Finite Group Databasebeta

← C5×#11037 #11933757

Subgroups — C5×#11037 #11933757

Order 1280.

1252 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic
2C2×C5×#421C211yesmaximal, characteristic, complemented
3C5×#2896C211yesmaximal, characteristic, complemented
4C2×C5×#413C211yesmaximal, characteristic, complemented
5C5×#2879C211yesmaximal, characteristic, complemented
6C2×C5×#344C211yesmaximal, characteristic, complemented
7C5×#1738C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×#41C2211yescharacteristic
10C5×#575—22no—
11C5×#575—22no—
12C5×#575—22no—
13C5×#575C414yescomplemented
14C2×C5×#137—21no—
15C2×C5×#137—21no—
16C2×C5×AGL(1,ℤ/8)—21no—
17C2×C5×AGL(1,ℤ/8)—21no—
18C2×C5×#135—22no—
19C22×C5×M16C2211yescharacteristic
20C22×C5×M16C2211yescharacteristic
21C22×C5×M16C2211yescharacteristic
22C22×C5×M16C2211yescharacteristic
23C2×C5×#117C2211yescharacteristic
24C5×#421—22no—
25C5×#421—22no—
26C2×C5×#104—22no—
27C5×#419—21no—
28C5×#418—21no—
29C5×#417—22no—
30C5×#416—22no—
31C5×#413—22no—
32C5×#413—22no—
33C2×C5×#101—21no—
34C2×C5×#100—21no—
35C5×#408—22no—
36C5×#408—22no—
37C5×#407—22no—
38C5×#344—22no—
39C5×#341—22no—
40#11037C511yesmaximal, characteristic, direct product factor, Sylow
41C2×C5×#41—21no—
42C2×C5×#41—21no—
43C2×C5×#41—21no—
44C2×C5×#41—21no—
45C2×C5×#41—21no—
46C2×C5×#41—21no—
47C2×C5×#41—21no—
48C2×C5×#41—21no—
49C2×C5×#41—21no—
50C2×C5×#41—21no—
51C2×C5×#41—21no—
52C2×C5×#41—21no—
53C2×C5×#41—21no—
54C2×C5×#41—21no—
55C2×C5×#41—21no—
56C2×C5×#41—21no—
57C2×C5×#41—21no—
58C2×C5×#41—21no—
59C2×C5×#41—21no—
60C2×C5×#41—21no—
61C2×C5×#41C2×C412yes—
62C2×C5×#41C2×C412yes—
63C2×C5×#41D412yes—
64C2×C5×#41D412yes—
65C22×C5×Q8D411yescharacteristic
66C22×C5×Q8D411yescharacteristic
67C22×C5×D4—21no—
68C22×C5×D4—21no—
69C22×C5×D4D411yescharacteristic
70C22×C5×D4D411yescharacteristic
71C23×C4×C5—21no—
72C23×C4×C5—21no—
73C23×C4×C5C2311yescharacteristic
74C5×#137—24no—
75C5×#137—24no—
76C5×#137—24no—
77C5×#137—24no—
78C5×AGL(1,ℤ/8)—24no—
79C5×AGL(1,ℤ/8)—24no—
80C5×AGL(1,ℤ/8)—24no—
81C5×AGL(1,ℤ/8)—24no—
82C5×#135—28no—
83C5×#135—28no—
84C2×C5×Q16—22no—
85C2×C5×SD16—22no—
86C2×C5×SD16—22no—
87C2×C5×D8—22no—
88C2×C5×M16—21no—
89C2×C5×M16—21no—
90C2×C5×M16—21no—
91C2×C5×M16—21no—
92C2×C5×M16—21no—
93C2×C5×M16—21no—
94C2×C5×M16—21no—
95C2×C5×M16—21no—
96C2×C5×M16—21no—
97C2×C5×M16—21no—
98C2×C5×M16—21no—
99C2×C5×M16—21no—
100C2×C5×M16—21no—
101C2×C5×M16—21no—
102C2×C5×M16—21no—
103C2×C5×M16—21no—
104C2×C5×M16—21no—
105C2×C5×M16—21no—
106C2×C5×M16—21no—
107C2×C5×M16C2×C412yes—
108C2×C5×M16D412yes—
109C2×C5×M16D412yes—
110C2×C5×M16D412yes—
111C2×C5×M16D412yes—
112C22×C5×C8—21no—
113C22×C5×C8—21no—
114C22×C5×C8—21no—
115C22×C5×C8D412yes—
116C5×#117—21no—
117C5×#117—21no—
118C5×#117—21no—
119C5×#117D412yes—
120C2×C5×C4⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C42×C5—21no—
123C5×#104—28no—
124C5×#103—24no—
125C5×#102—24no—
126C5×#101—24no—
127C5×#100—24no—
128C5×C22⋊C8—28no—
129C2×#575C2×C511yescharacteristic
130C2×#421C2×C511yescharacteristic, complemented
