Finite Group Databasebeta

← C2×C5×#2009 #11946131

Subgroups — C2×C5×#2009 #11946131

Order 1280.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic
2C22×C5×#137C211yesmaximal, characteristic, complemented
3C2×C5×#536C211yesmaximal, characteristic, complemented
4C2×C5×#421C211yesmaximal, characteristic, complemented
5C2×C5×#419C211yesmaximal, characteristic, complemented
6C2×C5×#410C211yesmaximal, characteristic, complemented
7C5×#2009C218yesmaximal, direct product factor
8C2×C5×#344C211yesmaximal, characteristic, complemented
9C22×C5×#41C2211yescharacteristic
10C22×C5×#41C2211yescharacteristic
11C23×C5×Q8C2211yescharacteristic
12C5×#575—22no—
13C5×#575—22no—
14C5×#575—22no—
15C5×#575C2214yes—
16C2×C5×#137—22no—
17C2×C5×#137—22no—
18C2×C5×#137—22no—
19C2×C5×#137—21no—
20C2×C5×#137—21no—
21C2×C5×#137—22no—
22C2×C5×#137—22no—
23C2×C5×#137C2214yescomplemented
24C2×C5×AGL(1,ℤ/8)—21no—
25C2×C5×AGL(1,ℤ/8)—21no—
26C2×C5×#135—22no—
27C22×C5×Q16—21no—
28C22×C5×SD16—21no—
29C22×C5×M16C2211yescharacteristic
30C22×C5×M16C2211yescharacteristic
31C5×#536—22no—
32C5×#536—22no—
33C5×#536—22no—
34C5×#536C2214yescomplemented
35C2×C5×C4⋊Q8—21no—
36C2×C5×#124—21no—
37C2×C5×#123—22no—
38C2×C5×C22⋊Q8—22no—
39C2×C5×#117C2211yescharacteristic
40C2×C5×#117C2211yescharacteristic
41C5×#421—22no—
42C5×#421C2214yescomplemented
43C2×C5×#104—22no—
44C5×#419—22no—
45C5×#419C2214yescomplemented
46C2×C5×#103—22no—
47C5×#410—22no—
48C5×#410C2214yescomplemented
49C2×C5×#99—22no—
50C5×#344C2214yescomplemented
51C2×#2009C511yesmaximal, characteristic, direct product factor, Sylow
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×#41—21no—
62C2×C5×#41—21no—
63C2×C5×#41—21no—
64C2×C5×#41—21no—
65C2×C5×#41—21no—
66C2×C5×#41—21no—
67C2×C5×#41—21no—
68C2×C5×#41—21no—
69C2×C5×#41—21no—
70C2×C5×#41—21no—
71C2×C5×#41—21no—
72C2×C5×#41D412yes—
73C2×C5×#41D412yes—
74C2×C5×#41C2312yes—
75C2×C5×#41C2312yes—
76C22×C5×Q8—21no—
77C22×C5×Q8—21no—
78C22×C5×Q8—21no—
79C22×C5×Q8—21no—
80C22×C5×Q8—21no—
81C22×C5×Q8—21no—
82C22×C5×Q8—21no—
83C22×C5×Q8—21no—
84C22×C5×Q8—21no—
85C22×C5×Q8—21no—
86C22×C5×Q8—21no—
87C22×C5×Q8D412yes—
88C22×C5×Q8D411yescharacteristic
89C22×C5×Q8D412yes—
90C22×C5×Q8D411yescharacteristic
91C22×C5×Q8C2312yes—
92C22×C5×D4—21no—
93C22×C5×D4—21no—
94C22×C5×D4D411yescharacteristic
95C22×C5×D4D411yescharacteristic
96C23×C4×C5—21no—
97C23×C4×C5—21no—
98C23×C4×C5—21no—
99C23×C4×C5C2311yescharacteristic
100C5×#137—28no—
101C5×#137—28no—
102C5×#137—24no—
103C5×#137—24no—
104C5×#137—28no—
105C5×#137—24no—
106C5×#137—24no—
107C5×#137—28no—
108C5×AGL(1,ℤ/8)—24no—
109C5×AGL(1,ℤ/8)—24no—
110C5×AGL(1,ℤ/8)—24no—
111C5×AGL(1,ℤ/8)—24no—
112C5×#135—28no—
113C5×#135—28no—
114C2×C5×Q16—24no—
115C2×C5×Q16—24no—
116C2×C5×Q16—22no—
117C2×C5×Q16—24no—
118C2×C5×SD16—24no—
