Finite Group Databasebeta

← #13007816

Subgroups — #13007816

Order 1280.

7220 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#10619186C211yesmaximal, characteristic, complemented
3#10619184C211yesmaximal, characteristic, complemented
4#10617807C212yesmaximal, complemented
5#10617805C213yesmaximal, complemented
6#10617802C211yesmaximal, characteristic, complemented
7#10617799C212yesmaximal, complemented
8#10617795C213yesmaximal, complemented
9#10617791C211yesmaximal, characteristic, complemented
10#10617771C216yesmaximal, complemented
11#10617770C213yesmaximal, complemented
12#10617766C216yesmaximal, complemented
13#10617764C213yesmaximal, complemented
14#10617745C212yesmaximal, complemented
15#10617743C212yesmaximal, complemented
16#10617737C213yesmaximal, complemented
17C4×D5×#41C211yesmaximal, characteristic, complemented
18#10617724C213yesmaximal, complemented
19C4×#4150C211yesmaximal, characteristic, complemented
20#10617686C216yesmaximal, complemented
21#10617678C213yesmaximal, complemented
22C2×#65891C213yesmaximal, complemented
23#10617665C216yesmaximal, complemented
24C2×C5×H(5,𝔽2)C2211yescharacteristic
25C2×#4150C2211yescharacteristic
26C2×D5×#41C2211yescharacteristic
27C5×#520C2211yescharacteristic
28C5×#520C2213yescomplemented
29C5×#520C2212yescomplemented
30C5×#518C2213yescomplemented
31C5×#518C2216yescomplemented
32C4×C5×#41C2211yescharacteristic
33C4×C5×#41C2213yescomplemented
34C4×C5×#41C2212yescomplemented
35C2×C4×C5×D4C2216yescomplemented
36C2×C4×C5×D4C2213yescomplemented
37#66168C2212yes—
38#66167C2213yes—
39#66166C2213yescomplemented
40#66165C2212yes—
41#66165C2212yescomplemented
42#66165C2212yescomplemented
43#66162C2213yes—
44#66161C2211yescharacteristic
45#41×Dic5C2211yescharacteristic
46#66159C2213yescomplemented
47#66140C2216yes—
48#66140C2216yescomplemented
49#66140C2216yescomplemented
50#66139C2213yes—
51#66139C2213yescomplemented
52D4×C22⋊D5C2216yes—
53C2×#4084C2213yes—
54C2×#4082C2213yescomplemented
55#66125C22112yescomplemented
56C2×C4×C22⋊D5C2216yescomplemented
57C2×#4072C2216yescomplemented
58#65917C2216yescomplemented
59#65914C2211yescharacteristic, complemented
60#65914C2213yescomplemented
61#65912C2213yescomplemented
62#65912C2213yescomplemented
63#65910C2212yescomplemented
64Q8×D20C2212yescomplemented
65C4×#713C2211yescharacteristic, complemented
66C4×#713C2211yescharacteristic, complemented
67#65906C2212yescomplemented
68C4×Q8×D5C2212yescomplemented
69C4×Q8×D5C2211yescharacteristic, complemented
70C4×Q8×D5C2211yescharacteristic, complemented
71#65904C2212yescomplemented
72#65903C2212yescomplemented
73#65899C22112yescomplemented
