Finite Group Databasebeta

← C5×#11019 #11933739

Subgroups — C5×#11019 #11933739

Order 1280.

1338 conjugacy classes of subgroups.

The subgroup lattice has 810 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
3C22×C5×#104C211yesmaximal, characteristic, complemented
4C2×C5×#410C211yesmaximal, characteristic, complemented
5C5×#2297C211yesmaximal, characteristic, complemented
6C2×C5×#344C211yesmaximal, characteristic, complemented
7C2×C5×#339C211yesmaximal, 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
21C2×C5×#117C2211yescharacteristic
22C2×C5×#117C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C5×#421—22no—
25C5×#421—22no—
26C2×C5×#104—22no—
27C2×C5×#104—22no—
28C2×C5×#104—22no—
29C2×C5×#104—22no—
30C5×#410—22no—
31C5×#410—22no—
32C2×C5×#99—22no—
33C5×#391—21no—
34C5×#390—21no—
35C5×#386—22no—
36C4×C5×C22⋊C4—22no—
37C5×#344—22no—
38C5×#339—22no—
39#11019C511yesmaximal, 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×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×M16C2×C412yes—
97C2×C5×M16D412yes—
98C2×C5×M16D412yes—
99C2×C5×M16D412yes—
100C22×C5×C8—21no—
101C22×C5×C8—21no—
102C5×#117—21no—
103C5×#117—21no—
104C5×#117—21no—
105C5×#117—21no—
106C5×#117—21no—
107C5×#117—21no—
108C5×#117—21no—
109C5×#117D412yes—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—24no—
114C2×C5×C22⋊C4D412yes—
115C2×C42×C5—21no—
116C2×C42×C5—21no—
117C2×C42×C5—21no—
118C2×C42×C5—21no—
119C2×C42×C5—21no—
120C2×C42×C5—21no—
121C2×C42×C5—21no—
122C2×C42×C5D412yes—
123C5×#104—28no—
124C5×#104—28no—
125C5×#99—28no—
126C5×#95—24no—
127C2×#575C2×C511yescharacteristic
128C2×#421C2×C511yescharacteristic, complemented
129C22×#104C2×C511yescharacteristic, complemented
130C2×#410C2×C511yescharacteristic, complemented
131#2297C2×C511yescharacteristic, complemented
132C2×#344C2×C511yescharacteristic, complemented
133C2×#339C2×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⋊C412yescomplemented
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⋊C412yescomplemented
205C22×C4×C5—21no—
206C22×C4×C5—22no—
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—44no—
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×C5—41no—
224C22×C4×C5—41no—
225C22×C4×C5C22×C411yescharacteristic
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×C5C2×D411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5#4111yescharacteristic
236C22×C4×C5#4111yescharacteristic
237C22×C4×C5#4111yescharacteristic
238C22×C4×C5#4111yescharacteristic
239C5×Q16—28no—
240C5×SD16—28no—
241C5×SD16—28no—
242C5×D8—28no—
243C5×M16—22no—
244C5×M16—22no—
245C5×M16—22no—
246C5×M16—22no—
247C5×M16—22no—
248C5×M16—41no—
249C5×M16—41no—
250C5×M16C22⋊C414yescomplemented
251C2×C5×C8—22no—
252C2×C5×C8—22no—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8—41no—
256C2×C5×C8—41no—
257C5×C4⋊C4—22no—
258C5×C4⋊C4—41no—
259C5×C4⋊C4—41no—
260C5×C4⋊C4—41no—
261C5×C22⋊C4—22no—
262C5×C22⋊C4—22no—
263C5×C22⋊C4—22no—
264C5×C22⋊C4—48no—
265C5×C22⋊C4—41no—
266C42×C5—22no—
267C42×C5—22no—
268C42×C5—22no—
269C42×C5—41no—
270C42×C5—41no—
271C42×C5—41no—
272C42×C5—41no—
273C42×C5—41no—
274C22×#41C22×C511yescharacteristic
275C22×#41C22×C511yescharacteristic
276#575—22no—
277#575—22no—
