Finite Group Databasebeta

← C5×#18742 #11941462

Subgroups — C5×#18742 #11941462

Order 1280.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3554C211yesmaximal, characteristic, complemented
2C5×#3246C211yesmaximal, characteristic, complemented
3C5×#3212C211yesmaximal, characteristic, complemented
4C5×#3184C211yesmaximal, characteristic, complemented
5C5×#1653C211yesmaximal, characteristic, complemented
6C5×#1651C211yesmaximal, characteristic, complemented
7C5×#1642C211yesmaximal, characteristic, complemented
8C5×#1640C211yesmaximal, characteristic, complemented
9C5×#1627C211yesmaximal, characteristic, complemented
10C5×#1626C211yesmaximal, characteristic, complemented
11C5×#1621C211yesmaximal, characteristic, complemented
12C5×#1620C211yesmaximal, characteristic, complemented
13C5×#1540C211yesmaximal, characteristic, complemented
14C5×#1485C211yesmaximal, characteristic, complemented
15C5×#1483C211yesmaximal, characteristic, complemented
16C5×#562—22no—
17C5×#559—21no—
18C5×#559C2211yescharacteristic
19C5×#557C2211yescharacteristic
20C5×#554—21no—
21C5×#550C2211yescharacteristic
22C5×D4×Q8C2211yescharacteristic
23C5×#548—21no—
24C5×#547—21no—
25C5×#542—21no—
26C5×#542—21no—
27C5×#540—21no—
28C5×#539—22no—
29C5×#536—21no—
30C5×#533C2211yescharacteristic
31C5×#532C2211yescharacteristic
32C5×#532C2211yescharacteristic
33C5×#529C2211yescharacteristic
34C5×#498C2211yescharacteristic
35C5×#495—21no—
36C5×#493C2211yescharacteristic
37C5×#488—21no—
38C5×#486C2211yescharacteristic
39C5×#486C2211yescharacteristic
40C5×#476—21no—
41C5×#475C2211yescharacteristic
42C5×#475C2211yescharacteristic
43C5×#469—22no—
44C5×#465—21no—
45C5×#465—21no—
46C5×#462C2211yescharacteristic
47C5×#461—21no—
48C5×#461C2211yescharacteristic
49C5×#460C2211yescharacteristic
50C5×#460C2211yescharacteristic
51C5×#460C2211yescharacteristic
52C5×#459C2211yescharacteristic
53C5×#452—21no—
54C5×#449—21no—
55C5×#442—22no—
56C5×#431C2211yescharacteristic
57C2×C5×C4⋊C8C2211yescharacteristic
58C4×C5×M16C2211yescharacteristic
59C5×#332C2211yescharacteristic
60C5×#332C2211yescharacteristic
61C5×#331C2211yescharacteristic
62C5×#331C2211yescharacteristic
63C5×Q8⋊C8C2211yescharacteristic
64C5×Q8⋊C8C2211yescharacteristic
65C5×Q8⋊C8C2211yescharacteristic
66C5×Q8⋊C8C2211yescharacteristic
67C5×Q8⋊C8C2211yescharacteristic
68C5×Q8⋊C8C2211yescharacteristic
69C5×D4⋊C8C2211yescharacteristic
70C5×D4⋊C8C2211yescharacteristic
71#18742C511yesmaximal, characteristic, direct product factor, Sylow
72C2×C5×#41—21no—
73C2×C5×#41—21no—
74C2×C5×#41—21no—
75C22×C5×Q8—21no—
76C2×C5×Q16—21no—
77C2×C5×SD16—21no—
78C2×C5×SD16—21no—
79C2×C5×SD16—21no—
80C2×C5×SD16—21no—
81C2×C5×D8—22no—
82C2×C5×D8—21no—
83C2×C5×M16—21no—
84C22×C5×C8—21no—
85C5×C4⋊Q8—21no—
86C5×C4⋊Q8—21no—
87C5×C4⋊Q8D411yescharacteristic
88C5×C4⋊Q8D411yescharacteristic
89C5×C4⋊Q8C2311yescharacteristic
90C5×C4⋊Q8C2311yescharacteristic
91C5×#127—21no—
92C5×#127C2311yescharacteristic
93C5×#127C2311yescharacteristic
94C5×#126—22no—
95C5×#126—21no—
96C5×#125—22no—
97C5×#125—21no—
98C5×#125—21no—
99C5×#125D411yescharacteristic
100C5×#124—22no—