74#65898C22112yescomplemented
75#65897C2216yescomplemented
76#65896C2216yescomplemented
77#65896C2216yescomplemented
78#65895C2216yescomplemented
79#65895C2216yescomplemented
80#65895C2216yescomplemented
81#65893C2216yescomplemented
82#65893C2216yescomplemented
83#65892C2216yescomplemented
84#65892C2216yescomplemented
85#65891C2216yescomplemented
86#65891C2216yescomplemented
87#65891C2213yescomplemented
88#65891C2216yescomplemented
89#65891C2216yescomplemented
90#65891C2216yescomplemented
91#65891C2216yescomplemented
92#65891C2216yescomplemented
93#65891C2216yescomplemented
94#65891C2213yescomplemented
95#65890C22112yescomplemented
96#65889C2216yescomplemented
97#65888C2216yescomplemented
98#65885C2216yescomplemented
99#65882C2213yescomplemented
100#65882C2216yescomplemented
101#65882C2213yescomplemented
102#65881C2216yescomplemented
103#65881C2216yescomplemented
104#65880C2216yescomplemented
105C4×D4×D5C2213yescomplemented
106C4×D4×D5C2213yescomplemented
107#65877C2216yescomplemented
108#65876C2216yescomplemented
109#65876C2216yescomplemented
110#65875C22112yescomplemented
111#65874C22112yescomplemented
112#65873C2216yescomplemented
113#65872C2216yescomplemented
114#65872C22112yescomplemented
115#65872C2216yescomplemented
116C4×#711C2213yescomplemented
117C4×#711C2216yescomplemented
118C4×#711C2213yescomplemented
119#65868C2216yescomplemented
120#65867C2216yescomplemented
121#65864C2216yescomplemented
122#65863C2216yescomplemented
123#65863C2216yescomplemented
124#65862C2216yescomplemented
125#65862C2216yescomplemented
126#65860C2213yescomplemented
127#65858C2213yescomplemented
128#65857C2213yescomplemented
129#65856C2213yescomplemented
130D5×#117C2213yescomplemented
131#65853C2213yescomplemented
132#65852C2216yescomplemented
133#65851C2213yescomplemented
134#65850C2213yescomplemented
135#65848C2216yescomplemented
136#65847C2216yescomplemented
137#65847C2216yescomplemented
138#65845C2216yescomplemented
139#65844C2213yescomplemented
140C2×#4043C2213yescomplemented
141#65834C2213yescomplemented
142C2×#4036C2213yescomplemented
143#65829C22112yescomplemented
144#65829C22112yescomplemented
145#65829C22112yescomplemented
146#65828C22112yescomplemented
147#65824C22112yescomplemented
148C2×#4029C2216yescomplemented
149C2×#4025C2216yescomplemented
150#65813C2216yescomplemented
151C4×#709C2216yescomplemented
152C4×#709C2213yescomplemented
153C4×#709C2213yescomplemented
154C4×#709C2216yescomplemented
155C2×C42×D5C2213yescomplemented
156#65804C2216yescomplemented
157C2×C4×Dic10C2213yescomplemented
158#62810—51nomaximal, Sylow
159C5×H(5,𝔽2)—28no—
160C2×C5×#41C2313yes—
