Finite Group Databasebeta

← #13007753

Subgroups — #13007753

Order 1280.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×2−1+4C211yesmaximal, characteristic, complemented
2#10619196C211yesmaximal, characteristic, complemented
3#10619193C211yesmaximal, characteristic, complemented
4#10617808C216yesmaximal, complemented
5#10617805C213yesmaximal, complemented
6#10617802C211yesmaximal, characteristic, complemented
7#10617796C216yesmaximal, complemented
8#10617794C213yesmaximal, complemented
9#10617790C211yesmaximal, characteristic, complemented
10#10617785C212yesmaximal, complemented
11#10617783C213yesmaximal, complemented
12#10617779C212yesmaximal, complemented
13#10617777C213yesmaximal, complemented
14#10617742C216yesmaximal, complemented
15#10617737C213yesmaximal, complemented
16C4×D5×#41C211yesmaximal, characteristic, complemented
17#10617727C216yesmaximal, complemented
18#10617724C213yesmaximal, complemented
19C4×#4150C211yesmaximal, characteristic, complemented
20#10617718C212yesmaximal, complemented
21Q8×#709C212yesmaximal, complemented
22#10617712C213yesmaximal, complemented
23C2×#65912C213yesmaximal, complemented
24C2×C5×2−1+4C2211yescharacteristic
25C2×#4150C2211yescharacteristic
26C2×D5×#41C2211yescharacteristic
27C5×#520C2211yescharacteristic
28C5×#520C2213yescomplemented
29C5×#520C2216yescomplemented
30C5×#519C2213yescomplemented
31C5×#519C2212yescomplemented
32C4×C5×#41C2211yescharacteristic
33C4×C5×#41C2213yescomplemented
34C4×C5×#41C2216yescomplemented
35C2×C4×C5×Q8C2213yescomplemented
36C2×C4×C5×Q8C2212yescomplemented
37#66167C2213yes—
38#66166C2213yescomplemented
39#66163C2216yes—
40#66162C2213yes—
41#66161C2211yescharacteristic
42#41×Dic5C2211yescharacteristic
43#66159C2213yescomplemented
44#66158C2216yes—
45#66158C2216yescomplemented
46#66158C2216yescomplemented
47#66151C2212yes—
48#66150C2213yes—
49#66150C2213yescomplemented
50Q8×C22⋊D5C2212yes—
51Q8×C22⋊D5C2212yescomplemented
52Q8×C22⋊D5C2212yescomplemented
53C2×#4092C2213yes—
54C2×#4090C2213yescomplemented
55#65918C2216yescomplemented
56#65917C2216yescomplemented
57#65917C2216yescomplemented
58#65917C2216yescomplemented
59#65916C2216yescomplemented
60#65916C2216yescomplemented
61#65915C2216yes—
62#65915C2216yescomplemented
63#65914C2213yes—
64#65914C2213yescomplemented
65#65914C2216yescomplemented
66#65913C2216yes—
67#65912C2213yes—
68#65912C2216yes—
69#65912C2216yes—
70#65912C2216yes—
71#65912C2216yescomplemented
72#65912C2216yescomplemented
73#65912C2216yescomplemented
74#65912C2216yescomplemented
75#65912C2216yescomplemented
76#65912C2213yescomplemented
77#65910C2212yes—
78Q8×D20C2212yes—
79C4×#713C2211yescharacteristic
80C4×#713C2211yescharacteristic
81#65906C2212yescomplemented
82C4×Q8×D5C2211yescharacteristic
83C4×Q8×D5C2211yescharacteristic
84C4×Q8×D5C2212yescomplemented
85#65903C2212yescomplemented
86#65902C2216yescomplemented
87#65902C2216yescomplemented
88#65901C2216yescomplemented
89#65901C2216yescomplemented
90Q8×Dic10C2212yescomplemented
91#65898C22112yescomplemented
92#65895C2216yescomplemented
93#65891C2213yes—
94#65891C2213yescomplemented
95#65890C22112yes—
96#65889C2216yes—
97#65888C2216yes—
98#65886C22112yescomplemented
99#65882C2211yescharacteristic
100#65882C2213yescomplemented
101#65881C2216yes—
102#65881C2216yes—
103#65880C2216yescomplemented
104C4×D4×D5C2213yes—
105C4×D4×D5C2213yes—
106#65875C22112yescomplemented
107#65874C22112yescomplemented
108#65873C2216yescomplemented
109#65872C22112yescomplemented
110#65872C2216yescomplemented
111#65872C2216yescomplemented
112D4×Dic10C2216yescomplemented
113C4×#711C2213yes—
114C4×#711C2213yes—
115C4×#711C2216yescomplemented
116#65868C2216yescomplemented
117#65867C2216yescomplemented
118#65867C2216yescomplemented
119#65866C2216yescomplemented
