Finite Group Databasebeta

← C2×#10615160 #12970013

Subgroups — C2×#10615160 #12970013

Order 1280.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#537C211yesmaximal, characteristic, complemented
2C2×#66167C211yesmaximal, characteristic, complemented
3C2×#65528C211yesmaximal, characteristic, complemented
4C2×#65527C211yesmaximal, characteristic, complemented
5C2×#65523C211yesmaximal, characteristic, complemented
6#10615160C2116yesmaximal, direct product factor
7C2×#65336C211yesmaximal, characteristic, complemented
8C2×#65341C211yesmaximal, characteristic, complemented
9C2×#65337C211yesmaximal, characteristic, complemented
10C2×#65332C211yesmaximal, characteristic, complemented
11C2×#65326C211yesmaximal, characteristic, complemented
12C2×#65328C211yesmaximal, characteristic, complemented
13C2×#65330C211yesmaximal, characteristic, complemented
14C2×#65323C211yesmaximal, characteristic, complemented
15C2×#65260C211yesmaximal, characteristic, complemented
16C2×#65257C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×#41C2211yescharacteristic
19C22×#709C2211yescharacteristic
20C5×#537—24no—
21C5×#537C2218yescomplemented
22C2×C5×C22⋊Q8—21no—
23C2×C5×C22⋊Q8C2211yescharacteristic
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121—21no—
26C2×C5×#121—21no—
27C2×C5×#121—21no—
28C2×C5×#121C2211yescharacteristic
29C2×C5×#121C2211yescharacteristic
30C22×C5×C4⋊C4C2211yescharacteristic
31#66167—24no—
32#66167C2218yescomplemented
33C2×#4092—21no—
34C22×#689C2211yescharacteristic
35C22×#688C2211yescharacteristic
36C2×#4085—21no—
37C2×#4085—21no—
38C2×#4084—21no—
39C22×#687C2211yescharacteristic
40C22×#686C2211yescharacteristic
41C2×#4076C2211yescharacteristic
42C2×#4076C2211yescharacteristic
43C22×C4⋊Dic5C2211yescharacteristic
44C2×#4070C2211yescharacteristic
45C2×#4070C2211yescharacteristic
46C22×#681C2211yescharacteristic
47C23×#168C2211yescharacteristic
48#65528C2218yescomplemented
49#65527C2218yescomplemented
50#65523C2218yescomplemented
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56C2×C22⋊#168C2211yescharacteristic
57C2×C22⋊#168C2211yescharacteristic
58C2×C22⋊#168C2211yescharacteristic
59#65341C2218yescomplemented
60#65337C2218yescomplemented
61#65336C2218yescomplemented
62#65332C2218yescomplemented
63#65330C2218yescomplemented
64#65328C2218yescomplemented
65#65326C2218yescomplemented
66#65323C2218yescomplemented
67#65260C2218yescomplemented
68C2×#3942C2211yescharacteristic
69C2×#3942C2211yescharacteristic
70#65257C2218yescomplemented
71C2×#3941C2211yescharacteristic
72C2×#3941C2211yescharacteristic
73C2×#3940C2211yescharacteristic
74C2×#3940C2211yescharacteristic
75C2×#3940C2211yescharacteristic
76C2×#3940C2211yescharacteristic
77C2×#3204—51nomaximal, Sylow
78C2×C5×#41—22no—
79C2×C5×#41—42no—
80C2×C5×#41—42no—
81C2×C5×#41—42no—
82C2×C5×#41—42no—
83C2×C5×#41D414yes—
84C2×C5×#41C2314yes—
85C2×C5×#41C2314yes—
86C22×C5×Q8D411yescharacteristic