119C2×C5×SD16—24no—
120C2×C5×SD16—22no—
121C2×C5×SD16—22no—
122C2×C5×SD16—24no—
123C2×C5×D8—22no—
124C2×C5×M16—21no—
125C2×C5×M16—21no—
126C2×C5×M16—21no—
127C2×C5×M16—21no—
128C2×C5×M16—21no—
129C2×C5×M16—21no—
130C2×C5×M16—21no—
131C2×C5×M16D412yes—
132C2×C5×M16D412yes—
133C2×C5×M16D412yes—
134C2×C5×M16C2312yes—
135C2×C5×M16C2312yes—
136C22×C5×C8—21no—
137C22×C5×C8D412yes—
138C5×C4⋊Q8—24no—
139C5×C4⋊Q8—24no—
140C5×#124—24no—
141C5×#124—24no—
142C5×#123—28no—
143C5×#123—28no—
144C5×C22⋊Q8—28no—
145C5×C22⋊Q8—28no—
146C5×#117—21no—
147C5×#117—21no—
148C5×#117—21no—
149C5×#117—21no—
150C5×#117—21no—
151C5×#117D412yes—
152C5×#117C2312yes—
153C5×#117C2312yes—
154C2×C5×C4⋊C4—24no—
155C2×C5×C4⋊C4—21no—
156C2×C5×C4⋊C4—21no—
157C2×C5×C22⋊C4—24no—
158C2×C5×C22⋊C4—21no—
159C2×C5×C22⋊C4D412yes—
160C2×C42×C5—21no—
161C2×C42×C5—21no—
162C5×#104—28no—
163C5×#103—28no—
164C5×#99—28no—
165C2×#575C2×C511yescharacteristic
166C22×#137C2×C511yescharacteristic, complemented
167C2×#536C2×C511yescharacteristic, complemented
168C2×#421C2×C511yescharacteristic, complemented
169C2×#419C2×C511yescharacteristic, complemented
170C2×#410C2×C511yescharacteristic, complemented
171#2009C2×C518yesdirect product factor
172C2×#344C2×C511yescharacteristic, complemented
173C24×C5—21no—
174C24×C5—21no—
175C24×C5C2×D411yescharacteristic
176C5×#41—22no—
177C5×#41—22no—
178C5×#41—22no—
179C5×#41—22no—
180C5×#41—22no—
181C5×#41—22no—
182C5×#41—22no—
183C5×#41—22no—
184C5×#41—22no—
185C5×#41—22no—
186C5×#41—22no—
187C5×#41—22no—
188C5×#41—22no—
189C5×#41—22no—
190C5×#41—22no—
191C5×#41—22no—
192C5×#41—41no—
193C5×#41—41no—
194C5×#41—41no—
195C5×#41—41no—
196C5×#41—41no—
197C5×#41—41no—
198C5×#41—41no—
199C5×#41—41no—
200C5×#41—41no—
201C5×#41—41no—
202C5×#41—41no—
203C5×#41—41no—
204C5×#41—41no—
205C5×#41—41no—
206C5×#41—41no—
207C5×#41—41no—
208C2×C5×Q8—22no—
209C2×C5×Q8—22no—
210C2×C5×Q8—21no—
211C2×C5×Q8—21no—
212C2×C5×Q8—22no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8—21no—
216C2×C5×Q8—21no—
217C2×C5×Q8—21no—
218C2×C5×Q8—21no—
219C2×C5×Q8—22no—
220C2×C5×Q8—22no—
221C2×C5×Q8—21no—
222C2×C5×Q8—21no—
223C2×C5×Q8—22no—
224C2×C5×Q8—22no—
225C2×C5×Q8—22no—
226C2×C5×Q8—22no—
227C2×C5×Q8—21no—
228C2×C5×Q8—21no—
229C2×C5×Q8—22no—
230C2×C5×Q8—22no—
231C2×C5×Q8—22no—
232C2×C5×Q8—22no—
233C2×C5×Q8—41no—
234C2×C5×Q8—41no—
235C2×C5×Q8—41no—
236C2×C5×Q8—41no—
237C2×C5×Q8—41no—
238C2×C5×Q8—41no—
239C2×C5×Q8—41no—
240C2×C5×Q8—41no—
241C2×C5×Q8—41no—
242C2×C5×Q8—41no—
243C2×C5×Q8—41no—
244C2×C5×Q8—41no—
245C2×C5×Q8C2×D414yes—
246C2×C5×Q8C2×D412yes—
247C2×C5×Q8C2×D412yes—
248C2×C5×D4—22no—
249C2×C5×D4—22no—
250C2×C5×D4—22no—
251C2×C5×D4—22no—
252C2×C5×D4—21no—
253C2×C5×D4—21no—
254C2×C5×D4—21no—
255C2×C5×D4—21no—
256C2×C5×D4—21no—
257C2×C5×D4—21no—
258C2×C5×D4—21no—