120#65865C22112yescomplemented
121#65865C22112yescomplemented
122#65865C22112yescomplemented
123#65863C2216yes—
124#65862C2216yes—
125#65862C2216yescomplemented
126#65861C22112yes—
127#65860C2213yes—
128#65858C2213yes—
129#65857C2213yescomplemented
130#65856C2213yes—
131D5×#117C2213yes—
132#65853C2213yescomplemented
133#65852C2216yescomplemented
134#65851C2213yescomplemented
135#65850C2213yescomplemented
136#65849C22112yescomplemented
137#65847C2216yescomplemented
138#65845C2216yes—
139#65845C2216yescomplemented
140#65844C2213yes—
141C2×#4043C2213yes—
142C2×#4042C2216yes—
143#65841C2216yescomplemented
144#65834C2213yescomplemented
145C2×#4035C2216yescomplemented
146C2×#4034C2213yescomplemented
147#65813C22112yescomplemented
148#65813C2216yescomplemented
149C4×#709C2213yes—
150C4×#709C2216yes—
151C4×#709C2213yescomplemented
152C4×#709C2216yescomplemented
153C2×#4018C2216yes—
154C2×C42×D5C2213yes—
155#65804C2216yescomplemented
156C2×C4×Dic10C2213yescomplemented
157C2×C4×Dic10C2216yescomplemented
158#62805—51nomaximal, Sylow
159C5×2−1+4—28no—
160C2×C5×#41C2316yes—
161C2×C5×#41C2313yes—
162C2×C5×#41C2311yescharacteristic
163C22×C5×Q8C2313yes—
164C22×C5×Q8C2312yes—
165#4150—28no—
166D5×#41—28no—
167C2×#713C2311yescharacteristic
168C2×Q8×D5C2311yescharacteristic
169C2×Q8×D5C2312yes—
170C2×#711C2313yes—
171C2×#711C2316yes—
172C2×D4×D5C2313yes—
173C2×#709C2312yes—
174C2×#709C2313yes—
175C2×#709C2313yes—
176C2×#709C2316yes—
177C22×C4×D5C2313yes—
178C22×C4×D5C2313yes—
179C22×C4×D5C2313yes—
180C22×Dic10C2313yes—
181C22×Dic10C2316yes—
182C4×C5×Q8C2312yes—
183C4×C5×Q8C2316yes—
184C4×C5×Q8C2316yes—
185C4×C5×Q8C2311yescharacteristic
186C4×C5×Q8C2311yescharacteristic
187C4×C5×Q8C2313yes—
188C4×C5×Q8C2316yes—
189C4×C5×Q8C2316yes—
190C4×C5×Q8C2316yes—
191C4×C5×Q8C2313yes—
192C4×C5×D4C2313yes—
193C4×C5×D4C2313yes—
194C4×C5×D4C2316yes—
195C4×C5×D4C2316yes—
196C4×C5×D4C2316yes—
197C4×C5×D4C23112yes—
198C4×C5×D4C2311yescharacteristic
199C4×C5×D4C2313yes—
200C5×#117C2313yes—
201C5×#117C2313yes—
202C5×#117C2316yes—
203C5×#117C23112yes—
204C5×#117C2316yes—
205C2×C5×C4⋊C4C2313yes—
206C2×C5×C4⋊C4C2316yes—
207C2×C5×C4⋊C4C2316yes—
208C2×C42×C5C2313yes—
209C2×C42×C5C2316yes—
210C2×C42×C5C2316yes—
211#4093C2316yes—
212#4093C2313yes—
213#4092C2313yes—
214#4092C2316yes—
215#4092C2316yes—
216#4092C2316yes—
217#4092C2316yes—
218#4092C2316yes—
219#4092C2313yes—
220Q8×Dic5C2312yes—
221Q8×Dic5C2311yescharacteristic
222Q8×Dic5C2311yescharacteristic
223#4090C2313yes—
224#4090C2316yes—
225#4090C2316yes—
226#4090C2316yes—
227#4090C2316yes—
228#4086C2311yescharacteristic
229#4085C2316yes—
230#4085C23112yes—
231#4085C2316yes—
232#4084C2311yescharacteristic
233#4084C2313yes—
234#4083C2316yes—
235#4082C2313yes—
236#4081C2316yes—
237#4081C23112yes—
238D4×Dic5C2313yes—
239D4×Dic5C2313yes—
240D4×Dic5C2316yes—
241#4076C2316yes—
242#4076C23112yes—
243#4075C23112yes—
244#4075C23112yes—
245#4075C23112yes—
246C4×C22⋊D5C2316yes—
247C4×C22⋊D5C2316yes—
248C4×C22⋊D5C2316yes—
249C4×C22⋊D5C2316yes—
250C4×C22⋊D5C2316yes—
251C4×C22⋊D5C2316yes—
252C4×C22⋊D5C2312yes—
253C4×C22⋊D5C2316yes—
254C4×C22⋊D5C2316yes—
255C4×C22⋊D5C2316yes—
256C4×C22⋊D5C2316yes—
257C4×C22⋊D5C2316yes—
258C2×#685C2316yes—
259C2×#685C2316yes—
260#4072C2316yes—
261#4072C2313yes—
262#4072C2313yes—
263#4072C2316yes—
264C2×C4⋊Dic5C2313yes—
265C2×C4⋊Dic5C2316yes—
266#4070C23112yes—
267#4070C2316yes—
268#4070C2316yes—
269#4070C23112yes—
270#4070C2316yes—
271C2×#683C2316yes—
272C2×#683C2316yes—
273C2×#683C2316yes—
274C2×#683C2316yes—
275C2×#683C2316yes—
276C2×C4×Dic5C2313yes—
277C2×C4×Dic5C2316yes—
278C2×C4×Dic5C2313yes—
279C2×C4×Dic5C2313yes—
280#4044C23112yes—
281#4044C2316yes—
282#4044C23112yes—
283#4044C2316yes—
284#4043C2313yes—
285#4043C2316yes—
286#4043C2316yes—
287#4043C2316yes—
