Finite Group Databasebeta

← #13007853

Subgroups — #13007853

Order 1280.

6930 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×Q8×#41C211yesmaximal, characteristic, complemented
2#10618947C211yesmaximal, characteristic, complemented
3#10618942C211yesmaximal, characteristic, complemented
4#10618933C212yesmaximal, complemented
5#10618932C211yesmaximal, characteristic, complemented
6#10618920C212yesmaximal, complemented
7#10618919C211yesmaximal, characteristic, complemented
8#10618850C216yesmaximal, complemented
9#10618849C213yesmaximal, complemented
10#10618828C216yesmaximal, complemented
11#10618827C213yesmaximal, complemented
12#10618662C213yesmaximal, complemented
13#10618648C213yesmaximal, complemented
14#10618178C213yesmaximal, complemented
15#10618178C216yesmaximal, complemented
16#10618175C216yesmaximal, complemented
17D5×#533C213yesmaximal, complemented
18#10617735C212yesmaximal
19C4×D5×#41C211yesmaximal, characteristic
20#41×Dic10C211yesmaximal, characteristic, complemented
21#41×Dic10C212yesmaximal, complemented
22Q8×#709C213yesmaximal, complemented
23C2×#65912C213yesmaximal, complemented
24C2×D5×#41C2211yescharacteristic
25C5×Q82C2211yescharacteristic, complemented
26C5×#557C2211yescharacteristic, complemented
27C5×#557C2212yescomplemented
28C5×#554C2213yescomplemented
29C5×#554C2216yescomplemented
30C5×D4×Q8C2213yescomplemented
31C5×#533C2213yescomplemented
32C5×#533C2216yescomplemented
33C4×C5×#41C2211yescharacteristic
34C4×C5×#41C2212yes—
35C2×C4×C5×Q8C2213yescomplemented
36#41×Dic5C2211yescharacteristic
37#41×Dic5C2212yes—
38Q8×C22⋊D5C2216yescomplemented
39C2×#4092C2213yes—
40C2×#4090C2213yescomplemented
41#66064C2216yescomplemented
42#66064C2213yescomplemented
43#66063C2216yes—
44#66063C2216yes—
45#66063C2216yescomplemented
46#66063C2216yescomplemented
47#66062C2213yes—
48#66062C2213yes—
49#66061C2213yescomplemented
50#66061C2216yescomplemented
51D5×C4⋊Q8C2213yescomplemented
52D5×C4⋊Q8C2213yescomplemented
53#66056C2216yescomplemented
54#66056C2213yescomplemented
55#66055C2213yescomplemented
56#66055C2216yescomplemented
57#66024C2216yescomplemented
58#66024C2216yescomplemented
59#66024C2216yescomplemented
60#66023C2216yes—
61#66023C2216yes—
62#66023C2216yescomplemented
63#66023C2216yescomplemented
64#66022C2216yes—
65D5×#125C2216yescomplemented
66#66019C2216yescomplemented
67#66019C2216yescomplemented
68#66019C2216yescomplemented
69#65970C22112yescomplemented
70#65970C22112yescomplemented
71#65970C22112yescomplemented
72#65969C2216yescomplemented
73#65969C22112yescomplemented
74#65968C22112yes—
75#65968C22112yes—
76#65966C2216yescomplemented
77#65966C22112yescomplemented
78D5×C22⋊Q8C2216yes—
79D5×C22⋊Q8C2216yes—
80#65957C22112yescomplemented
81#65957C22112yescomplemented
82#65956C2216yescomplemented
83#65956C2216yescomplemented
84#65913C2213yescomplemented
85#65913C2216yescomplemented
86#65912C2213yes—
87#65912C2213yes—
88#65912C2216yes—
89#65912C2213yes—
90#65912C2216yes—
91#65912C2216yes—
92#65912C2211yescharacteristic
93#65912C2213yescomplemented
94#65912C2213yescomplemented
95#65912C2216yescomplemented
96#65912C22112yescomplemented
97#65912C22112yescomplemented
98#65912C2213yescomplemented
99#65912C2216yescomplemented
100#65912C2213yescomplemented
101Q8×D20C2213yescomplemented
102#65908C2212yes—
103#65908C2212yes—
104C4×#713C2211yescharacteristic
105C4×#713C2211yescharacteristic
106#65906C2212yes—
107#65906C2212yes—
108C4×Q8×D5C2211yescharacteristic
109C4×Q8×D5C2211yescharacteristic
110C4×Q8×D5C2216yescomplemented
111C4×Q8×D5C2216yescomplemented
112#65904C2211yescharacteristic, complemented
113#65904C2212yescomplemented
114#65903C2212yescomplemented
115#65903C2212yescomplemented
116#65903C2212yescomplemented