101C5×#124—22no—
102C5×#124—21no—
103C5×#124—21no—
104C5×#124—21no—
105C5×#124—21no—
106C5×#124D411yescharacteristic
107C5×#123—22no—
108C5×#123—22no—
109C5×#123—22no—
110C5×#123—22no—
111C5×#123—22no—
112C5×#123—22no—
113C5×#123—21no—
114C5×C22⋊Q8—22no—
115C5×C22⋊Q8—22no—
116C5×C22⋊Q8—22no—
117C5×C22⋊Q8—22no—
118C5×C22⋊Q8—21no—
119C5×C22⋊Q8—22no—
120C5×C22⋊Q8—21no—
121C5×C22⋊Q8D411yescharacteristic
122C5×C22⋊Q8D411yescharacteristic
123C5×C22⋊Q8D411yescharacteristic
124C5×#121—22no—
125C5×#121—22no—
126C5×#121—22no—
127C5×#121—21no—
128C5×#121—21no—
129C5×#121—21no—
130C5×#121—21no—
131C5×#121D411yescharacteristic
132C5×#121D412yes—
133C4×C5×Q8—21no—
134C4×C5×Q8—21no—
135C4×C5×Q8—21no—
136C4×C5×Q8C2311yescharacteristic
137C4×C5×Q8C2311yescharacteristic
138C4×C5×Q8C2311yescharacteristic
139C4×C5×D4—22no—
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×D4D412yes—
149C4×C5×D4C2311yescharacteristic
150C5×#117—21no—
151C5×#117—21no—
152C2×C5×C4⋊C4—22no—
153C2×C42×C5C2311yescharacteristic
154C5×#106—22no—
155C5×#106—21no—
156C5×#106—21no—
157C5×C4⋊C8—21no—
158C5×C4⋊C8C2311yescharacteristic
159C5×C4⋊C8C2311yescharacteristic
160C5×C4⋊C8C2311yescharacteristic
161C5×C4⋊C8C2311yescharacteristic
162C5×#103—21no—
163C5×#103—21no—
164C5×#103—21no—
165C5×#103—21no—
166C5×#102—22no—
167C5×#102—22no—
168C5×#102—21no—
169C5×#102—21no—
170C5×#102—21no—
171C5×#102—21no—
172C5×C22⋊C8—21no—
173C5×#97—21no—
174C4×C5×C8—21no—
175C4×C5×C8C2311yescharacteristic
176C4×C5×C8C2311yescharacteristic
177#3554C2×C511yescharacteristic, complemented
178#3246C2×C511yescharacteristic, complemented
179#3212C2×C511yescharacteristic, complemented
180#3184C2×C511yescharacteristic, complemented
181#1653C2×C511yescharacteristic, complemented
182#1651C2×C511yescharacteristic, complemented
183#1642C2×C511yescharacteristic, complemented
184#1640C2×C511yescharacteristic, complemented
185#1627C2×C511yescharacteristic, complemented
186#1626C2×C511yescharacteristic, complemented
187#1621C2×C511yescharacteristic, complemented
188#1620C2×C511yescharacteristic, complemented
189#1540C2×C511yescharacteristic, complemented
190#1485C2×C511yescharacteristic, complemented
191#1483C2×C511yescharacteristic, complemented
192C5×#41—81no—
193C5×#41—81no—
194C5×#41—81no—
195C5×#41—81no—
196C5×#41—81no—
197C5×#41—81no—
198C2×C5×Q8—22no—
199C2×C5×Q8—21no—
200C2×C5×Q8—21no—
201C2×C5×Q8—21no—
202C2×C5×Q8—81no—
203C2×C5×Q8—81no—
204C2×C5×Q8C2×D411yescharacteristic
205C2×C5×Q8C2×D411yescharacteristic
206C2×C5×Q8C2×D411yescharacteristic
207C2×C5×D4—22no—
208C2×C5×D4—22no—
209C2×C5×D4—21no—
210C2×C5×D4—22no—
211C2×C5×D4—21no—
212C2×C5×D4—21no—
213C2×C5×D4—21no—
214C2×C5×D4—21no—
215C2×C5×D4—21no—
216C2×C5×D4—41no—
217C2×C5×D4C2×D411yescharacteristic
218C2×C5×D4C2×D412yes—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—21no—
223C22×C4×C5—22no—
224C22×C4×C5—41no—
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C5×Q16—81no—
229C5×SD16—81no—
230C5×SD16—81no—
231C5×SD16—81no—
232C5×SD16—81no—
233C5×D8—44no—
234C5×D8—81no—
235C5×M16—42no—
236C2×C5×C8—21no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C2×C5×C8—21no—