87C22×C5×Q8C2311yescharacteristic
88C22×C5×D4—21no—
89C22×C5×D4—21no—
90C22×C5×D4—21no—
91C22×C5×D4D411yescharacteristic
92C22×C5×D4D411yescharacteristic
93C22×C5×D4D411yescharacteristic
94C22×C5×D4C2311yescharacteristic
95C23×C4×C5—21no—
96C23×C4×C5—21no—
97C23×C4×C5C2311yescharacteristic
98C23×C4×C5C2311yescharacteristic
99C23×C4×C5C2311yescharacteristic
100C22×C22⋊D5—21no—
101C22×C22⋊D5—21no—
102C22×C22⋊D5—21no—
103C23×Dic5—21no—
104C2×#709—22no—
105C2×#709—42no—
106C2×#709—42no—
107C2×#709C2314yes—
108C22×D20C2311yescharacteristic
109C22×C4×D5—21no—
110C22×Dic10C2311yescharacteristic
111C5×C22⋊Q8—28no—
112C5×C22⋊Q8—22no—
113C5×C22⋊Q8—22no—
114C5×C22⋊Q8C2314yes—
115C5×C22⋊Q8C2314yes—
116C5×#121—28no—
117C5×#121—28no—
118C5×#121—28no—
119C5×#121—22no—
120C5×#121—22no—
121C5×#121C2314yes—
122C5×#121C2314yes—
123C2×C5×C4⋊C4—21no—
124C2×C5×C4⋊C4—22no—
125C2×C5×C4⋊C4—21no—
126C2×C5×C4⋊C4—21no—
127C2×C5×C4⋊C4C2311yescharacteristic
128C2×C5×C4⋊C4C2311yescharacteristic
129C2×C5×C4⋊C4C2314yes—
130C2×C5×C22⋊C4—21no—
131C2×C5×C22⋊C4—21no—
132C2×C5×C22⋊C4—21no—
133C2×C5×C22⋊C4—21no—
134C2×C22⋊Dic5—21no—
135C2×C22⋊Dic5—21no—
136#4092—28no—
137C2×#689—42no—
138C2×#689C2314yes—
139C2×#688—42no—
140C2×#688C2314yes—
141#4085—28no—
142#4085—28no—
143#4084—28no—
144C2×#687—42no—
145C2×#687C2314yes—
146C2×#686—42no—
147C2×#686C2314yes—
148#4076—22no—
149#4076—22no—
150#4076C2314yes—
151#4076C2314yes—
152C2×#685—21no—
153C2×#685—21no—
154C2×C4⋊Dic5—21no—
155C2×C4⋊Dic5—22no—
156C2×C4⋊Dic5C2314yes—
157C2×C4⋊Dic5C2311yescharacteristic
158C2×C4⋊Dic5C2311yescharacteristic
159#4070—22no—
160#4070—22no—
161#4070C2314yes—
162#4070C2314yes—
163C2×#683—21no—
164C2×#683—21no—
165C2×#681—42no—
166C2×#681C2314yes—
167C22×#168—42no—
168C22×#168C2311yescharacteristic
169C22×#168C2311yescharacteristic
170C22×#168C2311yescharacteristic
171C22×#168C2311yescharacteristic
172C22×#168C2314yes—
173#3967C2314yes—
174#3967C2314yes—
175#3964C2314yes—
176#3964C2314yes—
177C22⋊#168C2314yes—
178C22⋊#168C2314yes—
179C22⋊#168C2314yes—
180C22⋊#168C2314yes—
181#3942C2314yes—
182#3942C2314yes—
183#3941C2314yes—
184#3941C2314yes—
185#3940C2314yes—
186#3940C2314yes—
187#3940C2314yes—
188#3940C2314yes—
189C2×#537—51no—
190C2×#537D511yescharacteristic, complemented
191#3204—516no—
192C2×#481—51no—
193C2×#481—51no—
194C2×#483—51no—
195C2×#483—51no—
196C2×#470—51no—
197C2×#469—51no—
198C2×#465—51no—
199C2×#465—51no—
200C2×#452—51no—
201C2×#452—51no—
202C2×#449—51no—
203C2×#449—51no—
204C2×#408—51no—
205C24×C5—21no—
206C24×C5C2×D411yescharacteristic
207C24×C5C2×D411yescharacteristic
208C24×C5C2×D411yescharacteristic
209C23×D5—21no—
210C5×#41—48no—
211C5×#41—44no—
212C5×#41—44no—
213C5×#41—44no—
214C5×#41—44no—
215C5×#41—48no—
216C2×C5×Q8—21no—
217C2×C5×Q8—22no—
218C2×C5×Q8—22no—
219C2×C5×Q8—42no—
220C2×C5×Q8C2×D414yes—
221C2×C5×Q8C2412yes—
222C2×C5×D4—24no—
223C2×C5×D4—24no—
224C2×C5×D4—24no—
225C2×C5×D4—21no—