131#2896C2×C511yescharacteristic, complemented
132C2×#413C2×C511yescharacteristic, complemented
133#2879C2×C511yescharacteristic, complemented
134C2×#344C2×C511yescharacteristic, complemented
135#1738C2×C511yescharacteristic, complemented
136C24×C5—21no—
137C24×C5—21no—
138C24×C5#4111yescharacteristic
139C5×#41—22no—
140C5×#41—22no—
141C5×#41—22no—
142C5×#41—22no—
143C5×#41—22no—
144C5×#41—22no—
145C5×#41—22no—
146C5×#41—22no—
147C5×#41—22no—
148C5×#41—22no—
149C5×#41—22no—
150C5×#41—22no—
151C5×#41—22no—
152C5×#41—22no—
153C5×#41—22no—
154C5×#41—22no—
155C5×#41—41no—
156C5×#41—41no—
157C5×#41—41no—
158C5×#41—41no—
159C5×#41—41no—
160C5×#41—41no—
161C5×#41—41no—
162C5×#41—41no—
163C5×#41—41no—
164C5×#41—41no—
165C5×#41—41no—
166C5×#41—41no—
167C5×#41—41no—
168C5×#41—41no—
169C5×#41—41no—
170C5×#41—41no—
171C2×C5×Q8—21no—
172C2×C5×Q8—21no—
173C2×C5×Q8—21no—
174C2×C5×Q8—21no—
175C2×C5×Q8—21no—
176C2×C5×Q8—21no—
177C2×C5×Q8—21no—
178C2×C5×Q8—21no—
179C2×C5×Q8—21no—
180C2×C5×Q8—21no—
181C2×C5×Q8C22⋊C412yes—
182C2×C5×Q8C22⋊C412yes—
183C2×C5×D4—22no—
184C2×C5×D4—22no—
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4—21no—
192C2×C5×D4—21no—
193C2×C5×D4—21no—
194C2×C5×D4—21no—
195C2×C5×D4—21no—
196C2×C5×D4—21no—
197C2×C5×D4—41no—
198C2×C5×D4—41no—
199C2×C5×D4—41no—
200C2×C5×D4—41no—
201C2×C5×D4—41no—
202C2×C5×D4—41no—
203C2×C5×D4—41no—
204C2×C5×D4—41no—
205C2×C5×D4C22⋊C412yes—
206C2×C5×D4C22⋊C412yes—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—41no—
214C22×C4×C5—41no—
215C22×C4×C5—41no—
216C22×C4×C5—41no—
217C22×C4×C5—41no—
218C22×C4×C5—41no—
219C22×C4×C5—41no—
220C22×C4×C5—41no—
221C22×C4×C5—41no—
222C22×C4×C5C22×C411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D411yescharacteristic
233C22×C4×C5#4111yescharacteristic
234C22×C4×C5#4111yescharacteristic
235C22×C4×C5#4111yescharacteristic
236C5×Q16—28no—
237C5×SD16—28no—
238C5×SD16—28no—
239C5×D8—28no—
240C5×M16—22no—
241C5×M16—22no—
242C5×M16—22no—
243C5×M16—22no—
244C5×M16—22no—
245C5×M16—22no—
246C5×M16—22no—
247C5×M16—22no—
248C5×M16—22no—
249C5×M16—22no—
250C5×M16—41no—
251C5×M16—41no—
252C5×M16—41no—
253C5×M16—41no—
254C5×M16—41no—
255C5×M16—41no—
256C2×C5×C8—22no—
257C2×C5×C8—22no—
258C2×C5×C8—22no—
259C2×C5×C8—22no—
260C2×C5×C8—22no—
261C2×C5×C8—41no—
262C2×C5×C8—41no—
263C2×C5×C8—41no—
264C2×C5×C8—41no—
265C2×C5×C8—41no—
266C2×C5×C8—41no—
267C2×C5×C8C22⋊C414yes—
268C5×C4⋊C4—22no—
269C5×C4⋊C4—41no—
270C5×C22⋊C4—22no—
271C5×C22⋊C4—41no—
272C42×C5—22no—
273C42×C5—41no—
274C22×#41C22×C511yescharacteristic
275C22×#41C22×C511yescharacteristic
276#575—22no—
277#575—22no—
278#575—22no—
279#575C4×C514yescomplemented
280C2×#137—21no—
281C2×#137—21no—
282C2×AGL(1,ℤ/8)—21no—
283C2×AGL(1,ℤ/8)—21no—
284C2×#135—22no—
285C22×M16C22×C511yescharacteristic
286C22×M16C22×C511yescharacteristic
287C22×M16C22×C511yescharacteristic
288C22×M16C22×C511yescharacteristic
289C2×#117C22×C511yescharacteristic
290#421—22no—
291#421—22no—
292C2×#104—22no—
293#419—21no—
294#418—21no—
295#417—22no—
296#416—22no—
