Finite Group Databasebeta

← C5×#11032 #11933752

Subgroups — C5×#11032 #11933752

Order 1280.

1252 conjugacy classes of subgroups.

The subgroup lattice has 792 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
3C2×C5×#421C211yesmaximal, characteristic, complemented
4C2×C5×#413C211yesmaximal, characteristic, complemented
5C5×#2879C211yesmaximal, characteristic, complemented
6C5×#1742C211yesmaximal, characteristic, complemented
7C5×#1738C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×#41C2211yescharacteristic
10C5×#575—22no—
11C5×#575—22no—
12C5×#575—22no—
13C5×#575—22no—
14C2×C5×#137—21no—
15C2×C5×#137C412yescomplemented
16C2×C5×AGL(1,ℤ/8)—21no—
17C2×C5×AGL(1,ℤ/8)C412yescomplemented
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—
26C5×#421—22no—
27C5×#421—22no—
28C2×C5×#104—22no—
29C2×C5×#104—22no—
30C5×#413—22no—
31C5×#413—22no—
32C2×C5×#101—21no—
33C2×C5×#100—21no—
34C5×#408—22no—
35C5×#408—22no—
36C5×#407—22no—
37C5×#343—22no—
38C5×#341—22no—
39#11032C511yesmaximal, characteristic, direct product factor, Sylow
40C2×C5×#41—21no—
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×#41C2×C412yes—
61C2×C5×#41D412yes—
62C2×C5×#41D412yes—
63C2×C5×#41D412yes—
64C22×C5×Q8C2×C411yescharacteristic
65C22×C5×Q8D411yescharacteristic
66C22×C5×D4—21no—
67C22×C5×D4—21no—
68C22×C5×D4C2×C411yescharacteristic
69C22×C5×D4D411yescharacteristic
70C23×C4×C5—21no—
71C23×C4×C5—21no—
72C23×C4×C5C2311yescharacteristic
73C5×#137—24no—
74C5×#137—24no—
75C5×#137—24no—
76C5×#137—24no—
77C5×AGL(1,ℤ/8)—24no—
78C5×AGL(1,ℤ/8)—24no—
79C5×AGL(1,ℤ/8)—24no—
80C5×AGL(1,ℤ/8)—24no—
81C5×#135—28no—
82C5×#135—28no—
83C2×C5×Q16—22no—
84C2×C5×SD16—22no—
85C2×C5×SD16—22no—
86C2×C5×D8—22no—
87C2×C5×M16—21no—
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×M16C2×C412yes—
106C2×C5×M16D412yes—
107C2×C5×M16D412yes—
108C2×C5×M16D412yes—
109C2×C5×M16D412yes—
110C2×C5×M16D412yes—
111C22×C5×C8—21no—
112C22×C5×C8—21no—
113C22×C5×C8—21no—
114C22×C5×C8—21no—
115C5×#117—21no—
116C5×#117—21no—
117C5×#117—21no—
118C5×#117—21no—
119C2×C5×C4⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C42×C5D412yes—
122C5×#104—28no—
123C5×#104—28no—
124C5×#101—24no—
125C5×#100—24no—
126C5×C22⋊C8—28no—
127C2×#575C2×C511yescharacteristic
128C2×#421C2×C511yescharacteristic, complemented
129C2×#421C2×C511yescharacteristic, complemented
130C2×#413C2×C511yescharacteristic, complemented
131#2879C2×C511yescharacteristic, complemented
132#1742C2×C511yescharacteristic, complemented
133#1738C2×C511yescharacteristic, complemented
134C24×C5—21no—
135C24×C5—21no—
136C24×C5#4111yescharacteristic
137C5×#41—22no—
138C5×#41—22no—
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—41no—
154C5×#41—41no—
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—
169C2×C5×Q8—21no—
170C2×C5×Q8—21no—
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×Q8C22⋊C412yes—
180C2×C5×Q8C22⋊C412yes—
181C2×C5×D4—22no—
182C2×C5×D4—22no—
183C2×C5×D4—22no—
184C2×C5×D4—22no—
185C2×C5×D4—21no—
186C2×C5×D4—21no—
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—41no—
196C2×C5×D4—41no—
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×D4C22⋊C412yes—
204C2×C5×D4C22⋊C412yes—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—41no—
