Finite Group Databasebeta

← C5×#23412 #11946132

Subgroups — C5×#23412 #11946132

Order 1280.

1948 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#575C211yesmaximal, characteristic, complemented
2C2×C5×#575C211yesmaximal, characteristic, complemented
3C5×#3449C211yesmaximal, characteristic, complemented
4C2×C5×#421C211yesmaximal, characteristic, complemented
5C5×#2896C211yesmaximal, characteristic, complemented
6C2×C5×#410C211yesmaximal, characteristic, complemented
7C5×#2009C214yesmaximal, complemented
8C5×#2008C214yesmaximal, complemented
9C2×C5×#344C211yesmaximal, characteristic, complemented
10C22×C5×#41C2211yescharacteristic
11C22×C5×#41C2211yescharacteristic
12C22×C5×#41C2211yescharacteristic
13C5×#575—22no—
14C5×#575—22no—
15C5×#575—22no—
16C5×#575—22no—
17C5×#575—22no—
18C5×#575—22no—
19C5×#575—22no—
20C5×#575C2214yes—
21C2×C5×#137—21no—
22C2×C5×#137—21no—
23C2×C5×#137—21no—
24C2×C5×#137C2212yescomplemented
25C2×C5×AGL(1,ℤ/8)—21no—
26C2×C5×AGL(1,ℤ/8)—21no—
27C2×C5×AGL(1,ℤ/8)—21no—
28C2×C5×AGL(1,ℤ/8)C2212yescomplemented
29C2×C5×#135—22no—
30C2×C5×#135—22no—
31C22×C5×M16C2211yescharacteristic
32C22×C5×M16C2211yescharacteristic
33C5×#537—22no—
34C5×#536—21no—
35C5×#536C2212yescomplemented
36C5×#535—21no—
37C5×#535C2212yescomplemented
38C5×#534—22no—
39C5×#532—22no—
40C5×#525—22no—
41C5×#525—22no—
42C2×C5×#117C2211yescharacteristic
43C2×C5×#117C2211yescharacteristic
44C5×#421—22no—
45C5×#421C2214yescomplemented
46C2×C5×#104—22no—
47C5×#419C2212yescomplemented
48C5×#418C2212yescomplemented
49C5×#417—22no—
50C5×#416—22no—
51C5×#410—22no—
52C5×#410C2214yescomplemented
53C2×C5×#99—22no—
54C5×#344C2214yescomplemented
55#23412C511yesmaximal, characteristic, direct product factor, Sylow
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×#41—21no—
74C2×C5×#41—21no—
75C2×C5×#41—21no—
76C2×C5×#41—21no—
77C2×C5×#41—21no—
78C2×C5×#41—21no—
79C2×C5×#41—21no—
80C2×C5×#41—21no—
81C2×C5×#41—21no—
82C2×C5×#41—21no—
83C2×C5×#41—21no—
84C2×C5×#41—21no—
85C2×C5×#41—21no—
86C2×C5×#41D412yes—
87C2×C5×#41D412yes—
88C2×C5×#41D412yes—
89C2×C5×#41D412yescomplemented
90C2×C5×#41C2312yes—
91C2×C5×#41C2312yes—
92C22×C5×Q8D411yescharacteristic
93C22×C5×Q8D411yescharacteristic, complemented
94C22×C5×Q8C2311yescharacteristic
95C22×C5×D4—21no—
96C22×C5×D4—21no—
97C22×C5×D4—21no—
98C22×C5×D4D411yescharacteristic
99C22×C5×D4D411yescharacteristic, complemented
100C22×C5×D4C2311yescharacteristic
101C23×C4×C5—21no—
102C23×C4×C5—21no—
103C23×C4×C5—21no—
104C23×C4×C5C2311yescharacteristic
105C5×#137—24no—
106C5×#137—24no—
107C5×#137—24no—
108C5×#137—24no—
109C5×#137—24no—
110C5×#137—24no—
