Finite Group Databasebeta

← C5×#18581 #11941301

Subgroups — C5×#18581 #11941301

Order 1280.

866 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3523C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic
3C5×#3139C211yesmaximal, characteristic, complemented
4C2×C5×#477C211yesmaximal, characteristic, complemented
5C5×#1638C212yesmaximal, complemented
6C5×#1637C212yesmaximal, complemented
7C5×#1636C212yesmaximal, complemented
8C5×#1636C212yesmaximal, complemented
9C5×#1552C211yesmaximal, characteristic, complemented
10C5×#1491C211yesmaximal, characteristic, complemented
11C5×#1483C211yesmaximal, characteristic
12C5×#557—21no—
13C5×#557C2211yescharacteristic
14C5×#557C2211yescharacteristic
15C5×#556—21no—
16C5×#556C2211yescharacteristic
17C5×#552—22no—
18C5×#552—21no—
19C5×D4×Q8—21no—
20C5×D4×Q8C2211yescharacteristic
21C5×#541—22no—
22C5×#541—21no—
23C5×#533—21no—
24C5×#533C2211yescharacteristic
25C2×C5×C4⋊Q8C2211yescharacteristic
26C5×#529—21no—
27C5×#529C2211yescharacteristic
28C5×#519—21no—
29C2×C4×C5×Q8C2211yescharacteristic
30C5×#501—21no—
31C5×#491—22no—
32C5×#489—21no—
33C5×#487C2212yes—
34C5×#487C2212yes—
35C5×#483—21no—
36C5×#480—21no—
37C5×#477—21no—
38C5×#477—21no—
39C5×#477C2212yes—
40C5×#477C2212yes—
41C5×#477C2212yes—
42C5×#476C2212yes—
43C5×#432C2211yescharacteristic
44C2×C5×#107—21no—
45C2×C5×C4⋊C8C2211yescharacteristic
46C5×#419—22no—
47C2×C5×#103—21no—
48C4×C5×M16C2211yescharacteristic
49C5×#332C2212yes—
50C5×#332C2212yes—
51C5×Q8⋊C8C2212yes—
52C5×Q8⋊C8C2212yes—
53C5×Q8⋊C8C2212yes—
54C5×D4⋊C8C2212yes—
55#18581C511yesmaximal, characteristic, direct product factor, Sylow
56C22×C5×Q8—21no—
57C22×C5×Q8—21no—
58C22×C5×Q8D411yescharacteristic
59C2×C5×M16—21no—
60C22×C5×C8—21no—
61C5×C4⋊Q8—22no—
62C5×C4⋊Q8—21no—
63C5×C4⋊Q8—21no—
64C5×C4⋊Q8—21no—
65C5×C4⋊Q8—21no—
66C5×C4⋊Q8—21no—
67C5×C4⋊Q8—21no—
68C5×C4⋊Q8C2312yes—
69C5×C4⋊Q8C2311yescharacteristic
70C5×C4⋊Q8C2311yescharacteristic
71C5×#126—22no—
72C5×#126—22no—
73C5×#126—22no—
74C5×#126—22no—
75C5×#126—21no—
76C5×#125—22no—
77C5×#125—22no—
78C5×#125—22no—
79C5×#125—21no—
80C5×#125—22no—
81C5×#125—22no—
82C5×#125—21no—
83C5×#125D412yes—
84C5×#125D411yescharacteristic
85C5×#124—21no—
86C5×#124D411yescharacteristic
87C5×#123—22no—
88C5×#123—21no—
89C5×C22⋊Q8—22no—
90C5×C22⋊Q8—22no—
91C5×C22⋊Q8—21no—
92C5×C22⋊Q8—21no—
93C5×C22⋊Q8—21no—
94C5×C22⋊Q8—21no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8D411yescharacteristic
97C5×#121D411yescharacteristic
98C4×C5×Q8—22no—
99C4×C5×Q8—22no—
100C4×C5×Q8—21no—
101C4×C5×Q8—21no—
102C4×C5×Q8—21no—
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×Q8D411yescharacteristic
110C4×C5×Q8D411yescharacteristic
111C4×C5×Q8C2311yescharacteristic
112C4×C5×Q8C2311yescharacteristic
113C4×C5×Q8C2311yescharacteristic
114C4×C5×D4—22no—
115C4×C5×D4—21no—
116C4×C5×D4—21no—
117C4×C5×D4C2311yescharacteristic
118C5×#117—22no—
119C5×#117—22no—
120C5×#117—22no—
121C5×#117—21no—
122C5×#117—21no—
123C5×#117D412yes—