297#413—22no—
298#413—22no—
299C2×#101—21no—
300C2×#100—21no—
301#408—22no—
302#408—22no—
303#407—22no—
304#344—22no—
305#341—22no—
306C23×C5—22no—
307C23×C5—22no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5—41no—
312C23×C5—81no—
313C23×C5—82no—
314C23×C5—82no—
315C23×C5C4×D411yescharacteristic
316C23×C5#12111yescharacteristic
317C23×C5#12111yescharacteristic
318C23×C5#12111yescharacteristic
319C23×C5#12311yescharacteristic
320C23×C5#12311yescharacteristic
321C23×C5#12411yescharacteristic
322C5×Q8—22no—
323C5×Q8—22no—
324C5×Q8—22no—
325C5×Q8—22no—
326C5×Q8—41no—
327C5×Q8—41no—
328C5×Q8—41no—
329C5×Q8—41no—
330C5×D4—22no—
331C5×D4—22no—
332C5×D4—22no—
333C5×D4—22no—
334C5×D4—42no—
335C5×D4—42no—
336C5×D4—42no—
337C5×D4—42no—
338C5×D4—42no—
339C5×D4—42no—
340C5×D4—42no—
341C5×D4—42no—
342C5×D4—41no—
343C5×D4—41no—
344C5×D4—41no—
345C5×D4—41no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—42no—
353C2×C4×C5—42no—
354C2×C4×C5—42no—
355C2×C4×C5—42no—
356C2×C4×C5—42no—
357C2×C4×C5—42no—
358C2×C4×C5—42no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—82no—
362C2×C4×C5C2×C22⋊C411yescharacteristic
363C2×C4×C5C2×C22⋊C411yescharacteristic
364C2×C4×C5C2×C22⋊C411yescharacteristic
365C2×C4×C5C4×D411yescharacteristic
366C2×C4×C5C4×D411yescharacteristic
367C2×C4×C5C4×D411yescharacteristic
368C2×C4×C5#12011yescharacteristic
369C2×C4×C5#12011yescharacteristic
370C2×C4×C5#12011yescharacteristic
371C2×C4×C5#12011yescharacteristic
372C2×C4×C5#12011yescharacteristic
373C2×C4×C5#12011yescharacteristic
374C2×C4×C5#12011yescharacteristic
375C2×C4×C5#12011yescharacteristic
376C2×C4×C5#12111yescharacteristic
377C2×C4×C5#12111yescharacteristic
378C2×C4×C5#12111yescharacteristic
379C2×C4×C5#12111yescharacteristic
380C2×C4×C5#12111yescharacteristic
381C2×C4×C5#12111yescharacteristic
382C2×C4×C5#12111yescharacteristic
383C2×C4×C5#12111yescharacteristic
384C2×C4×C5#12111yescharacteristic
385C2×C4×C5#12311yescharacteristic
386C2×C4×C5#12311yescharacteristic
387C2×C4×C5#12411yescharacteristic
388C2×C4×C5#12711yescharacteristic
389C2×C4×C5#12711yescharacteristic
390C5×C8—24no—
391C5×C8—42no—
392C5×C8—42no—
393C5×C8—42no—
394C2×#41—21no—
395C2×#41—21no—
396C2×#41—21no—
397C2×#41—21no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—21no—
403C2×#41—21no—
404C2×#41—21no—
405C2×#41—21no—
406C2×#41—21no—
407C2×#41—21no—
408C2×#41—21no—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41C2×C4×C512yes—
415C2×#41C2×C4×C512yes—
416C2×#41C5×D412yes—
417C2×#41C5×D412yes—
418C22×Q8C5×D411yescharacteristic
419C22×Q8C5×D411yescharacteristic
420C22×D4—21no—
421C22×D4—21no—
422C22×D4C5×D411yescharacteristic
423C22×D4C5×D411yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4C23×C511yescharacteristic
427#137—24no—
428#137—24no—
429#137—24no—
430#137—24no—
431AGL(1,ℤ/8)—24no—
432AGL(1,ℤ/8)—24no—
433AGL(1,ℤ/8)—24no—
434AGL(1,ℤ/8)—24no—
435#135—28no—
436#135—28no—
437C2×Q16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×D8—22no—
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—21no—