111C5×#137—24no—
112C5×#137—24no—
113C5×AGL(1,ℤ/8)—24no—
114C5×AGL(1,ℤ/8)—24no—
115C5×AGL(1,ℤ/8)—24no—
116C5×AGL(1,ℤ/8)—24no—
117C5×AGL(1,ℤ/8)—24no—
118C5×AGL(1,ℤ/8)—24no—
119C5×AGL(1,ℤ/8)—24no—
120C5×AGL(1,ℤ/8)—24no—
121C5×#135—28no—
122C5×#135—28no—
123C5×#135—28no—
124C5×#135—28no—
125C2×C5×Q16—22no—
126C2×C5×Q16—22no—
127C2×C5×SD16—22no—
128C2×C5×SD16—22no—
129C2×C5×SD16—22no—
130C2×C5×SD16—22no—
131C2×C5×D8—22no—
132C2×C5×D8—22no—
133C2×C5×M16—21no—
134C2×C5×M16—21no—
135C2×C5×M16—21no—
136C2×C5×M16—21no—
137C2×C5×M16—21no—
138C2×C5×M16—21no—
139C2×C5×M16—21no—
140C2×C5×M16D412yescomplemented
141C2×C5×M16D412yescomplemented
142C2×C5×M16D412yescomplemented
143C2×C5×M16C2312yes—
144C2×C5×M16C2312yes—
145C22×C5×C8—21no—
146C22×C5×C8D412yescomplemented
147C5×C4⋊Q8—22no—
148C5×#127—22no—
149C5×#124—22no—
150C5×#124—22no—
151C5×#123—24no—
152C5×#123—24no—
153C5×C22⋊Q8—24no—
154C5×C22⋊Q8—24no—
155C5×#121—24no—
156C5×#121—28no—
157C5×#121—24no—
158C5×#120—24no—
159C5×#120—24no—
160C4×C5×D4—28no—
161C5×#117—21no—
162C5×#117—21no—
163C5×#117—21no—
164C5×#117—21no—
165C5×#117—21no—
166C5×#117D412yes—
167C5×#117C2312yes—
168C5×#117C2312yes—
169C2×C5×C4⋊C4—21no—
170C2×C5×C4⋊C4—21no—
171C2×C5×C22⋊C4—21no—
172C2×C5×C22⋊C4D412yes—
173C2×C42×C5—21no—
174C2×C42×C5—21no—
175C5×#104—28no—
176C5×#103—24no—
177C5×#102—24no—
178C5×#99—28no—
179C2×#575C2×C511yescharacteristic, complemented
180C2×#575C2×C511yescharacteristic, complemented
181#3449C2×C511yescharacteristic, complemented
182C2×#421C2×C511yescharacteristic, complemented
183#2896C2×C511yescharacteristic, complemented
184C2×#410C2×C511yescharacteristic, complemented
185#2009C2×C514yescomplemented
186#2008C2×C514yescomplemented
187C2×#344C2×C511yescharacteristic, complemented
188C24×C5—21no—
189C24×C5—21no—
190C24×C5—21no—
191C24×C5C2×D411yescharacteristic
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—22no—
201C5×#41—22no—
202C5×#41—22no—
203C5×#41—22no—
204C5×#41—22no—
205C5×#41—22no—
206C5×#41—22no—
207C5×#41—22no—
208C5×#41—22no—
209C5×#41—22no—
210C5×#41—22no—
211C5×#41—22no—
212C5×#41—22no—
213C5×#41—22no—
214C5×#41—22no—
215C5×#41—22no—
216C5×#41—41no—
217C5×#41—41no—
218C5×#41—41no—
219C5×#41—41no—
220C5×#41—41no—
221C5×#41—41no—
222C5×#41—41no—
223C5×#41—41no—
224C5×#41—41no—
225C5×#41—41no—
226C5×#41—41no—
227C5×#41—41no—
228C5×#41—41no—
229C5×#41—41no—
230C5×#41—41no—
231C5×#41—41no—
232C5×#41—41no—
233C5×#41—41no—
234C5×#41—41no—
235C5×#41—41no—
236C5×#41—41no—
237C5×#41—41no—
238C5×#41—41no—
239C5×#41—41no—
240C2×C5×Q8—21no—
241C2×C5×Q8—21no—
242C2×C5×Q8—21no—
243C2×C5×Q8—21no—
244C2×C5×Q8—21no—