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4D411yescharacteristic
128C2×C42×C5—21no—
129C2×C42×C5C2311yescharacteristic
130C5×#107—22no—
131C5×#107—22no—
132C5×#107—22no—
133C5×#106—22no—
134C5×C4⋊C8—21no—
135C5×C4⋊C8C2312yes—
136C5×C4⋊C8C2312yes—
137C5×#103—22no—
138C5×#103—22no—
139C5×#103—22no—
140C5×#103—24no—
141C5×#103—24no—
142C5×#102—22no—
143C5×C22⋊C8—21no—
144C5×#97—21no—
145C5×#97—21no—
146C4×C5×C8C2312yes—
147#3523C2×C511yescharacteristic
148#3238C2×C511yescharacteristic
149#3139C2×C511yescharacteristic, complemented
150C2×#477C2×C511yescharacteristic, complemented
151#1638C2×C512yescomplemented
152#1637C2×C512yescomplemented
153#1636C2×C512yescomplemented
154#1636C2×C512yescomplemented
155#1552C2×C511yescharacteristic, complemented
156#1491C2×C511yescharacteristic, complemented
157#1483C2×C511yescharacteristic
158C2×C5×Q8—22no—
159C2×C5×Q8—21no—
160C2×C5×Q8—21no—
161C2×C5×Q8—21no—
162C2×C5×Q8—22no—
163C2×C5×Q8—22no—
164C2×C5×Q8—41no—
165C2×C5×Q8—44no—
166C2×C5×Q8—42no—
167C2×C5×Q8—42no—
168C2×C5×Q8—41no—
169C2×C5×Q8C2×D411yescharacteristic
170C2×C5×Q8C2×D411yescharacteristic
171C2×C5×Q8C2×D411yescharacteristic
172C2×C5×D4—21no—
173C2×C5×D4C2×D411yescharacteristic
174C22×C4×C5—22no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—41no—
179C22×C4×C5C2×D411yescharacteristic
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C5×M16—42no—
183C2×C5×C8—22no—
184C2×C5×C8—22no—
185C2×C5×C8—22no—
186C2×C5×C8—42no—
187C5×C4⋊C4—22no—
188C5×C4⋊C4—22no—
189C5×C4⋊C4—22no—
190C5×C4⋊C4—22no—
191C5×C4⋊C4—22no—
192C5×C4⋊C4—22no—
193C5×C4⋊C4—22no—
194C5×C4⋊C4—22no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
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—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—22no—
209C5×C4⋊C4—22no—
210C5×C4⋊C4—41no—
211C5×C4⋊C4—41no—
212C5×C4⋊C4C2×D411yescharacteristic
213C5×C4⋊C4C2×D411yescharacteristic
214C5×C4⋊C4C2×D412yes—
215C5×C4⋊C4C2×D412yes—
216C5×C4⋊C4C2×D411yescharacteristic
217C5×C4⋊C4C2×D411yescharacteristic
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—21no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—21no—
224C5×C22⋊C4—21no—
225C5×C22⋊C4—21no—
226C5×C22⋊C4—21no—
227C42×C5—22no—
228C42×C5—22no—
229C42×C5—22no—
230C42×C5—21no—
231C42×C5—21no—
232C42×C5—22no—
233C42×C5—21no—
234C42×C5—21no—
235C42×C5—21no—
236C42×C5C2×D411yescharacteristic
237C42×C5C2×D411yescharacteristic
238C42×C5C2×D411yescharacteristic
239C42×C5C2411yescharacteristic
240#557—21no—
241#557C22×C511yescharacteristic
242#557C22×C511yescharacteristic
243#556—21no—
244#556C22×C511yescharacteristic
245#552—22no—
246#552—21no—
247D4×Q8—21no—
248D4×Q8C22×C511yescharacteristic
249#541—22no—
250#541—21no—
251#533—21no—
252#533C22×C511yescharacteristic
253C2×C4⋊Q8C22×C511yescharacteristic
254#529—21no—
255#529C22×C511yescharacteristic
256#519—21no—
257C2×C4×Q8C22×C511yescharacteristic
258#501—21no—
259#491—22no—
260#489—21no—
261#487C22×C512yes—
262#487C22×C512yes—
263#483—21no—
264#480—21no—
265#477—21no—