288#4043C2316yes—
289#4043C2313yes—
290#4042C23112yes—
291#4042C2316yes—
292#4042C23112yes—
293#4042C23112yes—
294#4042C23112yes—
295#4042C2316yes—
296#4041C2316yes—
297#4041C2313yes—
298#4041C2311yescharacteristic
299#4040C23112yes—
300#4040C2316yes—
301#4040C2316yes—
302#4039C2313yes—
303#4039C2313yes—
304#4038C2313yes—
305#4038C2313yes—
306#4038C2316yes—
307D5×C4⋊C4C2316yes—
308D5×C4⋊C4C2313yes—
309D5×C4⋊C4C2313yes—
310#4036C2313yes—
311#4036C2316yes—
312#4036C2313yes—
313#4035C2316yes—
314#4035C23112yes—
315#4035C23112yes—
316#4035C23112yes—
317#4035C23112yes—
318#4035C23112yes—
319#4035C2316yes—
320#4034C2313yes—
321#4034C2316yes—
322#4034C2316yes—
323#4034C2316yes—
324#4034C2316yes—
325#4034C2311yescharacteristic
326#4033C2316yes—
327#4033C2313yes—
328#4033C2316yes—
329#4033C2313yes—
330#4032C2316yes—
331#4032C23112yes—
332#4031C2316yes—
333#4031C2312yes—
334#4031C23112yes—
335#4030C2312yes—
336#4030C2316yes—
337#4029C2316yes—
338#4029C2316yes—
339#4028C2316yes—
340#4027C2316yes—
341#4027C2316yes—
342#4027C23112yes—
343D5×C22⋊C4C2316yes—
344#4025C2316yes—
345#4025C23112yes—
346#4025C2316yes—
347#4024C2316yes—
348#4024C2316yes—
349#4024C23112yes—
350#4023C23112yes—
351#4023C2316yes—
352#4022C23112yes—
353#4022C23112yes—
354#4022C23112yes—
355#4021C2316yes—
356#4021C23112yes—
357C4×D20C2313yes—
358C4×D20C2316yes—
359C4×D20C2316yes—
360C4×D20C2313yes—
361C4×D20C2311yescharacteristic
362C4×D20C2316yes—
363C4×D20C2313yes—
364C4×D20C2316yes—
365#4018C2316yes—
366#4018C23112yes—
367#4018C23112yes—
368#4018C23112yes—
369#4018C2316yes—
370#4018C2316yes—
371#4018C2316yes—
372#4018C2316yes—
373#4018C2316yes—
374C42×D5C2311yescharacteristic
375C42×D5C2313yes—
376C42×D5C2313yes—
377C42×D5C2313yes—
378C42×D5C2313yes—
379C42×D5C2313yes—
380C42×D5C2313yes—
381C42×D5C2313yes—
382C42×D5C2316yes—
383#4016C23112yes—
384#4016C2316yes—
385#4016C23112yes—
386#4015C2316yes—
387#4015C2316yes—
388C4×Dic10C2316yes—
389C4×Dic10C2313yes—
390C4×Dic10C2316yes—
391C4×Dic10C23112yes—
392C4×Dic10C2316yes—
393C4×Dic10C2316yes—
394C4×Dic10C23112yes—
395C4×Dic10C23112yes—
396C4×Dic10C2313yes—
397C4×Dic10C2316yes—
398C4×Dic10C2313yes—
399C4×Dic10C2316yes—
400C4×Dic10C2313yes—
401C4×Dic10C2316yes—
402#3523—52no—
403#3520—56no—
404#3518—52no—
405#3515—56no—
406#3511—53no—
407#3509—53no—
408#3503—51no—
409#3499—51no—
410#3495—53no—
411#3495—53no—
412#3489—51no—
413#3489—51no—
414#3482—56no—
415#3482—52no—
416Q8×#41—52no—
417#3475—56no—
418#3461—53no—
419#3461—53no—
420#3444—53no—
421C2×#533—53no—
422C4×2−1+4—51no—
423C4×2−1+4D511yescharacteristic, complemented
424C2×C4×#41—51no—
425C23×D5C2413yes—
426C5×#41—224no—
427C5×#41—212no—
428C5×#41#4118yescomplemented
429C2×C5×Q8—28no—
430C2×C5×Q8—212no—
431C2×C5×Q8C2416yes—
432C2×C5×Q8C2413yes—
433C2×C5×Q8C2411yescharacteristic
434C2×C5×D4C2416yes—
435C2×C5×D4C2411yescharacteristic
436C2×C5×D4C2413yes—
437C22×C4×C5C2413yes—
438C22×C4×C5C2412yes—
439C22×C4×C5C2416yes—
440C22×C4×C5C2416yes—
441C22×C4×C5C2416yes—
442C22×C4×C5C2413yes—
443C22×C4×C5C2416yes—
444C22×C4×C5C2413yes—
445C2×C22⋊D5C2412yes—
446C2×C22⋊D5C2416yes—
447C2×C22⋊D5C2416yes—
448C2×C22⋊D5C2412yes—
449C2×C22⋊D5C2412yes—
450C2×C22⋊D5C2416yes—
451C22×Dic5C2413yes—
452C22×Dic5C2416yes—
453C22×Dic5C2413yes—
454C22×Dic5C2413yes—
455C22×Dic5C2416yes—
456#713—24no—
457Q8×D5—24no—
458Q8×D5—28no—
459#711—212no—
460#711—224no—
461D4×D5—212no—
462#709—212no—
463#709—212no—
464#709—28no—
465#709—412no—
466C2×D20C2411yescharacteristic
467C2×D20C2413yes—
468C2×D20C2412yes—
469C2×D20C2416yes—
470C2×C4×D5—212no—
471C2×C4×D5—212no—
472C2×C4×D5—46no—
473C2×C4×D5C2411yescharacteristic
474C2×C4×D5C2411yescharacteristic
475C2×C4×D5C2413yes—
476C2×C4×D5C2413yes—
477C2×C4×D5C2413yes—
478C2×C4×D5C2413yes—
479C2×C4×D5C2413yes—
