Finite Group Databasebeta

← C5×#19000 #11941720

Subgroups — C5×#19000 #11941720

Order 1280.

896 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3529C211yesmaximal, characteristic
2C5×#3238C211yesmaximal, characteristic, complemented
3C5×#3218C211yesmaximal, characteristic, complemented
4C5×#3141C211yesmaximal, characteristic, complemented
5C5×#1664C212yesmaximal, complemented
6C5×#1662C212yesmaximal, complemented
7C5×#1661C212yesmaximal, complemented
8C5×#1659C212yesmaximal, complemented
9C5×#1536C211yesmaximal, characteristic, complemented
10C5×#1529C211yesmaximal, characteristic, complemented
11C5×#1529C211yesmaximal, characteristic, complemented
12C5×#563—21no—
13C5×#563C2211yescharacteristic
14C5×#562—21no—
15C5×#562—21no—
16C5×#562C2211yescharacteristic
17C5×#562C2211yescharacteristic
18C5×H(3,𝔽4)C2211yescharacteristic
19C5×#560—21no—
20C5×#560—21no—
21C5×#560—21no—
22C5×#532—21no—
23C5×#532C2211yescharacteristic
24C2×C5×C4⋊Q8C2211yescharacteristic, complemented
25C5×#529—21no—
26C5×#529—21no—
27C5×#529C2211yescharacteristic
28C5×#529C2211yescharacteristic
29C5×#525—21no—
30C5×#525—21no—
31C5×#525—21no—
32C5×#501C2212yescomplemented
33C5×#497C2212yes—
34C5×#491C2212yescomplemented
35C5×#489C2212yes—
36C5×#489C2212yes—
37C5×#489C2212yescomplemented
38C5×#487—21no—
39C5×#486—21no—
40C5×#483—21no—
41C5×#480—21no—
42C5×#477—21no—
43C5×#476—21no—
44C5×#462—21no—
45C5×#461—21no—
46C5×#451—21no—
47C5×#448—21no—
48C5×#432C2211yescharacteristic, complemented
49C5×#432C2211yescharacteristic, complemented
50C5×#417—21no—
51C5×#417—21no—
52C4×C5×M16C2211yescharacteristic, complemented
53C5×#330C2212yescomplemented
54C5×#330C2212yescomplemented
55C5×#329C2212yes—
56C5×#329C2212yes—
57C5×#329C2212yes—
58C5×#329C2212yescomplemented
59#19000C511yesmaximal, characteristic, direct product factor, Sylow
60C2×C5×#41—21no—
61C2×C5×#41D411yescharacteristic
62C2×C5×#41D411yescharacteristic
63C22×C5×Q8—21no—
64C23×C4×C5—21no—
65C2×C5×Q16—22no—
66C2×C5×SD16—22no—
67C2×C5×M16—21no—
68C5×C4⋊Q8—21no—
69C5×C4⋊Q8—21no—
70C5×C4⋊Q8—21no—
71C5×C4⋊Q8—21no—
72C5×C4⋊Q8D411yescharacteristic
73C5×C4⋊Q8C2312yes—
74C5×#127—21no—
75C5×#127D411yescharacteristic
76C5×#126—21no—
77C5×#126—21no—
78C5×#126—21no—
79C5×#126—21no—
80C5×#126—21no—
81C5×#126—21no—
82C5×#125—21no—
83C5×#125—21no—
84C5×#125C2311yescharacteristic
85C5×#125C2311yescharacteristic
86C5×#124—21no—
87C5×#124—21no—
88C5×#124—21no—
89C5×#124—21no—
90C5×#124C2311yescharacteristic
91C5×#124C2311yescharacteristic
92C5×#124C2311yescharacteristic
93C5×#124C2311yescharacteristic
94C5×#123—21no—
95C5×#123—21no—
96C5×#123—21no—
97C5×#123—21no—
98C5×#123—21no—
99C5×#123—21no—
100C5×#123—21no—
101C5×#123—21no—
102C5×#123—21no—
103C5×#123—21no—
104C5×#123—21no—
105C5×#123—21no—
106C5×C22⋊Q8—21no—
107C5×C22⋊Q8—21no—
108C5×C22⋊Q8—21no—
109C5×C22⋊Q8—21no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8D411yescharacteristic