161C2×C5×#41C2312yes—
162C2×C5×#41C2311yescharacteristic
163C22×C5×D4C2313yes—
164C22×C5×D4C2316yes—
165C23×C4×C5C2316yes—
166C22×C22⋊D5C2316yes—
167#4150—28no—
168D5×#41—28no—
169C2×#713C2311yescharacteristic
170C2×Q8×D5C2311yescharacteristic
171C2×Q8×D5C2312yes—
172C2×#711C2313yes—
173C2×#711C2316yes—
174C2×D4×D5C2313yes—
175C2×#709C2313yes—
176C2×#709C2313yes—
177C2×#709C2316yes—
178C2×#709C2316yes—
179C22×C4×D5C2313yes—
180C22×C4×D5C2313yes—
181C22×C4×D5C2313yes—
182C22×Dic10C2313yes—
183C4×C5×Q8C2312yes—
184C4×C5×Q8C2311yescharacteristic
185C4×C5×Q8C2311yescharacteristic
186C4×C5×Q8C2311yescharacteristic
187C4×C5×Q8C2313yes—
188C4×C5×D4C2313yes—
189C4×C5×D4C2313yes—
190C4×C5×D4C2316yes—
191C4×C5×D4C2316yes—
192C4×C5×D4C2316yes—
193C4×C5×D4C23112yes—
194C4×C5×D4C2316yes—
195C4×C5×D4C2316yes—
196C4×C5×D4C2313yes—
197C4×C5×D4C2316yes—
198C4×C5×D4C2313yes—
199C4×C5×D4C2316yes—
200C4×C5×D4C2316yes—
201C5×#117C2313yes—
202C5×#117C2313yes—
203C5×#117C2316yes—
204C5×#117C2316yes—
205C2×C5×C4⋊C4C2313yes—
206C2×C5×C4⋊C4C2316yes—
207C2×C5×C22⋊C4C2316yes—
208C2×C5×C22⋊C4C23112yes—
209C2×C42×C5C2313yes—
210C2×C42×C5C2316yes—
211#4099C23112yes—
212#4099C23112yes—
213C2×C22⋊Dic5C2316yes—
214C2×C22⋊Dic5C2316yes—
215C2×C22⋊Dic5C2316yes—
216#4093C2311yescharacteristic
217#4092C2311yescharacteristic
218#4092C2313yes—
219Q8×Dic5C2311yescharacteristic
220Q8×Dic5C2312yes—
221Q8×Dic5C2311yescharacteristic
222#4090C2313yes—
223#4086C2316yes—
224#4086C2313yes—
225#4085C2316yes—
226#4085C23112yes—
227#4085C2316yes—
228#4084C2313yes—
229#4084C2316yes—
230#4084C2316yes—
231#4084C2316yes—
232#4084C2313yes—
233#4084C2316yes—
234#4084C2316yes—
235#4083C2316yes—
236#4082C2313yes—
237#4082C2316yes—
238#4082C2316yes—
239#4082C2316yes—
240#4082C2316yes—
241#4081C2316yes—
242#4081C23112yes—
243D4×Dic5C2313yes—
244D4×Dic5C2316yes—
245D4×Dic5C2313yes—
246#4076C2316yes—
247#4076C23112yes—
248#4076C23112yes—
249#4075C23112yes—
250#4075C23112yes—
251#4075C23112yes—
252C4×C22⋊D5C2316yes—
253C4×C22⋊D5C2316yes—
254C4×C22⋊D5C2316yes—
255C4×C22⋊D5C2316yes—
256C4×C22⋊D5C2316yes—
257C4×C22⋊D5C2316yes—
258C4×C22⋊D5C2316yes—
259C4×C22⋊D5C2316yes—
260C4×C22⋊D5C2316yes—
261C4×C22⋊D5C2316yes—
262C4×C22⋊D5C2316yes—
263C4×C22⋊D5C2316yes—
264C4×C22⋊D5C23112yes—
265C4×C22⋊D5C23112yes—
266C4×C22⋊D5C23112yes—
267C2×#685C2316yes—
268#4072C23112yes—
269#4072C2316yes—
270#4072C2313yes—
271#4072C2313yes—
272#4072C2316yes—
273#4072C23112yes—
274#4072C23112yes—
275C2×C4⋊Dic5C2313yes—
276C2×C4⋊Dic5C2316yes—
277C2×C4⋊Dic5C2316yes—
278#4070C23112yes—
279#4070C2316yes—
280#4070C2316yes—
281#4070C2316yes—
282#4070C23112yes—
283#4070C23112yes—