117#65901C2213yescomplemented
118#65901C2216yescomplemented
119Q8×Dic10C2212yescomplemented
120Q8×Dic10C2211yescharacteristic, complemented
121Q8×Dic10C2213yescomplemented
122#65880C2216yes—
123#65880C2216yes—
124#65879C2216yes—
125#65879C2216yes—
126C4×D4×D5C2213yes—
127C4×D4×D5C2213yes—
128#65877C2213yescomplemented
129#65877C2216yescomplemented
130#65873C2216yescomplemented
131#65873C2216yescomplemented
132#65873C2216yescomplemented
133D4×Dic10C2213yescomplemented
134D4×Dic10C2216yescomplemented
135C4×#711C2213yes—
136C4×#711C2213yes—
137#65856C2213yes—
138#65856C2216yes—
139D5×#117C2216yes—
140D5×#117C2213yes—
141#65851C2216yescomplemented
142#65851C2216yescomplemented
143#65851C2216yescomplemented
144#65845C2216yescomplemented
145#65845C22112yescomplemented
146C2×#4043C2213yes—
147C2×#4042C2216yes—
148C2×#4035C2216yescomplemented
149C2×#4034C2213yescomplemented
150C4×#709C2213yes—
151C4×#709C2216yes—
152C2×#4018C2216yes—
153C2×C42×D5C2213yes—
154#65804C2213yescomplemented
155#65804C2216yescomplemented
156C2×C4×Dic10C2213yescomplemented
157C2×C4×Dic10C2216yescomplemented
158#62813—51nomaximal, Sylow
159C2×C5×#41C2311yescharacteristic
160C22×C5×Q8C2313yes—
161D5×#41Q8116yescomplemented
162C2×#713C2311yescharacteristic
163C2×Q8×D5C2316yes—
164C2×Q8×D5C2316yes—
165C2×Q8×D5C2311yescharacteristic
166C2×#711C2313yes—
167C2×D4×D5C2313yes—
168C2×#709C2313yes—
169C22×C4×D5C2313yes—
170C22×C4×D5C2313yes—
171C22×C4×D5C2313yes—
172C22×Dic10C2316yes—
173C22×Dic10C2313yes—
174C5×C4⋊Q8C2313yes—
175C5×C4⋊Q8C2316yes—
176C5×C4⋊Q8C2313yes—
177C5×C4⋊Q8C2316yes—
178C5×#125C2316yes—
179C5×#125C2316yes—
180C5×#125C2316yes—
181C5×C22⋊Q8C2316yes—
182C5×C22⋊Q8C2316yes—
183C5×C22⋊Q8C23112yes—
184C5×C22⋊Q8C23112yes—
185C4×C5×Q8C2311yescharacteristic
186C4×C5×Q8C2312yes—
187C4×C5×Q8C2313yes—
188C4×C5×Q8C2313yes—
189C4×C5×Q8C2316yes—
190C4×C5×Q8C2311yescharacteristic
191C4×C5×Q8C2312yes—
192C4×C5×Q8C2313yes—
193C4×C5×Q8C2316yes—
194C4×C5×Q8C2311yescharacteristic
195C4×C5×Q8C2316yes—
196C4×C5×D4C2313yes—
197C4×C5×D4C2313yes—
198C4×C5×D4C2316yes—
199C4×C5×D4C2316yes—
200C5×#117C2316yes—
201C5×#117C2313yes—
202C2×C5×C4⋊C4C2313yes—
203C2×C5×C4⋊C4C2316yes—
204C2×C42×C5C2313yes—
205C2×C42×C5C2316yes—
206#4092C2313yes—
207#4092C23112yes—
208#4092C2313yes—
209#4092C2316yes—
210#4092C2316yes—
211#4092C23112yes—
212#4092C2316yes—
213#4092C2311yescharacteristic
214#4092C2313yes—
215Q8×Dic5C2316yes—
216Q8×Dic5C2316yes—
217Q8×Dic5C2311yescharacteristic
218Q8×Dic5C2312yes—
219Q8×Dic5C2312yes—
220Q8×Dic5C2311yescharacteristic
221#4090C2313yes—
222#4090C23112yes—
223#4090C2316yes—
224#4090C23112yes—
225#4090C2313yes—
226#4090C2316yes—
227#4090C2316yes—
228#4090C2311yescharacteristic
229#4090C2313yes—
230D4×Dic5C2313yes—
231D4×Dic5C2313yes—
232D4×Dic5C2316yes—
233D4×Dic5C2316yes—
234C4×C22⋊D5C2316yes—
235C4×C22⋊D5C23112yes—
236C4×C22⋊D5C2316yes—
237C4×C22⋊D5C23112yes—
238C2×#685C2316yes—
239C2×#685C2316yes—
240#4072C2316yes—
241#4072C2313yes—
242C2×C4⋊Dic5C2313yes—
243C2×C4⋊Dic5C2316yes—
244#4070C23112yes—
245#4070C2316yes—
246#4070C2316yes—
247#4070C23112yes—
248C2×#683C2316yes—
249C2×#683C2316yes—
250C2×#683C2316yes—
251C2×#683C2316yes—
252C2×#683C2316yes—
253C2×C4×Dic5C2313yes—
254C2×C4×Dic5C2316yes—
255C2×C4×Dic5C2313yes—
256C2×C4×Dic5C2313yes—
257#4043C2313yes—
258#4043C2316yes—
259#4043C2313yes—
260#4043C23112yes—
261#4043C2311yescharacteristic
262#4043C2313yes—
263#4043C2316yes—
264#4043C2316yes—
265#4043C23112yes—
266#4042C2316yes—
267#4042C23112yes—
268#4042C23112yes—
269#4042C2316yes—
270#4042C23112yes—
271#4042C23112yes—
272#4042C2312yes—
273#4042C2316yes—
274#4042C2316yes—
275#4042C2316yes—
276#4042C2316yes—
277#4042C2316yes—
278#4042C23112yes—
279#4039C2313yes—
280#4039C2316yes—