278#575—22no—
279#575—22no—
280C2×#137—21no—
281C2×#137C4×C512yescomplemented
282C2×AGL(1,ℤ/8)—21no—
283C2×AGL(1,ℤ/8)C4×C512yescomplemented
284C2×#135—22no—
285C22×M16C22×C511yescharacteristic
286C22×M16C22×C511yescharacteristic
287C2×#117C22×C511yescharacteristic
288C2×#117C22×C511yescharacteristic
289C22×C42C22×C511yescharacteristic
290#421—22no—
291#421—22no—
292C2×#104—22no—
293C2×#104—22no—
294C2×#104—22no—
295C2×#104—22no—
296#410—22no—
297#410—22no—
298C2×#99—22no—
299#391—21no—
300#390—21no—
301#386—22no—
302C4×C22⋊C4—22no—
303#344—22no—
304#339—22no—
305C23×C5—22no—
306C23×C5—22no—
307C23×C5—42no—
308C23×C5—44no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5—41no—
312C23×C5—41no—
313C23×C5—82no—
314C23×C5C4×D411yescharacteristic
315C23×C5#12011yescharacteristic
316C23×C5#12011yescharacteristic
317C23×C5#12111yescharacteristic
318C23×C5#12111yescharacteristic
319C23×C5#12111yescharacteristic
320C23×C5#12711yescharacteristic
321C5×Q8—22no—
322C5×Q8—22no—
323C5×Q8—22no—
324C5×Q8—22no—
325C5×Q8—41no—
326C5×Q8—41no—
327C5×Q8—41no—
328C5×Q8—41no—
329C5×D4—22no—
330C5×D4—22no—
331C5×D4—22no—
332C5×D4—22no—
333C5×D4—42no—
334C5×D4—42no—
335C5×D4—42no—
336C5×D4—42no—
337C5×D4—42no—
338C5×D4—42no—
339C5×D4—42no—
340C5×D4—42no—
341C5×D4—41no—
342C5×D4—41no—
343C5×D4—41no—
344C5×D4—41no—
345C2×C4×C5—24no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—42no—
349C2×C4×C5—44no—
350C2×C4×C5—44no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—42no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—42no—
357C2×C4×C5—42no—
358C2×C4×C5—42no—
359C2×C4×C5—42no—
360C2×C4×C5—42no—
361C2×C4×C5—42no—
362C2×C4×C5—42no—
363C2×C4×C5—42no—
364C2×C4×C5—44no—
365C2×C4×C5—42no—
366C2×C4×C5—42no—
367C2×C4×C5—82no—
368C2×C4×C5C2×C22⋊C411yescharacteristic
369C2×C4×C5C2×C22⋊C411yescharacteristic
370C2×C4×C5C2×C22⋊C411yescharacteristic
371C2×C4×C5C4×D411yescharacteristic
372C2×C4×C5C4×D411yescharacteristic
373C2×C4×C5C4×D411yescharacteristic
374C2×C4×C5#12011yescharacteristic
375C2×C4×C5#12011yescharacteristic
376C2×C4×C5#12011yescharacteristic
377C2×C4×C5#12011yescharacteristic
378C2×C4×C5#12011yescharacteristic
379C2×C4×C5#12011yescharacteristic
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#12111yescharacteristic
387C2×C4×C5#12111yescharacteristic
388C2×C4×C5#12111yescharacteristic
389C2×C4×C5#12311yescharacteristic
390C2×C4×C5#12311yescharacteristic
391C2×C4×C5#12311yescharacteristic
392C2×C4×C5#12311yescharacteristic
393C2×C4×C5#12411yescharacteristic
394C2×C4×C5#12411yescharacteristic
395C2×C4×C5#12711yescharacteristic
396C5×C8—24no—
397C5×C8—42no—
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×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41C2×C4×C512yes—
419C2×#41C5×D412yes—
420C2×#41C5×D412yes—
421C2×#41C5×D412yes—
422C22×Q8C2×C4×C511yescharacteristic
423C22×Q8C5×D411yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4C2×C4×C511yescharacteristic
427C22×D4C5×D411yescharacteristic
428C23×C4—21no—
429C23×C4—21no—
430C23×C4—21no—
431C23×C4C23×C511yescharacteristic
432#137—24no—
433#137—24no—
434#137—24no—
435#137—24no—
436AGL(1,ℤ/8)—24no—
437AGL(1,ℤ/8)—24no—
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—24no—