284C2×#683C2316yes—
285C2×#683C2316yes—
286C2×C4×Dic5C2316yes—
287C2×C4×Dic5C2313yes—
288C2×C4×Dic5C2313yes—
289C2×C4×Dic5C2313yes—
290#4044C2316yes—
291#4044C23112yes—
292#4044C2312yes—
293#4043C2313yes—
294#4043C2316yes—
295#4043C2316yes—
296#4043C2316yes—
297#4043C2316yes—
298#4043C2313yes—
299#4042C2316yes—
300#4042C2316yes—
301#4041C2313yes—
302#4041C2316yes—
303#4041C2311yescharacteristic
304#4040C2316yes—
305#4040C2312yes—
306#4039C2313yes—
307#4039C2313yes—
308#4038C2313yes—
309#4038C2316yes—
310#4038C2313yes—
311D5×C4⋊C4C2313yes—
312D5×C4⋊C4C2313yes—
313D5×C4⋊C4C2316yes—
314#4036C2313yes—
315#4036C2316yes—
316#4036C2316yes—
317#4036C2316yes—
318#4036C2316yes—
319#4036C2311yescharacteristic
320#4035C23112yes—
321#4035C2316yes—
322#4035C2316yes—
323#4034C2313yes—
324#4034C2316yes—
325#4034C2313yes—
326#4033C2316yes—
327#4033C2313yes—
328#4033C2316yes—
329#4033C2313yes—
330#4032C2316yes—
331#4032C23112yes—
332#4031C23112yes—
333#4031C2316yes—
334#4031C23112yes—
335#4031C2316yes—
336#4030C2316yes—
337#4030C23112yes—
338#4030C2316yes—
339#4029C2316yes—
340#4029C23112yes—
341#4029C23112yes—
342#4029C23112yes—
343#4029C23112yes—
344#4029C2316yes—
345#4028C2316yes—
346#4027C23112yes—
347#4027C2316yes—
348#4027C2316yes—
349D5×C22⋊C4C2316yes—
350#4025C2316yes—
351#4025C23112yes—
352#4025C23112yes—
353#4025C23112yes—
354#4025C23112yes—
355#4025C23112yes—
356#4025C2316yes—
357#4024C23112yes—
358#4024C2316yes—
359#4024C2316yes—
360#4023C23112yes—
361#4023C2316yes—
362#4022C23112yes—
363#4021C2316yes—
364C4×D20C2312yes—
365C4×D20C2311yescharacteristic
366C4×D20C2313yes—
367C4×D20C2313yes—
368C4×D20C2316yes—
369C4×D20C2316yes—
370C4×D20C2316yes—
371C4×D20C2313yes—
372#4018C2312yes—
373#4018C2316yes—
374#4018C2316yes—
375#4018C2316yes—
376#4018C2316yes—
377#4018C2316yes—
378C42×D5C2311yescharacteristic
379C42×D5C2313yes—
380C42×D5C2313yes—
381C42×D5C2313yes—
382C42×D5C2313yes—
383C42×D5C2313yes—
384C42×D5C2313yes—
385C42×D5C2313yes—
386C42×D5C2316yes—
387#4016C23112yes—
388#4016C2316yes—
389#4015C2316yes—
390#4015C2316yes—
391C4×Dic10C2313yes—
392C4×Dic10C2316yes—
393C4×Dic10C2316yes—
394C4×Dic10C2316yes—
395C4×Dic10C2313yes—
396C4×Dic10C2316yes—
397C4×Dic10C2313yes—
398C4×Dic10C2316yes—
399C4×Dic10C2316yes—
400C4×Dic10C2313yes—
401C4×Dic10C2316yes—
402#3524—52no—
403#3521—56no—
404#3516—52no—
405#3513—56no—
406#3512—53no—
407#3510—53no—
408#3504—51no—
409#3500—51no—
410#3495—53no—
411#3494—53no—
412#3489—51no—
413#3488—51no—
414#3482—52no—
415#3481—56no—
416#3480—52no—
417#3475—56no—
418#3461—53no—
419#3460—53no—
420#3444—53no—
421C2×#529—53no—
422C4×2−1+4—51no—
