Finite Group Databasebeta

← C2×#10615156 #12969947

Subgroups — C2×#10615156 #12969947

Order 1280.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#537C211yesmaximal, characteristic, complemented
2C2×#66164C211yesmaximal, characteristic, complemented
3C2×#65527C211yesmaximal, characteristic, complemented
4C2×#65527C211yesmaximal, characteristic, complemented
5C2×#65523C211yesmaximal, characteristic, complemented
6#10615156C2116yesmaximal, direct product factor
7C2×#65335C211yesmaximal, characteristic, complemented
8C2×#65338C211yesmaximal, characteristic, complemented
9C2×#65337C211yesmaximal, characteristic, complemented
10C2×#65334C211yesmaximal, characteristic, complemented
11C2×#65325C211yesmaximal, characteristic, complemented
12C2×#65328C211yesmaximal, characteristic, complemented
13C2×#65327C211yesmaximal, characteristic, complemented
14C2×#65324C211yesmaximal, characteristic, complemented
15C2×#65257C211yesmaximal, characteristic, complemented
16C2×#65256C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×#41C2211yescharacteristic, complemented
19C23×D20C2211yescharacteristic
20C5×#537—24no—
21C5×#537C2218yescomplemented
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic, complemented
25C2×C5×#121—21no—
26C2×C5×#121—21no—
27C2×C5×#121—21no—
28C2×C5×#121C2211yescharacteristic
29C2×C5×#121C2211yescharacteristic, complemented
30C22×C5×C4⋊C4C2211yescharacteristic, complemented
31#66164—24no—
32#66164C2218yescomplemented
33C2×#4093—21no—
34C22×#688C2211yescharacteristic
35C22×#688C2211yescharacteristic
36C2×#4086—21no—
37C2×#4083—21no—
38C2×#4083—21no—
39C22×#686C2211yescharacteristic
40C22×#686C2211yescharacteristic
41C2×#4076C2211yescharacteristic
42C2×#4076C2211yescharacteristic
43C2×#4076C2211yescharacteristic
44C2×#4076C2211yescharacteristic
45C2×#4072C2211yescharacteristic
46C22×#681C2211yescharacteristic, complemented
47C23×#168C2211yescharacteristic, complemented
48#65527C2218yescomplemented
49#65527C2218yescomplemented
50#65523C2218yescomplemented
51C2×#3967C2211yescharacteristic, complemented
52C2×#3967C2211yescharacteristic, complemented
53C2×#3964C2211yescharacteristic, complemented
54C2×#3964C2211yescharacteristic, complemented
55C2×C22⋊#168C2211yescharacteristic
56C2×C22⋊#168C2211yescharacteristic
57C2×C22⋊#168C2211yescharacteristic, complemented
58C2×C22⋊#168C2211yescharacteristic, complemented
59#65338C2218yescomplemented
60#65337C2218yescomplemented
61#65335C2218yescomplemented
62#65334C2218yescomplemented
63#65328C2218yescomplemented
64#65327C2218yescomplemented
65#65325C2218yescomplemented
66#65324C2218yescomplemented
67#65257C2218yescomplemented
68#65256C2218yescomplemented
69C2×#3941C2211yescharacteristic
70C2×#3941C2211yescharacteristic
71C2×#3941C2211yescharacteristic
72C2×#3941C2211yescharacteristic