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×C5C22×C411yescharacteristic
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
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×C5#4111yescharacteristic
232C22×C4×C5#4111yescharacteristic
233C22×C4×C5#4111yescharacteristic
234C5×Q16—28no—
235C5×SD16—28no—
236C5×SD16—28no—
237C5×D8—28no—
238C5×M16—22no—
239C5×M16—22no—
240C5×M16—22no—
241C5×M16—22no—
242C5×M16—22no—
243C5×M16—22no—
244C5×M16—22no—
245C5×M16—22no—
246C5×M16—22no—
247C5×M16—41no—
248C5×M16—41no—
249C5×M16—41no—
250C5×M16—41no—
251C5×M16—41no—
252C5×M16—41no—
253C5×M16C22⋊C414yes—
254C2×C5×C8—22no—
255C2×C5×C8—22no—
256C2×C5×C8—22no—
257C2×C5×C8—22no—
258C2×C5×C8—22no—
259C2×C5×C8—22no—
260C2×C5×C8—41no—
261C2×C5×C8—41no—
262C2×C5×C8—41no—
263C2×C5×C8—41no—
264C2×C5×C8—41no—
265C2×C5×C8—41no—
266C5×C4⋊C4—41no—
267C5×C4⋊C4—41no—
268C5×C22⋊C4—41no—
269C5×C22⋊C4—41no—
270C42×C5—22no—
271C42×C5—22no—
272C22×#41C22×C511yescharacteristic
273C22×#41C22×C511yescharacteristic
274#575—22no—
275#575—22no—
276#575—22no—
277#575—22no—
278C2×#137—21no—
279C2×#137C4×C512yescomplemented
280C2×AGL(1,ℤ/8)—21no—
281C2×AGL(1,ℤ/8)C4×C512yescomplemented
282C2×#135—22no—
283C22×M16C22×C511yescharacteristic
284C22×M16C22×C511yescharacteristic
285C22×M16C22×C511yescharacteristic
286C22×M16C22×C511yescharacteristic
287C2×#117C22×C511yescharacteristic
288#421—22no—
289#421—22no—
290#421—22no—
291#421—22no—
292C2×#104—22no—
293C2×#104—22no—
294#413—22no—
295#413—22no—
296C2×#101—21no—
297C2×#100—21no—
298#408—22no—
299#408—22no—
300#407—22no—
301#343—22no—
302#341—22no—
303C23×C5—22no—
304C23×C5—22no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—81no—
310C23×C5—82no—
311C23×C5—82no—
312C23×C5C4×D411yescharacteristic
313C23×C5#12111yescharacteristic
314C23×C5#12111yescharacteristic
315C23×C5#12111yescharacteristic
316C23×C5#12311yescharacteristic
317C23×C5#12311yescharacteristic
318C23×C5#12411yescharacteristic
319C5×Q8—22no—
320C5×Q8—22no—
321C5×Q8—22no—
322C5×Q8—22no—
323C5×Q8—41no—
324C5×Q8—41no—
325C5×Q8—41no—
326C5×Q8—41no—
327C5×D4—22no—
328C5×D4—22no—
329C5×D4—22no—
330C5×D4—22no—
331C5×D4—42no—
332C5×D4—42no—
333C5×D4—42no—
334C5×D4—42no—
335C5×D4—42no—
336C5×D4—42no—
337C5×D4—42no—
338C5×D4—42no—
339C5×D4—41no—
340C5×D4—41no—
341C5×D4—41no—
342C5×D4—41no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—42no—
350C2×C4×C5—42no—
351C2×C4×C5—42no—
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—82no—
359C2×C4×C5C2×C22⋊C411yescharacteristic
360C2×C4×C5C2×C22⋊C411yescharacteristic
361C2×C4×C5C2×C22⋊C411yescharacteristic
362C2×C4×C5C4×D411yescharacteristic
363C2×C4×C5C4×D411yescharacteristic
364C2×C4×C5C4×D411yescharacteristic
365C2×C4×C5#12011yescharacteristic
366C2×C4×C5#12011yescharacteristic
367C2×C4×C5#12011yescharacteristic
368C2×C4×C5#12011yescharacteristic
369C2×C4×C5#12011yescharacteristic
370C2×C4×C5#12011yescharacteristic
371C2×C4×C5#12011yescharacteristic
372C2×C4×C5#12011yescharacteristic
373C2×C4×C5#12111yescharacteristic
374C2×C4×C5#12111yescharacteristic
375C2×C4×C5#12111yescharacteristic
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#12311yescharacteristic