448C2×M16—21no—
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16—21no—
453C2×M16—21no—
454C2×M16—21no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16C2×C4×C512yes—
461C2×M16C5×D412yes—
462C2×M16C5×D412yes—
463C2×M16C5×D412yes—
464C2×M16C5×D412yes—
465C22×C8—21no—
466C22×C8—21no—
467C22×C8—21no—
468C22×C8C5×D412yes—
469#117—21no—
470#117—21no—
471#117—21no—
472#117C5×D412yes—
473C2×C4⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C42—21no—
476#104—28no—
477#103—24no—
478#102—24no—
479#101—24no—
480#100—24no—
481C22⋊C8—28no—
482C22×C5—41no—
483C22×C5—41no—
484C22×C5—41no—
485C22×C5—41no—
486C22×C5—41no—
487C22×C5—41no—
488C22×C5—41no—
489C22×C5—44no—
490C22×C5—42no—
491C22×C5—42no—
492C22×C5—82no—
493C22×C5—82no—
494C22×C5—82no—
495C22×C5—82no—
496C22×C5—82no—
497C22×C5#38611yescharacteristic
498C22×C5#38611yescharacteristic
499C22×C5#39011yescharacteristic
500C22×C5#39211yescharacteristic
501C22×C5#39411yescharacteristic
502C22×C5#39411yescharacteristic
503C22×C5#39411yescharacteristic
504C4×C5—42no—
505C4×C5—42no—
506C4×C5—82no—
507C4×C5#37911yescharacteristic
508C4×C5#38611yescharacteristic
509C4×C5#38611yescharacteristic
510C4×C5#39011yescharacteristic
511C4×C5#39211yescharacteristic
512C4×C5#39211yescharacteristic
513C4×C5#39211yescharacteristic
514C4×C5#39411yescharacteristic
515C24—21no—
516C24—21no—
517C24C5×#4111yescharacteristic
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—41no—
538#41—41no—
539#41—41no—
540#41—41no—
541#41—41no—
542#41—41no—
543#41—41no—
544#41—41no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8C5×C22⋊C412yes—
561C2×Q8C5×C22⋊C412yes—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
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×D4—21no—
575C2×D4—21no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4C5×C22⋊C412yes—
585C2×D4C5×C22⋊C412yes—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4C22×C4×C511yescharacteristic
602C22×C4C2×C5×D411yescharacteristic
603C22×C4C2×C5×D411yescharacteristic
604C22×C4C2×C5×D411yescharacteristic
605C22×C4C2×C5×D411yescharacteristic
606C22×C4C2×C5×D411yescharacteristic
607C22×C4C2×C5×D411yescharacteristic
608C22×C4C2×C5×D411yescharacteristic
609C22×C4C2×C5×D411yescharacteristic
610C22×C4C2×C5×D411yescharacteristic
611C22×C4C2×C5×D411yescharacteristic
612C22×C4C5×#4111yescharacteristic
613C22×C4C5×#4111yescharacteristic
614C22×C4C5×#4111yescharacteristic
615Q16—28no—
616SD16—28no—
617SD16—28no—
618D8—28no—
619M16—22no—
620M16—22no—
621M16—22no—
622M16—22no—
623M16—22no—
624M16—22no—
625M16—22no—
626M16—22no—
627M16—22no—
628M16—22no—
629M16—41no—
630M16—41no—
631M16—41no—
632M16—41no—
633M16—41no—
634M16—41no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8C5×C22⋊C414yes—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C22⋊C4—22no—
650C22⋊C4—41no—
651C42—22no—
652C42—41no—
653C2×C5—21no—
654C2×C5—21no—
655C2×C5—21no—
656C2×C5—21no—
657C2×C5—21no—
658C2×C5—21no—
659C2×C5—21no—
660C2×C5—82no—
661C2×C5—82no—
662C2×C5#143811yescharacteristic