423C4×H(5,𝔽2)D511yescharacteristic, complemented
424C2×C4×#41—51no—
425C24×C5C2416yes—
426C23×D5C2413yes—
427C5×#41—28no—
428C5×#41—212no—
429C5×#41#4118yescomplemented
430C2×C5×Q8C2411yescharacteristic
431C2×C5×Q8C2411yescharacteristic
432C2×C5×D4—224no—
433C2×C5×D4—212no—
434C2×C5×D4C2416yes—
435C2×C5×D4C2416yes—
436C2×C5×D4C2413yes—
437C2×C5×D4C2413yes—
438C22×C4×C5—412no—
439C22×C4×C5C2416yes—
440C22×C4×C5C2413yes—
441C22×C4×C5C2416yes—
442C22×C4×C5C2413yes—
443C22×C4×C5C2416yes—
444C22×C4×C5C2416yes—
445C22×C4×C5C24112yes—
446C22×C4×C5C2413yes—
447C2×C22⋊D5—412no—
448C2×C22⋊D5C2416yes—
449C2×C22⋊D5C2416yes—
450C2×C22⋊D5C2416yes—
451C2×C22⋊D5C2416yes—
452C2×C22⋊D5C2416yes—
453C2×C22⋊D5C2416yes—
454C2×C22⋊D5C24112yes—
455C22×Dic5C2416yes—
456C22×Dic5C2413yes—
457C22×Dic5C2413yes—
458C22×Dic5C2413yes—
459C22×Dic5C2416yes—
460#713—24no—
461Q8×D5—24no—
462Q8×D5—28no—
463#711—212no—
464#711—224no—
465D4×D5—212no—
466#709—212no—
467#709—212no—
468#709—412no—
469#709—412no—
470C2×D20C2412yes—
471C2×D20C2411yescharacteristic
472C2×D20C2413yes—
473C2×D20C2416yes—
474C2×C4×D5—212no—
475C2×C4×D5—46no—
476C2×C4×D5—46no—
477C2×C4×D5C2411yescharacteristic
478C2×C4×D5C2411yescharacteristic
479C2×C4×D5C2411yescharacteristic
480C2×C4×D5C2413yes—
481C2×C4×D5C2413yes—
482C2×C4×D5C2413yes—
483C2×C4×D5C2413yes—
484C2×C4×D5C2413yes—
485C2×C4×D5C2412yes—
486C2×C4×D5C2416yes—
487C2×C4×D5C2413yes—
488C2×C4×D5C2413yes—
489C2×C4×D5C2413yes—
490C2×C4×D5C2413yes—
491C2×C4×D5C2416yes—
492C2×Dic10—212no—
493C2×Dic10C2413yes—
494C2×Dic10C2416yes—
495C2×Dic10C2413yes—
496C2×Dic10C2416yes—
497C2×Dic10C2416yes—
498C5×C4⋊C4C2413yes—
499C5×C4⋊C4C2413yes—
500C5×C4⋊C4C2416yes—
501C5×C4⋊C4C2416yes—
502C5×C4⋊C4C2413yes—
503C5×C4⋊C4C2411yescharacteristic
504C5×C4⋊C4C2412yes—
505C5×C22⋊C4C2416yes—
506C5×C22⋊C4C2416yes—
507C5×C22⋊C4C2416yes—
508C5×C22⋊C4C24112yes—
509C5×C22⋊C4C2416yes—
510C42×C5C2411yescharacteristic
511C42×C5C2413yes—
512C42×C5C2412yes—
513C42×C5C2413yes—
514C42×C5C2413yes—
515C42×C5C2416yes—
516C42×C5C2416yes—
517C22⋊Dic5C2416yes—
518C22⋊Dic5C2416yes—
519C22⋊Dic5C2416yes—
520C22⋊Dic5C24112yes—
521C22⋊Dic5C24112yes—
522C22⋊Dic5C24112yes—
523C22⋊Dic5C2416yes—
524C22⋊Dic5C2416yes—
525C22⋊Dic5C2416yes—
526#685C2412yes—
527#685C2412yes—
528#685C2412yes—
529#685C2412yes—
530#685C2412yes—
531#685C2416yes—
532#685C2416yes—
533#685C2416yes—
534#685C2416yes—
535#685C2416yes—
536#685C2416yes—
537#685C2416yes—
538#685C24112yes—
539C4⋊Dic5C2412yes—
540C4⋊Dic5C2411yescharacteristic
541C4⋊Dic5C2413yes—
542C4⋊Dic5C2416yes—
543C4⋊Dic5C2416yes—
544C4⋊Dic5C2413yes—
545C4⋊Dic5C2413yes—
546C4⋊Dic5C2416yes—
