Finite Group Databasebeta

← C2×C5×#2008 #11946130

Subgroups — C2×C5×#2008 #11946130

Order 1280.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic, complemented
2C22×C5×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C2×C5×#535C211yesmaximal, characteristic, complemented
4C2×C5×#421C211yesmaximal, characteristic, complemented
5C2×C5×#418C211yesmaximal, characteristic, complemented
6C2×C5×#410C211yesmaximal, characteristic, complemented
7C5×#2008C218yesmaximal, direct product factor
8C2×C5×#344C211yesmaximal, characteristic, complemented
9C22×C5×#41C2211yescharacteristic
10C22×C5×#41C2211yescharacteristic
11C23×C5×D4C2211yescharacteristic
12C5×#575—22no—
13C5×#575—22no—
14C5×#575—22no—
15C5×#575C2214yescomplemented
16C2×C5×#137—21no—
17C2×C5×#137—21no—
18C2×C5×AGL(1,ℤ/8)—22no—
19C2×C5×AGL(1,ℤ/8)—22no—
20C2×C5×AGL(1,ℤ/8)—22no—
21C2×C5×AGL(1,ℤ/8)—21no—
22C2×C5×AGL(1,ℤ/8)—21no—
23C2×C5×AGL(1,ℤ/8)—22no—
24C2×C5×AGL(1,ℤ/8)—22no—
25C2×C5×AGL(1,ℤ/8)C2214yescomplemented
26C2×C5×#135—22no—
27C22×C5×SD16—21no—
28C22×C5×D8—21no—
29C22×C5×M16C2211yescharacteristic
30C22×C5×M16C2211yescharacteristic
31C5×#535—22no—
32C5×#535—22no—
33C5×#535—22no—
34C5×#535C2214yescomplemented
35C2×C5×#127—21no—
36C2×C5×#124—21no—
37C2×C5×#121—22no—
38C2×C5×#120—22no—
39C2×C5×#117C2211yescharacteristic
40C2×C5×#117C2211yescharacteristic
41C5×#421—22no—
42C5×#421C2214yescomplemented
43C2×C5×#104—22no—
44C5×#418—22no—
45C5×#418C2214yescomplemented
46C2×C5×#102—22no—
47C5×#410—22no—
48C5×#410C2214yescomplemented
49C2×C5×#99—22no—
50C5×#344C2214yescomplemented
51C2×#2008C511yesmaximal, characteristic, direct product factor, Sylow
52C25×C5—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×#41—21no—
73C2×C5×#41D412yes—
74C2×C5×#41D412yescomplemented
75C2×C5×#41C2312yes—
76C2×C5×#41C2312yes—
77C22×C5×Q8D411yescharacteristic
78C22×C5×Q8D411yescharacteristic, complemented
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4—24no—
82C22×C5×D4—21no—
83C22×C5×D4—21no—
84C22×C5×D4—21no—
85C22×C5×D4—21no—
86C22×C5×D4—21no—
87C22×C5×D4—21no—
88C22×C5×D4—21no—
89C22×C5×D4—21no—
90C22×C5×D4—21no—
91C22×C5×D4—21no—
92C22×C5×D4—21no—
93C22×C5×D4D412yes—
94C22×C5×D4D411yescharacteristic
95C22×C5×D4D412yes—
96C22×C5×D4D411yescharacteristic, complemented
97C22×C5×D4C2312yes—
98C23×C4×C5—21no—
99C23×C4×C5—21no—
100C23×C4×C5C2311yescharacteristic
101C5×#137—24no—
102C5×#137—24no—
103C5×#137—24no—
104C5×#137—24no—
105C5×AGL(1,ℤ/8)—28no—
106C5×AGL(1,ℤ/8)—28no—
107C5×AGL(1,ℤ/8)—24no—
108C5×AGL(1,ℤ/8)—24no—
109C5×AGL(1,ℤ/8)—28no—
110C5×AGL(1,ℤ/8)—24no—
111C5×AGL(1,ℤ/8)—24no—
112C5×AGL(1,ℤ/8)—28no—
113C5×#135—28no—
114C5×#135—28no—
115C2×C5×Q16—22no—
116C2×C5×SD16—24no—
117C2×C5×SD16—24no—
118C2×C5×SD16—22no—
119C2×C5×SD16—22no—
120C2×C5×SD16—24no—
121C2×C5×D8—24no—
122C2×C5×D8—24no—