281#4039C2316yes—
282#4039C2313yes—
283#4038C2316yes—
284#4038C2316yes—
285#4038C2313yes—
286#4038C2313yes—
287D5×C4⋊C4C2316yes—
288D5×C4⋊C4C2316yes—
289D5×C4⋊C4C2316yes—
290D5×C4⋊C4C2316yes—
291D5×C4⋊C4C2313yes—
292D5×C4⋊C4C2313yes—
293D5×C4⋊C4C23112yes—
294D5×C4⋊C4C23112yes—
295#4036C2316yes—
296#4036C2316yes—
297#4036C2316yes—
298#4036C2316yes—
299#4036C2316yes—
300#4036C2316yes—
301#4035C2316yes—
302#4035C23112yes—
303#4035C23112yes—
304#4035C23112yes—
305#4035C2316yes—
306#4035C23112yes—
307#4035C2312yes—
308#4035C2316yes—
309#4035C2316yes—
310#4035C2316yes—
311#4035C2316yes—
312#4035C2316yes—
313#4035C23112yes—
314#4034C2313yes—
315#4034C2316yes—
316#4034C2316yes—
317#4034C2316yes—
318#4034C23112yes—
319#4034C2313yes—
320#4034C2316yes—
321#4034C2316yes—
322#4034C2316yes—
323#4034C2316yes—
324#4034C2311yescharacteristic
325#4034C2313yes—
326#4034C2316yes—
327#4034C2316yes—
328#4034C23112yes—
329#4033C2313yes—
330#4033C2316yes—
331#4033C2316yes—
332#4033C2313yes—
333#4033C2316yes—
334#4033C23112yes—
335#4033C2316yes—
336#4033C23112yes—
337#4027C2316yes—
338#4027C2316yes—
339#4027C23112yes—
340#4027C23112yes—
341D5×C22⋊C4C2316yes—
342D5×C22⋊C4C23112yes—
343#4024C23112yes—
344#4024C23112yes—
345#4024C23112yes—
346#4024C23112yes—
347#4024C23112yes—
348#4024C23112yes—
349#4023C2316yes—
350#4023C23112yes—
351C4×D20C2313yes—
352C4×D20C2316yes—
353C4×D20C2313yes—
354C4×D20C2316yes—
355#4018C2312yes—
356#4018C2316yes—
357#4018C2316yes—
358#4018C2316yes—
359#4018C2316yes—
360#4018C2316yes—
361#4018C2316yes—
362#4018C2316yes—
363#4018C2316yes—
364C42×D5C2313yes—
365C42×D5C2311yescharacteristic
366C42×D5C2313yes—
367C42×D5C2313yes—
368C42×D5C2313yes—
369C42×D5C2313yes—
370C42×D5C2313yes—
371C42×D5C2313yes—
372C42×D5C23112yes—
373#4016C2316yes—
374#4016C2316yes—
375#4016C2316yes—
376#4015C2313yes—
377#4015C2313yes—
378#4015C2316yes—
379#4015C2316yes—
380C4×Dic10C2313yes—
381C4×Dic10C2316yes—
382C4×Dic10C2313yes—
383C4×Dic10C2316yes—
384C4×Dic10C2316yes—
385C4×Dic10C2313yes—
386C4×Dic10C2312yes—
387C4×Dic10C2311yescharacteristic
388C4×Dic10C2313yes—
389C4×Dic10C2316yes—
390C4×Dic10C2316yes—
391C4×Dic10C2316yes—
392C4×Dic10C2316yes—
393C4×Dic10C2316yes—
394C4×Dic10C2316yes—
395C4×Dic10C2316yes—
396C4×Dic10C2316yes—
397C4×Dic10C23112yes—
398C4×Dic10C2313yes—
399C4×Dic10C2316yes—
400#3504—52no—
401#3504—56no—
402#3503—51no—
403#3503—51no—
404#3503—53no—
405#3503—53no—
406#3502—51no—
407#3502—51no—
408#3502—52no—
409#3501—53no—
410#3501—56no—
411#3501—53no—
412Q8×#41—56no—
413Q8×#41—53no—
414Q8×#41—52no—
415Q8×#41—51no—
416Q8×#41—53no—
417Q8×#41D511yescharacteristic, complemented
418#3458—56no—
419C2×#533—53no—
420C2×#533—53no—
421#3428—52no—
422C2×C4×#41—51no—
423C23×D5C2413yes—
424C5×#41C2×Q818yescomplemented
425C2×C5×Q8—46no—
426C2×C5×Q8C2411yescharacteristic
427C2×C5×Q8C2413yes—
428C2×C5×Q8C2416yes—
429C2×C5×Q8C2416yes—
430C2×C5×Q8C2411yescharacteristic
431C2×C5×D4C2413yes—
432C22×C4×C5C2413yes—
433C22×C4×C5C2416yes—
434C22×C4×C5C2413yes—
435C22×C4×C5C2416yes—
436C22×C4×C5C2413yes—
437C2×C22⋊D5C2416yes—
438C22×Dic5C2413yes—
439C22×Dic5C2416yes—
440C22×Dic5C2416yes—
441C22×Dic5C2413yes—
442C22×Dic5C2413yes—
443#713C2×Q818yescomplemented
444Q8×D5—412no—
445Q8×D5—412no—
446Q8×D5C2×Q818yescomplemented
447#711C2×Q8124yescomplemented
448D4×D5C2×Q8124yescomplemented
449#709C2×Q8124yescomplemented
450C2×D20C2413yes—
451C2×C4×D5—46no—
452C2×C4×D5—46no—
453C2×C4×D5C2×Q8124yescomplemented
454C2×C4×D5C2411yescharacteristic
455C2×C4×D5C2411yescharacteristic
456C2×C4×D5C2413yes—
457C2×C4×D5C2413yes—
458C2×C4×D5C2413yes—
459C2×C4×D5C2413yes—
460C2×C4×D5C2413yes—
461C2×C4×D5C2413yes—
462C2×C4×D5C24112yes—
463C2×C4×D5C24112yes—
464C2×C4×D5C2411yescharacteristic
465C2×C4×D5C2413yes—