226C2×C5×D4—22no—
227C2×C5×D4—22no—
228C2×C5×D4—42no—
229C2×C5×D4—42no—
230C2×C5×D4—42no—
231C2×C5×D4—44no—
232C2×C5×D4—82no—
233C2×C5×D4—82no—
234C2×C5×D4C2×D414yes—
235C2×C5×D4C2×D414yes—
236C2×C5×D4C2×D414yes—
237C2×C5×D4C2412yes—
238C22×C4×C5—22no—
239C22×C4×C5—22no—
240C22×C4×C5—22no—
241C22×C4×C5—22no—
242C22×C4×C5—22no—
243C22×C4×C5—22no—
244C22×C4×C5—21no—
245C22×C4×C5—21no—
246C22×C4×C5—21no—
247C22×C4×C5—24no—
248C22×C4×C5—24no—
249C22×C4×C5—44no—
250C22×C4×C5—82no—
251C22×C4×C5C2×D411yescharacteristic
252C22×C4×C5C2×D411yescharacteristic
253C22×C4×C5C2×D411yescharacteristic
254C22×C4×C5C2×D412yes—
255C22×C4×C5C2×D412yes—
256C22×C4×C5C2×D412yes—
257C22×C4×C5C2412yes—
258C22×C4×C5C2412yes—
259C22×C4×C5C2412yes—
260C22×C4×C5C2411yescharacteristic
261C2×C22⋊D5—24no—
262C2×C22⋊D5—24no—
263C2×C22⋊D5—24no—
264C2×C22⋊D5—44no—
265C2×C22⋊D5—82no—
266C2×C22⋊D5—82no—
267C22×Dic5—21no—
268C22×Dic5—21no—
269C22×Dic5—21no—
270C22×Dic5—24no—
271C22×Dic5—82no—
272#709—44no—
273#709—44no—
274#709—48no—
275C2×D20—22no—
276C2×D20—22no—
277C2×D20—21no—
278C2×D20C2412yes—
279C2×C4×D5—24no—
280C2×C4×D5—44no—
281C2×Dic10—22no—
282C2×Dic10—22no—
283C2×Dic10—21no—
284C2×Dic10C2412yes—
285C5×C4⋊C4—24no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4—24no—
289C5×C4⋊C4—24no—
290C5×C4⋊C4C2412yes—
291C5×C4⋊C4C2412yes—
292C5×C22⋊C4—24no—
293C5×C22⋊C4—24no—
294C5×C22⋊C4—24no—
295C5×C22⋊C4—24no—
296C22⋊Dic5—24no—
297C22⋊Dic5—24no—
298#689—44no—
299#688—44no—
300#687—44no—
301#686—44no—
302#685—24no—
303#685—24no—
304C4⋊Dic5—21no—
305C4⋊Dic5—21no—
306C4⋊Dic5—24no—
307C4⋊Dic5C2412yes—
308C4⋊Dic5C2412yes—
309#683—24no—
310#683—24no—
311#681—44no—
312C2×#168—22no—
313C2×#168—22no—
314C2×#168—22no—
315C2×#168—22no—
316C2×#168—44no—
317C2×#168C2412yes—
318C2×#168C2412yes—
319C2×#168C2412yes—
320C2×#168C2412yes—
321C22×#41—51no—
322C22×#41C2×D511yescharacteristic
323C22×#41C2×D511yescharacteristic
324C22×Q16—51no—
325C22×SD16—51no—
326C22×SD16—51no—
327C22×D8—51no—
328C22×M16—51no—
329C23×C8—51no—
330#537—24no—
331#537—58no—
332#537—104no—
333#537C2×D518yescomplemented
334C2×C22⋊Q8—21no—
335C2×C22⋊Q8—51no—
336C2×C22⋊Q8—51no—
337C2×C22⋊Q8—101no—
338C2×C22⋊Q8C2×D511yescharacteristic
339C2×C22⋊Q8C2×D511yescharacteristic
340C2×#121—21no—
341C2×#121—21no—
342C2×#121—21no—
343C2×#121—51no—
344C2×#121—51no—
345C2×#121—101no—
346C2×#121—101no—
347C2×#121—101no—
348C2×#121C2×D511yescharacteristic
349C2×#121C2×D511yescharacteristic
350C22×C4⋊C4—51no—
351C22×C4⋊C4C2×D511yescharacteristic
352#483—58no—
353#483—58no—
354#481—58no—
355#481—58no—
356#470—58no—
357#469—58no—
358#465—58no—
359#465—58no—
360#452—58no—
361#452—58no—
362#449—58no—
363#449—58no—
364C2×#106—51no—
365C2×#106—51no—
366C2×#106—51no—
367C2×#106—51no—
368C2×#103—51no—
369C2×#103—51no—
370C2×#103—51no—
371C2×#103—51no—
372C2×#102—51no—
373C2×#102—51no—
374C2×#102—51no—
375C2×#102—51no—
376#408—58no—
377C2×C22⋊C8—51no—
378C2×C22⋊C8—51no—