259C2×C5×D4—21no—
260C2×C5×D4—21no—
261C2×C5×D4—21no—
262C2×C5×D4—41no—
263C2×C5×D4—41no—
264C2×C5×D4—41no—
265C2×C5×D4—41no—
266C2×C5×D4—41no—
267C2×C5×D4—41no—
268C2×C5×D4—41no—
269C2×C5×D4—41no—
270C2×C5×D4C2×D412yes—
271C2×C5×D4C2×D412yes—
272C22×C4×C5—22no—
273C22×C4×C5—22no—
274C22×C4×C5—21no—
275C22×C4×C5—22no—
276C22×C4×C5—21no—
277C22×C4×C5—22no—
278C22×C4×C5—22no—
279C22×C4×C5—22no—
280C22×C4×C5—22no—
281C22×C4×C5—22no—
282C22×C4×C5—41no—
283C22×C4×C5—41no—
284C22×C4×C5—41no—
285C22×C4×C5—41no—
286C22×C4×C5—41no—
287C22×C4×C5—41no—
288C22×C4×C5—41no—
289C22×C4×C5—41no—
290C22×C4×C5—41no—
291C22×C4×C5—41no—
292C22×C4×C5—41no—
293C22×C4×C5—41no—
294C22×C4×C5—41no—
295C22×C4×C5C2×D411yescharacteristic
296C22×C4×C5C2×D411yescharacteristic
297C22×C4×C5C2×D411yescharacteristic
298C22×C4×C5C2×D411yescharacteristic
299C22×C4×C5C2×D411yescharacteristic
300C22×C4×C5C2×D411yescharacteristic
301C22×C4×C5C2×D411yescharacteristic
302C22×C4×C5C2×D411yescharacteristic
303C22×C4×C5C2×D411yescharacteristic
304C22×C4×C5C2×D411yescharacteristic
305C22×C4×C5C2×D411yescharacteristic
306C22×C4×C5#4111yescharacteristic
307C22×C4×C5#4111yescharacteristic
308C22×C4×C5C2411yescharacteristic
309C5×Q16—216no—
310C5×Q16—28no—
311C5×SD16—216no—
312C5×SD16—28no—
313C5×SD16—28no—
314C5×D8—28no—
315C5×M16—22no—
316C5×M16—22no—
317C5×M16—22no—
318C5×M16—22no—
319C5×M16—22no—
320C5×M16—22no—
321C5×M16—22no—
322C5×M16C2×D414yes—
323C2×C5×C8—22no—
324C2×C5×C8—22no—
325C2×C5×C8—22no—
326C2×C5×C8—22no—
327C2×C5×C8—22no—
328C2×C5×C8C2×D414yes—
329C5×C4⋊C4—216no—
330C5×C4⋊C4—22no—
331C5×C4⋊C4—22no—
332C5×C4⋊C4—22no—
333C5×C4⋊C4—41no—
334C5×C22⋊C4—216no—
335C5×C22⋊C4—22no—
336C5×C22⋊C4—22no—
337C5×C22⋊C4—41no—
338C5×C22⋊C4C2×D414yes—
339C42×C5—22no—
340C42×C5—22no—
341C42×C5—22no—
342C42×C5—41no—
343C22×#41C22×C511yescharacteristic
344C22×#41C22×C511yescharacteristic
345C23×Q8C22×C511yescharacteristic
346#575—22no—
347#575—22no—
348#575—22no—
349#575C22×C514yes—
350C2×#137—22no—
351C2×#137—22no—
352C2×#137—22no—
353C2×#137—21no—
354C2×#137—21no—
355C2×#137—22no—
356C2×#137—22no—
357C2×#137C22×C514yescomplemented
358C2×AGL(1,ℤ/8)—21no—
359C2×AGL(1,ℤ/8)—21no—
360C2×#135—22no—
361C22×Q16—21no—
362C22×SD16—21no—
363C22×M16C22×C511yescharacteristic
364C22×M16C22×C511yescharacteristic
365#536—22no—
366#536—22no—
367#536—22no—
368#536C22×C514yescomplemented
369C2×C4⋊Q8—21no—
370C2×#124—21no—
371C2×#123—22no—
372C2×C22⋊Q8—22no—
373C2×#117C22×C511yescharacteristic
374C2×#117C22×C511yescharacteristic
375#421—22no—
376#421C22×C514yescomplemented
377C2×#104—22no—
378#419—22no—
379#419C22×C514yescomplemented
380C2×#103—22no—
381#410—22no—
382#410C22×C514yescomplemented
383C2×#99—22no—
384#344C22×C514yescomplemented
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—42no—