245C2×C5×Q8—21no—
246C2×C5×Q8—21no—
247C2×C5×Q8—21no—
248C2×C5×Q8—21no—
249C2×C5×Q8—21no—
250C2×C5×Q8—21no—
251C2×C5×Q8—21no—
252C2×C5×Q8—21no—
253C2×C5×Q8—21no—
254C2×C5×Q8—21no—
255C2×C5×Q8C2×D412yes—
256C2×C5×Q8C2×D412yes—
257C2×C5×Q8C2×D412yes—
258C2×C5×D4—22no—
259C2×C5×D4—22no—
260C2×C5×D4—22no—
261C2×C5×D4—22no—
262C2×C5×D4—22no—
263C2×C5×D4—22no—
264C2×C5×D4—28no—
265C2×C5×D4—21no—
266C2×C5×D4—21no—
267C2×C5×D4—21no—
268C2×C5×D4—21no—
269C2×C5×D4—21no—
270C2×C5×D4—21no—
271C2×C5×D4—21no—
272C2×C5×D4—21no—
273C2×C5×D4—21no—
274C2×C5×D4—21no—
275C2×C5×D4—21no—
276C2×C5×D4—21no—
277C2×C5×D4—21no—
278C2×C5×D4—21no—
279C2×C5×D4—21no—
280C2×C5×D4—41no—
281C2×C5×D4—41no—
282C2×C5×D4—41no—
283C2×C5×D4—41no—
284C2×C5×D4—41no—
285C2×C5×D4—41no—
286C2×C5×D4—41no—
287C2×C5×D4—41no—
288C2×C5×D4—41no—
289C2×C5×D4—41no—
290C2×C5×D4—41no—
291C2×C5×D4—41no—
292C2×C5×D4C2×D412yes—
293C2×C5×D4C2×D412yes—
294C2×C5×D4C2×D412yes—
295C22×C4×C5—21no—
296C22×C4×C5—21no—
297C22×C4×C5—21no—
298C22×C4×C5—22no—
299C22×C4×C5—22no—
300C22×C4×C5—22no—
301C22×C4×C5—22no—
302C22×C4×C5—22no—
303C22×C4×C5—22no—
304C22×C4×C5—22no—
305C22×C4×C5—41no—
306C22×C4×C5—41no—
307C22×C4×C5—41no—
308C22×C4×C5—41no—
309C22×C4×C5—41no—
310C22×C4×C5—41no—
311C22×C4×C5—41no—
312C22×C4×C5—41no—
313C22×C4×C5—41no—
314C22×C4×C5—41no—
315C22×C4×C5—41no—
316C22×C4×C5—41no—
317C22×C4×C5—41no—
318C22×C4×C5C2×D411yescharacteristic
319C22×C4×C5C2×D411yescharacteristic
320C22×C4×C5C2×D411yescharacteristic
321C22×C4×C5C2×D411yescharacteristic
322C22×C4×C5C2×D411yescharacteristic
323C22×C4×C5C2×D411yescharacteristic
324C22×C4×C5C2×D411yescharacteristic
325C22×C4×C5C2×D411yescharacteristic
326C22×C4×C5C2×D411yescharacteristic
327C22×C4×C5C2×D411yescharacteristic
328C22×C4×C5C2×D411yescharacteristic
329C22×C4×C5#4111yescharacteristic
330C22×C4×C5#4111yescharacteristic
331C22×C4×C5C2411yescharacteristic
332C5×Q16—28no—
333C5×Q16—28no—
334C5×SD16—28no—
335C5×SD16—28no—
336C5×SD16—28no—
337C5×SD16—28no—
338C5×D8—28no—
339C5×D8—28no—
340C5×M16—22no—
341C5×M16—22no—
342C5×M16—22no—
343C5×M16—22no—
344C5×M16—22no—
345C5×M16—22no—
346C5×M16—22no—
347C5×M16C2×D414yes—
348C2×C5×C8—22no—
349C2×C5×C8—22no—
350C2×C5×C8—22no—
351C2×C5×C8—22no—
352C2×C5×C8—22no—
353C2×C5×C8C2×D414yes—
354C5×C4⋊C4—28no—
355C5×C4⋊C4—22no—
356C5×C4⋊C4—22no—
357C5×C4⋊C4—22no—
358C5×C4⋊C4—41no—
359C5×C22⋊C4—28no—
360C5×C22⋊C4—28no—
361C5×C22⋊C4—22no—
362C5×C22⋊C4—22no—
363C5×C22⋊C4—41no—
364C5×C22⋊C4C2×D414yes—
365C42×C5—22no—
366C42×C5—22no—
367C42×C5—22no—
368C42×C5—41no—
369C22×#41C22×C511yescharacteristic
370C22×#41C22×C511yescharacteristic