466C2×C4×D5C2413yes—
467C2×C4×D5C2413yes—
468C2×Dic10—412no—
469C2×Dic10—46no—
470C2×Dic10C2412yes—
471C2×Dic10C2411yescharacteristic
472C2×Dic10C2413yes—
473C2×Dic10C2416yes—
474C2×Dic10C2416yes—
475C2×Dic10C2416yes—
476C2×Dic10C2416yes—
477C2×Dic10C2416yes—
478C2×Dic10C24112yes—
479C2×Dic10C2413yes—
480C5×C4⋊C4C2411yescharacteristic
481C5×C4⋊C4C2412yes—
482C5×C4⋊C4C2416yes—
483C5×C4⋊C4C2416yes—
484C5×C4⋊C4C2416yes—
485C5×C4⋊C4C2413yes—
486C5×C4⋊C4C2416yes—
487C5×C4⋊C4C2413yes—
488C5×C4⋊C4C2413yes—
489C5×C4⋊C4C2416yes—
490C5×C4⋊C4C2416yes—
491C5×C4⋊C4C24112yes—
492C5×C4⋊C4C2416yes—
493C5×C22⋊C4C2416yes—
494C5×C22⋊C4C24112yes—
495C42×C5C2411yescharacteristic
496C42×C5C2412yes—
497C42×C5C2413yes—
498C42×C5C2416yes—
499C42×C5C2416yes—
500C42×C5C2413yes—
501C42×C5C2413yes—
502C42×C5C2416yes—
503C22⋊Dic5C2416yes—
504C22⋊Dic5C24112yes—
505#685C2412yes—
506#685C2412yes—
507#685C2416yes—
508#685C2416yes—
509#685C2416yes—
510#685C2416yes—
511#685C2416yes—
512#685C2416yes—
513#685C2416yes—
514#685C2416yes—
515C4⋊Dic5C2411yescharacteristic
516C4⋊Dic5C2412yes—
517C4⋊Dic5C2413yes—
518C4⋊Dic5C2416yes—
519C4⋊Dic5C2416yes—
520C4⋊Dic5C2416yes—
521C4⋊Dic5C2416yes—
522C4⋊Dic5C2413yes—
523C4⋊Dic5C2416yes—
524C4⋊Dic5C2413yes—
525C4⋊Dic5C2416yes—
526C4⋊Dic5C2416yes—
527C4⋊Dic5C24112yes—
528#683C2412yes—
529#683C2412yes—
530#683C2412yes—
531#683C2416yes—
532#683C2416yes—
533#683C2416yes—
534#683C2416yes—
535#683C2416yes—
536#683C2416yes—
537#683C2416yes—
538#683C2416yes—
539#683C2416yes—
540#683C2416yes—
541#683C2416yes—
542#683C24112yes—
543#683C24112yes—
544#683C24112yes—
545#683C2416yes—
546#683C2416yes—
547#683C2412yes—
548#683C2412yes—
549#683C2416yes—
550#683C2416yes—
551#683C2416yes—
552#683C2416yes—
553C4×Dic5C2411yescharacteristic
554C4×Dic5C2416yes—
555C4×Dic5C2413yes—
556C4×Dic5C2412yes—
557C4×Dic5C2413yes—
558C4×Dic5C2413yes—
559C4×Dic5C2416yes—
560C4×Dic5C2416yes—
561C4×Dic5C2413yes—
562C4×Dic5C2413yes—
563C4×Dic5C24112yes—
564C4×Dic5C24112yes—
565C4×Dic5C2411yescharacteristic
566C4×Dic5C2411yescharacteristic
567C4×Dic5C2413yes—
568C4×Dic5C2413yes—
569C4×Dic5C2413yes—
570C4×Dic5C2413yes—
571C22×#41—51no—
572Q82—56no—
573Q82—53no—
574Q82—52no—
575Q82—53no—
576Q82—51no—
577Q82C2×D511yescharacteristic, complemented
578#557—53no—
579#557—56no—
580#557—56no—
581#557—56no—
582#557—56no—
583#557—53no—
584#557—56no—
585#557—52no—
586#557—52no—
587#557—52no—
588#557—51no—
589#557—52no—
590#557C2×D511yescharacteristic, complemented
591#557C2×D512yescomplemented
592#554—53no—
593#554—56no—
594#554—56no—
595#554—56no—
596#554—56no—
597#554—56no—
598#554—512no—
599#554—512no—
600#554—512no—
601#554—512no—
602#554—53no—
603#554—56no—
604#554—56no—
605#554—56no—
606#554—56no—
607#554—53no—
608#554—56no—
609#554—56no—
610#554—512no—
611#554C2×D513yescomplemented
612#554C2×D516yescomplemented
613D4×Q8—56no—
614D4×Q8—56no—
615D4×Q8—53no—
616D4×Q8—56no—
617D4×Q8—512no—
618D4×Q8—53no—
619D4×Q8—56no—
620D4×Q8—53no—
621D4×Q8C2×D513yescomplemented
622#544—56no—
623#544—56no—
624#544—56no—
625#544—56no—
626#544—56no—
627#544—56no—
628#544—56no—
629#544—56no—
630#544—512no—
631#544—512no—
632#543—512no—
633#543—512no—
634#533—53no—
635#533—53no—
636#533—56no—
637#533—56no—
638#533—56no—
639#533—53no—
640#533—51no—
641#533—56no—
642#533—56no—
643#533—56no—
644#533—53no—
645#533—53no—
646#533—56no—
647#533—53no—
648#533—53no—
649#533—53no—
650#533—53no—
651#533—56no—
652#533—512no—
653#533—512no—
654#533—56no—
655#533—56no—
656#533—56no—
657#533—53no—
658#533—56no—
659#533C2×D513yescomplemented
660#533C2×D516yescomplemented
661C2×C4⋊Q8—53no—
662C2×C4⋊Q8—53no—
663C2×C4⋊Q8—53no—
664C2×C4⋊Q8—53no—
665C2×#125—56no—
666C2×#125—56no—
667C2×C22⋊Q8—53no—
668C2×C22⋊Q8—56no—
669C2×C22⋊Q8—56no—