388C23×C5—44no—
389C23×C5—41no—
390C23×C5—41no—
391C23×C5—41no—
392C23×C5—41no—
393C23×C5—82no—
394C23×C5#12011yescharacteristic
395C23×C5#12011yescharacteristic
396C23×C5#12111yescharacteristic
397C23×C5#12111yescharacteristic
398C23×C5#12711yescharacteristic
399C23×C5#12711yescharacteristic
400C23×C5C22×D411yescharacteristic
401C5×Q8—24no—
402C5×Q8—22no—
403C5×Q8—22no—
404C5×Q8—22no—
405C5×Q8—24no—
406C5×Q8—22no—
407C5×Q8—42no—
408C5×Q8—42no—
409C5×Q8—42no—
410C5×Q8—42no—
411C5×Q8—42no—
412C5×Q8—42no—
413C5×Q8—41no—
414C5×Q8—41no—
415C5×Q8—41no—
416C5×Q8—41no—
417C5×D4—22no—
418C5×D4—22no—
419C5×D4—22no—
420C5×D4—22no—
421C5×D4—42no—
422C5×D4—42no—
423C5×D4—42no—
424C5×D4—42no—
425C5×D4—42no—
426C5×D4—42no—
427C5×D4—42no—
428C5×D4—42no—
429C5×D4—41no—
430C5×D4—41no—
431C5×D4—41no—
432C5×D4—41no—
433C2×C4×C5—24no—
434C2×C4×C5—24no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—44no—
438C2×C4×C5—42no—
439C2×C4×C5—42no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—42no—
443C2×C4×C5—42no—
444C2×C4×C5—42no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—42no—
448C2×C4×C5—42no—
449C2×C4×C5—42no—
450C2×C4×C5—42no—
451C2×C4×C5—42no—
452C2×C4×C5—42no—
453C2×C4×C5—42no—
454C2×C4×C5—42no—
455C2×C4×C5—42no—
456C2×C4×C5—42no—
457C2×C4×C5—82no—
458C2×C4×C5#12011yescharacteristic
459C2×C4×C5#12011yescharacteristic
460C2×C4×C5#12011yescharacteristic
461C2×C4×C5#12011yescharacteristic
462C2×C4×C5#12011yescharacteristic
463C2×C4×C5#12011yescharacteristic
464C2×C4×C5#12011yescharacteristic
465C2×C4×C5#12011yescharacteristic
466C2×C4×C5#12011yescharacteristic
467C2×C4×C5#12011yescharacteristic
468C2×C4×C5#12111yescharacteristic
469C2×C4×C5#12111yescharacteristic
470C2×C4×C5#12111yescharacteristic
471C2×C4×C5#12111yescharacteristic
472C2×C4×C5#12111yescharacteristic
473C2×C4×C5#12111yescharacteristic
474C2×C4×C5#12111yescharacteristic
475C2×C4×C5#12111yescharacteristic
476C2×C4×C5#12111yescharacteristic
477C2×C4×C5#12111yescharacteristic
478C2×C4×C5#12711yescharacteristic
479C2×C4×C5#12711yescharacteristic
480C2×C4×C5C22×D411yescharacteristic
481C2×C4×C5C22×D411yescharacteristic
482C2×C4×C5C22×D411yescharacteristic
483C2×C4×C5C22×D411yescharacteristic
484C2×C4×C5C22×D411yescharacteristic
485C2×C4×C5C2×#4111yescharacteristic
486C5×C8—24no—
487C5×C8—24no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41—21no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—21no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—21no—
506C2×#41—21no—
507C2×#41—21no—
508C2×#41C5×D412yes—
509C2×#41C5×D412yes—
510C2×#41C23×C512yes—
511C2×#41C23×C512yes—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8—21no—
515C22×Q8—21no—
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8—21no—
522C22×Q8—21no—
523C22×Q8C5×D412yes—