242C2×C5×C8—81no—
243C5×C4⋊C4—22no—
244C5×C4⋊C4—22no—
245C5×C4⋊C4—22no—
246C5×C4⋊C4—22no—
247C5×C4⋊C4—21no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4—21no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4C2×D411yescharacteristic
262C5×C4⋊C4C2×D411yescharacteristic
263C5×C4⋊C4C2×D411yescharacteristic
264C5×C4⋊C4C2×D412yes—
265C5×C4⋊C4C2×D411yescharacteristic
266C5×C22⋊C4—22no—
267C5×C22⋊C4—22no—
268C5×C22⋊C4—22no—
269C5×C22⋊C4—22no—
270C5×C22⋊C4—22no—
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—22no—
278C5×C22⋊C4—22no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—41no—
281C5×C22⋊C4—41no—
282C42×C5—22no—
283C42×C5—21no—
284C42×C5—21no—
285C42×C5—21no—
286C42×C5C2×D411yescharacteristic
287C42×C5C2×D411yescharacteristic
288C42×C5C2×D411yescharacteristic
289C42×C5C2411yescharacteristic
290#562—22no—
291#559—21no—
292#559C22×C511yescharacteristic
293#557C22×C511yescharacteristic
294#554—21no—
295#550C22×C511yescharacteristic
296D4×Q8C22×C511yescharacteristic
297#548—21no—
298#547—21no—
299#542—21no—
300#542—21no—
301#540—21no—
302#539—22no—
303#536—21no—
304#533C22×C511yescharacteristic
305#532C22×C511yescharacteristic
306#532C22×C511yescharacteristic
307#529C22×C511yescharacteristic
308#498C22×C511yescharacteristic
309#495—21no—
310#493C22×C511yescharacteristic
311#488—21no—
312#486C22×C511yescharacteristic
313#486C22×C511yescharacteristic
314#476—21no—
315#475C22×C511yescharacteristic
316#475C22×C511yescharacteristic
317#469—22no—
318#465—21no—
319#465—21no—
320#462C22×C511yescharacteristic
321#461—21no—
322#461C22×C511yescharacteristic
323#460C22×C511yescharacteristic
324#460C22×C511yescharacteristic
325#460C22×C511yescharacteristic
326#459C22×C511yescharacteristic
327#452—21no—
328#449—21no—
329#442—22no—
330#431C22×C511yescharacteristic
331C2×C4⋊C8C22×C511yescharacteristic
332C4×M16C22×C511yescharacteristic
333#332C22×C511yescharacteristic
334#332C22×C511yescharacteristic
335#331C22×C511yescharacteristic
336#331C22×C511yescharacteristic
337Q8⋊C8C22×C511yescharacteristic
338Q8⋊C8C22×C511yescharacteristic
339Q8⋊C8C22×C511yescharacteristic
340Q8⋊C8C22×C511yescharacteristic
341Q8⋊C8C22×C511yescharacteristic
342Q8⋊C8C22×C511yescharacteristic
343D4⋊C8C22×C511yescharacteristic
344D4⋊C8C22×C511yescharacteristic
345C23×C5—21no—
346C23×C5—22no—
347C23×C5—41no—
348C23×C5#12011yescharacteristic
349C5×Q8—21no—
350C5×Q8—21no—
351C5×Q8—21no—
352C5×Q8—21no—
353C5×Q8—21no—
354C5×Q8—21no—
355C5×Q8—41no—
356C5×Q8—41no—
357C5×Q8—41no—
358C5×Q8—41no—
359C5×Q8—81no—
360C5×Q8—82no—
361C5×D4—21no—
362C5×D4—21no—
363C5×D4—42no—
364C5×D4—42no—
365C5×D4—41no—
366C5×D4—41no—
367C5×D4—41no—
368C5×D4—41no—
369C5×D4—41no—
370C5×D4—41no—
371C5×D4—41no—
372C5×D4—41no—
373C5×D4—81no—
374C5×D4—82no—
375C5×D4—82no—
376C5×D4—82no—
377C5×D4—82no—
378C2×C4×C5—21no—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—22no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—82no—
395C2×C4×C5—82no—
396C2×C4×C5—82no—
397C2×C4×C5—82no—
398C2×C4×C5—82no—
399C2×C4×C5#12011yescharacteristic
400C2×C4×C5#12011yescharacteristic