73C2×#3940C2211yescharacteristic, complemented
74C2×#3940C2211yescharacteristic, complemented
75C2×#3939C2211yescharacteristic, complemented
76C2×#3939C2211yescharacteristic, complemented
77C2×#3198—51nomaximal, Sylow
78C24×D5—21no—
79C2×C5×#41—22no—
80C2×C5×#41—42no—
81C2×C5×#41—42no—
82C2×C5×#41—42no—
83C2×C5×#41—42no—
84C2×C5×#41D414yes—
85C2×C5×#41C2314yes—
86C2×C5×#41C2314yescomplemented
87C22×C5×Q8D411yescharacteristic
88C22×C5×Q8C2311yescharacteristic
89C22×C5×D4—21no—
90C22×C5×D4—21no—
91C22×C5×D4—21no—
92C22×C5×D4D411yescharacteristic
93C22×C5×D4D411yescharacteristic
94C22×C5×D4D411yescharacteristic
95C22×C5×D4C2311yescharacteristic
96C23×C4×C5—21no—
97C23×C4×C5—21no—
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C23×C4×C5C2311yescharacteristic
101C22×C22⋊D5—21no—
102C22×C22⋊D5—21no—
103C22×C22⋊D5—21no—
104C22×C22⋊D5—21no—
105C22×D20—21no—
106C22×D20—22no—
107C22×D20—42no—
108C22×D20—42no—
109C22×D20C2311yescharacteristic
110C22×D20C2311yescharacteristic
111C22×D20C2314yes—
112C5×C22⋊Q8—28no—
113C5×C22⋊Q8—22no—
114C5×C22⋊Q8—22no—
115C5×C22⋊Q8C2314yes—
116C5×C22⋊Q8C2314yescomplemented
117C5×#121—28no—
118C5×#121—28no—
119C5×#121—28no—
120C5×#121—22no—
121C5×#121—22no—
122C5×#121C2314yes—
123C5×#121C2314yescomplemented
124C2×C5×C4⋊C4—21no—
125C2×C5×C4⋊C4—22no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4—21no—
128C2×C5×C4⋊C4C2311yescharacteristic
129C2×C5×C4⋊C4C2311yescharacteristic
130C2×C5×C4⋊C4C2314yescomplemented
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4—21no—
134C2×C5×C22⋊C4—21no—
135C2×C22⋊Dic5—21no—
136#4093—28no—
137C2×#688—42no—
138C2×#688—42no—
139C2×#688C2314yes—
140C2×#688C2314yes—
141#4086—28no—
142#4083—28no—
143#4083—28no—
144C2×#686—42no—
145C2×#686—42no—
146C2×#686C2314yes—
147C2×#686C2314yes—
148#4076—22no—
149#4076—22no—
150#4076—22no—
151#4076—22no—
152#4076C2314yes—
153#4076C2314yes—
154#4076C2314yes—
155#4076C2314yes—
156C2×#685—21no—
157C2×#685—21no—
158C2×#685—21no—
159C2×#685—21no—
160#4072—22no—
161#4072C2314yes—
162C2×C4⋊Dic5C2311yescharacteristic
163C2×C4⋊Dic5C2311yescharacteristic
164C2×C4×Dic5—21no—
165C2×#681—42no—
166C2×#681C2314yescomplemented
167C22×#168—42no—
168C22×#168C2311yescharacteristic
169C22×#168C2311yescharacteristic
170C22×#168C2311yescharacteristic
171C22×#168C2311yescharacteristic
172C22×#168C2314yescomplemented
173#3967C2314yescomplemented
174#3967C2314yescomplemented
175#3964C2314yescomplemented
176#3964C2314yescomplemented
177C22⋊#168C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yescomplemented
180C22⋊#168C2314yescomplemented
181#3941C2314yes—
182#3941C2314yes—
183#3941C2314yes—
184#3941C2314yes—
185#3940C2314yescomplemented
186#3940C2314yescomplemented
187#3939C2314yescomplemented
188#3939C2314yescomplemented
189C2×#537D511yescharacteristic, complemented