524C22×Q8C5×D411yescharacteristic
525C22×Q8C5×D412yes—
526C22×Q8C5×D411yescharacteristic
527C22×Q8C23×C512yes—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4C5×D411yescharacteristic
531C22×D4C5×D411yescharacteristic
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4C23×C511yescharacteristic
536#137—28no—
537#137—28no—
538#137—24no—
539#137—24no—
540#137—28no—
541#137—24no—
542#137—24no—
543#137—28no—
544AGL(1,ℤ/8)—24no—
545AGL(1,ℤ/8)—24no—
546AGL(1,ℤ/8)—24no—
547AGL(1,ℤ/8)—24no—
548#135—28no—
549#135—28no—
550C2×Q16—24no—
551C2×Q16—24no—
552C2×Q16—22no—
553C2×Q16—24no—
554C2×SD16—24no—
555C2×SD16—24no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—24no—
559C2×D8—22no—
560C2×M16—21no—
561C2×M16—21no—
562C2×M16—21no—
563C2×M16—21no—
564C2×M16—21no—
565C2×M16—21no—
566C2×M16—21no—
567C2×M16C5×D412yes—
568C2×M16C5×D412yes—
569C2×M16C5×D412yes—
570C2×M16C23×C512yes—
571C2×M16C23×C512yes—
572C22×C8—21no—
573C22×C8C5×D412yes—
574C4⋊Q8—24no—
575C4⋊Q8—24no—
576#124—24no—
577#124—24no—
578#123—28no—
579#123—28no—
580C22⋊Q8—28no—
581C22⋊Q8—28no—
582#117—21no—
583#117—21no—
584#117—21no—
585#117—21no—
586#117—21no—
587#117C5×D412yes—
588#117C23×C512yes—
589#117C23×C512yes—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4C5×D412yes—
596C2×C42—21no—
597C2×C42—21no—
598#104—28no—
599#103—28no—
600#99—28no—
601C22×C5—22no—
602C22×C5—22no—
603C22×C5—22no—
604C22×C5—41no—
605C22×C5—41no—
606C22×C5—41no—
607C22×C5—41no—
608C22×C5—44no—
609C22×C5—42no—
610C22×C5—42no—
611C22×C5—82no—
612C22×C5—82no—
613C22×C5—82no—
614C22×C5—82no—
615C22×C5—82no—
616C22×C5#39211yescharacteristic
617C22×C5#39211yescharacteristic
618C22×C5#39211yescharacteristic
619C22×C5#39211yescharacteristic
620C22×C5C2×#12011yescharacteristic
621C22×C5C2×#12111yescharacteristic
622C22×C5C2×#12711yescharacteristic
623C4×C5—44no—
624C4×C5—42no—
625C4×C5—42no—
626C4×C5—44no—
627C4×C5—82no—
628C4×C5#39211yescharacteristic
629C4×C5#39211yescharacteristic
630C4×C5#39211yescharacteristic
631C4×C5#39211yescharacteristic
632C4×C5C2×#12011yescharacteristic
633C4×C5C2×#12011yescharacteristic
634C4×C5C2×#12111yescharacteristic
635C4×C5C2×#12111yescharacteristic
636C24—21no—
637C24—21no—
638C24C2×C5×D411yescharacteristic
639#41—22no—
640#41—22no—
641#41—22no—
642#41—22no—
643#41—22no—
644#41—22no—
645#41—22no—
646#41—22no—
647#41—22no—
648#41—22no—
649#41—22no—
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—41no—
656#41—41no—
657#41—41no—
658#41—41no—
659#41—41no—
660#41—41no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665#41—41no—
666#41—41no—
667#41—41no—
668#41—41no—
669#41—41no—
670#41—41no—
671C2×Q8—22no—
672C2×Q8—22no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—21no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—22no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—22no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—22no—