371C22×#41C22×C511yescharacteristic
372#575—22no—
373#575—22no—
374#575—22no—
375#575—22no—
376#575—22no—
377#575—22no—
378#575—22no—
379#575C22×C514yes—
380C2×#137—21no—
381C2×#137—21no—
382C2×#137—21no—
383C2×#137C22×C512yescomplemented
384C2×AGL(1,ℤ/8)—21no—
385C2×AGL(1,ℤ/8)—21no—
386C2×AGL(1,ℤ/8)—21no—
387C2×AGL(1,ℤ/8)C22×C512yescomplemented
388C2×#135—22no—
389C2×#135—22no—
390C22×M16C22×C511yescharacteristic
391C22×M16C22×C511yescharacteristic
392#537—22no—
393#536—21no—
394#536C22×C512yescomplemented
395#535—21no—
396#535C22×C512yescomplemented
397#534—22no—
398#532—22no—
399#525—22no—
400#525—22no—
401C2×#117C22×C511yescharacteristic
402C2×#117C22×C511yescharacteristic
403#421—22no—
404#421C22×C514yescomplemented
405C2×#104—22no—
406#419C22×C512yescomplemented
407#418C22×C512yescomplemented
408#417—22no—
409#416—22no—
410#410—22no—
411#410C22×C514yescomplemented
412C2×#99—22no—
413#344C22×C514yescomplemented
414C23×C5—22no—
415C23×C5—22no—
416C23×C5—22no—
417C23×C5—41no—
418C23×C5—41no—
419C23×C5—41no—
420C23×C5—41no—
421C23×C5—41no—
422C23×C5—41no—
423C23×C5—81no—
424C23×C5—82no—
425C23×C5—82no—
426C23×C5—82no—
427C23×C5#12011yescharacteristic
428C23×C5#12011yescharacteristic
429C23×C5#12111yescharacteristic
430C23×C5#12111yescharacteristic
431C23×C5#12711yescharacteristic
432C23×C5#12711yescharacteristic
433C23×C5C22×D411yescharacteristic
434C5×Q8—22no—
435C5×Q8—22no—
436C5×Q8—22no—
437C5×Q8—22no—
438C5×Q8—22no—
439C5×Q8—22no—
440C5×Q8—41no—
441C5×Q8—41no—
442C5×Q8—41no—
443C5×Q8—41no—
444C5×Q8—41no—
445C5×Q8—41no—
446C5×D4—22no—
447C5×D4—22no—
448C5×D4—22no—
449C5×D4—22no—
450C5×D4—22no—
451C5×D4—22no—
452C5×D4—42no—
453C5×D4—42no—
454C5×D4—42no—
455C5×D4—42no—
456C5×D4—42no—
457C5×D4—42no—
458C5×D4—42no—
459C5×D4—42no—
460C5×D4—42no—
461C5×D4—42no—
462C5×D4—42no—
463C5×D4—42no—
464C5×D4—41no—
465C5×D4—41no—
466C5×D4—41no—
467C5×D4—41no—
468C5×D4—41no—
469C5×D4—41no—
470C5×D4—88no—
471C2×C4×C5—24no—
472C2×C4×C5—22no—
473C2×C4×C5—22no—
474C2×C4×C5—22no—
475C2×C4×C5—41no—
476C2×C4×C5—41no—
477C2×C4×C5—41no—
478C2×C4×C5—41no—
479C2×C4×C5—41no—
480C2×C4×C5—41no—
481C2×C4×C5—42no—
482C2×C4×C5—42no—
483C2×C4×C5—42no—
484C2×C4×C5—42no—
485C2×C4×C5—42no—
486C2×C4×C5—42no—
487C2×C4×C5—42no—
488C2×C4×C5—42no—
489C2×C4×C5—42no—
490C2×C4×C5—42no—
491C2×C4×C5—42no—
492C2×C4×C5—42no—
493C2×C4×C5—42no—
494C2×C4×C5—82no—
495C2×C4×C5—82no—
496C2×C4×C5#12011yescharacteristic
497C2×C4×C5#12011yescharacteristic
498C2×C4×C5#12011yescharacteristic
499C2×C4×C5#12011yescharacteristic
500C2×C4×C5#12011yescharacteristic
501C2×C4×C5#12011yescharacteristic
502C2×C4×C5#12011yescharacteristic
