Finite Group Databasebeta

← C5×#18465 #11941185

Subgroups — C5×#18465 #11941185

Order 1280.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3564C211yesmaximal, characteristic
2C5×#3218C211yesmaximal, characteristic, complemented
3C5×#3209C211yesmaximal, characteristic, complemented
4C5×#2821C211yesmaximal, characteristic, complemented
5C5×#1606C212yesmaximal
6C5×#1605C212yesmaximal, complemented
7C5×#1603C212yesmaximal, complemented
8C5×#1602C212yesmaximal, complemented
9C5×#1521C211yesmaximal, characteristic, complemented
10C5×#1515C211yesmaximal, characteristic, complemented
11C5×#1473C211yesmaximal, characteristic, complemented
12C5×#563—21no—
13C5×#563—21no—
14C5×#556—21no—
15C5×#554—21no—
16C5×#552—21no—
17C5×#552—21no—
18C5×#551—21no—
19C5×#551—21no—
20C5×#544C2211yescharacteristic
21C5×#543C2211yescharacteristic
22C5×#542—21no—
23C5×#541—21no—
24C5×#541—21no—
25C5×#539—21no—
26C5×#539C2211yescharacteristic
27C5×#538C2211yescharacteristic
28C5×#533C2211yescharacteristic
29C2×C5×C4⋊Q8C2211yescharacteristic
30C5×#529C2211yescharacteristic
31C2×C5×#126C2211yescharacteristic
32C5×#497—21no—
33C5×#494—21no—
34C5×#491—21no—
35C5×#487—21no—
36C5×#462—21no—
37C5×#462—21no—
38C5×#462—21no—
39C5×#461—21no—
40C5×#451C2212yes—
41C5×#451C2212yes—
42C5×#451C2212yes—
43C5×#448C2212yes—
44C5×#432C2211yescharacteristic
45C5×#431C2211yescharacteristic
46C5×#400—21no—
47C5×#399—21no—
48C5×#398—21no—
49C5×#397—21no—
50C5×#395C2212yes—
51C5×#393C2212yes—
52C5×#383C2211yescharacteristic
53C5×#328C2212yes—
54C5×#328C2212yes—
55C5×#328C2212yes—
56C5×#327C2212yes—
57C5×#324C2212yes—
58C5×#323C2212yes—
59#18465C511yesmaximal, characteristic, direct product factor, Sylow
60C22×C5×Q8C2312yes—
61C2×C5×Q16—22no—
62C2×C5×Q16—22no—
63C2×C5×Q16—22no—
64C2×C5×SD16—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⋊Q8—21no—
72C5×C4⋊Q8D411yescharacteristic
73C5×C4⋊Q8D411yescharacteristic
74C5×#126—21no—
75C5×#126—21no—
76C5×#126—21no—
77C5×#126—21no—
78C5×#126—21no—
79C5×#126—21no—
80C5×#126—21no—
81C5×#126—21no—
82C5×#126—21no—
83C5×#126—21no—
84C5×#126—21no—
85C5×#126—21no—
86C5×#126—21no—
87C5×#125—21no—
88C5×#125—21no—
89C5×#125—21no—
90C5×#125—21no—
91C5×#125—21no—
92C5×#125—21no—
93C5×#125—21no—
94C5×#125—21no—
95C5×#125—21no—
96C5×#125D411yescharacteristic
97C5×#124—21no—
98C5×#124—21no—
99C5×#124—21no—
100C5×#124D411yescharacteristic
101C5×#123—21no—
102C5×#123—21no—
103C5×#123—21no—
104C5×#123—21no—
105C5×#123—21no—
106C5×#123—21no—
107C5×#123—21no—
108C5×#123—21no—
109C5×C22⋊Q8—21no—
110C5×C22⋊Q8—21no—
111C5×C22⋊Q8—21no—
112C5×C22⋊Q8—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8—21no—
115C5×C22⋊Q8—21no—
116C5×C22⋊Q8—21no—
117C5×C22⋊Q8—21no—
118C5×C22⋊Q8—21no—
119C5×C22⋊Q8—21no—
120C5×C22⋊Q8—21no—
121C5×C22⋊Q8—21no—
122C5×C22⋊Q8—21no—
123C5×C22⋊Q8C2311yescharacteristic
124C5×C22⋊Q8C2311yescharacteristic
125C5×C22⋊Q8C2311yescharacteristic
126C5×#121—21no—
127C5×#121C2311yescharacteristic
128C5×#120—21no—
129C4×C5×Q8—21no—
130C4×C5×Q8—21no—
131C4×C5×Q8—21no—
132C4×C5×Q8D411yescharacteristic
133C4×C5×Q8D411yescharacteristic
134C4×C5×Q8D411yescharacteristic
135C4×C5×D4—21no—
136C4×C5×D4—21no—
137C4×C5×D4—21no—
138C4×C5×D4—21no—
139C4×C5×D4—21no—
140C4×C5×D4D411yescharacteristic
141C5×#117—21no—
142C5×#117—21no—
143C5×#117—21no—
