23×C511yescharacteristic
392C4×Q8C23×C511yescharacteristic
393C4×Q8C23×C511yescharacteristic
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4C23×C511yescharacteristic
398#117—22no—
399#117—22no—
400#117—22no—
401#117—21no—
402#117—21no—
403#117C5×D412yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4C5×D411yescharacteristic
408C2×C42—21no—
409C2×C42C23×C511yescharacteristic
410#107—24no—
411#107—22no—
412#106—24no—
413#106—22no—
414C4⋊C8—21no—
415C4⋊C8C23×C512yes—
416C4⋊C8C23×C512yes—
417#103—22no—
418#103—22no—
419#103—22no—
420#102—22no—
421C22⋊C8—21no—
422#97—21no—
423#97—21no—
424C4×C8C23×C512yes—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5—41no—
430C22×C5#45612yes—
431C22×C5C2×#12011yescharacteristic
432C4×C5—21no—
433C4×C5—22no—
434C4×C5—21no—
435C4×C5—21no—
436C4×C5—21no—
437C4×C5—41no—
438C4×C5—42no—
439C4×C5—41no—
440C4×C5—41no—
441C4×C5—42no—
442C4×C5—41no—
443C4×C5—41no—
444C4×C5—41no—
445C4×C5—82no—
446C4×C5C2×AGL(1,ℤ/8)11yescharacteristic
447C4×C5#57511yescharacteristic
448C4×C5#57812yes—
449C2×Q8—22no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—41no—
456C2×Q8—42no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—41no—
461C2×Q8C2×C5×D411yescharacteristic
462C2×Q8C2×C5×D411yescharacteristic
463C2×Q8C2×C5×D411yescharacteristic
464C2×D4—21no—
465C2×D4C2×C5×D411yescharacteristic
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4C2×C5×D411yescharacteristic
472C22×C4C2×C5×D411yescharacteristic
473C22×C4C2×C5×D411yescharacteristic
474Q16—44no—
475Q16—44no—
476M16—24no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—42no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×C5×D411yescharacteristic
507C4⋊C4C2×C5×D411yescharacteristic
508C4⋊C4C2×C5×D412yes—
509C4⋊C4C2×C5×D411yescharacteristic
510C4⋊C4C2×C5×D412yes—
511C4⋊C4C2×C5×D411yescharacteristic
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—21no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—21no—
525C42—21no—
526C42—22no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42C2×C5×D411yescharacteristic
531C42C2×C5×D411yescharacteristic
532C42C2×C5×D411yescharacteristic
533C42C24×C511yescharacteristic
534C2×C5—22no—
535C2×C5—81no—
536C2×C5#300611yescharacteristic
537C2×C5#301111yescharacteristic
538C2×C5C2×#45611yescharacteristic
539C23—21no—
540C23C5×#12011yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—21no—
544Q8—22no—
545Q8—42no—
546Q8—44no—
547Q8—41no—
548Q8—41no—
549Q8—42no—
550Q8—42no—
551Q8—42no—
552Q8—82no—
553Q8C5×AGL(1,ℤ/8)12yes—
554D4—22no—
555D4—42no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—82no—
576C2×C4C5×#12011yescharacteristic
577C2×C4C5×#12011yescharacteristic
578C2×C4C5×#12011yescharacteristic
579C2×C4C22×C5×D411yescharacteristic
580C2×C4C22×C5×D411yescharacteristic
581C2×C4C22×C5×D411yescharacteristic
582C8—24no—
583C8—42no—
584C8—42no—
585C5#1858811yescharacteristic, direct product factor, Sylow
586C22—21no—
587C22—21no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C5×#45612yes—
592C22C2×C5×#12011yescharacteristic
593C4—21no—
594C4—22no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—82no—
607C4C2×C5×AGL(1,ℤ/8)11yescharacteristic
608C4C5×#57511yescharacteristic
609C4C5×#57812yes—
610C2—22no—
611C2—81no—
612C2C5×#300611yescharacteristic
613C2C5×#301111yescharacteristic
614C2C2×C5×#45611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#121D4
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
3. C5×#3165C2semidirect
4. C2×C5×#462C2semidirect
5. C5×#1653C2semidirect
6. C5×#1652C2semidirect
7. C5×#1649C2semidirect
8. C5×#1648C2semidirect
9. C5×#1552C2semidirect
10. C5×#1491C2semidirect
55. #18588C5direct (N × H)
150. #3165C2×C5semidirect
151. C2×#462C2×C5semidirect
152. #1653C2×C5semidirect
153. #1652C2×C5semidirect
154. #1649C2×C5semidirect
155. #1648C2×C5semidirect
156. #1552C2×C5semidirect
157. #1491C2×C5semidirect
585. C5#18588direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35232
C5×#32392
C5×#31652
C2×C5×#4622
C5×#16532
C5×#16522
C5×#16492
C5×#16482
C5×#15522
C5×#14912
C5×#14832
#185885