696C2×Q8—41no—
697C2×Q8—41no—
698C2×Q8—41no—
699C2×Q8—41no—
700C2×Q8—41no—
701C2×Q8—41no—
702C2×Q8—41no—
703C2×Q8—41no—
704C2×Q8—41no—
705C2×Q8—41no—
706C2×Q8—41no—
707C2×Q8—41no—
708C2×Q8C2×C5×D414yes—
709C2×Q8C2×C5×D412yes—
710C2×Q8C2×C5×D412yes—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—41no—
728C2×D4—41no—
729C2×D4—41no—
730C2×D4—41no—
731C2×D4—41no—
732C2×D4—41no—
733C2×D4C2×C5×D412yes—
734C2×D4C2×C5×D412yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—41no—
751C22×C4—41no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4C2×C5×D411yescharacteristic
759C22×C4C2×C5×D411yescharacteristic
760C22×C4C2×C5×D411yescharacteristic
761C22×C4C2×C5×D411yescharacteristic
762C22×C4C2×C5×D411yescharacteristic
763C22×C4C2×C5×D411yescharacteristic
764C22×C4C2×C5×D411yescharacteristic
765C22×C4C2×C5×D411yescharacteristic
766C22×C4C2×C5×D411yescharacteristic
767C22×C4C2×C5×D411yescharacteristic
768C22×C4C2×C5×D411yescharacteristic
769C22×C4C5×#4111yescharacteristic
770C22×C4C5×#4111yescharacteristic
771C22×C4C24×C511yescharacteristic
772Q16—216no—
773Q16—28no—
774SD16—216no—
775SD16—28no—
776SD16—28no—
777D8—28no—
778M16—22no—
779M16—22no—
780M16—22no—
781M16—22no—
782M16—22no—
783M16—22no—
784M16—22no—
785M16C2×C5×D414yes—
786C2×C8—22no—
787C2×C8—22no—
788C2×C8—22no—
789C2×C8—22no—
790C2×C8—22no—
791C2×C8C2×C5×D414yes—
792C4⋊C4—216no—
793C4⋊C4—22no—
794C4⋊C4—22no—
795C4⋊C4—22no—
796C4⋊C4—41no—
797C22⋊C4—216no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—41no—
801C22⋊C4C2×C5×D414yes—
802C42—22no—
803C42—22no—
804C42—22no—
805C42—41no—
806C2×C5—21no—
807C2×C5—21no—
808C2×C5—21no—
809C2×C5—21no—
810C2×C5—21no—
811C2×C5—21no—
812C2×C5—82no—
813C2×C5—82no—
814C2×C5#200912yesdirect product factor
815C2×C5C2×#39211yescharacteristic
816C23—22no—
817C23—22no—
818C23—42no—
819C23—44no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—82no—
825C23C5×#12011yescharacteristic
826C23C5×#12011yescharacteristic
827C23C5×#12111yescharacteristic
828C23C5×#12111yescharacteristic
829C23C5×#12711yescharacteristic
830C23C5×#12711yescharacteristic
831C23C22×C5×D411yescharacteristic
832Q8—24no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—24no—
837Q8—22no—
838Q8—42no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—41no—
843Q8—41no—
844Q8—41no—
845Q8—41no—
846Q8—42no—
847Q8—42no—
848D4—22no—
849D4—22no—
850D4—22no—
851D4—22no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—42no—
860D4—41no—
861D4—41no—
862D4—41no—
863D4—41no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—44no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—82no—
889C2×C4C5×#12011yescharacteristic
890C2×C4C5×#12011yescharacteristic