190C2×#535—51no—
191#3198—516no—
192C2×#481—51no—
193C2×#485—51no—
194C2×#482—51no—
195C2×#480—51no—
196C2×#469—51no—
197C2×#468—51no—
198C2×#466—51no—
199C2×#465—51no—
200C2×#449—51no—
201C2×#449—51no—
202C2×#450—51no—
203C2×#447—51no—
204C2×#408—51no—
205C24×C5—21no—
206C24×C5C2×D411yescharacteristic
207C24×C5C2×D411yescharacteristic
208C24×C5C2×D411yescharacteristic
209C23×D5—21no—
210C23×D5—21no—
211C23×D5—24no—
212C23×D5—44no—
213C23×D5—82no—
214C23×D5—82no—
215C5×#41—48no—
216C5×#41—44no—
217C5×#41—44no—
218C5×#41—44no—
219C5×#41—44no—
220C5×#41—48no—
221C2×C5×Q8—21no—
222C2×C5×Q8—22no—
223C2×C5×Q8—22no—
224C2×C5×Q8—42no—
225C2×C5×Q8C2×D414yes—
226C2×C5×Q8C2412yes—
227C2×C5×D4—24no—
228C2×C5×D4—24no—
229C2×C5×D4—24no—
230C2×C5×D4—21no—
231C2×C5×D4—22no—
232C2×C5×D4—22no—
233C2×C5×D4—42no—
234C2×C5×D4—42no—
235C2×C5×D4—42no—
236C2×C5×D4—44no—
237C2×C5×D4—82no—
238C2×C5×D4—82no—
239C2×C5×D4C2×D414yes—
240C2×C5×D4C2×D414yes—
241C2×C5×D4C2×D414yes—
242C2×C5×D4C2412yes—
243C22×C4×C5—22no—
244C22×C4×C5—22no—
245C22×C4×C5—22no—
246C22×C4×C5—22no—
247C22×C4×C5—22no—
248C22×C4×C5—22no—
249C22×C4×C5—21no—
250C22×C4×C5—21no—
251C22×C4×C5—21no—
252C22×C4×C5—24no—
253C22×C4×C5—24no—
254C22×C4×C5—44no—
255C22×C4×C5—82no—
256C22×C4×C5C2×D411yescharacteristic
257C22×C4×C5C2×D411yescharacteristic
258C22×C4×C5C2×D411yescharacteristic
259C22×C4×C5C2×D412yes—
260C22×C4×C5C2×D412yes—
261C22×C4×C5C2×D412yes—
262C22×C4×C5C2412yes—
263C22×C4×C5C2412yes—
264C22×C4×C5C2412yes—
265C22×C4×C5C2411yescharacteristic
266C2×C22⋊D5—24no—
267C2×C22⋊D5—24no—
268C2×C22⋊D5—24no—
269C2×C22⋊D5—24no—
270C2×C22⋊D5—82no—
271C2×C22⋊D5—82no—
272C2×C22⋊D5—82no—
273C2×C22⋊D5—82no—
274C22×Dic5—21no—
275C22×Dic5—21no—
276C2×D20—22no—
277C2×D20—22no—
278C2×D20—22no—
279C2×D20—22no—
280C2×D20—21no—
281C2×D20—21no—
282C2×D20—24no—
283C2×D20—44no—
284C2×D20—44no—
285C2×D20—44no—
286C2×D20—48no—
287C2×D20C2412yes—
288C2×D20C2412yes—
289C5×C4⋊C4—21no—
290C5×C4⋊C4—21no—
291C5×C4⋊C4—24no—
292C5×C4⋊C4—24no—
293C5×C4⋊C4—24no—
294C5×C4⋊C4C2412yes—
295C5×C4⋊C4C2412yes—
296C5×C22⋊C4—24no—
297C5×C22⋊C4—24no—
298C5×C22⋊C4—24no—
299C5×C22⋊C4—24no—
300C22⋊Dic5—24no—
301#688—44no—
302#688—44no—
303#686—44no—
304#686—44no—
305#685—24no—
306#685—24no—
307#685—24no—
308#685—24no—
309C4⋊Dic5—21no—
310C4⋊Dic5—21no—
311C4⋊Dic5C2412yes—
312C4⋊Dic5C2412yes—
313C4×Dic5—24no—
314#681—44no—
315C2×#168—22no—
316C2×#168—22no—
317C2×#168—22no—
318C2×#168—22no—
319C2×#168—44no—
320C2×#168C2412yes—
321C2×#168C2412yes—
322C2×#168C2412yes—
323C2×#168C2412yes—
324C22×#41C2×D511yescharacteristic
325C22×#41C2×D511yescharacteristic, complemented
326C23×D4—51no—
327C22×SD16—51no—
328C22×SD16—51no—
329C22×D8—51no—
330C22×D8—51no—
331C22×M16—51no—
332C23×C8—51no—
333#537—24no—
334#537C2×D518yescomplemented
335#535—58no—