547C4⋊Dic5C2416yes—
548C4⋊Dic5C24112yes—
549C4⋊Dic5C24112yes—
550#683C2412yes—
551#683C2416yes—
552#683C2412yes—
553#683C24112yes—
554#683C2416yes—
555#683C2416yes—
556#683C2416yes—
557#683C2416yes—
558#683C2416yes—
559#683C2416yes—
560#683C2416yes—
561#683C2416yes—
562#683C2416yes—
563#683C24112yes—
564C4×Dic5C2413yes—
565C4×Dic5C2416yes—
566C4×Dic5C2413yes—
567C4×Dic5C2413yes—
568C4×Dic5C2413yes—
569C4×Dic5C2413yes—
570C4×Dic5C2416yes—
571C4×Dic5C2416yes—
572C4×Dic5C24112yes—
573C4×Dic5C2411yescharacteristic
574C4×Dic5C2411yescharacteristic
575C4×Dic5C2411yescharacteristic
576C4×Dic5C2413yes—
577C4×Dic5C2413yes—
578C4×Dic5C2413yes—
579C4×Dic5C2413yes—
580C2×2−1+4—51no—
581C2×H(5,𝔽2)C2×D511yescharacteristic
582C22×#41—51no—
583#559—56no—
584#559—56no—
585#557—52no—
586#557—52no—
587#556—56no—
588#556—56no—
589#556—56no—
590#555—56no—
591#554—56no—
592#554—56no—
593#554—56no—
594#553—512no—
595#553—56no—
596#553—56no—
597#553—512no—
598#553—56no—
599#553—56no—
600#552—512no—
601#552—56no—
602#552—56no—
603#552—56no—
604#552—56no—
605#551—512no—
606#551—512no—
607#551—512no—
608#551—512no—
609#550—52no—
610D4×Q8—52no—
611#548—52no—
612#548—52no—
613#548—52no—
614#548—52no—
615#547—56no—
616#547—56no—
617#546—56no—
618#546—56no—
619#546—56no—
620#546—56no—
621#546—512no—
622D42—56no—
623#544—53no—
624#544—53no—
625#542—56no—
626#542—56no—
627#542—56no—
628#542—56no—
629#541—56no—
630#541—56no—
631#540—56no—
632#540—56no—
633#539—512no—
634#538—512no—
635#537—53no—
636#537—53no—
637#536—53no—
638#536—53no—
639#535—53no—
640#535—53no—
641#533—53no—
642#533—53no—
643#533—53no—
644#533—56no—
645#532—53no—
646#532—53no—
647#532—53no—
648#532—56no—
649#529—51no—
650#529—53no—
651#529—56no—
652#529—56no—
653#529—512no—
654#529—53no—
655#529—56no—
656#529—56no—
657#529—56no—
658#529—56no—
659#529—56no—
660#529—56no—
661#529—56no—
662#529—53no—
663#529—56no—
664#529—56no—
665#529—56no—
666#529—56no—
667C2×#126—56no—
668C2×#125—53no—
669C2×#124—53no—
670#525—53no—
671#525—512no—
672#525—56no—
673#525—56no—
674#525—53no—
675C2×#123—56no—
676C2×C22⋊Q8—53no—
677C2×#121—53no—
678#520—51no—
679#520—56no—
680#520—53no—
681#520C2×D511yescharacteristic
682#520C2×D513yescomplemented
683#520C2×D512yescomplemented
684#519—52no—
685#519—53no—
686#518C2×D513yescomplemented
687#518C2×D516yescomplemented
688C4×#41—51no—
689C4×#41—51no—
690C4×#41—51no—
691C4×#41—53no—
692C4×#41—53no—
693C4×#41—56no—
694C4×#41—53no—
695C4×#41—53no—
696C4×#41—53no—
697C4×#41—56no—
698C4×#41—56no—
699C4×#41C2×D511yescharacteristic
700C4×#41C2×D513yescomplemented
701C4×#41C2×D512yescomplemented
702C2×C4×Q8—51no—