115C5×C22⋊Q8D411yescharacteristic
116C5×#121—21no—
117C5×#121—21no—
118C5×#121—21no—
119C5×#121—21no—
120C5×#121—21no—
121C5×#121—21no—
122C5×#121—21no—
123C5×#121—21no—
124C5×#121—21no—
125C5×#121—21no—
126C5×#121—21no—
127C5×#121—21no—
128C5×#121—21no—
129C5×#121—21no—
130C5×#121D411yescharacteristic
131C5×#121D411yescharacteristic
132C5×#120—21no—
133C5×#120—21no—
134C5×#120—21no—
135C5×#120—21no—
136C5×#120—21no—
137C5×#120—21no—
138C4×C5×Q8D411yescharacteristic
139C4×C5×Q8D411yescharacteristic
140C4×C5×D4—21no—
141C4×C5×D4—21no—
142C4×C5×D4—21no—
143C4×C5×D4—21no—
144C4×C5×D4—21no—
145C4×C5×D4—21no—
146C4×C5×D4—21no—
147C4×C5×D4—21no—
148C4×C5×D4D411yescharacteristic
149C4×C5×D4D411yescharacteristic
150C5×#117—21no—
151C5×#117—21no—
152C5×#117—21no—
153C2×C5×C4⋊C4—21no—
154C2×C5×C4⋊C4—21no—
155C2×C42×C5—21no—
156C2×C42×C5C2311yescharacteristic
157C5×#107—22no—
158C5×#106—22no—
159C5×C4⋊C8—21no—
160C5×C4⋊C8—21no—
161C5×#103—22no—
162C5×#103—22no—
163C5×#103—22no—
164C5×#103—22no—
165C5×#103—22no—
166C5×#102—22no—
167C5×#102—22no—
168C5×#102—22no—
169C5×C22⋊C8—21no—
170C5×C22⋊C8—21no—
171C5×#97C2312yes—
172C5×#97C2312yes—
173C5×#97C2312yes—
174C4×C5×C8—21no—
175#3529C2×C511yescharacteristic
176#3238C2×C511yescharacteristic, complemented
177#3218C2×C511yescharacteristic, complemented
178#3141C2×C511yescharacteristic, complemented
179#1664C2×C512yescomplemented
180#1662C2×C512yescomplemented
181#1661C2×C512yescomplemented
182#1659C2×C512yescomplemented
183#1536C2×C511yescharacteristic, complemented
184#1529C2×C511yescharacteristic, complemented
185#1529C2×C511yescharacteristic, complemented
186C24×C5—21no—
187C5×#41—42no—
188C5×#41—42no—
189C5×#41—82no—
190C2×C5×Q8—21no—
191C2×C5×Q8—22no—
192C2×C5×Q8—41no—
193C2×C5×Q8—82no—
194C2×C5×Q8C2×D411yescharacteristic
195C2×C5×Q8C2×D411yescharacteristic
196C2×C5×Q8C2×D411yescharacteristic
197C2×C5×Q8C2×D411yescharacteristic
198C2×C5×D4—21no—
199C2×C5×D4—21no—
200C2×C5×D4—21no—
201C2×C5×D4—21no—
202C2×C5×D4—21no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—21no—
208C2×C5×D4—21no—
209C2×C5×D4—21no—
210C2×C5×D4—21no—
211C2×C5×D4C2×D411yescharacteristic
212C2×C5×D4C2×D411yescharacteristic
213C2×C5×D4C2×D411yescharacteristic
214C2×C5×D4C2×D411yescharacteristic
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—21no—
224C22×C4×C5—41no—
225C22×C4×C5—82no—
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C5×Q16—82no—
230C5×SD16—82no—
231C5×M16—42no—
232C2×C5×C8—22no—
233C2×C5×C8—22no—
234C2×C5×C8—22no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4—21no—
239C5×C4⋊C4—21no—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—21no—
242C5×C4⋊C4—21no—
243C5×C4⋊C4—21no—
244C5×C4⋊C4—21no—
245C5×C4⋊C4—21no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—22no—
252C5×C4⋊C4—22no—
253C5×C4⋊C4—41no—
254C5×C4⋊C4—41no—
255C5×C4⋊C4C2×D411yescharacteristic
256C5×C4⋊C4C2×D411yescharacteristic
257C5×C4⋊C4C2×D411yescharacteristic