336#535—104no—
337C2×#127—101no—
338C2×#124—101no—
339C2×C22⋊Q8—21no—
340C2×C22⋊Q8C2×D511yescharacteristic
341C2×C22⋊Q8C2×D511yescharacteristic, complemented
342C2×#121—21no—
343C2×#121—21no—
344C2×#121—21no—
345C2×#121—51no—
346C2×#121—51no—
347C2×#121—51no—
348C2×#121—51no—
349C2×#121C2×D511yescharacteristic
350C2×#121C2×D511yescharacteristic, complemented
351C2×#120—101no—
352C2×#120—101no—
353C2×#117—51no—
354C22×C4⋊C4C2×D511yescharacteristic, complemented
355#485—58no—
356#482—58no—
357#481—58no—
358#480—58no—
359#469—58no—
360#468—58no—
361#466—58no—
362#465—58no—
363#450—58no—
364#449—58no—
365#449—58no—
366#447—58no—
367C2×#107—51no—
368C2×#107—51no—
369C2×#106—51no—
370C2×#106—51no—
371C2×#103—51no—
372C2×#103—51no—
373C2×#102—51no—
374C2×#102—51no—
375C2×#102—51no—
376C2×#102—51no—
377C2×#102—51no—
378C2×#102—51no—
379#408—58no—
380C2×C22⋊C8—51no—
381C2×C22⋊C8—51no—
382C2×C22⋊C8—51no—
383C2×C22⋊C8—51no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—22no—
392C23×C5—22no—
393C23×C5—22no—
394C23×C5—42no—
395C23×C5—42no—
396C23×C5—42no—
397C23×C5C22×D412yes—
398C23×C5C22×D412yes—
399C23×C5C22×D412yes—
400C23×C5C22×D411yescharacteristic
401C22×D5—22no—
402C22×D5—22no—
403C22×D5—48no—
404C22×D5—42no—
405C22×D5—42no—
406C22×D5—42no—
407C22×D5—42no—
408C22×D5—42no—
409C22×D5—42no—
410C22×D5—84no—
411C22×D5—84no—
412C22×D5—816no—
413C5×Q8—22no—
414C5×Q8—22no—
415C5×Q8—44no—
416C5×Q8—42no—
417C5×D4—22no—
418C5×D4—22no—
419C5×D4—44no—
420C5×D4—44no—
421C5×D4—44no—
422C5×D4—48no—
423C5×D4—42no—
424C5×D4—84no—
425C5×D4—84no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—24no—
430C2×C4×C5—24no—
431C2×C4×C5—24no—
432C2×C4×C5—22no—
433C2×C4×C5—22no—
434C2×C4×C5—22no—
435C2×C4×C5—22no—
436C2×C4×C5—22no—
437C2×C4×C5—22no—
438C2×C4×C5—22no—
439C2×C4×C5—22no—
440C2×C4×C5—22no—
441C2×C4×C5—48no—
442C2×C4×C5—42no—
443C2×C4×C5—42no—
444C2×C4×C5—42no—
445C2×C4×C5—84no—
446C2×C4×C5C22×D412yes—
447C2×C4×C5C22×D412yes—
448C2×C4×C5C22×D412yes—
449C2×C4×C5C22×D411yescharacteristic
450C2×C4×C5H(5,𝔽2)12yes—
451C2×C4×C5H(5,𝔽2)12yes—
452C2×C4×C5C2511yescharacteristic
453C22⋊D5—84no—
454C22⋊D5—84no—
455C22⋊D5—84no—
456C22⋊D5—84no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—42no—
460C2×Dic5—42no—
461D20—22no—
462D20—22no—
463D20—22no—
464D20—22no—
465D20—48no—
466D20—42no—
467D20—42no—
468#168—22no—
469#168—22no—
470#168—22no—
471#168—22no—
472C25—101no—
473C2×#41—22no—
474C2×#41—42no—
475C2×#41—42no—
476C2×#41—42no—
477C2×#41—42no—
478C2×#41C22⋊D514yes—
479C2×#41C22×D514yes—
480C2×#41C22×D514yescomplemented
481C22×Q8C22⋊D511yescharacteristic
482C22×Q8C22×D511yescharacteristic
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—51no—
487C22×D4—51no—
488C22×D4—54no—
489C22×D4—101no—
490C22×D4—101no—
491C22×D4—101no—
492C22×D4—101no—