503C2×C4×C5#12011yescharacteristic
504C2×C4×C5#12011yescharacteristic
505C2×C4×C5#12011yescharacteristic
506C2×C4×C5#12111yescharacteristic
507C2×C4×C5#12111yescharacteristic
508C2×C4×C5#12111yescharacteristic
509C2×C4×C5#12111yescharacteristic
510C2×C4×C5#12111yescharacteristic
511C2×C4×C5#12111yescharacteristic
512C2×C4×C5#12111yescharacteristic
513C2×C4×C5#12111yescharacteristic
514C2×C4×C5#12111yescharacteristic
515C2×C4×C5#12111yescharacteristic
516C2×C4×C5#12711yescharacteristic
517C2×C4×C5#12711yescharacteristic
518C2×C4×C5C22×D411yescharacteristic
519C2×C4×C5C22×D411yescharacteristic
520C2×C4×C5C22×D411yescharacteristic
521C2×C4×C5C22×D411yescharacteristic
522C2×C4×C5C22×D411yescharacteristic
523C2×C4×C5C2×#4111yescharacteristic
524C5×C8—24no—
525C5×C8—24no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—21no—
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—21no—
546C2×#41—21no—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41C5×D412yes—
557C2×#41C5×D412yes—
558C2×#41C5×D412yes—
559C2×#41C5×D412yescomplemented
560C2×#41C23×C512yes—
561C2×#41C23×C512yes—
562C22×Q8C5×D411yescharacteristic
563C22×Q8C5×D411yescharacteristic, complemented
564C22×Q8C23×C511yescharacteristic
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4C5×D411yescharacteristic
569C22×D4C5×D411yescharacteristic, complemented
570C22×D4C23×C511yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C511yescharacteristic
575#137—24no—
576#137—24no—
577#137—24no—
578#137—24no—
579#137—24no—
580#137—24no—
581#137—24no—
582#137—24no—
583AGL(1,ℤ/8)—24no—
584AGL(1,ℤ/8)—24no—
585AGL(1,ℤ/8)—24no—
586AGL(1,ℤ/8)—24no—
587AGL(1,ℤ/8)—24no—
588AGL(1,ℤ/8)—24no—
589AGL(1,ℤ/8)—24no—
590AGL(1,ℤ/8)—24no—
591#135—28no—
592#135—28no—
593#135—28no—
594#135—28no—
595C2×Q16—22no—
596C2×Q16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×D8—22no—
602C2×D8—22no—
603C2×M16—21no—
604C2×M16—21no—
605C2×M16—21no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—21no—
610C2×M16C5×D412yescomplemented
611C2×M16C5×D412yescomplemented
612C2×M16C5×D412yescomplemented
613C2×M16C23×C512yes—
614C2×M16C23×C512yes—
615C22×C8—21no—
616C22×C8C5×D412yescomplemented
617C4⋊Q8—22no—
618#127—22no—
619#124—22no—
620#124—22no—
621#123—24no—
622#123—24no—
623C22⋊Q8—24no—
624C22⋊Q8—24no—
625#121—24no—
626#121—28no—
627#121—24no—
628#120—24no—
629#120—24no—
630C4×D4—28no—
631#117—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117C5×D412yes—
637#117C23×C512yes—
638#117C23×C512yes—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4C5×D412yes—
643C2×C42—21no—
644C2×C42—21no—
645#104—28no—
646#103—24no—
647#102—24no—