379C2×C22⋊C8—51no—
380C2×C22⋊C8—51no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—22no—
385C23×C5—22no—
386C23×C5—22no—
387C23×C5—22no—
388C23×C5—22no—
389C23×C5—22no—
390C23×C5—22no—
391C23×C5—42no—
392C23×C5—42no—
393C23×C5—42no—
394C23×C5C22×D412yes—
395C23×C5C22×D412yes—
396C23×C5C22×D412yes—
397C23×C5C22×D411yescharacteristic
398C22×D5—22no—
399C22×D5—42no—
400C22×D5—42no—
401C22×D5—42no—
402C5×Q8—22no—
403C5×Q8—22no—
404C5×Q8—44no—
405C5×Q8—42no—
406C5×D4—22no—
407C5×D4—22no—
408C5×D4—44no—
409C5×D4—44no—
410C5×D4—44no—
411C5×D4—48no—
412C5×D4—42no—
413C5×D4—84no—
414C5×D4—84no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—24no—
419C2×C4×C5—24no—
420C2×C4×C5—24no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—48no—
431C2×C4×C5—42no—
432C2×C4×C5—42no—
433C2×C4×C5—42no—
434C2×C4×C5—84no—
435C2×C4×C5C22×D412yes—
436C2×C4×C5C22×D412yes—
437C2×C4×C5C22×D412yes—
438C2×C4×C5C22×D411yescharacteristic
439C2×C4×C5H(5,𝔽2)12yes—
440C2×C4×C5H(5,𝔽2)12yes—
441C2×C4×C5C2511yescharacteristic
442C22⋊D5—48no—
443C22⋊D5—84no—
444C22⋊D5—84no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—42no—
449C2×Dic5—42no—
450C2×Dic5—42no—
451C2×Dic5—84no—
452D20—22no—
453D20—22no—
454D20—42no—
455C4×D5—48no—
456Dic10—22no—
457Dic10—22no—
458Dic10—42no—
459#168—22no—
460#168—22no—
461#168—22no—
462#168—22no—
463C2×#41—22no—
464C2×#41—42no—
465C2×#41—42no—
466C2×#41—42no—
467C2×#41—42no—
468C2×#41—54no—
469C2×#41—102no—
470C2×#41—202no—
471C2×#41—202no—
472C2×#41C22⋊D514yes—
473C2×#41C22×D514yes—
474C2×#41C22×D514yes—
475C22×Q8—51no—
476C22×Q8C22⋊D511yescharacteristic
477C22×Q8C22×D511yescharacteristic
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—51no—
482C22×D4—101no—
483C22×D4—101no—
484C22×D4—101no—
485C22×D4C22⋊D511yescharacteristic
486C22×D4C22⋊D511yescharacteristic
487C22×D4C22⋊D511yescharacteristic
488C22×D4C22×D511yescharacteristic
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—101no—
492C23×C4—101no—
493C23×C4C22×D511yescharacteristic
494C23×C4C22×D511yescharacteristic
495C23×C4C22×D511yescharacteristic
496C2×Q16—54no—
497C2×Q16—202no—
498C2×SD16—54no—
499C2×SD16—54no—
500C2×SD16—202no—
501C2×SD16—202no—
502C2×D8—54no—
503C2×D8—202no—
504C2×M16—54no—
505C2×M16—202no—
506C22×C8—51no—
507C22×C8—51no—
508C22×C8—51no—
509C22×C8—51no—
510C22×C8—54no—
511C22×C8—202no—
512C22⋊Q8—28no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—54no—
516C22⋊Q8—54no—
517C22⋊Q8—108no—
518C22⋊Q8—102no—
519C22⋊Q8—102no—
520C22⋊Q8C22×D514yes—
521C22⋊Q8C22×D514yes—
522#121—28no—
523#121—28no—
524#121—28no—
525#121—22no—
526#121—22no—
527#121—54no—
528#121—54no—
529#121—108no—
530#121—108no—
531#121—108no—
532#121—102no—
533#121—102no—
534#121C22×D514yes—
535#121C22×D514yes—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—54no—
543C2×C4⋊C4—101no—
544C2×C4⋊C4—102no—
545C2×C4⋊C4—101no—
546C2×C4⋊C4—101no—
547C2×C4⋊C4C22×D511yescharacteristic