144C5×#117—21no—
145C5×#117—21no—
146C5×#117—21no—
147C2×C5×C4⋊C4—21no—
148C2×C5×C4⋊C4—21no—
149C2×C5×C4⋊C4—21no—
150C2×C5×C4⋊C4—22no—
151C2×C5×C4⋊C4D411yescharacteristic
152C2×C5×C4⋊C4D411yescharacteristic
153C2×C5×C4⋊C4C2311yescharacteristic
154C2×C5×C22⋊C4—21no—
155C2×C5×C22⋊C4—22no—
156C2×C5×C22⋊C4D411yescharacteristic
157C2×C5×C22⋊C4D411yescharacteristic
158C2×C5×C22⋊C4C2311yescharacteristic
159C2×C42×C5C2311yescharacteristic
160C5×C4⋊C8—21no—
161C5×C4⋊C8—21no—
162C5×#103—22no—
163C5×#103—22no—
164C5×#103—22no—
165C5×#103—22no—
166C5×C22⋊C8C2312yes—
167C5×C22⋊C8C2312yes—
168C5×#97—21no—
169C4×C5×C8—21no—
170C5×#95—21no—
171C5×#95—21no—
172C5×#95—22no—
173C5×#95—22no—
174C5×#95C2312yes—
175#3564C2×C511yescharacteristic
176#3218C2×C511yescharacteristic, complemented
177#3209C2×C511yescharacteristic, complemented
178#2821C2×C511yescharacteristic, complemented
179#1606C2×C512yes—
180#1605C2×C512yescomplemented
181#1603C2×C512yescomplemented
182#1602C2×C512yescomplemented
183#1521C2×C511yescharacteristic, complemented
184#1515C2×C511yescharacteristic, complemented
185#1473C2×C511yescharacteristic, complemented
186C24×C5C2×D411yescharacteristic
187C2×C5×Q8—21no—
188C2×C5×Q8—21no—
189C2×C5×Q8—21no—
190C2×C5×Q8—22no—
191C2×C5×Q8—22no—
192C2×C5×Q8—82no—
193C2×C5×Q8C2×D411yescharacteristic
194C2×C5×Q8C2×D411yescharacteristic
195C2×C5×Q8C2×D411yescharacteristic
196C2×C5×D4—21no—
197C2×C5×D4—21no—
198C2×C5×D4—21no—
199C2×C5×D4C2×D411yescharacteristic
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5C2×D411yescharacteristic
208C22×C4×C5C2×D411yescharacteristic
209C22×C4×C5C2×D411yescharacteristic
210C22×C4×C5C2×D411yescharacteristic
211C22×C4×C5C2×D411yescharacteristic
212C22×C4×C5C2411yescharacteristic
213C5×Q16—82no—
214C5×Q16—82no—
215C5×Q16—82no—
216C5×SD16—82no—
217C2×C5×C8—22no—
218C2×C5×C8—22no—
219C5×C4⋊C4—21no—
220C5×C4⋊C4—21no—
221C5×C4⋊C4—21no—
222C5×C4⋊C4—21no—
223C5×C4⋊C4—21no—
224C5×C4⋊C4—21no—
225C5×C4⋊C4—21no—
226C5×C4⋊C4—21no—
227C5×C4⋊C4—21no—
228C5×C4⋊C4—21no—
229C5×C4⋊C4—21no—
230C5×C4⋊C4—21no—
231C5×C4⋊C4—21no—
232C5×C4⋊C4—21no—
233C5×C4⋊C4—21no—
234C5×C4⋊C4—21no—
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—41no—
249C5×C4⋊C4—41no—
250C5×C4⋊C4—41no—
251C5×C4⋊C4—41no—
252C5×C4⋊C4—82no—
253C5×C4⋊C4C2×D411yescharacteristic
254C5×C4⋊C4C2×D411yescharacteristic
255C5×C4⋊C4C2×D411yescharacteristic
256C5×C4⋊C4C2×D411yescharacteristic
257C5×C22⋊C4—21no—
258C5×C22⋊C4—21no—
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—82no—
279C42×C5—21no—
280C42×C5—21no—
281C42×C5—21no—
282C42×C5—21no—
283C42×C5—21no—
284C42×C5—21no—
285C42×C5—21no—
286C42×C5C2×D411yescharacteristic
287C42×C5C2×D411yescharacteristic
288C42×C5C2×D411yescharacteristic
289C42×C5C2×D411yescharacteristic
290#563—21no—
291#563—21no—
292#556—21no—
293#554—21no—
294#552—21no—
295#552—21no—
296#551—21no—
297#551—21no—
298#544C22×C511yescharacteristic
299#543C22×C511yescharacteristic
300#542—21no—
301#541—21no—
302#541—21no—
303#539—21no—
304#539C22×C511yescharacteristic
305#538C22×C511yescharacteristic
306#533C22×C511yescharacteristic
307C2×C4⋊Q8C22×C511yescharacteristic
308#529C22×C511yescharacteristic
309C2×#126C22×C511yescharacteristic
310#497—21no—
311#494—21no—
312#491—21no—
313#487—21no—
314#462—21no—
315#462—21no—
316#462—21no—
317#461—21no—