258C5×C4⋊C4C2×D411yescharacteristic
259C5×C22⋊C4—21no—
260C5×C22⋊C4—21no—
261C5×C22⋊C4—21no—
262C5×C22⋊C4—21no—
263C5×C22⋊C4—21no—
264C5×C22⋊C4—21no—
265C5×C22⋊C4—21no—
266C5×C22⋊C4—21no—
267C5×C22⋊C4—21no—
268C5×C22⋊C4—21no—
269C5×C22⋊C4—21no—
270C5×C22⋊C4—21no—
271C5×C22⋊C4—21no—
272C5×C22⋊C4—21no—
273C5×C22⋊C4—21no—
274C5×C22⋊C4—21no—
275C5×C22⋊C4—21no—
276C5×C22⋊C4—21no—
277C5×C22⋊C4—21no—
278C5×C22⋊C4—21no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—21no—
281C5×C22⋊C4—21no—
282C5×C22⋊C4—21no—
283C42×C5—21no—
284C42×C5—21no—
285C42×C5—21no—
286C42×C5—21no—
287C42×C5C2×D411yescharacteristic
288C42×C5C2×D411yescharacteristic
289C42×C5C2×D411yescharacteristic
290C42×C5C2411yescharacteristic
291#563—21no—
292#563C22×C511yescharacteristic
293#562—21no—
294#562—21no—
295#562C22×C511yescharacteristic
296#562C22×C511yescharacteristic
297H(3,𝔽4)C22×C511yescharacteristic
298#560—21no—
299#560—21no—
300#560—21no—
301#532—21no—
302#532C22×C511yescharacteristic
303C2×C4⋊Q8C22×C511yescharacteristic, complemented
304#529—21no—
305#529—21no—
306#529C22×C511yescharacteristic
307#529C22×C511yescharacteristic
308#525—21no—
309#525—21no—
310#525—21no—
311#501C22×C512yescomplemented
312#497C22×C512yes—
313#491C22×C512yescomplemented
314#489C22×C512yes—
315#489C22×C512yes—
316#489C22×C512yescomplemented
317#487—21no—
318#486—21no—
319#483—21no—
320#480—21no—
321#477—21no—
322#476—21no—
323#462—21no—
324#461—21no—
325#451—21no—
326#448—21no—
327#432C22×C511yescharacteristic, complemented
328#432C22×C511yescharacteristic, complemented
329#417—21no—
330#417—21no—
331C4×M16C22×C511yescharacteristic, complemented
332#330C22×C512yescomplemented
333#330C22×C512yescomplemented
334#329C22×C512yes—
335#329C22×C512yes—
336#329C22×C512yes—
337#329C22×C512yescomplemented
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—21no—
341C23×C5—21no—
342C23×C5—81no—
343C23×C5—81no—
344C23×C5—81no—
345C23×C5#12011yescharacteristic
346C5×Q8—41no—
347C5×Q8—41no—
348C5×Q8—41no—
349C5×Q8—41no—
350C5×Q8—42no—
351C5×Q8—42no—
352C5×Q8—82no—
353C5×Q8—81no—
354C5×D4—41no—
355C5×D4—41no—
356C5×D4—41no—
357C5×D4—41no—
358C5×D4—81no—
359C5×D4—81no—
360C5×D4—81no—
361C5×D4—81no—
362C5×D4—81no—
363C5×D4—81no—
364C5×D4—81no—
365C5×D4—81no—
366C5×D4—81no—
367C5×D4—81no—
368C5×D4—81no—
369C5×D4—81no—
370C5×D4—81no—
371C2×C4×C5—22no—
372C2×C4×C5—21no—
373C2×C4×C5—21no—
374C2×C4×C5—21no—
375C2×C4×C5—21no—
376C2×C4×C5—21no—
377C2×C4×C5—21no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—81no—
388C2×C4×C5—81no—
389C2×C4×C5—81no—
390C2×C4×C5—81no—
391C2×C4×C5—81no—
392C2×C4×C5—82no—
393C2×C4×C5#12011yescharacteristic
394C2×C4×C5#12011yescharacteristic
395C2×C4×C5#12011yescharacteristic
396C2×C4×C5C22×D411yescharacteristic
397C2×C4×C5C22×D411yescharacteristic
398C2×C4×C5C22×D411yescharacteristic
399C5×C8—42no—
400C5×C8—42no—
401C5×C8—42no—
402C2×#41—21no—
403C2×#41C5×D411yescharacteristic
404C2×#41C5×D411yescharacteristic