670C2×C22⋊Q8—56no—
671C2×C22⋊Q8—53no—
672#520—52no—
673#520—52no—
674#520—56no—
675#520—56no—
676#519—52no—
677#519—52no—
678#518—56no—
679#518—56no—
680C4×#41—51no—
681C4×#41—52no—
682C4×#41—51no—
683C4×#41—51no—
684C4×#41—53no—
685C4×#41—53no—
686C4×#41—53no—
687C4×#41—56no—
688C4×#41—53no—
689C4×#41—56no—
690C4×#41C2×D511yescharacteristic
691C4×#41C2×D512yes—
692C2×C4×Q8—51no—
693C2×C4×Q8—51no—
694C2×C4×Q8—56no—
695C2×C4×Q8—56no—
696C2×C4×Q8—53no—
697C2×C4×Q8—56no—
698C2×C4×Q8C2×D513yescomplemented
699C2×C4×D4—53no—
700C2×C4×D4—53no—
701C2×#117—53no—
702C2×#117—56no—
703C2×#117—56no—
704C22×C42—53no—
705C23×C5C2513yes—
706C22×D5—43no—
707C22×D5—43no—
708C22×D5C22×Q8112yes—
709C22×D5C2511yescharacteristic
710C22×D5C2513yes—
711C5×Q8—26no—
712C5×Q8—22no—
713C5×Q8—46no—
714C5×Q8—46no—
715C5×Q8C22×Q814yes—
716C5×D4C22×Q8112yes—
717C2×C4×C5—26no—
718C2×C4×C5—46no—
719C2×C4×C5—43no—
720C2×C4×C5—46no—
721C2×C4×C5C22×Q8112yes—
722C2×C4×C5C2511yescharacteristic
723C2×C4×C5C2516yes—
724C2×C4×C5C2513yes—
725C2×C4×C5C2513yes—
726C2×C4×C5C2516yes—
727C2×C4×C5C2512yes—
728C2×C4×C5C2512yes—
729C2×C4×C5C2513yes—
730C2×C4×C5C2511yescharacteristic
731C2×C4×C5C2511yescharacteristic
732C22⋊D5C22×Q8124yes—
733C2×Dic5—26no—
734C2×Dic5—46no—
735C2×Dic5—46no—
736C2×Dic5—43no—
737C2×Dic5C22×Q8112yes—
738C2×Dic5C2511yescharacteristic
739C2×Dic5C2512yes—
740C2×Dic5C2512yes—
741C2×Dic5C2516yes—
742C2×Dic5C2516yes—
743C2×Dic5C2513yes—
744C2×Dic5C2513yes—
745C2×Dic5C2513yes—
746C2×Dic5C2511yescharacteristic
747C2×Dic5C2511yescharacteristic
748D20C22×Q8112yes—
749C4×D5—22no—
750C4×D5—26no—
751C4×D5—22no—
752C4×D5—26no—
753C4×D5—43no—
754C4×D5—43no—
755C4×D5—43no—
756C4×D5—43no—
757C4×D5—412no—
758C4×D5—412no—
759C4×D5C22×Q814yes—
760C4×D5C22×Q8112yes—
761C4×D5C22×Q8112yes—
762C4×D5C22×Q8112yes—
763Dic10—22no—
764Dic10—26no—
765Dic10—24no—
766Dic10—212no—
767Dic10—46no—
768Dic10—46no—
769Dic10—46no—
770Dic10—46no—
771Dic10—412no—
772Dic10C22×Q8112yes—
773C2×#41—516no—
774C2×#41—51no—
775C2×#41—53no—
776C2×#41—53no—
777C2×#41C22×D511yescharacteristic
778C22×Q8—51no—
779C22×Q8—56no—
780C22×Q8—56no—
781C22×Q8—56no—
782C22×Q8—53no—
783C22×Q8C22×D513yes—
784C22×D4—53no—
785C23×C4—53no—
786C23×C4—53no—
787C23×C4—53no—
788C4⋊Q8—53no—
789C4⋊Q8—51no—
790C4⋊Q8—56no—
791C4⋊Q8—56no—
792C4⋊Q8—53no—
793C4⋊Q8—53no—
794C4⋊Q8—56no—
795C4⋊Q8—512no—
796C4⋊Q8—512no—
797C4⋊Q8—53no—
798C4⋊Q8—51no—
799C4⋊Q8—56no—
800C4⋊Q8—56no—
801C4⋊Q8—56no—
802C4⋊Q8—56no—
803C4⋊Q8—56no—
804C4⋊Q8—53no—
805C4⋊Q8—53no—
806C4⋊Q8—512no—
807C4⋊Q8—512no—
808C4⋊Q8—56no—
809C4⋊Q8—56no—
810C4⋊Q8—56no—
811C4⋊Q8—56no—
812C4⋊Q8—53no—
813C4⋊Q8—53no—
814C4⋊Q8—56no—
815C4⋊Q8—56no—
816C4⋊Q8C22×D513yes—
817C4⋊Q8C22×D513yes—
818C4⋊Q8C22×D516yes—
819C4⋊Q8C22×D516yes—
820#125—56no—
821#125—52no—
822#125—512no—
823#125—56no—
824#125—56no—
825#125—56no—
826#125—56no—
827#125—56no—
828#125—56no—
829#125—56no—
830#125—56no—
831#125—512no—
832#125—512no—
833#125—512no—
834#125—512no—
835#125—56no—
836#125—56no—
837#125—56no—
838#125—56no—
839#125—56no—
840#125—56no—
841#125—56no—
842#125C22×D516yes—
843#125C22×D516yes—
844#125C22×D516yes—
845C22⋊Q8—53no—
846C22⋊Q8—51no—
847C22⋊Q8—56no—
848C22⋊Q8—56no—
849C22⋊Q8—53no—
850C22⋊Q8—53no—
851C22⋊Q8—56no—
852C22⋊Q8—512no—
853C22⋊Q8—512no—
854C22⋊Q8—56no—
855C22⋊Q8—56no—
856C22⋊Q8—512no—
857C22⋊Q8—512no—
858C22⋊Q8—56no—
859C22⋊Q8—52no—
860C22⋊Q8—53no—
861C22⋊Q8—51no—
862C22⋊Q8—512no—
863C22⋊Q8—56no—
864C22⋊Q8—56no—
865C22⋊Q8—56no—
866C22⋊Q8—56no—
867C22⋊Q8—56no—
868C22⋊Q8—56no—
869C22⋊Q8—53no—
870C22⋊Q8—53no—
871C22⋊Q8—56no—
872C22⋊Q8—56no—
873C22⋊Q8—56no—
874C22⋊Q8—512no—
875C22⋊Q8—512no—
876C22⋊Q8—512no—
877C22⋊Q8—512no—
878C22⋊Q8—512no—
879C22⋊Q8—512no—
880C22⋊Q8—512no—
881C22⋊Q8—512no—