383C2×C4×C5#12311yescharacteristic
384C2×C4×C5#12411yescharacteristic
385C2×C4×C5#12711yescharacteristic
386C2×C4×C5#12711yescharacteristic
387C5×C8—24no—
388C5×C8—42no—
389C5×C8—42no—
390C5×C8—42no—
391C2×#41—21no—
392C2×#41—21no—
393C2×#41—21no—
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×#41C2×C4×C512yes—
412C2×#41C5×D412yes—
413C2×#41C5×D412yes—
414C2×#41C5×D412yes—
415C22×Q8C2×C4×C511yescharacteristic
416C22×Q8C5×D411yescharacteristic
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C2×C4×C511yescharacteristic
420C22×D4C5×D411yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4C23×C511yescharacteristic
424#137—24no—
425#137—24no—
426#137—24no—
427#137—24no—
428AGL(1,ℤ/8)—24no—
429AGL(1,ℤ/8)—24no—
430AGL(1,ℤ/8)—24no—
431AGL(1,ℤ/8)—24no—
432#135—28no—
433#135—28no—
434C2×Q16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×D8—22no—
438C2×M16—21no—
439C2×M16—21no—
440C2×M16—21no—
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×M16C2×C4×C512yes—
457C2×M16C5×D412yes—
458C2×M16C5×D412yes—
459C2×M16C5×D412yes—
460C2×M16C5×D412yes—
461C2×M16C5×D412yes—
462C22×C8—21no—
463C22×C8—21no—
464C22×C8—21no—
465C22×C8—21no—
466#117—21no—
467#117—21no—
468#117—21no—
469#117—21no—
470C2×C4⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C42C5×D412yes—
473#104—28no—
474#104—28no—
475#101—24no—
476#100—24no—
477C22⋊C8—28no—
478C22×C5—41no—
479C22×C5—41no—
480C22×C5—41no—
481C22×C5—41no—
482C22×C5—41no—
483C22×C5—41no—
484C22×C5—41no—
485C22×C5—44no—
486C22×C5—42no—
487C22×C5—42no—
488C22×C5—82no—
489C22×C5—82no—
490C22×C5—82no—
491C22×C5—82no—
492C22×C5—82no—
493C22×C5#38611yescharacteristic
494C22×C5#38611yescharacteristic
495C22×C5#39011yescharacteristic
496C22×C5#39211yescharacteristic
497C22×C5#39411yescharacteristic
498C22×C5#39411yescharacteristic
499C22×C5#39411yescharacteristic
500C4×C5—42no—
501C4×C5—42no—
502C4×C5—82no—
503C4×C5#37911yescharacteristic
504C4×C5#38611yescharacteristic
505C4×C5#38611yescharacteristic
506C4×C5#39011yescharacteristic
507C4×C5#39211yescharacteristic
508C4×C5#39211yescharacteristic
509C4×C5#39211yescharacteristic
510C4×C5#39411yescharacteristic
511C24—21no—
512C24—21no—
513C24C5×#4111yescharacteristic
514#41—22no—
515#41—22no—
516#41—22no—
517#41—22no—
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—41no—
531#41—41no—
532#41—41no—
533#41—41no—
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—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8C5×C22⋊C412yes—
557C2×Q8C5×C22⋊C412yes—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
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—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4C5×C22⋊C412yes—
581C2×D4C5×C22⋊C412yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—41no—
597C22×C4C22×C4×C511yescharacteristic
598C22×C4C2×C5×D411yescharacteristic
599C22×C4C2×C5×D411yescharacteristic
600C22×C4C2×C5×D411yescharacteristic
601C22×C4C2×C5×D411yescharacteristic
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×C4C5×#4111yescharacteristic
609C22×C4C5×#4111yescharacteristic
610C22×C4C5×#4111yescharacteristic
611Q16—28no—
612SD16—28no—
613SD16—28no—
614D8—28no—
615M16—22no—
616M16—22no—
617M16—22no—
618M16—22no—
619M16—22no—