663C23—22no—
664C23—22no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—81no—
670C23—82no—
671C23—82no—
672C23C4×C5×D411yescharacteristic
673C23C5×#12111yescharacteristic
674C23C5×#12111yescharacteristic
675C23C5×#12111yescharacteristic
676C23C5×#12311yescharacteristic
677C23C5×#12311yescharacteristic
678C23C5×#12411yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687D4—22no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—82no—
719C2×C4C2×C5×C22⋊C411yescharacteristic
720C2×C4C2×C5×C22⋊C411yescharacteristic
721C2×C4C2×C5×C22⋊C411yescharacteristic
722C2×C4C4×C5×D411yescharacteristic
723C2×C4C4×C5×D411yescharacteristic
724C2×C4C4×C5×D411yescharacteristic
725C2×C4C5×#12011yescharacteristic
726C2×C4C5×#12011yescharacteristic
727C2×C4C5×#12011yescharacteristic
728C2×C4C5×#12011yescharacteristic
729C2×C4C5×#12011yescharacteristic
730C2×C4C5×#12011yescharacteristic
731C2×C4C5×#12011yescharacteristic
732C2×C4C5×#12011yescharacteristic
733C2×C4C5×#12111yescharacteristic
734C2×C4C5×#12111yescharacteristic
735C2×C4C5×#12111yescharacteristic
736C2×C4C5×#12111yescharacteristic
737C2×C4C5×#12111yescharacteristic
738C2×C4C5×#12111yescharacteristic
739C2×C4C5×#12111yescharacteristic
740C2×C4C5×#12111yescharacteristic
741C2×C4C5×#12111yescharacteristic
742C2×C4C5×#12311yescharacteristic
743C2×C4C5×#12311yescharacteristic
744C2×C4C5×#12411yescharacteristic
745C2×C4C5×#12711yescharacteristic
746C2×C4C5×#12711yescharacteristic
747C8—24no—
748C8—42no—
749C8—42no—
750C8—42no—
751C5#1103711yescharacteristic, direct product factor, Sylow
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22C5×#38611yescharacteristic
768C22C5×#38611yescharacteristic
769C22C5×#39011yescharacteristic
770C22C5×#39211yescharacteristic
771C22C5×#39411yescharacteristic
772C22C5×#39411yescharacteristic
773C22C5×#39411yescharacteristic
774C4—42no—
775C4—42no—
776C4—82no—
777C4C5×#37911yescharacteristic
778C4C5×#38611yescharacteristic
779C4C5×#38611yescharacteristic
780C4C5×#39011yescharacteristic
781C4C5×#39211yescharacteristic
782C4C5×#39211yescharacteristic
783C4C5×#39211yescharacteristic
784C4C5×#39411yescharacteristic
785C2—21no—
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—21no—
791C2—21no—
792C2—82no—
793C2—82no—
794C2C5×#143811yescharacteristic
subgroupG/H
centerC4×C5#392
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
socleC2×C5#1438
prime radicalC2×C5×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C23×C4×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C5×#421C2semidirect
3. C5×#2896C2semidirect
4. C2×C5×#413C2semidirect
5. C5×#2879C2semidirect
6. C2×C5×#344C2semidirect
7. C5×#1738C2semidirect
13. C5×#575C4semidirect
40. #11037C5direct (N × H)
130. C2×#421C2×C5semidirect
131. #2896C2×C5semidirect
132. C2×#413C2×C5semidirect
133. #2879C2×C5semidirect
134. C2×#344C2×C5semidirect
135. #1738C2×C5semidirect
279. #575C4×C5semidirect
751. C5#11037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5752
C2×C5×#4212
C5×#28962
C2×C5×#4132
C5×#28792
C2×C5×#3442
C5×#17382
#110375