648#99—28no—
649C22×C5—41no—
650C22×C5—41no—
651C22×C5—41no—
652C22×C5—41no—
653C22×C5—41no—
654C22×C5—41no—
655C22×C5—41no—
656C22×C5—44no—
657C22×C5—44no—
658C22×C5—42no—
659C22×C5—42no—
660C22×C5—42no—
661C22×C5—82no—
662C22×C5—82no—
663C22×C5—82no—
664C22×C5—82no—
665C22×C5—82no—
666C22×C5—82no—
667C22×C5—82no—
668C22×C5#39211yescharacteristic
669C22×C5#39211yescharacteristic
670C22×C5#39211yescharacteristic
671C22×C5#39211yescharacteristic
672C22×C5C2×#12011yescharacteristic
673C22×C5C2×#12111yescharacteristic
674C22×C5C2×#12711yescharacteristic
675C4×C5—44no—
676C4×C5—42no—
677C4×C5—42no—
678C4×C5—42no—
679C4×C5—82no—
680C4×C5#39211yescharacteristic
681C4×C5#39211yescharacteristic
682C4×C5#39211yescharacteristic
683C4×C5#39211yescharacteristic
684C4×C5C2×#12011yescharacteristic
685C4×C5C2×#12011yescharacteristic
686C4×C5C2×#12111yescharacteristic
687C4×C5C2×#12111yescharacteristic
688C24—21no—
689C24—21no—
690C24—21no—
691C24C2×C5×D411yescharacteristic
692#41—22no—
693#41—22no—
694#41—22no—
695#41—22no—
696#41—22no—
697#41—22no—
698#41—22no—
699#41—22no—
700#41—22no—
701#41—22no—
702#41—22no—
703#41—22no—
704#41—22no—
705#41—22no—
706#41—22no—
707#41—22no—
708#41—22no—
709#41—22no—
710#41—22no—
711#41—22no—
712#41—22no—
713#41—22no—
714#41—22no—
715#41—22no—
716#41—41no—
717#41—41no—
718#41—41no—
719#41—41no—
720#41—41no—
721#41—41no—
722#41—41no—
723#41—41no—
724#41—41no—
725#41—41no—
726#41—41no—
727#41—41no—
728#41—41no—
729#41—41no—
730#41—41no—
731#41—41no—
732#41—41no—
733#41—41no—
734#41—41no—
735#41—41no—
736#41—41no—
737#41—41no—
738#41—41no—
739#41—41no—
740C2×Q8—21no—
741C2×Q8—21no—
742C2×Q8—21no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8C2×C5×D412yes—
756C2×Q8C2×C5×D412yes—
757C2×Q8C2×C5×D412yes—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—28no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—41no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—41no—
784C2×D4—41no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—41no—
791C2×D4—41no—
792C2×D4C2×C5×D412yes—
793C2×D4C2×C5×D412yes—
794C2×D4C2×C5×D412yes—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—41no—
818C22×C4C2×C5×D411yescharacteristic
819C22×C4C2×C5×D411yescharacteristic
820C22×C4C2×C5×D411yescharacteristic
821C22×C4C2×C5×D411yescharacteristic
822C22×C4C2×C5×D411yescharacteristic
823C22×C4C2×C5×D411yescharacteristic
824C22×C4C2×C5×D411yescharacteristic
825C22×C4C2×C5×D411yescharacteristic
826C22×C4C2×C5×D411yescharacteristic
827C22×C4C2×C5×D411yescharacteristic
828C22×C4C2×C5×D411yescharacteristic
829C22×C4C5×#4111yescharacteristic