123C2×C5×D8—22no—
124C2×C5×D8—24no—
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×M16—21no—
132C2×C5×M16D412yescomplemented
133C2×C5×M16D412yescomplemented
134C2×C5×M16D412yescomplemented
135C2×C5×M16C2312yes—
136C2×C5×M16C2312yes—
137C22×C5×C8—21no—
138C22×C5×C8D412yescomplemented
139C5×#127—24no—
140C5×#127—24no—
141C5×#124—24no—
142C5×#124—24no—
143C5×#121—28no—
144C5×#121—28no—
145C5×#120—28no—
146C5×#120—28no—
147C5×#117—21no—
148C5×#117—21no—
149C5×#117—21no—
150C5×#117—21no—
151C5×#117—21no—
152C5×#117D412yes—
153C5×#117C2312yes—
154C5×#117C2312yes—
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×#102—28no—
164C5×#99—28no—
165C2×#575C2×C511yescharacteristic, complemented
166C22×AGL(1,ℤ/8)C2×C511yescharacteristic, complemented
167C2×#535C2×C511yescharacteristic, complemented
168C2×#421C2×C511yescharacteristic, complemented
169C2×#418C2×C511yescharacteristic, complemented
170C2×#410C2×C511yescharacteristic, complemented
171#2008C2×C518yesdirect product factor
172C2×#344C2×C511yescharacteristic, complemented
173C24×C5—22no—
174C24×C5—21no—
175C24×C5—22no—
176C24×C5—21no—
177C24×C5—22no—
178C24×C5—41no—
179C24×C5—41no—
180C24×C5—41no—
181C24×C5—41no—
182C24×C5—84no—
183C24×C5C2×D411yescharacteristic
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—22no—
193C5×#41—22no—
194C5×#41—22no—
195C5×#41—22no—
196C5×#41—22no—
197C5×#41—22no—
198C5×#41—22no—
199C5×#41—22no—
200C5×#41—41no—
201C5×#41—41no—
202C5×#41—41no—
203C5×#41—41no—
204C5×#41—41no—
205C5×#41—41no—
206C5×#41—41no—
207C5×#41—41no—
208C5×#41—41no—
209C5×#41—41no—
210C5×#41—41no—
211C5×#41—41no—
212C5×#41—41no—
213C5×#41—41no—
214C5×#41—41no—
215C5×#41—41no—
216C2×C5×Q8—21no—
217C2×C5×Q8—21no—
218C2×C5×Q8—21no—
219C2×C5×Q8—21no—
220C2×C5×Q8—21no—
221C2×C5×Q8—21no—
222C2×C5×Q8—21no—
223C2×C5×Q8—21no—
224C2×C5×Q8—21no—
225C2×C5×Q8—21no—
226C2×C5×Q8C2×D412yes—
227C2×C5×Q8C2×D412yescomplemented
228C2×C5×D4—22no—
229C2×C5×D4—22no—
230C2×C5×D4—22no—
231C2×C5×D4—22no—
232C2×C5×D4—216no—
233C2×C5×D4—21no—
234C2×C5×D4—21no—
235C2×C5×D4—22no—
236C2×C5×D4—22no—
237C2×C5×D4—21no—
238C2×C5×D4—21no—
239C2×C5×D4—22no—
240C2×C5×D4—22no—
241C2×C5×D4—21no—
242C2×C5×D4—21no—
243C2×C5×D4—22no—
244C2×C5×D4—22no—
245C2×C5×D4—21no—
246C2×C5×D4—22no—
247C2×C5×D4—22no—
248C2×C5×D4—22no—
249C2×C5×D4—22no—
250C2×C5×D4—21no—
251C2×C5×D4—21no—
252C2×C5×D4—21no—
253C2×C5×D4—22no—
254C2×C5×D4—22no—
255C2×C5×D4—22no—
256C2×C5×D4—22no—
257C2×C5×D4—22no—
258C2×C5×D4—41no—
259C2×C5×D4—41no—
260C2×C5×D4—41no—
261C2×C5×D4—41no—
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×D4—41no—
271C2×C5×D4—41no—
272C2×C5×D4—41no—
273C2×C5×D4—41no—
274C2×C5×D4—41no—
275C2×C5×D4—41no—
276C2×C5×D4—41no—
277C2×C5×D4—41no—
278C2×C5×D4—88no—
279C2×C5×D4C2×D414yes—
280C2×C5×D4C2×D412yes—
281C2×C5×D4C2×D412yescomplemented