882C22⋊Q8—512no—
883C22⋊Q8—512no—
884C22⋊Q8—512no—
885C22⋊Q8—512no—
886C22⋊Q8C22×D516yes—
887C22⋊Q8C22×D516yes—
888C22⋊Q8C22×D5112yes—
889C22⋊Q8C22×D5112yes—
890C4×Q8—51no—
891C4×Q8—51no—
892C4×Q8—56no—
893C4×Q8—56no—
894C4×Q8—52no—
895C4×Q8—52no—
896C4×Q8—53no—
897C4×Q8—53no—
898C4×Q8—512no—
899C4×Q8—56no—
900C4×Q8—56no—
901C4×Q8—512no—
902C4×Q8—56no—
903C4×Q8—56no—
904C4×Q8—56no—
905C4×Q8—52no—
906C4×Q8—53no—
907C4×Q8—51no—
908C4×Q8—53no—
909C4×Q8—53no—
910C4×Q8—512no—
911C4×Q8—56no—
912C4×Q8—56no—
913C4×Q8—56no—
914C4×Q8—56no—
915C4×Q8—56no—
916C4×Q8—56no—
917C4×Q8—53no—
918C4×Q8—53no—
919C4×Q8—56no—
920C4×Q8—56no—
921C4×Q8—56no—
922C4×Q8—56no—
923C4×Q8—56no—
924C4×Q8C22×D513yes—
925C4×Q8C22×D511yescharacteristic
926C4×Q8C22×D511yescharacteristic
927C4×Q8C22×D516yes—
928C4×Q8C22×D511yescharacteristic
929C4×Q8C22×D516yes—
930C4×Q8C22×D513yes—
931C4×Q8C22×D513yes—
932C4×Q8C22×D516yes—
933C4×Q8C22×D512yes—
934C4×Q8C22×D512yes—
935C4×D4—53no—
936C4×D4—53no—
937C4×D4—56no—
938C4×D4—56no—
939C4×D4—56no—
940C4×D4—56no—
941C4×D4—512no—
942C4×D4—512no—
943C4×D4—53no—
944C4×D4—53no—
945C4×D4—56no—
946C4×D4—56no—
947C4×D4—56no—
948C4×D4—56no—
949C4×D4—512no—
950C4×D4—512no—
951C4×D4—53no—
952C4×D4—53no—
953C4×D4—56no—
954C4×D4—56no—
955C4×D4C22×D513yes—
956C4×D4C22×D513yes—
957C4×D4C22×D516yes—
958C4×D4C22×D516yes—
959#117—53no—
960#117—56no—
961#117—53no—
962#117—53no—
963#117—56no—
964#117—56no—
965#117—56no—
966#117—512no—
967#117—56no—
968#117—52no—
969#117—56no—
970#117—56no—
971#117—56no—
972#117—56no—
973#117—56no—
974#117—56no—
975#117—56no—
976#117C22×D513yes—
977#117C22×D516yes—
978C2×C4⋊C4—56no—
979C2×C4⋊C4—56no—
980C2×C4⋊C4—56no—
981C2×C4⋊C4—56no—
982C2×C4⋊C4—56no—
983C2×C4⋊C4—56no—
984C2×C4⋊C4—53no—
985C2×C4⋊C4—53no—
986C2×C4⋊C4—53no—
987C2×C4⋊C4—56no—
988C2×C4⋊C4—56no—
989C2×C4⋊C4—512no—
990C2×C4⋊C4—512no—
991C2×C4⋊C4—56no—
992C2×C4⋊C4—56no—
993C2×C4⋊C4C22×D516yes—
994C2×C4⋊C4C22×D513yes—
995C2×C22⋊C4—56no—
996C2×C22⋊C4—56no—
997C2×C22⋊C4—56no—
998C2×C22⋊C4—512no—
999C2×C42—56no—
1000C2×C42—53no—
1001C2×C42—53no—
1002C2×C42—53no—
1003C2×C42—53no—
1004C2×C42—512no—
1005C2×C42—53no—
1006C2×C42—53no—
1007C2×C42—53no—
1008C2×C42—53no—
1009C2×C42—53no—
1010C2×C42—53no—
1011C2×C42—51no—
1012C2×C42C22×D516yes—
1013C2×C42C22×D513yes—
1014C22×C5—23no—
1015C22×C5—23no—
1016C22×C5C23×Q816yes—
1017C22×C5C2611yescharacteristic
1018C2×D5—23no—
1019C2×D5—23no—
1020C2×D5—21no—
1021C2×D5—21no—
1022C2×D5—412no—
1023C2×D5C23×Q812yes—
1024C2×D5C23×Q816yes—
1025C4×C5—22no—
1026C4×C5—26no—
1027C4×C5—23no—
1028C4×C5—23no—
1029C4×C5—26no—
1030C4×C5—21no—
1031C4×C5—22no—
1032C4×C5C23×Q816yes—
1033C4×C5C23×Q812yes—
1034C4×C5#58512yes—
1035Dic5—26no—
1036Dic5—26no—
1037Dic5—22no—
1038Dic5—22no—
1039Dic5—23no—
1040Dic5—23no—
1041Dic5—21no—
1042Dic5C23×Q816yes—
1043Dic5C23×Q812yes—
1044Dic5#58512yes—
1045C24—53no—
1046#41—58no—
1047#41—524no—
1048#41—524no—
1049#41Q8×D518yescomplemented
1050C2×Q8—46no—
1051C2×Q8—58no—
1052C2×Q8—53no—
1053C2×Q8—56no—
1054C2×Q8—52no—
1055C2×Q8—53no—
1056C2×Q8—51no—
1057C2×Q8—56no—
1058C2×Q8—512no—
1059C2×Q8—56no—
1060C2×Q8—56no—
1061C2×Q8—56no—
1062C2×Q8—206no—
1063C2×Q8—2012no—
1064C2×Q8—2012no—
1065C2×Q8—2012no—
1066C2×Q8C23×D513yes—
1067C2×Q8C23×D511yescharacteristic
1068C2×Q8C23×D516yes—
1069C2×Q8C23×D516yes—
1070C2×Q8C23×D511yescharacteristic
1071C2×D4—56no—
1072C2×D4—524no—
1073C2×D4—53no—
1074C2×D4C23×D513yes—
1075C22×C4—53no—
1076C22×C4—524no—
1077C22×C4—53no—
1078C22×C4—53no—
1079C22×C4—53no—
1080C22×C4—51no—
1081C22×C4—53no—
1082C22×C4—53no—
1083C22×C4—56no—
1084C22×C4—56no—
1085C22×C4—51no—
1086C22×C4—51no—
1087C22×C4—53no—
1088C22×C4—53no—
1089C22×C4—53no—
1090C22×C4—53no—
1091C22×C4—53no—
1092C22×C4—53no—
1093C22×C4—512no—