440#135—28no—
441#135—28no—
442C2×Q16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×D8—22no—
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×M16C2×C4×C512yes—
455C2×M16C5×D412yes—
456C2×M16C5×D412yes—
457C2×M16C5×D412yes—
458C22×C8—21no—
459C22×C8—21no—
460#117—21no—
461#117—21no—
462#117—21no—
463#117—21no—
464#117—21no—
465#117—21no—
466#117—21no—
467#117C5×D412yes—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4C5×D412yes—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42C5×D412yes—
481#104—28no—
482#104—28no—
483#99—28no—
484#95—24no—
485C22×C5—22no—
486C22×C5—22no—
487C22×C5—22no—
488C22×C5—41no—
489C22×C5—41no—
490C22×C5—41no—
491C22×C5—41no—
492C22×C5—44no—
493C22×C5—42no—
494C22×C5—42no—
495C22×C5—82no—
496C22×C5—82no—
497C22×C5—82no—
498C22×C5—82no—
499C22×C5—82no—
500C22×C5#38611yescharacteristic
501C22×C5#38611yescharacteristic
502C22×C5#39011yescharacteristic
503C22×C5#39211yescharacteristic
504C22×C5#39211yescharacteristic
505C22×C5#39211yescharacteristic
506C22×C5#39411yescharacteristic
507C4×C5—44no—
508C4×C5—42no—
509C4×C5—42no—
510C4×C5—82no—
511C4×C5—82no—
512C4×C5#37911yescharacteristic
513C4×C5#38611yescharacteristic
514C4×C5#38611yescharacteristic
515C4×C5#39011yescharacteristic
516C4×C5#39211yescharacteristic
517C4×C5#39411yescharacteristic
518C4×C5#39411yescharacteristic
519C4×C5#39411yescharacteristic
520C24—21no—
521C24—21no—
522C24C2×C5×D411yescharacteristic
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—22no—
536#41—22no—
537#41—22no—
538#41—22no—
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—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8C5×C22⋊C412yes—
566C2×Q8C5×C22⋊C412yescomplemented
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4C5×C22⋊C412yes—
590C2×D4C5×C22⋊C412yescomplemented
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—44no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4C22×C4×C511yescharacteristic
612C22×C4C2×C5×D411yescharacteristic
613C22×C4C2×C5×D411yescharacteristic
614C22×C4C2×C5×D411yescharacteristic
615C22×C4C2×C5×D411yescharacteristic
616C22×C4C2×C5×D411yescharacteristic
617C22×C4C2×C5×D411yescharacteristic
618C22×C4C2×C5×D411yescharacteristic
619C22×C4C2×C5×D411yescharacteristic
620C22×C4C2×C5×D411yescharacteristic
621C22×C4C5×#4111yescharacteristic
622C22×C4C5×#4111yescharacteristic
623C22×C4C5×#4111yescharacteristic
624C22×C4C5×#4111yescharacteristic
625Q16—28no—
626SD16—28no—
627SD16—28no—
628D8—28no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—41no—
635M16—41no—
636M16C5×C22⋊C414yescomplemented
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—41no—
642C2×C8—41no—
643C4⋊C4—22no—
644C4⋊C4—41no—
645C4⋊C4—41no—
646C4⋊C4—41no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—48no—
651C22⋊C4—41no—
652C42—22no—
653C42—22no—
654C42—22no—
655C42—41no—
656C42—41no—
657C42—41no—
658C42—41no—
659C42—41no—
660C2×C5—21no—
661C2×C5—21no—
662C2×C5—21no—
663C2×C5—21no—
664C2×C5—21no—
665C2×C5—21no—
666C2×C5—82no—
667C2×C5—82no—
668C2×C5#143811yescharacteristic
669C2×C5#190612yes—
670C23—22no—
671C23—22no—
672C23—42no—
673C23—44no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—82no—
679C23C4×C5×D411yescharacteristic