830C22×C4C5×#4111yescharacteristic
831C22×C4C24×C511yescharacteristic
832Q16—28no—
833Q16—28no—
834SD16—28no—
835SD16—28no—
836SD16—28no—
837SD16—28no—
838D8—28no—
839D8—28no—
840M16—22no—
841M16—22no—
842M16—22no—
843M16—22no—
844M16—22no—
845M16—22no—
846M16—22no—
847M16C2×C5×D414yes—
848C2×C8—22no—
849C2×C8—22no—
850C2×C8—22no—
851C2×C8—22no—
852C2×C8—22no—
853C2×C8C2×C5×D414yes—
854C4⋊C4—28no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—41no—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—41no—
864C22⋊C4C2×C5×D414yes—
865C42—22no—
866C42—22no—
867C42—22no—
868C42—41no—
869C2×C5—21no—
870C2×C5—21no—
871C2×C5—21no—
872C2×C5—21no—
873C2×C5—21no—
874C2×C5—21no—
875C2×C5—21no—
876C2×C5—82no—
877C2×C5—82no—
878C2×C5—82no—
879C2×C5C2×#39211yescharacteristic
880C23—22no—
881C23—22no—
882C23—22no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—81no—
890C23—82no—
891C23—82no—
892C23—82no—
893C23C5×#12011yescharacteristic
894C23C5×#12011yescharacteristic
895C23C5×#12111yescharacteristic
896C23C5×#12111yescharacteristic
897C23C5×#12711yescharacteristic
898C23C5×#12711yescharacteristic
899C23C22×C5×D411yescharacteristic
900Q8—22no—
901Q8—22no—
902Q8—22no—
903Q8—22no—
904Q8—22no—
905Q8—22no—
906Q8—41no—
907Q8—41no—
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912D4—22no—
913D4—22no—
914D4—22no—
915D4—22no—
916D4—22no—
917D4—22no—
918D4—42no—
919D4—42no—
920D4—42no—
921D4—42no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—88no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—42no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—82no—
961C2×C4—82no—
962C2×C4C5×#12011yescharacteristic
963C2×C4C5×#12011yescharacteristic
964C2×C4C5×#12011yescharacteristic
965C2×C4C5×#12011yescharacteristic
966C2×C4C5×#12011yescharacteristic
967C2×C4C5×#12011yescharacteristic
968C2×C4C5×#12011yescharacteristic
969C2×C4C5×#12011yescharacteristic
970C2×C4C5×#12011yescharacteristic
971C2×C4C5×#12011yescharacteristic
972C2×C4C5×#12111yescharacteristic
973C2×C4C5×#12111yescharacteristic
974C2×C4C5×#12111yescharacteristic
975C2×C4C5×#12111yescharacteristic
976C2×C4C5×#12111yescharacteristic
977C2×C4C5×#12111yescharacteristic
978C2×C4C5×#12111yescharacteristic
979C2×C4C5×#12111yescharacteristic
980C2×C4C5×#12111yescharacteristic
981C2×C4C5×#12111yescharacteristic
982C2×C4C5×#12711yescharacteristic
983C2×C4C5×#12711yescharacteristic
984C2×C4C22×C5×D411yescharacteristic
985C2×C4C22×C5×D411yescharacteristic
986C2×C4C22×C5×D411yescharacteristic
987C2×C4C22×C5×D411yescharacteristic
988C2×C4C22×C5×D411yescharacteristic
989C2×C4C2×C5×#4111yescharacteristic
990C8—24no—
991C8—24no—