1094C22×C4—512no—
1095C22×C4—206no—
1096C22×C4—206no—
1097C22×C4C23×D513yes—
1098C22×C4C23×D513yes—
1099C22×C4C23×D516yes—
1100C22×C4C23×D516yes—
1101C22×C4C23×D513yes—
1102C4⋊C4—56no—
1103C4⋊C4—56no—
1104C4⋊C4—52no—
1105C4⋊C4—52no—
1106C4⋊C4—56no—
1107C4⋊C4—52no—
1108C4⋊C4—52no—
1109C4⋊C4—56no—
1110C4⋊C4—56no—
1111C4⋊C4—52no—
1112C4⋊C4—56no—
1113C4⋊C4—52no—
1114C4⋊C4—51no—
1115C4⋊C4—53no—
1116C4⋊C4—56no—
1117C4⋊C4—56no—
1118C4⋊C4—56no—
1119C4⋊C4—56no—
1120C4⋊C4—56no—
1121C4⋊C4—56no—
1122C4⋊C4—53no—
1123C4⋊C4—53no—
1124C4⋊C4—56no—
1125C4⋊C4—56no—
1126C4⋊C4—56no—
1127C4⋊C4—56no—
1128C4⋊C4—56no—
1129C4⋊C4—56no—
1130C4⋊C4—512no—
1131C4⋊C4—512no—
1132C4⋊C4—512no—
1133C4⋊C4—56no—
1134C4⋊C4—56no—
1135C4⋊C4—56no—
1136C4⋊C4—56no—
1137C4⋊C4—512no—
1138C4⋊C4—56no—
1139C4⋊C4—56no—
1140C4⋊C4C23×D516yes—
1141C4⋊C4C23×D513yes—
1142C4⋊C4C23×D513yes—
1143C4⋊C4C23×D513yes—
1144C4⋊C4C23×D516yes—
1145C4⋊C4C23×D516yes—
1146C4⋊C4C23×D5112yes—
1147C4⋊C4C23×D516yes—
1148C4⋊C4C23×D512yes—
1149C4⋊C4C23×D511yescharacteristic
1150C4⋊C4C23×D516yes—
1151C4⋊C4C23×D516yes—
1152C4⋊C4C23×D516yes—
1153C22⋊C4—56no—
1154C22⋊C4—512no—
1155C22⋊C4—56no—
1156C22⋊C4—56no—
1157C22⋊C4—52no—
1158C22⋊C4—52no—
1159C22⋊C4—56no—
1160C22⋊C4—56no—
1161C22⋊C4—56no—
1162C22⋊C4—56no—
1163C22⋊C4—56no—
1164C22⋊C4—56no—
1165C22⋊C4C23×D516yes—
1166C22⋊C4C23×D5112yes—
1167C42—51no—
1168C42—51no—
1169C42—53no—
1170C42—53no—
1171C42—53no—
1172C42—53no—
1173C42—53no—
1174C42—53no—
1175C42—53no—
1176C42—53no—
1177C42—512no—
1178C42—512no—
1179C42—56no—
1180C42—56no—
1181C42—51no—
1182C42—52no—
1183C42—56no—
1184C42—53no—
1185C42C23×D513yes—
1186C42C23×D513yes—
1187C42C23×D516yes—
1188C42C23×D516yes—
1189C42C23×D511yescharacteristic
1190C42C23×D513yes—
1191C42C23×D516yes—
1192C42C23×D512yes—
1193C2×C5—26no—
1194C2×C5C24×Q811yescharacteristic
1195C2×C5C2×#58511yescharacteristic
1196C2×C5C2×#58511yescharacteristic
1197D5—22no—
1198D5—26no—
1199C23—51no—
1200C23—53no—
1201C23—512no—
1202C23—203no—
1203C23—203no—
1204C23C24×D513yes—
1205Q8—22no—
1206Q8—26no—
1207Q8—46no—
1208Q8—46no—
1209Q8—512no—
1210Q8—104no—
1211Q8—1012no—
1212Q8—102no—
1213Q8—106no—
1214Q8—206no—
1215Q8—2012no—
1216Q8—206no—
1217Q8—206no—
1218Q8—206no—
1219Q8C2×Q8×D514yes—
1220D4—524no—
1221D4—512no—
1222D4C2×Q8×D5112yes—
1223C2×C4—26no—
1224C2×C4—43no—
1225C2×C4—46no—
1226C2×C4—46no—
1227C2×C4—512no—
1228C2×C4—53no—
1229C2×C4—51no—
1230C2×C4—51no—
1231C2×C4—54no—
1232C2×C4—512no—
1233C2×C4—512no—
1234C2×C4—512no—
1235C2×C4—51no—
1236C2×C4—53no—
1237C2×C4—56no—
1238C2×C4—52no—
1239C2×C4—53no—
1240C2×C4—56no—
1241C2×C4—52no—
1242C2×C4—102no—
1243C2×C4—106no—
1244C2×C4—106no—
1245C2×C4—102no—
1246C2×C4—106no—
1247C2×C4—203no—
1248C2×C4—203no—
1249C2×C4—203no—
1250C2×C4—203no—
1251C2×C4—2012no—
1252C2×C4—2012no—
1253C2×C4—203no—
1254C2×C4—206no—
1255C2×C4—206no—
1256C2×C4C2×Q8×D5112yes—
1257C2×C4C24×D511yescharacteristic
1258C2×C4C24×D513yes—
1259C2×C4C24×D516yes—
1260C2×C4C24×D513yes—
1261C2×C4C24×D516yes—
1262C2×C4C24×D512yes—
1263C2×C4C24×D512yes—
1264C2×C4C24×D513yes—
1265C2×C4C24×D511yescharacteristic
1266C2×C4C24×D511yescharacteristic
1267C5#6281311yescharacteristic, complemented, Sylow
1268C22—23no—
1269C22—23no—
1270C22—52no—
1271C22—56no—
1272C22—103no—
1273C22—101no—
1274C22—103no—
1275C22—101no—
1276C22—2012no—
1277C22C22×Q8×D516yes—
1278C22C25×D511yescharacteristic
1279C4—23no—
1280C4—22no—
1281C4—26no—
1282C4—21no—
1283C4—22no—
1284C4—23no—
1285C4—26no—
1286C4—52no—
1287C4—56no—
1288C4—52no—
1289C4—101no—
1290C4—103no—
1291C4—106no—
1292C4—102no—
1293C4—103no—
1294C4—106no—
1295C4—102no—
1296C4C22×Q8×D512yes—
1297C4C22×Q8×D516yes—
1298C4#6628312yes—
1299C2—26no—
1300C2—102no—
1301C2—106no—
1302C2C23×Q8×D511yescharacteristic