480C2×C4×D5C2413yes—
481C2×C4×D5C2413yes—
482C2×C4×D5C2416yes—
483C2×C4×D5C2412yes—
484C2×C4×D5C2413yes—
485C2×C4×D5C2413yes—
486C2×C4×D5C2416yes—
487C2×C4×D5C2411yescharacteristic
488C2×Dic10—212no—
489C2×Dic10—412no—
490C2×Dic10C2416yes—
491C2×Dic10C2413yes—
492C2×Dic10C2416yes—
493C2×Dic10C2413yes—
494C2×Dic10C2412yes—
495C2×Dic10C24112yes—
496C5×C4⋊C4C2413yes—
497C5×C4⋊C4C2413yes—
498C5×C4⋊C4C2416yes—
499C5×C4⋊C4C2416yes—
500C5×C4⋊C4C24112yes—
501C5×C4⋊C4C2413yes—
502C5×C4⋊C4C2411yescharacteristic
503C5×C4⋊C4C2416yes—
504C5×C22⋊C4C2416yes—
505C5×C22⋊C4C2416yes—
506C5×C22⋊C4C2412yes—
507C5×C22⋊C4C2416yes—
508C42×C5C2411yescharacteristic
509C42×C5C2413yes—
510C42×C5C2416yes—
511C42×C5C2413yes—
512C42×C5C2413yes—
513C42×C5C2416yes—
514C42×C5C24112yes—
515C42×C5C2416yes—
516C22⋊Dic5C2416yes—
517C22⋊Dic5C2416yes—
518C22⋊Dic5C2416yes—
519C22⋊Dic5C2416yes—
520C22⋊Dic5C2412yes—
521C22⋊Dic5C2416yes—
522#685C2412yes—
523#685C2416yes—
524#685C2412yes—
525#685C2416yes—
526#685C24112yes—
527#685C24112yes—
528#685C2416yes—
529#685C2416yes—
530#685C2416yes—
531#685C2416yes—
532#685C2416yes—
533#685C2416yes—
534#685C2416yes—
535#685C2416yes—
536C4⋊Dic5C2416yes—
537C4⋊Dic5C2413yes—
538C4⋊Dic5C2411yescharacteristic
539C4⋊Dic5C24112yes—
540C4⋊Dic5C2416yes—
541C4⋊Dic5C2416yes—
542C4⋊Dic5C2416yes—
543C4⋊Dic5C2413yes—
544C4⋊Dic5C2416yes—
545C4⋊Dic5C2413yes—
546#683C2412yes—
547#683C2416yes—
548#683C2416yes—
549#683C2416yes—
550#683C24112yes—
551#683C24112yes—
552#683C24112yes—
553#683C2416yes—
554#683C2416yes—
555#683C2416yes—
556#683C2416yes—
557#683C2416yes—
558#683C2416yes—
559#683C2416yes—
560#683C2416yes—
561#683C24112yes—
562#683C24112yes—
563C4×Dic5C2411yescharacteristic
564C4×Dic5C2413yes—
565C4×Dic5C2416yes—
566C4×Dic5C2413yes—
567C4×Dic5C2413yes—
568C4×Dic5C24112yes—
569C4×Dic5C2413yes—
570C4×Dic5C2413yes—
571C4×Dic5C2413yes—
572C4×Dic5C2413yes—
573C4×Dic5C2416yes—
574C4×Dic5C2416yes—
575C4×Dic5C2411yescharacteristic
576C4×Dic5C2411yescharacteristic
577C4×Dic5C2413yes—
578C4×Dic5C2413yes—
579C2×2−1+4—51no—
580C2×2−1+4C2×D511yescharacteristic
581C22×#41—51no—
582Q82—52no—
583#557—56no—
584#557—56no—
585#557—52no—
586#556—56no—
587#556—56no—
588#556—56no—
589#556—56no—
590#556—56no—
591#555—56no—
592#554—56no—
593#554—56no—
594#554—56no—
595#554—56no—
596#553—512no—
597#552—56no—
598#552—56no—
599#552—512no—
600#552—56no—
601#552—512no—
602#552—512no—
603#552—512no—
604#552—56no—
605#551—512no—
606#551—512no—
607D4×Q8—52no—
608D4×Q8—52no—
609D4×Q8—52no—
610D4×Q8—52no—
611D4×Q8—56no—
612#548—52no—
613#548—52no—
614#548—512no—
615#547—56no—
616#547—56no—
617#547—56no—
618#547—56no—
619#547—56no—
620#546—56no—
621#546—56no—
622#544—53no—
623#544—53no—
624#542—56no—
625#542—56no—
626#542—56no—
627#542—56no—
628#541—56no—
629#541—56no—
630#541—56no—
631#541—56no—
632#539—512no—
633#539—512no—
634#537—53no—
635#537—53no—
636#536—53no—
637#536—53no—
638#536—53no—
639#536—53no—
640#533—53no—
641#533—56no—
642#533—56no—
643#533—56no—
644#533—56no—
645#533—56no—
646#533—56no—
647#533—56no—
648#533—53no—
649#533—56no—
650#533—53no—
651#533—56no—
652#532—53no—
653#532—51no—
654#532—53no—
655C2×C4⋊Q8—53no—
656C2×C4⋊Q8—53no—
657#529—53no—
658#529—53no—
659#529—56no—
660#529—56no—
661#529—56no—
662#529—512no—
663#529—53no—
664#529—53no—
665#529—56no—
666#529—56no—
667#529—512no—
668#529—56no—
669C2×#125—56no—
670#525—53no—
671#525—56no—
672#525—56no—
673#525—53no—
674C2×C22⋊Q8—53no—
675C2×C22⋊Q8—56no—
676C2×C22⋊Q8—53no—
677#520—51no—
678#520—56no—
679#520—53no—
680#520C2×D511yescharacteristic
681#520C2×D513yescomplemented
682#520C2×D516yescomplemented
683#519—52no—
684#519—53no—
685#519C2×D513yescomplemented
686#519C2×D512yescomplemented
687C4×#41—51no—
688C4×#41—51no—
689C4×#41—51no—
690C4×#41—53no—
691C4×#41—53no—