548C2×C4⋊C4C22×D511yescharacteristic
549C2×C4⋊C4C22×D514yes—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—101no—
555C2×C22⋊C4—101no—
556C2×C22⋊C4—101no—
557C2×C22⋊C4—101no—
558#106—54no—
559#106—54no—
560#106—54no—
561#106—54no—
562#103—54no—
563#103—54no—
564#103—54no—
565#103—54no—
566#102—54no—
567#102—54no—
568#102—54no—
569#102—54no—
570C22⋊C8—54no—
571C22⋊C8—54no—
572C22⋊C8—54no—
573C22⋊C8—54no—
574C22×C5—22no—
575C22×C5—22no—
576C22×C5—22no—
577C22×C5—22no—
578C22×C5—22no—
579C22×C5—22no—
580C22×C5—22no—
581C22×C5—22no—
582C22×C5—22no—
583C22×C5—44no—
584C22×C5—44no—
585C22×C5—44no—
586C22×C5—42no—
587C22×C5—42no—
588C22×C5—42no—
589C22×C5—84no—
590C22×C5#53412yes—
591C22×C5#57712yes—
592C22×C5#57712yes—
593C22×C5C23×D411yescharacteristic
594C2×D5—42no—
595C2×D5—42no—
596C2×D5—42no—
597C2×D5—84no—
598C4×C5—22no—
599C4×C5—22no—
600C4×C5—22no—
601C4×C5—42no—
602C4×C5—42no—
603C4×C5—42no—
604C4×C5#53412yes—
605C4×C5C2×H(5,𝔽2)11yescharacteristic
606C4×C5C2×H(5,𝔽2)11yescharacteristic
607Dic5—42no—
608Dic5—42no—
609Dic5—42no—
610C24—21no—
611C24—101no—
612C24C2×C22⋊D511yescharacteristic
613C24C2×C22⋊D511yescharacteristic
614C24C2×C22⋊D511yescharacteristic
615#41—48no—
616#41—44no—
617#41—44no—
618#41—44no—
619#41—44no—
620#41—48no—
621#41—204no—
622#41—204no—
623#41—208no—
624C2×Q8—21no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—42no—
628C2×Q8—52no—
629C2×Q8—101no—
630C2×Q8—102no—
631C2×Q8—102no—
632C2×Q8C2×C22⋊D514yes—
633C2×Q8C23×D512yes—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—21no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—52no—
645C2×D4—82no—
646C2×D4—82no—
647C2×D4—104no—
648C2×D4—104no—
649C2×D4—104no—
650C2×D4—102no—
651C2×D4—102no—
652C2×D4—101no—
653C2×D4—204no—
654C2×D4—402no—
655C2×D4—402no—
656C2×D4C2×C22⋊D514yes—
657C2×D4C2×C22⋊D514yes—
658C2×D4C2×C22⋊D514yes—
659C2×D4C23×D512yes—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—44no—
672C22×C4—82no—
673C22×C4—101no—
674C22×C4—101no—
675C22×C4—101no—
676C22×C4—104no—
677C22×C4—104no—
678C22×C4—204no—
679C22×C4—402no—
680C22×C4C2×C22⋊D512yes—
681C22×C4C2×C22⋊D512yes—
682C22×C4C2×C22⋊D512yes—
683C22×C4C2×C22⋊D511yescharacteristic
684C22×C4C2×C22⋊D511yescharacteristic
685C22×C4C2×C22⋊D511yescharacteristic
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C22×C4C23×D511yescharacteristic
690Q16—204no—
691SD16—204no—
692SD16—204no—
693D8—204no—
694M16—204no—
695C2×C8—52no—
696C2×C8—52no—
697C2×C8—52no—
698C2×C8—52no—
699C2×C8—102no—
700C2×C8—102no—
701C2×C8—102no—
702C2×C8—102no—
703C2×C8—204no—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—52no—
710C4⋊C4—52no—
711C4⋊C4—104no—
712C4⋊C4—101no—
713C4⋊C4—101no—
714C4⋊C4—104no—
715C4⋊C4—104no—
716C4⋊C4C23×D512yes—
717C4⋊C4C23×D512yes—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—104no—
723C22⋊C4—104no—
724C22⋊C4—104no—
725C22⋊C4—104no—
726C2×C5—42no—
727C2×C5—42no—
728C2×C5—42no—
729C2×C5—82no—