401C2×C4×C5#12011yescharacteristic
402C2×C4×C5C22×D411yescharacteristic
403C2×C4×C5C22×D411yescharacteristic
404C2×C4×C5C22×D411yescharacteristic
405C5×C8—22no—
406C5×C8—41no—
407C5×C8—41no—
408C5×C8—41no—
409C5×C8—41no—
410C5×C8—41no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C22×Q8—21no—
415C2×Q16—21no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—21no—
420C2×D8—22no—
421C2×D8—21no—
422C2×M16—21no—
423C22×C8—21no—
424C4⋊Q8—21no—
425C4⋊Q8—21no—
426C4⋊Q8C5×D411yescharacteristic
427C4⋊Q8C5×D411yescharacteristic
428C4⋊Q8C23×C511yescharacteristic
429C4⋊Q8C23×C511yescharacteristic
430#127—21no—
431#127C23×C511yescharacteristic
432#127C23×C511yescharacteristic
433#126—22no—
434#126—21no—
435#125—22no—
436#125—21no—
437#125—21no—
438#125C5×D411yescharacteristic
439#124—22no—
440#124—22no—
441#124—21no—
442#124—21no—
443#124—21no—
444#124—21no—
445#124C5×D411yescharacteristic
446#123—22no—
447#123—22no—
448#123—22no—
449#123—22no—
450#123—22no—
451#123—22no—
452#123—21no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—21no—
458C22⋊Q8—22no—
459C22⋊Q8—21no—
460C22⋊Q8C5×D411yescharacteristic
461C22⋊Q8C5×D411yescharacteristic
462C22⋊Q8C5×D411yescharacteristic
463#121—22no—
464#121—22no—
465#121—22no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121C5×D411yescharacteristic
471#121C5×D412yes—
472C4×Q8—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8C23×C511yescharacteristic
476C4×Q8C23×C511yescharacteristic
477C4×Q8C23×C511yescharacteristic
478C4×D4—22no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4C5×D412yes—
488C4×D4C23×C511yescharacteristic
489#117—21no—
490#117—21no—
491C2×C4⋊C4—22no—
492C2×C42C23×C511yescharacteristic
493#106—22no—
494#106—21no—
495#106—21no—
496C4⋊C8—21no—
497C4⋊C8C23×C511yescharacteristic
498C4⋊C8C23×C511yescharacteristic
499C4⋊C8C23×C511yescharacteristic
500C4⋊C8C23×C511yescharacteristic
501#103—21no—
502#103—21no—
503#103—21no—
504#103—21no—
505#102—22no—
506#102—22no—
507#102—21no—
508#102—21no—
509#102—21no—
510#102—21no—
511C22⋊C8—21no—
512#97—21no—
513C4×C8—21no—
514C4×C8C23×C511yescharacteristic
515C4×C8C23×C511yescharacteristic
516C22×C5—21no—
517C22×C5—21no—
518C22×C5—21no—
519C22×C5—41no—
520C22×C5—42no—
521C22×C5—41no—
522C22×C5—42no—
523C22×C5—42no—
524C22×C5—41no—
525C22×C5—81no—
526C22×C5—81no—
527C22×C5—81no—
528C22×C5C2×#12011yescharacteristic
529C4×C5—21no—
530C4×C5—21no—
531C4×C5—21no—
532C4×C5—21no—
533C4×C5—41no—
534C4×C5—41no—
535C4×C5—41no—
536C4×C5—42no—
537C4×C5—41no—
538C4×C5—41no—
539C4×C5—41no—
540C4×C5—41no—
541C4×C5—81no—
542C4×C5#57611yescharacteristic
543C4×C5#57711yescharacteristic
544C4×C5#57711yescharacteristic
545C4×C5#57711yescharacteristic
546#41—81no—
547#41—81no—
548#41—81no—
549#41—81no—
550#41—81no—
551#41—81no—
552C2×Q8—22no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—81no—
557C2×Q8—81no—
558C2×Q8C2×C5×D411yescharacteristic
559C2×Q8C2×C5×D411yescharacteristic
560C2×Q8C2×C5×D411yescharacteristic
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—41no—
571C2×D4C2×C5×D411yescharacteristic
572C2×D4C2×C5×D412yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—41no—