891C2×C4C5×#12011yescharacteristic
892C2×C4C5×#12011yescharacteristic
893C2×C4C5×#12011yescharacteristic
894C2×C4C5×#12011yescharacteristic
895C2×C4C5×#12011yescharacteristic
896C2×C4C5×#12011yescharacteristic
897C2×C4C5×#12011yescharacteristic
898C2×C4C5×#12011yescharacteristic
899C2×C4C5×#12111yescharacteristic
900C2×C4C5×#12111yescharacteristic
901C2×C4C5×#12111yescharacteristic
902C2×C4C5×#12111yescharacteristic
903C2×C4C5×#12111yescharacteristic
904C2×C4C5×#12111yescharacteristic
905C2×C4C5×#12111yescharacteristic
906C2×C4C5×#12111yescharacteristic
907C2×C4C5×#12111yescharacteristic
908C2×C4C5×#12111yescharacteristic
909C2×C4C5×#12711yescharacteristic
910C2×C4C5×#12711yescharacteristic
911C2×C4C22×C5×D411yescharacteristic
912C2×C4C22×C5×D411yescharacteristic
913C2×C4C22×C5×D411yescharacteristic
914C2×C4C22×C5×D411yescharacteristic
915C2×C4C22×C5×D411yescharacteristic
916C2×C4C2×C5×#4111yescharacteristic
917C8—24no—
918C8—24no—
919C5C2×#200911yescharacteristic, direct product factor, Sylow
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22C5×#39211yescharacteristic
936C22C5×#39211yescharacteristic
937C22C5×#39211yescharacteristic
938C22C5×#39211yescharacteristic
939C22C2×C5×#12011yescharacteristic
940C22C2×C5×#12111yescharacteristic
941C22C2×C5×#12711yescharacteristic
942C4—44no—
943C4—42no—
944C4—42no—
945C4—44no—
946C4—82no—
947C4C5×#39211yescharacteristic
948C4C5×#39211yescharacteristic
949C4C5×#39211yescharacteristic
950C4C5×#39211yescharacteristic
951C4C2×C5×#12011yescharacteristic
952C4C2×C5×#12011yescharacteristic
953C4C2×C5×#12111yescharacteristic
954C4C2×C5×#12111yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—82no—
963C2C5×#200912yesdirect product factor
964C2C2×C5×#39211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC2×C5×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C5×#137C2semidirect
3. C2×C5×#536C2semidirect
4. C2×C5×#421C2semidirect
5. C2×C5×#419C2semidirect
6. C2×C5×#410C2semidirect
7. C5×#2009C2direct (N × H)
8. C2×C5×#344C2semidirect
23. C2×C5×#137C22semidirect
34. C5×#536C22semidirect
42. C5×#421C22semidirect
45. C5×#419C22semidirect
48. C5×#410C22semidirect
50. C5×#344C22semidirect
51. C2×#2009C5direct (N × H)
166. C22×#137C2×C5semidirect
167. C2×#536C2×C5semidirect
168. C2×#421C2×C5semidirect
169. C2×#419C2×C5semidirect
170. C2×#410C2×C5semidirect
171. #2009C2×C5direct (N × H)
172. C2×#344C2×C5semidirect
357. C2×#137C22×C5semidirect
368. #536C22×C5semidirect
376. #421C22×C5semidirect
379. #419C22×C5semidirect
382. #410C22×C5semidirect
384. #344C22×C5semidirect
814. C2×C5#2009direct (N × H)
919. C5C2×#2009direct (N × H)
963. C2C5×#2009direct (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
C22×C5×#1372
C2×C5×#5362
C2×C5×#4212
C2×C5×#4192
C2×C5×#4102
C5×#20092
C2×C5×#3442
C2×#20095