703C2×C4×Q8—51no—
704C2×C4×Q8—52no—
705C2×C4×Q8—53no—
706C2×C4×D4—56no—
707C2×C4×D4—53no—
708C2×C4×D4—53no—
709C2×C4×D4C2×D513yescomplemented
710C2×C4×D4C2×D516yescomplemented
711C2×#117—56no—
712C2×#117—53no—
713C22×C42—53no—
714C23×C5—212no—
715C23×C5—46no—
716C23×C5—46no—
717C23×C5C2516yes—
718C23×C5C2513yes—
719C22×D5—26no—
720C22×D5—26no—
721C22×D5—43no—
722C22×D5C2513yes—
723C22×D5C2512yes—
724C22×D5C2511yescharacteristic
725C5×Q8—22no—
726C5×Q8C2×#4114yes—
727C5×D4—212no—
728C5×D4—212no—
729C5×D4—26no—
730C5×D4C2×#41112yes—
731C2×C4×C5—212no—
732C2×C4×C5—26no—
733C2×C4×C5—212no—
734C2×C4×C5—43no—
735C2×C4×C5—46no—
736C2×C4×C5—46no—
737C2×C4×C5—412no—
738C2×C4×C5C2×#41112yes—
739C2×C4×C5C2513yes—
740C2×C4×C5C2513yes—
741C2×C4×C5C2511yescharacteristic
742C2×C4×C5C2512yes—
743C2×C4×C5C2516yes—
744C2×C4×C5C2512yes—
745C2×C4×C5C2513yes—
746C2×C4×C5C2511yescharacteristic
747C2×C4×C5C2511yescharacteristic
748C22⋊D5—212no—
749C22⋊D5—212no—
750C22⋊D5—212no—
751C22⋊D5—46no—
752C22⋊D5—46no—
753C22⋊D5—46no—
754C22⋊D5—412no—
755C2×Dic5—212no—
756C2×Dic5—26no—
757C2×Dic5—43no—
758C2×Dic5—43no—
759C2×Dic5—46no—
760C2×Dic5C2511yescharacteristic
761C2×Dic5C2511yescharacteristic
762C2×Dic5C2511yescharacteristic
763C2×Dic5C2512yes—
764C2×Dic5C2513yes—
765C2×Dic5C2516yes—
766C2×Dic5C2513yes—
767C2×Dic5C2513yes—
768C2×Dic5C2516yes—
769D20—24no—
770D20—22no—
771D20—26no—
772D20—46no—
773C4×D5—22no—
774C4×D5—26no—
775C4×D5—22no—
776C4×D5—26no—
777C4×D5—26no—
778C4×D5—26no—
779C4×D5—212no—
780C4×D5—22no—
781C4×D5—26no—
782C4×D5—24no—
783C4×D5—43no—
784C4×D5—43no—
785C4×D5—43no—
786C4×D5—43no—
787C4×D5—46no—
788Dic10—26no—
789Dic10—212no—
790Dic10—26no—
791Dic10—46no—
792Dic10—46no—
7932−1+4—108no—
794H(5,𝔽2)—28no—
795C2×#41—51no—
796C2×#41—53no—
797C2×#41—56no—
798C2×#41—53no—
799C2×#41—53no—
800C2×#41—56no—
801C2×#41—56no—
802C2×#41—108no—
803C2×#41C22×D513yes—
804C2×#41C22×D512yes—
805C2×#41C22×D511yescharacteristic
806C22×Q8—51no—
807C22×Q8—52no—
808C22×Q8—53no—
809C22×D4—56no—
810C22×D4—53no—
811C22×D4C22×D513yes—
812C22×D4C22×D516yes—
813C23×C4—53no—
814C23×C4—53no—
815C23×C4—53no—
816C23×C4C22×D516yes—
817C4⋊Q8—53no—
818C4⋊Q8—53no—
819C4⋊Q8—53no—
820C4⋊Q8—56no—
821C4⋊Q8—56no—
822C4⋊Q8—56no—
823#127—53no—
824#127—56no—
825#126—52no—
826#126—56no—
827#126—512no—
828#126—56no—
829#126—512no—
830#126—512no—
831#126—512no—
832#126—56no—
833#126—512no—
834#126—512no—
835#126—512no—
836#125—53no—
837#125—56no—
838#125—56no—
839#125—56no—
840#125—51no—
841#125—56no—
842#125—56no—
843#125—56no—
844#125—512no—
845#125—56no—
846#125—512no—
847#124—51no—
848#124—53no—
849#124—56no—
850#124—56no—
