Finite Group Databasebeta

← C5×#11003 #11933723

Subgroups — C5×#11003 #11933723

Order 1280.

1292 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3449C211yesmaximal, characteristic
2C2×C5×#421C211yesmaximal, characteristic, complemented
3C2×C5×#421C211yesmaximal, characteristic, complemented
4C2×C5×#421C211yesmaximal, characteristic, complemented
5C5×#2896C211yesmaximal, characteristic, complemented
6C2×C5×#344C211yesmaximal, characteristic, complemented
7C5×#1740C211yesmaximal, characteristic, complemented
8C22×C5×#41C2211yescharacteristic
9C22×C5×#41C2211yescharacteristic
10C22×C5×M16C2211yescharacteristic
11C22×C5×M16C2211yescharacteristic
12C5×#537—22no—
13C5×#536—21no—
14C5×#536C412yescomplemented
15C5×#535—21no—
16C5×#535C412yescomplemented
17C5×#534—22no—
18C5×#532—22no—
19C5×#525—22no—
20C5×#525—22no—
21C2×C5×#117C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C2×C5×#117C2211yescharacteristic
24C5×#421—22no—
25C5×#421—22no—
26C5×#421—22no—
27C5×#421—22no—
28C5×#421—22no—
29C5×#421—22no—
30C2×C5×#104—22no—
31C2×C5×#104—22no—
32C2×C5×#104—22no—
33C5×#419—21no—
34C5×#418—21no—
35C5×#417—22no—
36C5×#416—22no—
37C5×#344—22no—
38C5×#342—22no—
39#11003C511yesmaximal, 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
73C2×C5×M16—21no—
74C2×C5×M16—21no—
75C2×C5×M16—21no—
76C2×C5×M16—21no—
77C2×C5×M16—21no—
78C2×C5×M16—21no—
79C2×C5×M16—21no—
80C2×C5×M16—21no—
81C2×C5×M16—21no—
82C2×C5×M16—21no—
83C2×C5×M16D412yescomplemented
84C2×C5×M16D412yescomplemented
85C22×C5×C8—21no—
86C22×C5×C8—21no—
87C5×C4⋊Q8—22no—
88C5×#127—22no—
89C5×#124—22no—
90C5×#124—22no—
91C5×#123—24no—
92C5×#123—24no—
93C5×C22⋊Q8—24no—
94C5×C22⋊Q8—24no—
95C5×#121—24no—
96C5×#121—28no—
97C5×#121—24no—
98C5×#120—24no—
99C5×#120—24no—
100C4×C5×D4—28no—
101C5×#117—21no—
102C5×#117—21no—
103C5×#117—21no—
104C5×#117—21no—
105C5×#117—21no—
106C5×#117—21no—
107C5×#117—21no—
108C5×#117—21no—
109C5×#117—21no—
110C5×#117C2×C412yes—
111C5×#117D412yes—
112C5×#117D412yescomplemented
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4D412yes—
119C2×C42×C5—21no—
120C2×C42×C5—21no—
121C2×C42×C5D412yescomplemented
122C5×#104—28no—
123C5×#104—28no—
124C5×#104—28no—
125C5×#103—24no—
126C5×#102—24no—
127#3449C2×C511yescharacteristic
128C2×#421C2×C511yescharacteristic, complemented
129C2×#421C2×C511yescharacteristic, complemented
130C2×#421C2×C511yescharacteristic, complemented
131#2896C2×C511yescharacteristic, complemented
132C2×#344C2×C511yescharacteristic, complemented
133#1740C2×C511yescharacteristic, complemented
134C24×C5—21no—
135C24×C5—21no—
136C24×C5C2×D411yescharacteristic
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—28no—
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—21no—
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×D4—41no—
204C2×C5×D4C22⋊C412yes—
205C2×C5×D4C22⋊C412yes—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
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×C5—41no—
223C22×C4×C5C22×C411yescharacteristic
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
236C22×C4×C5#4111yescharacteristic
237C5×M16—22no—
238C5×M16—22no—
239C5×M16—22no—
240C5×M16—22no—
241C5×M16—41no—
242C5×M16—41no—
243C5×M16—41no—
244C5×M16—41no—
245C2×C5×C8—22no—
246C2×C5×C8—22no—
247C2×C5×C8—41no—
248C2×C5×C8—41no—
249C2×C5×C8—41no—
250C2×C5×C8—41no—
251C5×C4⋊C4—28no—
252C5×C4⋊C4—22no—
253C5×C4⋊C4—22no—
254C5×C4⋊C4—22no—
255C5×C4⋊C4—41no—
256C5×C4⋊C4—41no—
257C5×C4⋊C4—41no—
258C5×C22⋊C4—28no—
259C5×C22⋊C4—28no—
260C5×C22⋊C4—22no—
261C5×C22⋊C4—22no—
262C5×C22⋊C4—41no—
263C5×C22⋊C4—41no—
264C5×C22⋊C4—41no—
265C5×C22⋊C4C22⋊C414yes—
266C42×C5—22no—
267C42×C5—22no—
268C42×C5—22no—
269C42×C5—22no—
270C42×C5—22no—
271C42×C5—41no—
272C22×#41C22×C511yescharacteristic
273C22×#41C22×C511yescharacteristic
274C22×M16C22×C511yescharacteristic
275C22×M16C22×C511yescharacteristic
276#537—22no—
277#536—21no—
278#536C4×C512yescomplemented
279#535—21no—
280#535C4×C512yescomplemented
281#534—22no—
282#532—22no—
283#525—22no—
284#525—22no—