282C22×C4×C5—22no—
283C22×C4×C5—21no—
284C22×C4×C5—21no—
285C22×C4×C5—22no—
286C22×C4×C5—22no—
287C22×C4×C5—22no—
288C22×C4×C5—22no—
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×C5—41no—
296C22×C4×C5—41no—
297C22×C4×C5—41no—
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×C5C2×D411yescharacteristic
307C22×C4×C5C2×D411yescharacteristic
308C22×C4×C5C2×D411yescharacteristic
309C22×C4×C5#4111yescharacteristic
310C22×C4×C5#4111yescharacteristic
311C22×C4×C5C2411yescharacteristic
312C5×Q16—28no—
313C5×SD16—216no—
314C5×SD16—28no—
315C5×SD16—28no—
316C5×D8—216no—
317C5×D8—28no—
318C5×M16—22no—
319C5×M16—22no—
320C5×M16—22no—
321C5×M16—22no—
322C5×M16—22no—
323C5×M16—22no—
324C5×M16—22no—
325C5×M16C2×D414yescomplemented
326C2×C5×C8—22no—
327C2×C5×C8—22no—
328C2×C5×C8—22no—
329C2×C5×C8—22no—
330C2×C5×C8—22no—
331C2×C5×C8C2×D414yescomplemented
332C5×C4⋊C4—22no—
333C5×C4⋊C4—22no—
334C5×C4⋊C4—22no—
335C5×C4⋊C4—41no—
336C5×C22⋊C4—216no—
337C5×C22⋊C4—22no—
338C5×C22⋊C4—22no—
339C5×C22⋊C4—41no—
340C5×C22⋊C4C2×D414yes—
341C42×C5—22no—
342C42×C5—22no—
343C42×C5—22no—
344C42×C5—41no—
345C22×#41C22×C511yescharacteristic
346C22×#41C22×C511yescharacteristic
347C23×D4C22×C511yescharacteristic
348#575—22no—
349#575—22no—
350#575—22no—
351#575C22×C514yescomplemented
352C2×#137—21no—
353C2×#137—21no—
354C2×AGL(1,ℤ/8)—22no—
355C2×AGL(1,ℤ/8)—22no—
356C2×AGL(1,ℤ/8)—22no—
357C2×AGL(1,ℤ/8)—21no—
358C2×AGL(1,ℤ/8)—21no—
359C2×AGL(1,ℤ/8)—22no—
360C2×AGL(1,ℤ/8)—22no—
361C2×AGL(1,ℤ/8)C22×C514yescomplemented
362C2×#135—22no—
363C22×SD16—21no—
364C22×D8—21no—
365C22×M16C22×C511yescharacteristic
366C22×M16C22×C511yescharacteristic
367#535—22no—
368#535—22no—
369#535—22no—
370#535C22×C514yescomplemented
371C2×#127—21no—
372C2×#124—21no—
373C2×#121—22no—
374C2×#120—22no—
375C2×#117C22×C511yescharacteristic
376C2×#117C22×C511yescharacteristic
377#421—22no—
378#421C22×C514yescomplemented
379C2×#104—22no—
380#418—22no—
381#418C22×C514yescomplemented
382C2×#102—22no—
383#410—22no—
384#410C22×C514yescomplemented
385C2×#99—22no—
386#344C22×C514yescomplemented
387C23×C5—24no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—42no—
391C23×C5—44no—
392C23×C5—48no—
393C23×C5—42no—
394C23×C5—42no—
395C23×C5—41no—
396C23×C5—41no—
397C23×C5—42no—
398C23×C5—42no—
399C23×C5—42no—
400C23×C5—41no—
401C23×C5—41no—
402C23×C5—42no—
403C23×C5—82no—
404C23×C5—84no—
405C23×C5—84no—
406C23×C5—84no—
407C23×C5—84no—
408C23×C5—84no—
409C23×C5—84no—
410C23×C5#12011yescharacteristic
411C23×C5#12011yescharacteristic
412C23×C5#12111yescharacteristic
413C23×C5#12111yescharacteristic
414C23×C5#12711yescharacteristic
415C23×C5#12711yescharacteristic
416C23×C5C22×D411yescharacteristic
417C5×Q8—22no—
418C5×Q8—22no—
419C5×Q8—22no—
420C5×Q8—22no—
421C5×Q8—41no—
422C5×Q8—41no—
423C5×Q8—41no—
424C5×Q8—41no—