405C22×Q8—21no—
406C23×C4—21no—
407C2×Q16—22no—
408C2×SD16—22no—
409C2×M16—21no—
410C4⋊Q8—21no—
411C4⋊Q8—21no—
412C4⋊Q8—21no—
413C4⋊Q8—21no—
414C4⋊Q8C5×D411yescharacteristic
415C4⋊Q8C23×C512yes—
416#127—21no—
417#127C5×D411yescharacteristic
418#126—21no—
419#126—21no—
420#126—21no—
421#126—21no—
422#126—21no—
423#126—21no—
424#125—21no—
425#125—21no—
426#125C23×C511yescharacteristic
427#125C23×C511yescharacteristic
428#124—21no—
429#124—21no—
430#124—21no—
431#124—21no—
432#124C23×C511yescharacteristic
433#124C23×C511yescharacteristic
434#124C23×C511yescharacteristic
435#124C23×C511yescharacteristic
436#123—21no—
437#123—21no—
438#123—21no—
439#123—21no—
440#123—21no—
441#123—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445#123—21no—
446#123—21no—
447#123—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8—21no—
456C22⋊Q8C5×D411yescharacteristic
457C22⋊Q8C5×D411yescharacteristic
458#121—21no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—21no—
472#121C5×D411yescharacteristic
473#121C5×D411yescharacteristic
474#120—21no—
475#120—21no—
476#120—21no—
477#120—21no—
478#120—21no—
479#120—21no—
480C4×Q8C5×D411yescharacteristic
481C4×Q8C5×D411yescharacteristic
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4C5×D411yescharacteristic
491C4×D4C5×D411yescharacteristic
492#117—21no—
493#117—21no—
494#117—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C42—21no—
498C2×C42C23×C511yescharacteristic
499#107—22no—
500#106—22no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#103—22no—
504#103—22no—
505#103—22no—
506#103—22no—
507#103—22no—
508#102—22no—
509#102—22no—
510#102—22no—
511C22⋊C8—21no—
512C22⋊C8—21no—
513#97C23×C512yes—
514#97C23×C512yes—
515#97C23×C512yes—
516C4×C8—21no—
517C22×C5—21no—
518C22×C5—21no—
519C22×C5—21no—
520C22×C5—41no—
521C22×C5—41no—
522C22×C5—41no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5—41no—
528C22×C5—41no—
529C22×C5—41no—
530C22×C5—41no—
531C22×C5—41no—
532C22×C5—84no—
533C22×C5C2×#12011yescharacteristic
534C4×C5—21no—
535C4×C5—21no—
536C4×C5—21no—
537C4×C5—21no—
538C4×C5—21no—
539C4×C5—41no—
540C4×C5—41no—
541C4×C5—41no—
542C4×C5—41no—
543C4×C5—41no—
544C4×C5—41no—
545C4×C5—41no—
546C4×C5—41no—
547C4×C5—82no—
548C4×C5#45512yes—
549C24—21no—
550#41—42no—
551#41—42no—
552#41—82no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—41no—
556C2×Q8—82no—
557C2×Q8C2×C5×D411yescharacteristic
558C2×Q8C2×C5×D411yescharacteristic
559C2×Q8C2×C5×D411yescharacteristic
560C2×Q8C2×C5×D411yescharacteristic
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4C2×C5×D411yescharacteristic
575C2×D4C2×C5×D411yescharacteristic
576C2×D4C2×C5×D411yescharacteristic
577C2×D4C2×C5×D411yescharacteristic
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—82no—
589C22×C4C2×C5×D411yescharacteristic
590C22×C4C2×C5×D411yescharacteristic
591C22×C4C2×C5×D411yescharacteristic
592Q16—82no—
593SD16—82no—