285C2×#117C22×C511yescharacteristic
286C2×#117C22×C511yescharacteristic
287C2×#117C22×C511yescharacteristic
288#421—22no—
289#421—22no—
290#421—22no—
291#421—22no—
292#421—22no—
293#421—22no—
294C2×#104—22no—
295C2×#104—22no—
296C2×#104—22no—
297#419—21no—
298#418—21no—
299#417—22no—
300#416—22no—
301#344—22no—
302#342—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×C5C2×C22⋊C411yescharacteristic
313C23×C5#12011yescharacteristic
314C23×C5#12011yescharacteristic
315C23×C5#12111yescharacteristic
316C23×C5#12111yescharacteristic
317C23×C5#12411yescharacteristic
318C23×C5#12711yescharacteristic
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—
343C5×D4—88no—
344C2×C4×C5—24no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
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—42no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—82no—
362C2×C4×C5—82no—
363C2×C4×C5—82no—
364C2×C4×C5C2×C22⋊C411yescharacteristic
365C2×C4×C5C2×C22⋊C411yescharacteristic
366C2×C4×C5C4×D411yescharacteristic
367C2×C4×C5C4×D411yescharacteristic
368C2×C4×C5C4×D411yescharacteristic
369C2×C4×C5C4×D411yescharacteristic
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#12111yescharacteristic
386C2×C4×C5#12311yescharacteristic
387C2×C4×C5#12311yescharacteristic
388C2×C4×C5#12311yescharacteristic
389C2×C4×C5#12311yescharacteristic
390C2×C4×C5#12411yescharacteristic
391C2×C4×C5#12711yescharacteristic
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×#41C5×D412yes—
416C2×#41C5×D412yes—
417C2×#41C5×D412yes—
418C22×Q8C2×C4×C511yescharacteristic
419C22×Q8C5×D411yescharacteristic
420C22×D4—21no—
421C22×D4—21no—
422C22×D4C2×C4×C511yescharacteristic
423C22×D4C5×D411yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4C23×C511yescharacteristic
427C2×M16—21no—
428C2×M16—21no—
429C2×M16—21no—
430C2×M16—21no—
431C2×M16—21no—
432C2×M16—21no—
433C2×M16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C2×M16—21no—
437C2×M16C5×D412yescomplemented
438C2×M16C5×D412yescomplemented
439C22×C8—21no—
440C22×C8—21no—
441C4⋊Q8—22no—
442#127—22no—
443#124—22no—
444#124—22no—
445#123—24no—
446#123—24no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449#121—24no—
450#121—28no—
451#121—24no—
452#120—24no—
453#120—24no—
454C4×D4—28no—
455#117—21no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117—21no—
462#117—21no—
463#117—21no—
464#117C2×C4×C512yes—
465#117C5×D412yes—
466#117C5×D412yescomplemented
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4C5×D412yes—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C5×D412yescomplemented
476#104—28no—
477#104—28no—
478#104—28no—
479#103—24no—
480#102—24no—
481C22×C5—41no—
482C22×C5—41no—
483C22×C5—41no—
484C22×C5—41no—
485C22×C5—41no—
486C22×C5—41no—
487C22×C5—41no—
488C22×C5—44no—
489C22×C5—44no—
490C22×C5—42no—
491C22×C5—42no—
492C22×C5—82no—
493C22×C5—82no—
494C22×C5—82no—
495C22×C5—82no—
496C22×C5#37911yescharacteristic
497C22×C5#39011yescharacteristic
498C22×C5#39011yescharacteristic
499C22×C5#39211yescharacteristic
500C22×C5#39211yescharacteristic
501C22×C5#39411yescharacteristic
502C22×C5#39411yescharacteristic
503C4×C5—44no—
504C4×C5—42no—
505C4×C5—42no—
506C4×C5—82no—
507C4×C5—82no—
508C4×C5#38611yescharacteristic
509C4×C5#38611yescharacteristic
510C4×C5#38611yescharacteristic
511C4×C5#38611yescharacteristic
512C4×C5#39211yescharacteristic
513C4×C5#39211yescharacteristic
514C4×C5#39411yescharacteristic
515C4×C5#39411yescharacteristic
516C24—21no—
517C24—21no—
518C24C2×C5×D411yescharacteristic
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—22no—
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—
550#41—41no—
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×Q8—21no—
561C2×Q8C5×C22⋊C412yes—
562C2×Q8C5×C22⋊C412yes—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—28no—
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—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4C5×C22⋊C412yes—
587C2×D4C5×C22⋊C412yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4C22×C4×C511yescharacteristic