992C5#2341211yescharacteristic, direct product factor, Sylow
993C22—41no—
994C22—41no—
995C22—41no—
996C22—41no—
997C22—41no—
998C22—41no—
999C22—41no—
1000C22—44no—
1001C22—44no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22C5×#39211yescharacteristic
1013C22C5×#39211yescharacteristic
1014C22C5×#39211yescharacteristic
1015C22C5×#39211yescharacteristic
1016C22C2×C5×#12011yescharacteristic
1017C22C2×C5×#12111yescharacteristic
1018C22C2×C5×#12711yescharacteristic
1019C4—44no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—82no—
1024C4C5×#39211yescharacteristic
1025C4C5×#39211yescharacteristic
1026C4C5×#39211yescharacteristic
1027C4C5×#39211yescharacteristic
1028C4C2×C5×#12011yescharacteristic
1029C4C2×C5×#12011yescharacteristic
1030C4C2×C5×#12111yescharacteristic
1031C4C2×C5×#12111yescharacteristic
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2—21no—
1039C2—82no—
1040C2—82no—
1041C2—82no—
1042C2C2×C5×#39211yescharacteristic
subgroupG/H
centerC4×C5#392
commutator, Frattini, cosocleC22×C4C24×C5
socleC2×C5C2×#392
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
1. C2×C5×#575C2semidirect
2. C2×C5×#575C2semidirect
3. C5×#3449C2semidirect
4. C2×C5×#421C2semidirect
5. C5×#2896C2semidirect
6. C2×C5×#410C2semidirect
7. C5×#2009C2semidirect
8. C5×#2008C2semidirect
9. C2×C5×#344C2semidirect
24. C2×C5×#137C22semidirect
28. C2×C5×AGL(1,ℤ/8)C22semidirect
35. C5×#536C22semidirect
37. C5×#535C22semidirect
45. C5×#421C22semidirect
47. C5×#419C22semidirect
48. C5×#418C22semidirect
52. C5×#410C22semidirect
54. C5×#344C22semidirect
55. #23412C5direct (N × H)
89. C2×C5×#41D4semidirect
93. C22×C5×Q8D4semidirect
99. C22×C5×D4D4semidirect
140. C2×C5×M16D4semidirect
141. C2×C5×M16D4semidirect
142. C2×C5×M16D4semidirect
146. C22×C5×C8D4semidirect
179. C2×#575C2×C5semidirect
180. C2×#575C2×C5semidirect
181. #3449C2×C5semidirect
182. C2×#421C2×C5semidirect
183. #2896C2×C5semidirect
184. C2×#410C2×C5semidirect
185. #2009C2×C5semidirect
186. #2008C2×C5semidirect
187. C2×#344C2×C5semidirect
383. C2×#137C22×C5semidirect
387. C2×AGL(1,ℤ/8)C22×C5semidirect
394. #536C22×C5semidirect
396. #535C22×C5semidirect
404. #421C22×C5semidirect
406. #419C22×C5semidirect
407. #418C22×C5semidirect
411. #410C22×C5semidirect
413. #344C22×C5semidirect
559. C2×#41C5×D4semidirect
563. C22×Q8C5×D4semidirect
569. C22×D4C5×D4semidirect
610. C2×M16C5×D4semidirect
611. C2×M16C5×D4semidirect
612. C2×M16C5×D4semidirect
616. C22×C8C5×D4semidirect
992. C5#23412direct (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
C5×#34492
C2×C5×#4212
C5×#28962
C2×C5×#4102
C5×#20092
C5×#20082
C2×C5×#3442
#234125