493C22×D4—101no—
494C22×D4—102no—
495C22×D4—202no—
496C22×D4—202no—
497C22×D4C22⋊D511yescharacteristic
498C22×D4C22⋊D511yescharacteristic
499C22×D4C22⋊D511yescharacteristic
500C22×D4C22×D511yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506C2×SD16—54no—
507C2×SD16—54no—
508C2×SD16—202no—
509C2×SD16—202no—
510C2×D8—54no—
511C2×D8—54no—
512C2×D8—202no—
513C2×D8—202no—
514C2×M16—54no—
515C2×M16—202no—
516C22×C8—51no—
517C22×C8—51no—
518C22×C8—51no—
519C22×C8—51no—
520C22×C8—54no—
521C22×C8—202no—
522#127—108no—
523#124—108no—
524C22⋊Q8—28no—
525C22⋊Q8—22no—
526C22⋊Q8—22no—
527C22⋊Q8C22×D514yes—
528C22⋊Q8C22×D514yescomplemented
529#121—28no—
530#121—28no—
531#121—28no—
532#121—22no—
533#121—22no—
534#121—54no—
535#121—54no—
536#121—54no—
537#121—54no—
538#121—102no—
539#121—102no—
540#121—102no—
541#121—102no—
542#121C22×D514yes—
543#121C22×D514yescomplemented
544#120—108no—
545#120—108no—
546#117—54no—
547#117—102no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—51no—
553C2×C4⋊C4—51no—
554C2×C4⋊C4C22×D511yescharacteristic
555C2×C4⋊C4C22×D511yescharacteristic
556C2×C4⋊C4C22×D514yescomplemented
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—101no—
562C2×C22⋊C4—101no—
563C2×C22⋊C4—101no—
564C2×C22⋊C4—101no—
565C2×C22⋊C4—101no—
566C2×C42—101no—
567#107—54no—
568#107—54no—
569#106—54no—
570#106—54no—
571#103—54no—
572#103—54no—
573#102—54no—
574#102—54no—
575#102—54no—
576#102—54no—
577#102—54no—
578#102—54no—
579C22⋊C8—54no—
580C22⋊C8—54no—
581C22⋊C8—54no—
582C22⋊C8—54no—
583C22×C5—22no—
584C22×C5—22no—
585C22×C5—22no—
586C22×C5—22no—
587C22×C5—22no—
588C22×C5—22no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—44no—
593C22×C5—44no—
594C22×C5—44no—
595C22×C5—42no—
596C22×C5—42no—
597C22×C5—42no—
598C22×C5—84no—
599C22×C5#53412yes—
600C22×C5#57612yes—
601C22×C5#57712yes—
602C22×C5C23×D411yescharacteristic
603C2×D5—42no—
604C2×D5—42no—
605C2×D5—42no—
606C2×D5—42no—
607C2×D5—42no—
608C2×D5—42no—
609C2×D5—816no—
610C2×D5—84no—
611C2×D5—84no—
612C4×C5—22no—
613C4×C5—22no—
614C4×C5—22no—
615C4×C5—42no—
616C4×C5—42no—
617C4×C5—42no—
618C4×C5#53412yes—
619C4×C5C2×H(5,𝔽2)11yescharacteristic
620C4×C5C2×H(5,𝔽2)11yescharacteristic
621Dic5—42no—
622Dic5—42no—
623C24—21no—
624C24—101no—
625C24—101no—
626C24—104no—
627C24—204no—
628C24—402no—
629C24—402no—
630C24C2×C22⋊D511yescharacteristic
631C24C2×C22⋊D511yescharacteristic
632C24C2×C22⋊D511yescharacteristic
633#41—48no—
634#41—44no—
635#41—44no—
636#41—44no—
637#41—44no—
638#41—48no—
639C2×Q8—21no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—42no—
643C2×Q8C2×C22⋊D514yes—
644C2×Q8C23×D512yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—21no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—52no—
656C2×D4—52no—
657C2×D4—82no—
658C2×D4—82no—
659C2×D4—104no—
660C2×D4—104no—