692C4×#41—56no—
693C4×#41—53no—
694C4×#41—53no—
695C4×#41—56no—
696C4×#41—53no—
697C4×#41—56no—
698C4×#41C2×D511yescharacteristic
699C4×#41C2×D513yescomplemented
700C4×#41C2×D516yescomplemented
701C2×C4×Q8—51no—
702C2×C4×Q8—51no—
703C2×C4×Q8—52no—
704C2×C4×Q8—53no—
705C2×C4×Q8—56no—
706C2×C4×Q8C2×D513yescomplemented
707C2×C4×Q8C2×D512yescomplemented
708C2×C4×D4—53no—
709C2×C4×D4—53no—
710C2×#117—53no—
711C2×#117—56no—
712C22×C42—53no—
713C23×C5C2512yes—
714C23×C5C2513yes—
715C22×D5—26no—
716C22×D5—26no—
717C22×D5—43no—
718C22×D5C2513yes—
719C22×D5C2512yes—
720C22×D5C2511yescharacteristic
721C5×Q8—212no—
722C5×Q8—26no—
723C5×Q8C2×#4114yes—
724C5×D4—212no—
725C5×D4—22no—
726C5×D4C2×#41112yes—
727C2×C4×C5—212no—
728C2×C4×C5—212no—
729C2×C4×C5—26no—
730C2×C4×C5—24no—
731C2×C4×C5—46no—
732C2×C4×C5—43no—
733C2×C4×C5—46no—
734C2×C4×C5C2×#41112yes—
735C2×C4×C5C2513yes—
736C2×C4×C5C2511yescharacteristic
737C2×C4×C5C2513yes—
738C2×C4×C5C2516yes—
739C2×C4×C5C2512yes—
740C2×C4×C5C2516yes—
741C2×C4×C5C2513yes—
742C2×C4×C5C2511yescharacteristic
743C2×C4×C5C2511yescharacteristic
744C22⋊D5—212no—
745C22⋊D5—212no—
746C22⋊D5—24no—
747C22⋊D5—24no—
748C22⋊D5—24no—
749C22⋊D5—46no—
750C2×Dic5—212no—
751C2×Dic5—26no—
752C2×Dic5—26no—
753C2×Dic5—26no—
754C2×Dic5—46no—
755C2×Dic5C2511yescharacteristic
756C2×Dic5C2512yes—
757C2×Dic5C2513yes—
758C2×Dic5C2513yes—
759C2×Dic5C2516yes—
760C2×Dic5C2516yes—
761C2×Dic5C2513yes—
762C2×Dic5C2511yescharacteristic
763C2×Dic5C2511yescharacteristic
764D20—24no—
765D20—22no—
766D20—26no—
767D20—46no—
768C4×D5—26no—
769C4×D5—22no—
770C4×D5—26no—
771C4×D5—26no—
772C4×D5—26no—
773C4×D5—212no—
774C4×D5—26no—
775C4×D5—24no—
776C4×D5—26no—
777C4×D5—22no—
778C4×D5—26no—
779C4×D5—43no—
780C4×D5—43no—
781C4×D5—46no—
782C4×D52−1+414yescomplemented
783Dic10—26no—
784Dic10—212no—
785Dic10—26no—
786Dic10—24no—
787Dic10—212no—
788Dic10—412no—
7892−1+4—28no—
7902−1+4—108no—
791C2×#41—51no—
792C2×#41—53no—
793C2×#41—56no—
794C2×#41—52no—
795C2×#41—53no—
796C2×#41—53no—
797C2×#41—56no—
798C2×#41—108no—
799C2×#41C22×D513yes—
800C2×#41C22×D516yes—
801C2×#41C22×D511yescharacteristic
802C22×Q8—51no—
803C22×Q8—52no—
804C22×Q8—53no—
805C22×Q8—56no—
806C22×Q8C22×D513yes—
807C22×Q8C22×D512yes—
808C22×D4—53no—
809C23×C4—53no—
810C23×C4—53no—
811C23×C4—53no—
812C4⋊Q8—53no—
813C4⋊Q8—56no—
814C4⋊Q8—56no—
815C4⋊Q8—56no—
816C4⋊Q8—56no—
817C4⋊Q8—53no—
818C4⋊Q8—56no—
819C4⋊Q8—56no—
820C4⋊Q8—56no—
821C4⋊Q8—51no—
822C4⋊Q8—56no—
823C4⋊Q8—56no—
824C4⋊Q8—56no—
825#127—51no—
826#126—56no—
827#126—56no—
828#126—512no—
829#126—512no—
830#126—56no—
831#126—56no—
832#126—512no—
833#126—512no—
834#126—512no—
835#126—512no—
836#125—56no—
837#125—512no—
838#125—512no—
839#125—512no—
840#125—53no—
841#125—53no—
842#125—56no—
843#125—512no—
844#125—56no—
845#125—512no—
846#125—512no—
847#125—56no—
848#125—512no—
849#124—53no—
850#124—56no—
851#124—53no—
852#124—52no—
853#124—56no—
854#124—512no—
855#124—56no—
856#124—512no—
857#123—56no—
858#123—512no—
859#123—512no—
860#123—512no—
861#123—512no—
862#123—56no—
863#123—56no—
864#123—512no—
865#123—56no—
866#123—56no—
867#123—56no—
868#123—512no—
869C22⋊Q8—53no—
870C22⋊Q8—56no—
871C22⋊Q8—56no—
872C22⋊Q8—56no—
873C22⋊Q8—53no—
874C22⋊Q8—56no—
875C22⋊Q8—56no—
876C22⋊Q8—56no—
877C22⋊Q8—512no—
878C22⋊Q8—56no—
879C22⋊Q8—56no—
880C22⋊Q8—512no—
881C22⋊Q8—56no—
882C22⋊Q8—53no—
883C22⋊Q8—56no—
884C22⋊Q8—512no—
885C22⋊Q8—56no—
886C22⋊Q8—512no—
887C22⋊Q8—56no—
888C22⋊Q8—512no—
889C22⋊Q8—53no—
890C22⋊Q8—56no—
891C22⋊Q8—56no—
892C22⋊Q8—512no—
893C22⋊Q8—56no—
894C22⋊Q8—56no—
895C22⋊Q8—512no—
896#121—51no—
897#121—53no—
898#121—56no—
899#121—56no—
900#121—512no—
901#121—512no—
902#121—56no—
903#121—51no—
904#121—53no—
905#121—56no—
906#121—52no—
907#121—56no—
908#120—56no—
909#120—56no—