266#477—21no—
267#477C22×C512yes—
268#477C22×C512yes—
269#477C22×C512yes—
270#476C22×C512yes—
271#432C22×C511yescharacteristic
272C2×#107—21no—
273C2×C4⋊C8C22×C511yescharacteristic
274#419—22no—
275C2×#103—21no—
276C4×M16C22×C511yescharacteristic
277#332C22×C512yes—
278#332C22×C512yes—
279Q8⋊C8C22×C512yes—
280Q8⋊C8C22×C512yes—
281Q8⋊C8C22×C512yes—
282D4⋊C8C22×C512yes—
283C23×C5—21no—
284C23×C5#12011yescharacteristic
285C5×Q8—21no—
286C5×Q8—21no—
287C5×Q8—21no—
288C5×Q8—22no—
289C5×Q8—42no—
290C5×Q8—44no—
291C5×Q8—44no—
292C5×Q8—41no—
293C5×Q8—41no—
294C5×Q8—42no—
295C5×Q8—82no—
296C5×Q8#13712yes—
297C5×D4—22no—
298C5×D4—42no—
299C2×C4×C5—21no—
300C2×C4×C5—22no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—22no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—22no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—42no—
313C2×C4×C5—44no—
314C2×C4×C5—42no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—42no—
318C2×C4×C5—82no—
319C2×C4×C5#12011yescharacteristic
320C2×C4×C5#12011yescharacteristic
321C2×C4×C5#12011yescharacteristic
322C2×C4×C5C22×D411yescharacteristic
323C2×C4×C5C22×D411yescharacteristic
324C2×C4×C5C22×D411yescharacteristic
325C5×C8—42no—
326C5×C8—42no—
327C5×C8—42no—
328C22×Q8—21no—
329C22×Q8—21no—
330C22×Q8C5×D411yescharacteristic
331C2×M16—21no—
332C22×C8—21no—
333C4⋊Q8—22no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8C23×C512yes—
341C4⋊Q8C23×C511yescharacteristic
342C4⋊Q8C23×C511yescharacteristic
343#126—22no—
344#126—22no—
345#126—22no—
346#126—22no—
347#126—21no—
348#125—22no—
349#125—22no—
350#125—22no—
351#125—21no—
352#125—22no—
353#125—22no—
354#125—21no—
355#125C5×D411yescharacteristic
356#125C5×D412yes—
357#124—21no—
358#124C5×D411yescharacteristic
359#123—22no—
360#123—21no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8C5×D411yescharacteristic
369#121C5×D411yescharacteristic
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C5×D411yescharacteristic
382C4×Q8C5×D411yescharacteristic
383C4×Q8C23×C511yescharacteristic
384C4×Q8C23×C511yescharacteristic
385C4×Q8C23×C511yescharacteristic
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C23×C511yescharacteristic
390#117—22no—
391#117—22no—
392#117—22no—
393#117—21no—
394#117—21no—
395#117C5×D412yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4C5×D411yescharacteristic
400C2×C42—21no—
401C2×C42C23×C511yescharacteristic
402#107—22no—
403#107—22no—
404#107—22no—
405#106—22no—
406C4⋊C8—21no—
407C4⋊C8C23×C512yes—
408C4⋊C8C23×C512yes—
409#103—22no—
410#103—22no—
411#103—22no—
412#103—24no—
413#103—24no—
414#102—22no—
415C22⋊C8—21no—
416#97—21no—
417#97—21no—
418C4×C8C23×C512yes—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5#45412yes—
425C22×C5C2×#12011yescharacteristic
426C4×C5—21no—
427C4×C5—22no—
428C4×C5—21no—
429C4×C5—21no—
430C4×C5—21no—
431C4×C5—41no—
432C4×C5—42no—
433C4×C5—41no—
434C4×C5—41no—
435C4×C5—42no—
436C4×C5—41no—
437C4×C5—41no—
438C4×C5—41no—
439C4×C5—82no—
440C4×C5C2×#13711yescharacteristic