425C5×D4—22no—
426C5×D4—24no—
427C5×D4—22no—
428C5×D4—22no—
429C5×D4—24no—
430C5×D4—22no—
431C5×D4—42no—
432C5×D4—42no—
433C5×D4—42no—
434C5×D4—42no—
435C5×D4—42no—
436C5×D4—42no—
437C5×D4—42no—
438C5×D4—42no—
439C5×D4—42no—
440C5×D4—42no—
441C5×D4—42no—
442C5×D4—42no—
443C5×D4—42no—
444C5×D4—42no—
445C5×D4—41no—
446C5×D4—41no—
447C5×D4—41no—
448C5×D4—41no—
449C5×D4—816no—
450C2×C4×C5—24no—
451C2×C4×C5—22no—
452C2×C4×C5—22no—
453C2×C4×C5—44no—
454C2×C4×C5—41no—
455C2×C4×C5—41no—
456C2×C4×C5—41no—
457C2×C4×C5—41no—
458C2×C4×C5—42no—
459C2×C4×C5—42no—
460C2×C4×C5—42no—
461C2×C4×C5—42no—
462C2×C4×C5—42no—
463C2×C4×C5—42no—
464C2×C4×C5—42no—
465C2×C4×C5—42no—
466C2×C4×C5—42no—
467C2×C4×C5—82no—
468C2×C4×C5#12011yescharacteristic
469C2×C4×C5#12011yescharacteristic
470C2×C4×C5#12011yescharacteristic
471C2×C4×C5#12011yescharacteristic
472C2×C4×C5#12011yescharacteristic
473C2×C4×C5#12011yescharacteristic
474C2×C4×C5#12011yescharacteristic
475C2×C4×C5#12011yescharacteristic
476C2×C4×C5#12011yescharacteristic
477C2×C4×C5#12011yescharacteristic
478C2×C4×C5#12111yescharacteristic
479C2×C4×C5#12111yescharacteristic
480C2×C4×C5#12111yescharacteristic
481C2×C4×C5#12111yescharacteristic
482C2×C4×C5#12111yescharacteristic
483C2×C4×C5#12111yescharacteristic
484C2×C4×C5#12111yescharacteristic
485C2×C4×C5#12111yescharacteristic
486C2×C4×C5#12111yescharacteristic
487C2×C4×C5#12111yescharacteristic
488C2×C4×C5#12711yescharacteristic
489C2×C4×C5#12711yescharacteristic
490C2×C4×C5C22×D411yescharacteristic
491C2×C4×C5C22×D411yescharacteristic
492C2×C4×C5C22×D411yescharacteristic
493C2×C4×C5C22×D411yescharacteristic
494C2×C4×C5C22×D411yescharacteristic
495C2×C4×C5C2×#4111yescharacteristic
496C5×C8—24no—
497C5×C8—24no—
498C25—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×#41—21no—
509C2×#41—21no—
510C2×#41—21no—
511C2×#41—21no—
512C2×#41—21no—
513C2×#41—21no—
514C2×#41—21no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41—21no—
518C2×#41—21no—
519C2×#41C5×D412yes—
520C2×#41C5×D412yescomplemented
521C2×#41C23×C512yes—
522C2×#41C23×C512yes—
523C22×Q8C5×D411yescharacteristic
524C22×Q8C5×D411yescharacteristic, complemented
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—24no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4C5×D412yes—
540C22×D4C5×D411yescharacteristic
541C22×D4C5×D412yes—
542C22×D4C5×D411yescharacteristic, complemented
543C22×D4C23×C512yes—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C511yescharacteristic
547#137—24no—
548#137—24no—
549#137—24no—
550#137—24no—
551AGL(1,ℤ/8)—28no—
552AGL(1,ℤ/8)—28no—
553AGL(1,ℤ/8)—24no—
554AGL(1,ℤ/8)—24no—
555AGL(1,ℤ/8)—28no—
556AGL(1,ℤ/8)—24no—
557AGL(1,ℤ/8)—24no—
558AGL(1,ℤ/8)—28no—
559#135—28no—
560#135—28no—
561C2×Q16—22no—
562C2×SD16—24no—
563C2×SD16—24no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—24no—