910C4×Q8—51no—
911C4×Q8—51no—
912C4×Q8—52no—
913C4×Q8—53no—
914C4×Q8—53no—
915C4×Q8—56no—
916C4×Q8—56no—
917C4×Q8—56no—
918C4×Q8—56no—
919C4×Q8—53no—
920C4×Q8—53no—
921C4×Q8—53no—
922C4×Q8—56no—
923C4×Q8—56no—
924C4×Q8—512no—
925C4×Q8—512no—
926C4×Q8—512no—
927C4×Q8—53no—
928C4×Q8—56no—
929C4×Q8—56no—
930C4×Q8—56no—
931C4×Q8C22×D511yescharacteristic
932C4×Q8C22×D511yescharacteristic
933C4×Q8C22×D513yes—
934C4×Q8C22×D516yes—
935C4×Q8C22×D512yes—
936C4×Q8C22×D516yes—
937C4×Q8C22×D516yes—
938C4×Q8C22×D516yes—
939C4×Q8C22×D513yes—
940C4×Q8C22×D516yes—
941C4×D4—53no—
942C4×D4—53no—
943C4×D4—56no—
944C4×D4—56no—
945C4×D4—56no—
946C4×D4—56no—
947C4×D4—52no—
948C4×D4—56no—
949C4×D4—56no—
950C4×D4—56no—
951C4×D4—56no—
952C4×D4—56no—
953C4×D4—56no—
954C4×D4—56no—
955C4×D4—56no—
956C4×D4—53no—
957C4×D4—53no—
958C4×D4—56no—
959C4×D4—56no—
960C4×D4—512no—
961C4×D4—53no—
962C4×D4—53no—
963C4×D4—51no—
964C4×D4—53no—
965C4×D4—56no—
966C4×D4—56no—
967C4×D4—56no—
968C4×D4—56no—
969C4×D4C22×D513yes—
970C4×D4C22×D513yes—
971C4×D4C22×D516yes—
972C4×D4C22×D511yescharacteristic
973C4×D4C22×D516yes—
974C4×D4C22×D516yes—
975C4×D4C22×D513yes—
976C4×D4C22×D5112yes—
977#117—53no—
978#117—53no—
979#117—56no—
980#117—56no—
981#117—53no—
982#117—53no—
983#117—56no—
984#117—56no—
985#117—512no—
986#117—56no—
987#117—56no—
988#117—512no—
989#117—512no—
990#117—512no—
991#117—56no—
992#117—56no—
993#117—56no—
994#117—56no—
995#117C22×D513yes—
996#117C22×D513yes—
997#117C22×D516yes—
998#117C22×D5112yes—
999#117C22×D516yes—
1000C2×C4⋊C4—56no—
1001C2×C4⋊C4—56no—
1002C2×C4⋊C4—56no—
1003C2×C4⋊C4—53no—
1004C2×C4⋊C4—56no—
1005C2×C4⋊C4—56no—
1006C2×C4⋊C4—56no—
1007C2×C4⋊C4—53no—
1008C2×C4⋊C4—53no—
1009C2×C4⋊C4—56no—
1010C2×C4⋊C4C22×D513yes—
1011C2×C4⋊C4C22×D516yes—
1012C2×C4⋊C4C22×D516yes—
1013C2×C22⋊C4—56no—
1014C2×C22⋊C4—56no—
1015C2×C22⋊C4—56no—
1016C2×C42—56no—
1017C2×C42—53no—
1018C2×C42—53no—
1019C2×C42—53no—
1020C2×C42—53no—
1021C2×C42—53no—
1022C2×C42—53no—
1023C2×C42—56no—
1024C2×C42—53no—
1025C2×C42—53no—
1026C2×C42—53no—
1027C2×C42—53no—
1028C2×C42—51no—
1029C2×C42C22×D516yes—
1030C2×C42C22×D513yes—
1031C2×C42C22×D516yes—
1032C22×C5—23no—
1033C22×C5—23no—
1034C22×C5—22no—
1035C22×C5—22no—
1036C22×C5—22no—
1037C22×C5C22×#4116yes—
1038C22×C5C2611yescharacteristic
1039C2×D5—21no—
1040C2×D5—21no—
1041C2×D5—22no—
1042C2×D5—23no—
1043C2×D5—23no—
1044C2×D5—22no—
1045C2×D5—23no—
1046C2×D5—22no—
1047C2×D5—412no—
1048C2×D5C2×2−1+412yes—
1049C4×C5—26no—
1050C4×C5—22no—
1051C4×C5—23no—
1052C4×C5—26no—
1053C4×C5—21no—
1054C4×C5—23no—
1055C4×C5C22×#4116yes—
1056C4×C5C22×#4112yes—
1057C4×C5C2×2−1+412yes—
1058Dic5—26no—
1059Dic5—23no—
1060Dic5—21no—
1061Dic5—22no—
1062Dic5—23no—
1063Dic5—26no—
1064Dic5—23no—
1065Dic5C2×2−1+412yes—
1066Dic5#58512yes—
1067C24—53no—
1068#41—224no—
1069#41—212no—
1070#41—108no—
1071#41—104no—
1072#41—1012no—
1073#41—1024no—
1074#41—1012no—
1075#41—1012no—
1076#41—2012no—
1077#41#70918yescomplemented
1078C2×Q8—28no—
1079C2×Q8—212no—
1080C2×Q8—52no—
1081C2×Q8—56no—
1082C2×Q8—56no—
1083C2×Q8—53no—
1084C2×Q8—53no—
1085C2×Q8—512no—
1086C2×Q8—104no—
1087C2×Q8—108no—
1088C2×Q8—1012no—
1089C2×Q8—2012no—
1090C2×Q8C23×D513yes—
1091C2×Q8C23×D516yes—
1092C2×Q8C23×D511yescharacteristic
1093C2×D4—52no—
1094C2×D4—52no—
1095C2×D4—56no—
1096C2×D4—56no—
1097C2×D4—52no—
1098C2×D4—56no—
1099C2×D4—52no—
1100C2×D4—53no—
1101C2×D4—51no—
1102C2×D4—56no—
1103C2×D4—1012no—
1104C2×D4C23×D516yes—
1105C2×D4C23×D511yescharacteristic
1106C2×D4C23×D513yes—
1107C22×C4—51no—
1108C22×C4—53no—
1109C22×C4—53no—
1110C22×C4—53no—
1111C22×C4—56no—
1112C22×C4—56no—
1113C22×C4—51no—
1114C22×C4—51no—
1115C22×C4—53no—
1116C22×C4—53no—
1117C22×C4—53no—
1118C22×C4—53no—
1119C22×C4—53no—
1120C22×C4—53no—
1121C22×C4—56no—
1122C22×C4—52no—
1123C22×C4—53no—