441C4×C5#57511yescharacteristic
442C4×C5#57812yes—
443C2×Q8—22no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—41no—
450C2×Q8—44no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—41no—
454C2×Q8C2×C5×D411yescharacteristic
455C2×Q8C2×C5×D411yescharacteristic
456C2×Q8C2×C5×D411yescharacteristic
457C2×D4—21no—
458C2×D4C2×C5×D411yescharacteristic
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4C2×C5×D411yescharacteristic
465C22×C4C2×C5×D411yescharacteristic
466C22×C4C2×C5×D411yescharacteristic
467M16—42no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—42no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4C2×C5×D412yes—
498C4⋊C4C2×C5×D412yes—
499C4⋊C4C2×C5×D411yescharacteristic
500C4⋊C4C2×C5×D411yescharacteristic
501C4⋊C4C2×C5×D411yescharacteristic
502C4⋊C4C2×C5×D411yescharacteristic
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C42—22no—
513C42—22no—
514C42—22no—
515C42—21no—
516C42—21no—
517C42—22no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42C2×C5×D411yescharacteristic
522C42C2×C5×D411yescharacteristic
523C42C2×C5×D411yescharacteristic
524C42C24×C511yescharacteristic
525C2×C5—22no—
526C2×C5—81no—
527C2×C5#300711yescharacteristic
528C2×C5#301111yescharacteristic
529C2×C5C2×#45411yescharacteristic
530C23—21no—
531C23C5×#12011yescharacteristic
532Q8—21no—
533Q8—21no—
534Q8—21no—
535Q8—22no—
536Q8—42no—
537Q8—44no—
538Q8—44no—
539Q8—41no—
540Q8—41no—
541Q8—42no—
542Q8—82no—
543Q8C5×#13712yes—
544D4—22no—
545D4—42no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—42no—
560C2×C4—44no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—82no—
566C2×C4C5×#12011yescharacteristic
567C2×C4C5×#12011yescharacteristic
568C2×C4C5×#12011yescharacteristic
569C2×C4C22×C5×D411yescharacteristic
570C2×C4C22×C5×D411yescharacteristic
571C2×C4C22×C5×D411yescharacteristic
572C8—42no—
573C8—42no—
574C8—42no—
575C5#1858111yescharacteristic, direct product factor, Sylow
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C5×#45412yes—
582C22C2×C5×#12011yescharacteristic
583C4—21no—
584C4—22no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—82no—
597C4C2×C5×#13711yescharacteristic
598C4C5×#57511yescharacteristic
599C4C5×#57812yes—
600C2—22no—
601C2—81no—
602C2C5×#300711yescharacteristic
603C2C5×#301111yescharacteristic
604C2C2×C5×#45411yescharacteristic
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×#3139C2semidirect
4. C2×C5×#477C2semidirect
5. C5×#1638C2semidirect
6. C5×#1637C2semidirect
7. C5×#1636C2semidirect
8. C5×#1636C2semidirect
9. C5×#1552C2semidirect
10. C5×#1491C2semidirect
55. #18581C5direct (N × H)
149. #3139C2×C5semidirect
150. C2×#477C2×C5semidirect
151. #1638C2×C5semidirect
152. #1637C2×C5semidirect
153. #1636C2×C5semidirect
154. #1636C2×C5semidirect
155. #1552C2×C5semidirect
156. #1491C2×C5semidirect
575. C5#18581direct (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×#32382
C5×#31392
C2×C5×#4772
C5×#16382
C5×#16372
C5×#16362
C5×#15522
C5×#14912
C5×#14832
#185815