567C2×D8—24no—
568C2×D8—24no—
569C2×D8—22no—
570C2×D8—24no—
571C2×M16—21no—
572C2×M16—21no—
573C2×M16—21no—
574C2×M16—21no—
575C2×M16—21no—
576C2×M16—21no—
577C2×M16—21no—
578C2×M16C5×D412yescomplemented
579C2×M16C5×D412yescomplemented
580C2×M16C5×D412yescomplemented
581C2×M16C23×C512yes—
582C2×M16C23×C512yes—
583C22×C8—21no—
584C22×C8C5×D412yescomplemented
585#127—24no—
586#127—24no—
587#124—24no—
588#124—24no—
589#121—28no—
590#121—28no—
591#120—28no—
592#120—28no—
593#117—21no—
594#117—21no—
595#117—21no—
596#117—21no—
597#117—21no—
598#117C5×D412yes—
599#117C23×C512yes—
600#117C23×C512yes—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4C5×D412yes—
606C2×C42—21no—
607C2×C42—21no—
608#104—28no—
609#102—28no—
610#99—28no—
611C22×C5—22no—
612C22×C5—22no—
613C22×C5—22no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5—44no—
619C22×C5—48no—
620C22×C5—42no—
621C22×C5—42no—
622C22×C5—44no—
623C22×C5—82no—
624C22×C5—82no—
625C22×C5—84no—
626C22×C5—82no—
627C22×C5—84no—
628C22×C5—84no—
629C22×C5—84no—
630C22×C5—84no—
631C22×C5—82no—
632C22×C5—84no—
633C22×C5—82no—
634C22×C5#39211yescharacteristic
635C22×C5#39211yescharacteristic
636C22×C5#39211yescharacteristic
637C22×C5#39211yescharacteristic
638C22×C5C2×#12011yescharacteristic
639C22×C5C2×#12111yescharacteristic
640C22×C5C2×#12711yescharacteristic
641C4×C5—44no—
642C4×C5—42no—
643C4×C5—42no—
644C4×C5—82no—
645C4×C5#39211yescharacteristic
646C4×C5#39211yescharacteristic
647C4×C5#39211yescharacteristic
648C4×C5#39211yescharacteristic
649C4×C5C2×#12011yescharacteristic
650C4×C5C2×#12011yescharacteristic
651C4×C5C2×#12111yescharacteristic
652C4×C5C2×#12111yescharacteristic
653C24—22no—
654C24—21no—
655C24—22no—
656C24—21no—
657C24—22no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24—84no—
663C24C2×C5×D411yescharacteristic
664#41—22no—
665#41—22no—
666#41—22no—
667#41—22no—
668#41—22no—
669#41—22no—
670#41—22no—
671#41—22no—
672#41—22no—
673#41—22no—
674#41—22no—
675#41—22no—
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—41no—
681#41—41no—
682#41—41no—
683#41—41no—
684#41—41no—
685#41—41no—
686#41—41no—
687#41—41no—
688#41—41no—
689#41—41no—
690#41—41no—
691#41—41no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8C2×C5×D412yes—
707C2×Q8C2×C5×D412yescomplemented
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—216no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—21no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—22no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—41no—
745C2×D4—41no—
746C2×D4—41no—
747C2×D4—41no—
748C2×D4—41no—
749C2×D4—41no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—88no—
759C2×D4C2×C5×D414yes—
760C2×D4C2×C5×D412yes—
761C2×D4C2×C5×D412yescomplemented
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4C2×C5×D411yescharacteristic