1124C22×C4—53no—
1125C22×C4—53no—
1126C22×C4—56no—
1127C22×C4—1012no—
1128C22×C4—1012no—
1129C22×C4—206no—
1130C22×C4C23×D516yes—
1131C22×C4C23×D516yes—
1132C22×C4C23×D513yes—
1133C22×C4C23×D512yes—
1134C22×C4C23×D513yes—
1135C22×C4C23×D516yes—
1136C22×C4C23×D516yes—
1137C22×C4C23×D513yes—
1138C4⋊C4—56no—
1139C4⋊C4—56no—
1140C4⋊C4—56no—
1141C4⋊C4—53no—
1142C4⋊C4—56no—
1143C4⋊C4—56no—
1144C4⋊C4—56no—
1145C4⋊C4—512no—
1146C4⋊C4—56no—
1147C4⋊C4—56no—
1148C4⋊C4—53no—
1149C4⋊C4—53no—
1150C4⋊C4—56no—
1151C4⋊C4—512no—
1152C4⋊C4—512no—
1153C4⋊C4—512no—
1154C4⋊C4—512no—
1155C4⋊C4—512no—
1156C4⋊C4—52no—
1157C4⋊C4—51no—
1158C4⋊C4—56no—
1159C4⋊C4—56no—
1160C4⋊C4—56no—
1161C4⋊C4—56no—
1162C4⋊C4—56no—
1163C4⋊C4—56no—
1164C4⋊C4—56no—
1165C4⋊C4C23×D513yes—
1166C4⋊C4C23×D513yes—
1167C4⋊C4C23×D513yes—
1168C4⋊C4C23×D516yes—
1169C4⋊C4C23×D516yes—
1170C4⋊C4C23×D5112yes—
1171C4⋊C4C23×D511yescharacteristic
1172C4⋊C4C23×D516yes—
1173C22⋊C4—56no—
1174C22⋊C4—56no—
1175C22⋊C4—52no—
1176C22⋊C4—56no—
1177C22⋊C4—56no—
1178C22⋊C4—56no—
1179C22⋊C4—56no—
1180C22⋊C4—56no—
1181C22⋊C4—56no—
1182C22⋊C4—56no—
1183C22⋊C4—512no—
1184C22⋊C4—512no—
1185C22⋊C4—52no—
1186C22⋊C4—52no—
1187C22⋊C4—56no—
1188C22⋊C4—56no—
1189C22⋊C4—56no—
1190C22⋊C4—56no—
1191C22⋊C4—56no—
1192C22⋊C4—56no—
1193C22⋊C4C23×D516yes—
1194C22⋊C4C23×D516yes—
1195C22⋊C4C23×D512yes—
1196C22⋊C4C23×D516yes—
1197C42—51no—
1198C42—51no—
1199C42—53no—
1200C42—53no—
1201C42—53no—
1202C42—53no—
1203C42—53no—
1204C42—53no—
1205C42—53no—
1206C42—53no—
1207C42—56no—
1208C42—512no—
1209C42—56no—
1210C42—51no—
1211C42—53no—
1212C42—56no—
1213C42C23×D513yes—
1214C42C23×D513yes—
1215C42C23×D516yes—
1216C42C23×D5112yes—
1217C42C23×D516yes—
1218C42C23×D513yes—
1219C42C23×D511yescharacteristic
1220C42C23×D516yes—
1221C2×C5—26no—
1222C2×C5—42no—
1223C2×C5C23×#4111yescharacteristic
1224C2×C5C22×2−1+411yescharacteristic
1225C2×C5C2×#58511yescharacteristic
1226D5—22no—
1227D5—42no—
1228D5—43no—
1229C23—51no—
1230C23—53no—
1231C23—52no—
1232C23—106no—
1233C23—106no—
1234C23—203no—
1235C23C24×D512yes—
1236C23C24×D513yes—
1237Q8—212no—
1238Q8—26no—
1239Q8—1012no—
1240Q8—104no—
1241Q8—1012no—
1242Q8—106no—
1243Q8—106no—
1244Q8—2012no—
1245Q8C2×#70914yes—
1246D4—212no—
1247D4—22no—
1248D4—104no—
1249D4—104no—
1250D4—104no—
1251D4—104no—
1252D4—1012no—
1253D4—1012no—
1254D4—106no—
1255D4—102no—
1256D4—206no—
1257D4—206no—
1258D4C2×#709112yes—
1259C2×C4—212no—
1260C2×C4—212no—
1261C2×C4—26no—
1262C2×C4—24no—
1263C2×C4—43no—
1264C2×C4—46no—
1265C2×C4—46no—
1266C2×C4—51no—
1267C2×C4—51no—
1268C2×C4—54no—
1269C2×C4—51no—
1270C2×C4—52no—
1271C2×C4—53no—
1272C2×C4—53no—
1273C2×C4—56no—
1274C2×C4—56no—
1275C2×C4—53no—
1276C2×C4—106no—
1277C2×C4—102no—
1278C2×C4—106no—
1279C2×C4—106no—
1280C2×C4—106no—
1281C2×C4—106no—
1282C2×C4—106no—
1283C2×C4—1012no—
1284C2×C4—102no—
1285C2×C4—106no—
1286C2×C4—106no—
1287C2×C4—106no—
1288C2×C4—1012no—
1289C2×C4—106no—
1290C2×C4—104no—
1291C2×C4—203no—
1292C2×C4—203no—
1293C2×C4—206no—
1294C2×C4—206no—
1295C2×C4C2×#709112yes—
1296C2×C4C24×D513yes—
1297C2×C4C24×D511yescharacteristic
1298C2×C4C24×D513yes—
1299C2×C4C24×D512yes—
1300C2×C4C24×D516yes—
1301C2×C4C24×D516yes—
1302C2×C4C24×D513yes—
1303C2×C4C24×D511yescharacteristic
1304C2×C4C24×D511yescharacteristic
1305C5#6280511yescharacteristic, complemented, Sylow
1306C22—23no—
1307C22—23no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—52no—
1312C22—101no—
1313C22—101no—
1314C22—102no—
1315C22—103no—
1316C22—103no—
1317C22—102no—
1318C22—103no—
1319C22—102no—
1320C22—2012no—
1321C22C22×#70916yes—
1322C22C25×D511yescharacteristic
1323C4—26no—
1324C4—23no—
1325C4—22no—
1326C4—21no—
1327C4—23no—
1328C4—26no—
1329C4—52no—
1330C4—52no—
1331C4—101no—
1332C4—103no—
1333C4—106no—
1334C4—103no—
1335C4—102no—