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×C4C2×C5×D411yescharacteristic
613C22×C4C2×C5×D411yescharacteristic
614C22×C4C2×C5×D411yescharacteristic
615C22×C4C5×#4111yescharacteristic
616C22×C4C5×#4111yescharacteristic
617C22×C4C5×#4111yescharacteristic
618C22×C4C5×#4111yescharacteristic
619M16—22no—
620M16—22no—
621M16—22no—
622M16—22no—
623M16—41no—
624M16—41no—
625M16—41no—
626M16—41no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C4⋊C4—28no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—41no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C22⋊C4C5×C22⋊C414yes—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—41no—
654C2×C5—21no—
655C2×C5—21no—
656C2×C5—21no—
657C2×C5—21no—
658C2×C5—21no—
659C2×C5—21no—
660C2×C5—21no—
661C2×C5—82no—
662C2×C5—82no—
663C2×C5#143811yescharacteristic
664C23—22no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—81no—
671C23—82no—
672C23—82no—
673C23C2×C5×C22⋊C411yescharacteristic
674C23C5×#12011yescharacteristic
675C23C5×#12011yescharacteristic
676C23C5×#12111yescharacteristic
677C23C5×#12111yescharacteristic
678C23C5×#12411yescharacteristic
679C23C5×#12711yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—88no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4C2×C5×C22⋊C411yescharacteristic
726C2×C4C2×C5×C22⋊C411yescharacteristic
727C2×C4C4×C5×D411yescharacteristic
728C2×C4C4×C5×D411yescharacteristic
729C2×C4C4×C5×D411yescharacteristic
730C2×C4C4×C5×D411yescharacteristic
731C2×C4C5×#12011yescharacteristic
732C2×C4C5×#12011yescharacteristic
733C2×C4C5×#12011yescharacteristic
734C2×C4C5×#12011yescharacteristic
735C2×C4C5×#12011yescharacteristic
736C2×C4C5×#12011yescharacteristic
737C2×C4C5×#12111yescharacteristic
738C2×C4C5×#12111yescharacteristic
739C2×C4C5×#12111yescharacteristic
740C2×C4C5×#12111yescharacteristic
741C2×C4C5×#12111yescharacteristic
742C2×C4C5×#12111yescharacteristic
743C2×C4C5×#12111yescharacteristic
744C2×C4C5×#12111yescharacteristic
745C2×C4C5×#12111yescharacteristic
746C2×C4C5×#12111yescharacteristic
747C2×C4C5×#12311yescharacteristic
748C2×C4C5×#12311yescharacteristic
749C2×C4C5×#12311yescharacteristic
750C2×C4C5×#12311yescharacteristic
751C2×C4C5×#12411yescharacteristic
752C2×C4C5×#12711yescharacteristic
753C8—42no—
754C8—42no—
755C5#1100311yescharacteristic, direct product factor, Sylow
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—44no—
765C22—42no—
766C22—42no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C5×#37911yescharacteristic
772C22C5×#39011yescharacteristic
773C22C5×#39011yescharacteristic
774C22C5×#39211yescharacteristic
775C22C5×#39211yescharacteristic
776C22C5×#39411yescharacteristic
777C22C5×#39411yescharacteristic
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—82no—
783C4C5×#38611yescharacteristic
784C4C5×#38611yescharacteristic
785C4C5×#38611yescharacteristic
786C4C5×#38611yescharacteristic
787C4C5×#39211yescharacteristic
788C4C5×#39211yescharacteristic
789C4C5×#39411yescharacteristic
790C4C5×#39411yescharacteristic
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—82no—
799C2—82no—
800C2C5×#143811yescharacteristic
subgroupG/H
centerC4×C5#392
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
socleC2×C5#1438
prime radicalC5×#3449C2
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×#421C2semidirect
5. C5×#2896C2semidirect
6. C2×C5×#344C2semidirect
7. C5×#1740C2semidirect
14. C5×#536C4semidirect
16. C5×#535C4semidirect
39. #11003C5direct (N × H)
83. C2×C5×M16D4semidirect
84. C2×C5×M16D4semidirect
112. C5×#117D4semidirect
121. C2×C42×C5D4semidirect
128. C2×#421C2×C5semidirect
129. C2×#421C2×C5semidirect
130. C2×#421C2×C5semidirect
131. #2896C2×C5semidirect
132. C2×#344C2×C5semidirect
133. #1740C2×C5semidirect
278. #536C4×C5semidirect
280. #535C4×C5semidirect
437. C2×M16C5×D4semidirect
438. C2×M16C5×D4semidirect
466. #117C5×D4semidirect
475. C2×C42C5×D4semidirect
755. C5#11003direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34492
C2×C5×#4212
C5×#28962
C2×C5×#3442
C5×#17402
#110035