318#451C22×C512yes—
319#451C22×C512yes—
320#451C22×C512yes—
321#448C22×C512yes—
322#432C22×C511yescharacteristic
323#431C22×C511yescharacteristic
324#400—21no—
325#399—21no—
326#398—21no—
327#397—21no—
328#395C22×C512yes—
329#393C22×C512yes—
330#383C22×C511yescharacteristic
331#328C22×C512yes—
332#328C22×C512yes—
333#328C22×C512yes—
334#327C22×C512yes—
335#324C22×C512yes—
336#323C22×C512yes—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—22no—
340C23×C5—41no—
341C23×C5—41no—
342C23×C5C22×D411yescharacteristic
343C5×Q8—41no—
344C5×Q8—41no—
345C5×Q8—41no—
346C5×Q8—42no—
347C5×Q8—42no—
348C5×Q8—42no—
349C5×Q8—42no—
350C5×Q8—81no—
351C5×Q8—81no—
352C5×Q8—81no—
353C5×D4—41no—
354C5×D4—42no—
355C5×D4—81no—
356C5×D4—81no—
357C2×C4×C5—22no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—21no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—22no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—42no—
374C2×C4×C5—42no—
375C2×C4×C5—42no—
376C2×C4×C5—42no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—81no—
380C2×C4×C5—81no—
381C2×C4×C5—81no—
382C2×C4×C5—81no—
383C2×C4×C5—81no—
384C2×C4×C5#12011yescharacteristic
385C2×C4×C5#12011yescharacteristic
386C2×C4×C5#12011yescharacteristic
387C2×C4×C5#12011yescharacteristic
388C2×C4×C5C22×D411yescharacteristic
389C2×C4×C5C22×D411yescharacteristic
390C5×C8—42no—
391C5×C8—42no—
392C22×Q8C23×C512yes—
393C2×Q16—22no—
394C2×Q16—22no—
395C2×Q16—22no—
396C2×SD16—22no—
397C4⋊Q8—21no—
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400C4⋊Q8—21no—
401C4⋊Q8—21no—
402C4⋊Q8—21no—
403C4⋊Q8—21no—
404C4⋊Q8C5×D411yescharacteristic
405C4⋊Q8C5×D411yescharacteristic
406#126—21no—
407#126—21no—
408#126—21no—
409#126—21no—
410#126—21no—
411#126—21no—
412#126—21no—
413#126—21no—
414#126—21no—
415#126—21no—
416#126—21no—
417#126—21no—
418#126—21no—
419#125—21no—
420#125—21no—
421#125—21no—
422#125—21no—
423#125—21no—
424#125—21no—
425#125—21no—
426#125—21no—
427#125—21no—
428#125C5×D411yescharacteristic
429#124—21no—
430#124—21no—
431#124—21no—
432#124C5×D411yescharacteristic
433#123—21no—
434#123—21no—
435#123—21no—
436#123—21no—
437#123—21no—
438#123—21no—
439#123—21no—
440#123—21no—
441C22⋊Q8—21no—
442C22⋊Q8—21no—
443C22⋊Q8—21no—
444C22⋊Q8—21no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8C23×C511yescharacteristic
456C22⋊Q8C23×C511yescharacteristic
457C22⋊Q8C23×C511yescharacteristic
458#121—21no—
459#121C23×C511yescharacteristic
460#120—21no—
461C4×Q8—21no—
462C4×Q8—21no—
463C4×Q8—21no—
464C4×Q8C5×D411yescharacteristic
465C4×Q8C5×D411yescharacteristic
466C4×Q8C5×D411yescharacteristic
467C4×D4—21no—
468C4×D4—21no—
469C4×D4—21no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4C5×D411yescharacteristic
473#117—21no—
474#117—21no—
475#117—21no—
476#117—21no—
477#117—21no—
478#117—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4C5×D411yescharacteristic
484C2×C4⋊C4C5×D411yescharacteristic
485C2×C4⋊C4C23×C511yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4C5×D411yescharacteristic
489C2×C22⋊C4C5×D411yescharacteristic
490C2×C22⋊C4C23×C511yescharacteristic
491C2×C42C23×C511yescharacteristic
492C4⋊C8—21no—
493C4⋊C8—21no—
494#103—22no—
495#103—22no—
496#103—22no—
497#103—22no—
498C22⋊C8C23×C512yes—
499C22⋊C8C23×C512yes—
500#97—21no—
501C4×C8—21no—
502#95—21no—
503#95—21no—