620M16—22no—
621M16—22no—
622M16—22no—
623M16—22no—
624M16—41no—
625M16—41no—
626M16—41no—
627M16—41no—
628M16—41no—
629M16—41no—
630M16C5×C22⋊C414yes—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C4⋊C4—41no—
644C4⋊C4—41no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—22no—
648C42—22no—
649C2×C5—21no—
650C2×C5—21no—
651C2×C5—21no—
652C2×C5—21no—
653C2×C5—21no—
654C2×C5—21no—
655C2×C5—21no—
656C2×C5—82no—
657C2×C5—82no—
658C2×C5#143811yescharacteristic
659C23—22no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23C4×C5×D411yescharacteristic
669C23C5×#12111yescharacteristic
670C23C5×#12111yescharacteristic
671C23C5×#12111yescharacteristic
672C23C5×#12311yescharacteristic
673C23C5×#12311yescharacteristic
674C23C5×#12411yescharacteristic
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—82no—
715C2×C4C2×C5×C22⋊C411yescharacteristic
716C2×C4C2×C5×C22⋊C411yescharacteristic
717C2×C4C2×C5×C22⋊C411yescharacteristic
718C2×C4C4×C5×D411yescharacteristic
719C2×C4C4×C5×D411yescharacteristic
720C2×C4C4×C5×D411yescharacteristic
721C2×C4C5×#12011yescharacteristic
722C2×C4C5×#12011yescharacteristic
723C2×C4C5×#12011yescharacteristic
724C2×C4C5×#12011yescharacteristic
725C2×C4C5×#12011yescharacteristic
726C2×C4C5×#12011yescharacteristic
727C2×C4C5×#12011yescharacteristic
728C2×C4C5×#12011yescharacteristic
729C2×C4C5×#12111yescharacteristic
730C2×C4C5×#12111yescharacteristic
731C2×C4C5×#12111yescharacteristic
732C2×C4C5×#12111yescharacteristic
733C2×C4C5×#12111yescharacteristic
734C2×C4C5×#12111yescharacteristic
735C2×C4C5×#12111yescharacteristic
736C2×C4C5×#12111yescharacteristic
737C2×C4C5×#12111yescharacteristic
738C2×C4C5×#12311yescharacteristic
739C2×C4C5×#12311yescharacteristic
740C2×C4C5×#12411yescharacteristic
741C2×C4C5×#12711yescharacteristic
742C2×C4C5×#12711yescharacteristic
743C8—24no—
744C8—42no—
745C8—42no—
746C8—42no—
747C5#1103211yescharacteristic, direct product factor, Sylow
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22C5×#38611yescharacteristic
764C22C5×#38611yescharacteristic
765C22C5×#39011yescharacteristic
766C22C5×#39211yescharacteristic
767C22C5×#39411yescharacteristic
768C22C5×#39411yescharacteristic
769C22C5×#39411yescharacteristic
770C4—42no—
771C4—42no—
772C4—82no—
773C4C5×#37911yescharacteristic
774C4C5×#38611yescharacteristic
775C4C5×#38611yescharacteristic
776C4C5×#39011yescharacteristic
777C4C5×#39211yescharacteristic
778C4C5×#39211yescharacteristic
779C4C5×#39211yescharacteristic
780C4C5×#39411yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—21no—
788C2—82no—
789C2—82no—
790C2C5×#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. C2×C5×#421C2semidirect
4. C2×C5×#413C2semidirect
5. C5×#2879C2semidirect
6. C5×#1742C2semidirect
7. C5×#1738C2semidirect
15. C2×C5×#137C4semidirect
17. C2×C5×AGL(1,ℤ/8)C4semidirect
39. #11032C5direct (N × H)
128. C2×#421C2×C5semidirect
129. C2×#421C2×C5semidirect
130. C2×#413C2×C5semidirect
131. #2879C2×C5semidirect
132. #1742C2×C5semidirect
133. #1738C2×C5semidirect
279. C2×#137C4×C5semidirect
281. C2×AGL(1,ℤ/8)C4×C5semidirect
747. C5#11032direct (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
C2×C5×#4132
C5×#28792
C5×#17422
C5×#17382
#110325