730C2×C5#320414yescomplemented
731C2×C5C2×#53411yescharacteristic
732C2×C5C2×#57711yescharacteristic
733C2×C5C2×#57711yescharacteristic
734D5—82no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—102no—
749C23—202no—
750C23—202no—
751C23—202no—
752C23C22×C22⋊D512yes—
753C23C22×C22⋊D512yes—
754C23C22×C22⋊D512yes—
755C23C22×C22⋊D511yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—44no—
759Q8—42no—
760Q8—102no—
761Q8—102no—
762Q8—202no—
763D4—22no—
764D4—22no—
765D4—44no—
766D4—44no—
767D4—44no—
768D4—48no—
769D4—42no—
770D4—84no—
771D4—84no—
772D4—102no—
773D4—102no—
774D4—208no—
775D4—202no—
776D4—404no—
777D4—404no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—84no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—208no—
802C2×C4—202no—
803C2×C4—202no—
804C2×C4—202no—
805C2×C4—404no—
806C2×C4#414412yes—
807C2×C4#414412yes—
808C2×C4C22×C22⋊D512yes—
809C2×C4C22×C22⋊D512yes—
810C2×C4C22×C22⋊D512yes—
811C2×C4C22×C22⋊D511yescharacteristic
812C2×C4C24×D511yescharacteristic
813C8—102no—
814C8—102no—
815C8—102no—
816C8—102no—
817C5C2×#320411yescharacteristic, complemented, Sylow
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—84no—
834C22—202no—
835C22—202no—
836C22—202no—
837C22—404no—
838C22#6613812yes—
839C22#6617012yes—
840C22#6617112yes—
841C22C23×C22⋊D511yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—202no—
849C4—202no—
850C4—202no—
851C4#6613812yes—
852C4C2×#414411yescharacteristic
853C4C2×#414411yescharacteristic
854C2—42no—
855C2—42no—
856C2—42no—
857C2—82no—
858C2—402no—
859C2#1061516014yesdirect product factor
860C2C2×#6613811yescharacteristic
861C2C2×#6617011yescharacteristic
862C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#537C2
socleC23×C5C22×D4
hypercenterC2×#537D5
hypocenterC5C2×#3204
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×#66167C2semidirect
3. C2×#65528C2semidirect
4. C2×#65527C2semidirect
5. C2×#65523C2semidirect
6. #10615160C2direct (N × H)
7. C2×#65336C2semidirect
8. C2×#65341C2semidirect
9. C2×#65337C2semidirect
10. C2×#65332C2semidirect
11. C2×#65326C2semidirect
12. C2×#65328C2semidirect
13. C2×#65330C2semidirect
14. C2×#65323C2semidirect
15. C2×#65260C2semidirect
16. C2×#65257C2semidirect
21. C5×#537C22semidirect
32. #66167C22semidirect
48. #65528C22semidirect
49. #65527C22semidirect
50. #65523C22semidirect
59. #65341C22semidirect
60. #65337C22semidirect
61. #65336C22semidirect
62. #65332C22semidirect
63. #65330C22semidirect
64. #65328C22semidirect
65. #65326C22semidirect
66. #65323C22semidirect
67. #65260C22semidirect
70. #65257C22semidirect
190. C2×#537D5semidirect
333. #537C2×D5semidirect
730. C2×C5#3204semidirect
817. C5C2×#3204semidirect
859. C2#10615160direct (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×#661672
C2×#655282
C2×#655272
C2×#655232
#106151602
C2×#653362
C2×#653412
C2×#653372
C2×#653322
C2×#653262
C2×#653282
C2×#653302
C2×#653232
C2×#652602
C2×#652572
C2×#32045