579C22×C4C2×C5×D411yescharacteristic
580C22×C4C2×C5×D411yescharacteristic
581C22×C4C2×C5×D411yescharacteristic
582Q16—81no—
583SD16—81no—
584SD16—81no—
585SD16—81no—
586SD16—81no—
587D8—44no—
588D8—81no—
589M16—42no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—81no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
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—21no—
615C4⋊C4C2×C5×D411yescharacteristic
616C4⋊C4C2×C5×D411yescharacteristic
617C4⋊C4C2×C5×D411yescharacteristic
618C4⋊C4C2×C5×D412yes—
619C4⋊C4C2×C5×D411yescharacteristic
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—41no—
635C22⋊C4—41no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42C2×C5×D411yescharacteristic
641C42C2×C5×D411yescharacteristic
642C42C2×C5×D411yescharacteristic
643C42C24×C511yescharacteristic
644C2×C5—41no—
645C2×C5—81no—
646C2×C5—82no—
647C2×C5—161no—
648C2×C5#301011yescharacteristic
649C2×C5#301211yescharacteristic
650C2×C5#301811yescharacteristic
651C23—21no—
652C23—22no—
653C23—41no—
654C23C5×#12011yescharacteristic
655Q8—21no—
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—81no—
666Q8—82no—
667D4—21no—
668D4—21no—
669D4—42no—
670D4—42no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—82no—
680D4—81no—
681D4—82no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4C5×#12011yescharacteristic
706C2×C4C5×#12011yescharacteristic
707C2×C4C5×#12011yescharacteristic
708C2×C4C22×C5×D411yescharacteristic
709C2×C4C22×C5×D411yescharacteristic
710C2×C4C22×C5×D411yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C5#1874211yescharacteristic, direct product factor, Sylow
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×C5×#12011yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4C5×#57611yescharacteristic
745C4C5×#57711yescharacteristic
746C4C5×#57711yescharacteristic
747C4C5×#57711yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C5×#301011yescharacteristic
753C2C5×#301211yescharacteristic
754C2C5×#301811yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
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
1. C5×#3554C2semidirect
2. C5×#3246C2semidirect
3. C5×#3212C2semidirect
4. C5×#3184C2semidirect
5. C5×#1653C2semidirect
6. C5×#1651C2semidirect
7. C5×#1642C2semidirect
8. C5×#1640C2semidirect
9. C5×#1627C2semidirect
10. C5×#1626C2semidirect
11. C5×#1621C2semidirect
12. C5×#1620C2semidirect
13. C5×#1540C2semidirect
14. C5×#1485C2semidirect
15. C5×#1483C2semidirect
71. #18742C5direct (N × H)
177. #3554C2×C5semidirect
178. #3246C2×C5semidirect
179. #3212C2×C5semidirect
180. #3184C2×C5semidirect
181. #1653C2×C5semidirect
182. #1651C2×C5semidirect
183. #1642C2×C5semidirect
184. #1640C2×C5semidirect
185. #1627C2×C5semidirect
186. #1626C2×C5semidirect
187. #1621C2×C5semidirect
188. #1620C2×C5semidirect
189. #1540C2×C5semidirect
190. #1485C2×C5semidirect
191. #1483C2×C5semidirect
717. C5#18742direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35542
C5×#32462
C5×#32122
C5×#31842
C5×#16532
C5×#16512
C5×#16422
C5×#16402
C5×#16272
C5×#16262
C5×#16212
C5×#16202
C5×#15402
C5×#14852
C5×#14832
#187425