661C2×D4—104no—
662C2×D4—104no—
663C2×D4—102no—
664C2×D4—102no—
665C2×D4—102no—
666C2×D4—102no—
667C2×D4—101no—
668C2×D4—101no—
669C2×D4—104no—
670C2×D4—204no—
671C2×D4—204no—
672C2×D4—204no—
673C2×D4—208no—
674C2×D4—402no—
675C2×D4—402no—
676C2×D4—402no—
677C2×D4—402no—
678C2×D4C2×C22⋊D514yes—
679C2×D4C2×C22⋊D514yes—
680C2×D4C2×C22⋊D514yes—
681C2×D4C23×D512yes—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—44no—
694C22×C4—82no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4C2×C22⋊D512yes—
698C22×C4C2×C22⋊D512yes—
699C22×C4C2×C22⋊D512yes—
700C22×C4C2×C22⋊D511yescharacteristic
701C22×C4C2×C22⋊D511yescharacteristic
702C22×C4C2×C22⋊D511yescharacteristic
703C22×C4C23×D512yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D511yescharacteristic
707SD16—204no—
708SD16—204no—
709D8—204no—
710D8—204no—
711M16—204no—
712C2×C8—52no—
713C2×C8—52no—
714C2×C8—52no—
715C2×C8—52no—
716C2×C8—102no—
717C2×C8—102no—
718C2×C8—102no—
719C2×C8—102no—
720C2×C8—204no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—24no—
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—52no—
727C4⋊C4—52no—
728C4⋊C4—101no—
729C4⋊C4—101no—
730C4⋊C4C23×D512yes—
731C4⋊C4C23×D512yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—104no—
737C22⋊C4—104no—
738C22⋊C4—104no—
739C22⋊C4—104no—
740C22⋊C4—104no—
741C42—104no—
742C2×C5—42no—
743C2×C5—42no—
744C2×C5—42no—
745C2×C5—82no—
746C2×C5#319814yescomplemented
747C2×C5C2×#53411yescharacteristic
748C2×C5C2×#57611yescharacteristic
749C2×C5C2×#57711yescharacteristic
750D5—82no—
751D5—82no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—102no—
766C23—102no—
767C23—208no—
768C23—202no—
769C23—202no—
770C23—202no—
771C23—202no—
772C23—202no—
773C23—202no—
774C23—404no—
775C23—404no—
776C23—4016no—
777C23C22×C22⋊D512yes—
778C23C22×C22⋊D512yes—
779C23C22×C22⋊D512yes—
780C23C22×C22⋊D511yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—44no—
784Q8—42no—
785D4—22no—
786D4—22no—
787D4—44no—
788D4—44no—
789D4—44no—
790D4—48no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4—102no—
795D4—102no—
796D4—102no—
797D4—102no—
798D4—208no—
799D4—202no—
800D4—202no—
801D4—404no—
802D4—404no—
803D4—404no—
804D4—404no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—48no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—84no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—202no—
828C2×C4—202no—
829C2×C4#414412yes—
830C2×C4#414412yes—
831C2×C4C22×C22⋊D512yes—
832C2×C4C22×C22⋊D512yes—
833C2×C4C22×C22⋊D512yes—
834C2×C4C22×C22⋊D511yescharacteristic
835C2×C4C24×D511yescharacteristic
836C8—102no—
837C8—102no—
838C8—102no—
839C8—102no—
840C5C2×#319811yescharacteristic, complemented, Sylow
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—84no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—4016no—
864C22—404no—