680C23C5×#12011yescharacteristic
681C23C5×#12011yescharacteristic
682C23C5×#12111yescharacteristic
683C23C5×#12111yescharacteristic
684C23C5×#12111yescharacteristic
685C23C5×#12711yescharacteristic
686Q8—22no—
687Q8—22no—
688Q8—22no—
689Q8—22no—
690Q8—41no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—82no—
733C2×C4C2×C5×C22⋊C411yescharacteristic
734C2×C4C2×C5×C22⋊C411yescharacteristic
735C2×C4C2×C5×C22⋊C411yescharacteristic
736C2×C4C4×C5×D411yescharacteristic
737C2×C4C4×C5×D411yescharacteristic
738C2×C4C4×C5×D411yescharacteristic
739C2×C4C5×#12011yescharacteristic
740C2×C4C5×#12011yescharacteristic
741C2×C4C5×#12011yescharacteristic
742C2×C4C5×#12011yescharacteristic
743C2×C4C5×#12011yescharacteristic
744C2×C4C5×#12011yescharacteristic
745C2×C4C5×#12111yescharacteristic
746C2×C4C5×#12111yescharacteristic
747C2×C4C5×#12111yescharacteristic
748C2×C4C5×#12111yescharacteristic
749C2×C4C5×#12111yescharacteristic
750C2×C4C5×#12111yescharacteristic
751C2×C4C5×#12111yescharacteristic
752C2×C4C5×#12111yescharacteristic
753C2×C4C5×#12111yescharacteristic
754C2×C4C5×#12311yescharacteristic
755C2×C4C5×#12311yescharacteristic
756C2×C4C5×#12311yescharacteristic
757C2×C4C5×#12311yescharacteristic
758C2×C4C5×#12411yescharacteristic
759C2×C4C5×#12411yescharacteristic
760C2×C4C5×#12711yescharacteristic
761C8—24no—
762C8—42no—
763C5#1101911yescharacteristic, direct product factor, Sylow
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—44no—
772C22—42no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22C5×#38611yescharacteristic
780C22C5×#38611yescharacteristic
781C22C5×#39011yescharacteristic
782C22C5×#39211yescharacteristic
783C22C5×#39211yescharacteristic
784C22C5×#39211yescharacteristic
785C22C5×#39411yescharacteristic
786C4—44no—
787C4—42no—
788C4—42no—
789C4—82no—
790C4—82no—
791C4C5×#37911yescharacteristic
792C4C5×#38611yescharacteristic
793C4C5×#38611yescharacteristic
794C4C5×#39011yescharacteristic
795C4C5×#39211yescharacteristic
796C4C5×#39411yescharacteristic
797C4C5×#39411yescharacteristic
798C4C5×#39411yescharacteristic
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—82no—
806C2—82no—
807C2C5×#143811yescharacteristic
808C2C5×#190612yes—
subgroupG/H
centerC2×C4×C5#121
commutatorC22×C4C22×C4×C5
Frattini, cosocleC23×C4C23×C5
socleC22×C5#386
prime radicalC2×C5×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×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. C22×C5×#104C2semidirect
4. C2×C5×#410C2semidirect
5. C5×#2297C2semidirect
6. C2×C5×#344C2semidirect
7. C2×C5×#339C2semidirect
15. C2×C5×#137C4semidirect
17. C2×C5×AGL(1,ℤ/8)C4semidirect
39. #11019C5direct (N × H)
128. C2×#421C2×C5semidirect
129. C22×#104C2×C5semidirect
130. C2×#410C2×C5semidirect
131. #2297C2×C5semidirect
132. C2×#344C2×C5semidirect
133. C2×#339C2×C5semidirect
180. C2×C5×Q8C22⋊C4semidirect
204. C2×C5×D4C22⋊C4semidirect
250. C5×M16C22⋊C4semidirect
281. C2×#137C4×C5semidirect
283. C2×AGL(1,ℤ/8)C4×C5semidirect
566. C2×Q8C5×C22⋊C4semidirect
590. C2×D4C5×C22⋊C4semidirect
636. M16C5×C22⋊C4semidirect
763. C5#11019direct (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
C22×C5×#1042
C2×C5×#4102
C5×#22972
C2×C5×#3442
C2×C5×#3392
#110195