779C22×C4C2×C5×D411yescharacteristic
780C22×C4C2×C5×D411yescharacteristic
781C22×C4C2×C5×D411yescharacteristic
782C22×C4C2×C5×D411yescharacteristic
783C22×C4C2×C5×D411yescharacteristic
784C22×C4C2×C5×D411yescharacteristic
785C22×C4C2×C5×D411yescharacteristic
786C22×C4C2×C5×D411yescharacteristic
787C22×C4C2×C5×D411yescharacteristic
788C22×C4C2×C5×D411yescharacteristic
789C22×C4C5×#4111yescharacteristic
790C22×C4C5×#4111yescharacteristic
791C22×C4C24×C511yescharacteristic
792Q16—28no—
793SD16—216no—
794SD16—28no—
795SD16—28no—
796D8—216no—
797D8—28no—
798M16—22no—
799M16—22no—
800M16—22no—
801M16—22no—
802M16—22no—
803M16—22no—
804M16—22no—
805M16C2×C5×D414yescomplemented
806C2×C8—22no—
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—22no—
810C2×C8—22no—
811C2×C8C2×C5×D414yescomplemented
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—41no—
816C22⋊C4—216no—
817C22⋊C4—22no—
818C22⋊C4—22no—
819C22⋊C4—41no—
820C22⋊C4C2×C5×D414yes—
821C42—22no—
822C42—22no—
823C42—22no—
824C42—41no—
825C2×C5—21no—
826C2×C5—21no—
827C2×C5—21no—
828C2×C5—21no—
829C2×C5—21no—
830C2×C5—21no—
831C2×C5—82no—
832C2×C5—84no—
833C2×C5—82no—
834C2×C5#200812yesdirect product factor
835C2×C5C2×#39211yescharacteristic
836C23—24no—
837C23—22no—
838C23—22no—
839C23—42no—
840C23—44no—
841C23—48no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—82no—
853C23—84no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23C5×#12011yescharacteristic
860C23C5×#12011yescharacteristic
861C23C5×#12111yescharacteristic
862C23C5×#12111yescharacteristic
863C23C5×#12711yescharacteristic
864C23C5×#12711yescharacteristic
865C23C22×C5×D411yescharacteristic
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874D4—22no—
875D4—24no—
876D4—22no—
877D4—22no—
878D4—24no—
879D4—22no—
880D4—42no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—41no—
896D4—42no—
897D4—42no—
898D4—816no—
899C2×C4—24no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—44no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—82no—
917C2×C4C5×#12011yescharacteristic
918C2×C4C5×#12011yescharacteristic
919C2×C4C5×#12011yescharacteristic
920C2×C4C5×#12011yescharacteristic
921C2×C4C5×#12011yescharacteristic
922C2×C4C5×#12011yescharacteristic
923C2×C4C5×#12011yescharacteristic
924C2×C4C5×#12011yescharacteristic
925C2×C4C5×#12011yescharacteristic
926C2×C4C5×#12011yescharacteristic
927C2×C4C5×#12111yescharacteristic
928C2×C4C5×#12111yescharacteristic
929C2×C4C5×#12111yescharacteristic
930C2×C4C5×#12111yescharacteristic
931C2×C4C5×#12111yescharacteristic
932C2×C4C5×#12111yescharacteristic
933C2×C4C5×#12111yescharacteristic
934C2×C4C5×#12111yescharacteristic
935C2×C4C5×#12111yescharacteristic
936C2×C4C5×#12111yescharacteristic
937C2×C4C5×#12711yescharacteristic
938C2×C4C5×#12711yescharacteristic