594M16—42no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4C2×C5×D411yescharacteristic
619C4⋊C4C2×C5×D411yescharacteristic
620C4⋊C4C2×C5×D411yescharacteristic
621C4⋊C4C2×C5×D411yescharacteristic
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42C2×C5×D411yescharacteristic
651C42C2×C5×D411yescharacteristic
652C42C2×C5×D411yescharacteristic
653C42C24×C511yescharacteristic
654C2×C5—41no—
655C2×C5—81no—
656C2×C5—81no—
657C2×C5—81no—
658C2×C5—81no—
659C2×C5C2×#45511yescharacteristic
660C2×C5#302111yescharacteristic
661C2×C5#302211yescharacteristic
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—81no—
667C23—81no—
668C23—81no—
669C23C5×#12011yescharacteristic
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—42no—
675Q8—42no—
676Q8—82no—
677Q8—81no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—81no—
683D4—81no—
684D4—81no—
685D4—81no—
686D4—81no—
687D4—81no—
688D4—81no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—82no—
717C2×C4C5×#12011yescharacteristic
718C2×C4C5×#12011yescharacteristic
719C2×C4C5×#12011yescharacteristic
720C2×C4C22×C5×D411yescharacteristic
721C2×C4C22×C5×D411yescharacteristic
722C2×C4C22×C5×D411yescharacteristic
723C8—42no—
724C8—42no—
725C8—42no—
726C5#1900011yescharacteristic, direct product factor, Sylow
727C22—21no—
728C22—21no—
729C22—21no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—84no—
743C22C2×C5×#12011yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—82no—
758C4C5×#45512yes—
759C2—41no—
760C2—81no—
761C2—81no—
762C2—81no—
763C2—81no—
764C2C2×C5×#45511yescharacteristic
765C2C5×#302111yescharacteristic
766C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#3529C2
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
2. C5×#3238C2semidirect
3. C5×#3218C2semidirect
4. C5×#3141C2semidirect
5. C5×#1664C2semidirect
6. C5×#1662C2semidirect
7. C5×#1661C2semidirect
8. C5×#1659C2semidirect
9. C5×#1536C2semidirect
10. C5×#1529C2semidirect
11. C5×#1529C2semidirect
24. C2×C5×C4⋊Q8C22semidirect
32. C5×#501C22semidirect
34. C5×#491C22semidirect
37. C5×#489C22semidirect
48. C5×#432C22semidirect
49. C5×#432C22semidirect
52. C4×C5×M16C22semidirect
53. C5×#330C22semidirect
54. C5×#330C22semidirect
58. C5×#329C22semidirect
59. #19000C5direct (N × H)
176. #3238C2×C5semidirect
177. #3218C2×C5semidirect
178. #3141C2×C5semidirect
179. #1664C2×C5semidirect
180. #1662C2×C5semidirect
181. #1661C2×C5semidirect
182. #1659C2×C5semidirect
183. #1536C2×C5semidirect
184. #1529C2×C5semidirect
185. #1529C2×C5semidirect
303. C2×C4⋊Q8C22×C5semidirect
311. #501C22×C5semidirect
313. #491C22×C5semidirect
316. #489C22×C5semidirect
327. #432C22×C5semidirect
328. #432C22×C5semidirect
331. C4×M16C22×C5semidirect
332. #330C22×C5semidirect
333. #330C22×C5semidirect
337. #329C22×C5semidirect
726. C5#19000direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35292
C5×#32382
C5×#32182
C5×#31412
C5×#16642
C5×#16622
C5×#16612
C5×#16592
C5×#15362
C5×#15292
#190005