504#95—22no—
505#95—22no—
506#95C23×C512yes—
507C22×C5—21no—
508C22×C5—21no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—82no—
516C22×C5C2×#12011yescharacteristic
517C22×C5#57812yes—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—21no—
524C4×C5—41no—
525C4×C5—41no—
526C4×C5—41no—
527C4×C5—41no—
528C4×C5—41no—
529C4×C5—41no—
530C4×C5—41no—
531C4×C5—41no—
532C4×C5—41no—
533C4×C5—41no—
534C4×C5—82no—
535C4×C5—82no—
536C24C2×C5×D411yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—82no—
543C2×Q8C2×C5×D411yescharacteristic
544C2×Q8C2×C5×D411yescharacteristic
545C2×Q8C2×C5×D411yescharacteristic
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4C2×C5×D411yescharacteristic
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4C2×C5×D411yescharacteristic
558C22×C4C2×C5×D411yescharacteristic
559C22×C4C2×C5×D411yescharacteristic
560C22×C4C2×C5×D411yescharacteristic
561C22×C4C2×C5×D411yescharacteristic
562C22×C4C24×C511yescharacteristic
563Q16—82no—
564Q16—82no—
565Q16—82no—
566SD16—82no—
567C2×C8—22no—
568C2×C8—22no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—82no—
603C4⋊C4C2×C5×D411yescharacteristic
604C4⋊C4C2×C5×D411yescharacteristic
605C4⋊C4C2×C5×D411yescharacteristic
606C4⋊C4C2×C5×D411yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—82no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42C2×C5×D411yescharacteristic
637C42C2×C5×D411yescharacteristic
638C42C2×C5×D411yescharacteristic
639C42C2×C5×D411yescharacteristic
640C2×C5—22no—
641C2×C5—81no—
642C2×C5—81no—
643C2×C5#301111yescharacteristic
644C2×C5#302211yescharacteristic
645C2×C5#302711yescharacteristic
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23C22×C5×D411yescharacteristic
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—81no—
660Q8—81no—
661Q8—81no—
662D4—41no—
663D4—42no—
664D4—81no—
665D4—81no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4C5×#12011yescharacteristic
694C2×C4C5×#12011yescharacteristic
695C2×C4C5×#12011yescharacteristic
696C2×C4C5×#12011yescharacteristic
697C2×C4C22×C5×D411yescharacteristic
698C2×C4C22×C5×D411yescharacteristic
699C8—42no—
700C8—42no—
701C5#1846511yescharacteristic, direct product factor, Sylow
702C22—21no—
703C22—21no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—82no—
711C22C2×C5×#12011yescharacteristic
712C22C5×#57812yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—82no—
730C4—82no—
731C2—22no—
732C2—81no—
733C2—81no—
734C2C5×#301111yescharacteristic
735C2C5×#302211yescharacteristic
736C2C5×#302711yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#538C22
LCSG ▷ C22×C4 ▷ 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×#3218C2semidirect
3. C5×#3209C2semidirect
4. C5×#2821C2semidirect
6. C5×#1605C2semidirect
7. C5×#1603C2semidirect
8. C5×#1602C2semidirect
9. C5×#1521C2semidirect
10. C5×#1515C2semidirect
11. C5×#1473C2semidirect
59. #18465C5direct (N × H)
176. #3218C2×C5semidirect
177. #3209C2×C5semidirect
178. #2821C2×C5semidirect
180. #1605C2×C5semidirect
181. #1603C2×C5semidirect
182. #1602C2×C5semidirect
183. #1521C2×C5semidirect
184. #1515C2×C5semidirect
185. #1473C2×C5semidirect
701. C5#18465direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35642
C5×#32182
C5×#32092
C5×#28212
C5×#16062
C5×#16052
C5×#16032
C5×#16022
C5×#15212
C5×#15152
C5×#14732
#184655