1336C4—103no—
1337C4—106no—
1338C4C22×#70916yes—
1339C4C22×#70912yes—
1340C4D5×2−1+412yes—
1341C2—26no—
1342C2—42no—
1343C2—102no—
1344C2—203no—
1345C2—202no—
1346C2C23×#70911yescharacteristic
1347C2C2×D5×2−1+411yescharacteristic
1348C2D5×#58511yescharacteristic
subgroupG/H
centerC2×C4C24×D5
commutator, socle, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC4×C5×2−1+4C2
hypercenterC4×2−1+4D5
hypocenterC5#62805
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. C4×C5×2−1+4C2semidirect
2. #10619196C2semidirect
3. #10619193C2semidirect
4. #10617808C2semidirect
5. #10617805C2semidirect
6. #10617802C2semidirect
7. #10617796C2semidirect
8. #10617794C2semidirect
9. #10617790C2semidirect
10. #10617785C2semidirect
11. #10617783C2semidirect
12. #10617779C2semidirect
13. #10617777C2semidirect
14. #10617742C2semidirect
15. #10617737C2semidirect
16. C4×D5×#41C2semidirect
17. #10617727C2semidirect
18. #10617724C2semidirect
19. C4×#4150C2semidirect
20. #10617718C2semidirect
21. Q8×#709C2semidirect
22. #10617712C2semidirect
23. C2×#65912C2semidirect
28. C5×#520C22semidirect
29. C5×#520C22semidirect
30. C5×#519C22semidirect
31. C5×#519C22semidirect
33. C4×C5×#41C22semidirect
34. C4×C5×#41C22semidirect
35. C2×C4×C5×Q8C22semidirect
36. C2×C4×C5×Q8C22semidirect
38. #66166C22semidirect
43. #66159C22semidirect
45. #66158C22semidirect
46. #66158C22semidirect
49. #66150C22semidirect
51. Q8×C22⋊D5C22semidirect
52. Q8×C22⋊D5C22semidirect
54. C2×#4090C22semidirect
55. #65918C22semidirect
56. #65917C22semidirect
57. #65917C22semidirect
58. #65917C22semidirect
59. #65916C22semidirect
60. #65916C22semidirect
62. #65915C22semidirect
64. #65914C22semidirect
65. #65914C22semidirect
71. #65912C22semidirect
72. #65912C22semidirect
73. #65912C22semidirect
74. #65912C22semidirect
75. #65912C22semidirect
76. #65912C22semidirect
81. #65906C22semidirect
84. C4×Q8×D5C22semidirect
85. #65903C22semidirect
86. #65902C22semidirect
87. #65902C22semidirect
88. #65901C22semidirect
89. #65901C22semidirect
90. Q8×Dic10C22semidirect
91. #65898C22semidirect
92. #65895C22semidirect
94. #65891C22semidirect
98. #65886C22semidirect
100. #65882C22semidirect
103. #65880C22semidirect
106. #65875C22semidirect
107. #65874C22semidirect
108. #65873C22semidirect
109. #65872C22semidirect
110. #65872C22semidirect
111. #65872C22semidirect
112. D4×Dic10C22semidirect
115. C4×#711C22semidirect
116. #65868C22semidirect
117. #65867C22semidirect
118. #65867C22semidirect
119. #65866C22semidirect
120. #65865C22semidirect
121. #65865C22semidirect
122. #65865C22semidirect
125. #65862C22semidirect
129. #65857C22semidirect
132. #65853C22semidirect
133. #65852C22semidirect
134. #65851C22semidirect
135. #65850C22semidirect
136. #65849C22semidirect
137. #65847C22semidirect
139. #65845C22semidirect
143. #65841C22semidirect
144. #65834C22semidirect
145. C2×#4035C22semidirect
146. C2×#4034C22semidirect
147. #65813C22semidirect
148. #65813C22semidirect
151. C4×#709C22semidirect
152. C4×#709C22semidirect
155. #65804C22semidirect
156. C2×C4×Dic10C22semidirect
157. C2×C4×Dic10C22semidirect
423. C4×2−1+4D5semidirect
428. C5×#41#41semidirect
681. #520C2×D5semidirect
682. #520C2×D5semidirect
685. #519C2×D5semidirect
686. #519C2×D5semidirect
699. C4×#41C2×D5semidirect
700. C4×#41C2×D5semidirect
706. C2×C4×Q8C2×D5semidirect
707. C2×C4×Q8C2×D5semidirect
782. C4×D52−1+4semidirect
1077. #41#709semidirect
1305. C5#62805semidirect

Maximal subgroups

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

subgroupindex
C4×C5×2−1+42
#106191962
#106191932
#106178082
#106178052
#106178022
#106177962
#106177942
#106177902
#106177852
#106177832
#106177792
#106177772
#106177422
#106177372
C4×D5×#412
#106177272
#106177242
C4×#41502
#106177182
Q8×#7092
#106177122
C2×#659122
#628055