865C22—404no—
866C22#6613812yes—
867C22#6616912yes—
868C22#6617112yes—
869C22C23×C22⋊D511yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—202no—
877C4—202no—
878C4#6613812yes—
879C4C2×#414411yescharacteristic
880C4C2×#414411yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—82no—
885C2—402no—
886C2—402no—
887C2#1061515614yesdirect product factor
888C2C2×#6613811yescharacteristic
889C2C2×#6616911yescharacteristic
890C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#537C2
socleC23×C5C22×D4
hypercenterC2×#537D5
hypocenterC5C2×#3198
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×C5×#537C2semidirect
2. C2×#66164C2semidirect
3. C2×#65527C2semidirect
4. C2×#65527C2semidirect
5. C2×#65523C2semidirect
6. #10615156C2direct (N × H)
7. C2×#65335C2semidirect
8. C2×#65338C2semidirect
9. C2×#65337C2semidirect
10. C2×#65334C2semidirect
11. C2×#65325C2semidirect
12. C2×#65328C2semidirect
13. C2×#65327C2semidirect
14. C2×#65324C2semidirect
15. C2×#65257C2semidirect
16. C2×#65256C2semidirect
18. C22×C5×#41C22semidirect
21. C5×#537C22semidirect
24. C2×C5×C22⋊Q8C22semidirect
29. C2×C5×#121C22semidirect
30. C22×C5×C4⋊C4C22semidirect
32. #66164C22semidirect
46. C22×#681C22semidirect
47. C23×#168C22semidirect
48. #65527C22semidirect
49. #65527C22semidirect
50. #65523C22semidirect
51. C2×#3967C22semidirect
52. C2×#3967C22semidirect
53. C2×#3964C22semidirect
54. C2×#3964C22semidirect
57. C2×C22⋊#168C22semidirect
58. C2×C22⋊#168C22semidirect
59. #65338C22semidirect
60. #65337C22semidirect
61. #65335C22semidirect
62. #65334C22semidirect
63. #65328C22semidirect
64. #65327C22semidirect
65. #65325C22semidirect
66. #65324C22semidirect
67. #65257C22semidirect
68. #65256C22semidirect
73. C2×#3940C22semidirect
74. C2×#3940C22semidirect
75. C2×#3939C22semidirect
76. C2×#3939C22semidirect
86. C2×C5×#41C23semidirect
116. C5×C22⋊Q8C23semidirect
123. C5×#121C23semidirect
130. C2×C5×C4⋊C4C23semidirect
166. C2×#681C23semidirect
172. C22×#168C23semidirect
173. #3967C23semidirect
174. #3967C23semidirect
175. #3964C23semidirect
176. #3964C23semidirect
179. C22⋊#168C23semidirect
180. C22⋊#168C23semidirect
185. #3940C23semidirect
186. #3940C23semidirect
187. #3939C23semidirect
188. #3939C23semidirect
189. C2×#537D5semidirect
325. C22×#41C2×D5semidirect
334. #537C2×D5semidirect
341. C2×C22⋊Q8C2×D5semidirect
350. C2×#121C2×D5semidirect
354. C22×C4⋊C4C2×D5semidirect
480. C2×#41C22×D5semidirect
528. C22⋊Q8C22×D5semidirect
543. #121C22×D5semidirect
556. C2×C4⋊C4C22×D5semidirect
746. C2×C5#3198semidirect
840. C5C2×#3198semidirect
887. C2#10615156direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5372
C2×#661642
C2×#655272
C2×#655232
#106151562
C2×#653352
C2×#653382
C2×#653372
C2×#653342
C2×#653252
C2×#653282
C2×#653272
C2×#653242
C2×#652572
C2×#652562
C2×#31985