1303C2C2×#6628311yescharacteristic
1304C2D5×#58511yescharacteristic
subgroupG/H
centerC2×C4C24×D5
commutator, socle, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC5×Q8×#41C2
prime radicalC2×D5×#41C22
hypercenterQ8×#41D5
hypocenterC5#62813
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. C5×Q8×#41C2semidirect
2. #10618947C2semidirect
3. #10618942C2semidirect
4. #10618933C2semidirect
5. #10618932C2semidirect
6. #10618920C2semidirect
7. #10618919C2semidirect
8. #10618850C2semidirect
9. #10618849C2semidirect
10. #10618828C2semidirect
11. #10618827C2semidirect
12. #10618662C2semidirect
13. #10618648C2semidirect
14. #10618178C2semidirect
15. #10618178C2semidirect
16. #10618175C2semidirect
17. D5×#533C2semidirect
20. #41×Dic10C2semidirect
21. #41×Dic10C2semidirect
22. Q8×#709C2semidirect
23. C2×#65912C2semidirect
25. C5×Q82C22semidirect
26. C5×#557C22semidirect
27. C5×#557C22semidirect
28. C5×#554C22semidirect
29. C5×#554C22semidirect
30. C5×D4×Q8C22semidirect
31. C5×#533C22semidirect
32. C5×#533C22semidirect
35. C2×C4×C5×Q8C22semidirect
38. Q8×C22⋊D5C22semidirect
40. C2×#4090C22semidirect
41. #66064C22semidirect
42. #66064C22semidirect
45. #66063C22semidirect
46. #66063C22semidirect
49. #66061C22semidirect
50. #66061C22semidirect
51. D5×C4⋊Q8C22semidirect
52. D5×C4⋊Q8C22semidirect
53. #66056C22semidirect
54. #66056C22semidirect
55. #66055C22semidirect
56. #66055C22semidirect
57. #66024C22semidirect
58. #66024C22semidirect
59. #66024C22semidirect
62. #66023C22semidirect
63. #66023C22semidirect
65. D5×#125C22semidirect
66. #66019C22semidirect
67. #66019C22semidirect
68. #66019C22semidirect
69. #65970C22semidirect
70. #65970C22semidirect
71. #65970C22semidirect
72. #65969C22semidirect
73. #65969C22semidirect
76. #65966C22semidirect
77. #65966C22semidirect
80. #65957C22semidirect
81. #65957C22semidirect
82. #65956C22semidirect
83. #65956C22semidirect
84. #65913C22semidirect
85. #65913C22semidirect
93. #65912C22semidirect
94. #65912C22semidirect
95. #65912C22semidirect
96. #65912C22semidirect
97. #65912C22semidirect
98. #65912C22semidirect
99. #65912C22semidirect
100. #65912C22semidirect
101. Q8×D20C22semidirect
110. C4×Q8×D5C22semidirect
111. C4×Q8×D5C22semidirect
112. #65904C22semidirect
113. #65904C22semidirect
114. #65903C22semidirect
115. #65903C22semidirect
116. #65903C22semidirect
117. #65901C22semidirect
118. #65901C22semidirect
119. Q8×Dic10C22semidirect
120. Q8×Dic10C22semidirect
121. Q8×Dic10C22semidirect
128. #65877C22semidirect
129. #65877C22semidirect
130. #65873C22semidirect
131. #65873C22semidirect
132. #65873C22semidirect
133. D4×Dic10C22semidirect
134. D4×Dic10C22semidirect
141. #65851C22semidirect
142. #65851C22semidirect
143. #65851C22semidirect
144. #65845C22semidirect
145. #65845C22semidirect
148. C2×#4035C22semidirect
149. C2×#4034C22semidirect
154. #65804C22semidirect
155. #65804C22semidirect
156. C2×C4×Dic10C22semidirect
157. C2×C4×Dic10C22semidirect
161. D5×#41Q8semidirect
417. Q8×#41D5semidirect
424. C5×#41C2×Q8semidirect
443. #713C2×Q8semidirect
446. Q8×D5C2×Q8semidirect
447. #711C2×Q8semidirect
448. D4×D5C2×Q8semidirect
449. #709C2×Q8semidirect
453. C2×C4×D5C2×Q8semidirect
577. Q82C2×D5semidirect
590. #557C2×D5semidirect
591. #557C2×D5semidirect
611. #554C2×D5semidirect
612. #554C2×D5semidirect
621. D4×Q8C2×D5semidirect
659. #533C2×D5semidirect
660. #533C2×D5semidirect
698. C2×C4×Q8C2×D5semidirect
1049. #41Q8×D5semidirect
1267. C5#62813semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×#412
#106189472
#106189422
#106189332
#106189322
#106189202
#106189192
#106188502
#106188492
#106188282
#106188272
#106186622
#106186482
#106181782
#106181752
D5×#5332
#106177352
C4×D5×#412
#41×Dic102
Q8×#7092
C2×#659122
#628135