939C2×C4C22×C5×D411yescharacteristic
940C2×C4C22×C5×D411yescharacteristic
941C2×C4C22×C5×D411yescharacteristic
942C2×C4C22×C5×D411yescharacteristic
943C2×C4C22×C5×D411yescharacteristic
944C2×C4C2×C5×#4111yescharacteristic
945C8—24no—
946C8—24no—
947C5C2×#200811yescharacteristic, direct product factor, Sylow
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22C5×#39211yescharacteristic
972C22C5×#39211yescharacteristic
973C22C5×#39211yescharacteristic
974C22C5×#39211yescharacteristic
975C22C2×C5×#12011yescharacteristic
976C22C2×C5×#12111yescharacteristic
977C22C2×C5×#12711yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4C5×#39211yescharacteristic
983C4C5×#39211yescharacteristic
984C4C5×#39211yescharacteristic
985C4C5×#39211yescharacteristic
986C4C2×C5×#12011yescharacteristic
987C4C2×C5×#12011yescharacteristic
988C4C2×C5×#12111yescharacteristic
989C4C2×C5×#12111yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C5×#200812yesdirect product factor
1000C2C2×C5×#39211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC22×C4C24×C5
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
1. C2×C5×#575C2semidirect
2. C22×C5×AGL(1,ℤ/8)C2semidirect
3. C2×C5×#535C2semidirect
4. C2×C5×#421C2semidirect
5. C2×C5×#418C2semidirect
6. C2×C5×#410C2semidirect
7. C5×#2008C2direct (N × H)
8. C2×C5×#344C2semidirect
15. C5×#575C22semidirect
25. C2×C5×AGL(1,ℤ/8)C22semidirect
34. C5×#535C22semidirect
42. C5×#421C22semidirect
45. C5×#418C22semidirect
48. C5×#410C22semidirect
50. C5×#344C22semidirect
51. C2×#2008C5direct (N × H)
74. C2×C5×#41D4semidirect
78. C22×C5×Q8D4semidirect
96. C22×C5×D4D4semidirect
132. C2×C5×M16D4semidirect
133. C2×C5×M16D4semidirect
134. C2×C5×M16D4semidirect
138. C22×C5×C8D4semidirect
165. C2×#575C2×C5semidirect
166. C22×AGL(1,ℤ/8)C2×C5semidirect
167. C2×#535C2×C5semidirect
168. C2×#421C2×C5semidirect
169. C2×#418C2×C5semidirect
170. C2×#410C2×C5semidirect
171. #2008C2×C5direct (N × H)
172. C2×#344C2×C5semidirect
227. C2×C5×Q8C2×D4semidirect
281. C2×C5×D4C2×D4semidirect
325. C5×M16C2×D4semidirect
331. C2×C5×C8C2×D4semidirect
351. #575C22×C5semidirect
361. C2×AGL(1,ℤ/8)C22×C5semidirect
370. #535C22×C5semidirect
378. #421C22×C5semidirect
381. #418C22×C5semidirect
384. #410C22×C5semidirect
386. #344C22×C5semidirect
520. C2×#41C5×D4semidirect
524. C22×Q8C5×D4semidirect
542. C22×D4C5×D4semidirect
578. C2×M16C5×D4semidirect
579. C2×M16C5×D4semidirect
580. C2×M16C5×D4semidirect
584. C22×C8C5×D4semidirect
707. C2×Q8C2×C5×D4semidirect
761. C2×D4C2×C5×D4semidirect
805. M16C2×C5×D4semidirect
811. C2×C8C2×C5×D4semidirect
834. C2×C5#2008direct (N × H)
947. C5C2×#2008direct (N × H)
999. C2C5×#2008direct (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×AGL(1,ℤ/8)2
C2×C5×#5352
C2×C5×#4212
C2×C5×#4182
C2×C5×#4102
C5×#20082
C2×C5×#3442
C2×#20085