851#124—56no—
852#124—56no—
853#124—56no—
854#124—56no—
855#124—512no—
856#124—512no—
857#124—56no—
858#123—56no—
859#123—512no—
860#123—512no—
861#123—512no—
862#123—512no—
863#123—52no—
864#123—56no—
865#123—56no—
866#123—512no—
867#123—512no—
868#123—512no—
869#123—56no—
870#123—56no—
871#123—512no—
872#123—512no—
873C22⋊Q8—51no—
874C22⋊Q8—53no—
875C22⋊Q8—512no—
876C22⋊Q8—512no—
877C22⋊Q8—56no—
878C22⋊Q8—56no—
879C22⋊Q8—56no—
880C22⋊Q8—512no—
881C22⋊Q8—53no—
882C22⋊Q8—56no—
883C22⋊Q8—56no—
884C22⋊Q8—56no—
885C22⋊Q8—53no—
886C22⋊Q8—56no—
887C22⋊Q8—56no—
888C22⋊Q8—56no—
889C22⋊Q8—56no—
890C22⋊Q8—56no—
891C22⋊Q8—512no—
892#121—53no—
893#121—56no—
894#121—56no—
895#121—56no—
896#121—53no—
897#121—56no—
898#121—56no—
899#121—56no—
900#121—512no—
901#121—56no—
902#121—512no—
903#121—512no—
904#121—56no—
905#121—51no—
906#121—53no—
907#121—56no—
908#121—56no—
909#121—56no—
910#121—512no—
911#120—512no—
912#120—512no—
913#120—56no—
914#120—56no—
915C4×Q8—51no—
916C4×Q8—51no—
917C4×Q8—52no—
918C4×Q8—53no—
919C4×Q8—53no—
920C4×Q8—56no—
921C4×Q8—56no—
922C4×Q8—56no—
923C4×Q8—53no—
924C4×Q8—53no—
925C4×Q8—53no—
926C4×Q8—56no—
927C4×Q8—56no—
928C4×Q8—53no—
929C4×Q8—56no—
930C4×Q8—56no—
931C4×Q8—56no—
932C4×Q8—56no—
933C4×Q8C22×D511yescharacteristic
934C4×Q8C22×D511yescharacteristic
935C4×Q8C22×D511yescharacteristic
936C4×Q8C22×D512yes—
937C4×Q8C22×D513yes—
938C4×D4—53no—
939C4×D4—53no—
940C4×D4—56no—
941C4×D4—56no—
942C4×D4—56no—
943C4×D4—56no—
944C4×D4—512no—
945C4×D4—512no—
946C4×D4—512no—
947C4×D4—56no—
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—52no—
964C4×D4—51no—
965C4×D4—53no—
966C4×D4—56no—
967C4×D4—56no—
968C4×D4—56no—
969C4×D4C22×D513yes—
970C4×D4C22×D513yes—
971C4×D4C22×D516yes—
972C4×D4C22×D513yes—
973C4×D4C22×D516yes—
974C4×D4C22×D516yes—
975C4×D4C22×D516yes—
976C4×D4C22×D516yes—
977C4×D4C22×D5112yes—
978C4×D4C22×D516yes—
979C4×D4C22×D516yes—
980C4×D4C22×D513yes—
981C4×D4C22×D516yes—
982#117—56no—
983#117—53no—
984#117—512no—
985#117—512no—
986#117—512no—
987#117—53no—
988#117—56no—
989#117—53no—
990#117—53no—
991#117—56no—
992#117—56no—
993#117—512no—
994#117—56no—
995#117—52no—
996#117—56no—
997#117—56no—
998#117—56no—
999#117—56no—
1000#117C22×D513yes—
1001#117C22×D513yes—
1002#117C22×D516yes—
1003#117C22×D516yes—
1004C2×C4⋊C4—56no—
1005C2×C4⋊C4—56no—
1006C2×C4⋊C4—56no—
1007C2×C4⋊C4—53no—
1008C2×C4⋊C4—56no—
1009C2×C4⋊C4—53no—
1010C2×C4⋊C4—53no—
1011C2×C4⋊C4—56no—
1012C2×C4⋊C4C22×D513yes—
1013C2×C4⋊C4C22×D516yes—
1014C2×C22⋊C4—56no—
1015C2×C22⋊C4—56no—
1016C2×C22⋊C4—56no—
1017C2×C22⋊C4—56no—
1018C2×C22⋊C4—56no—
1019C2×C22⋊C4C22×D516yes—
1020C2×C22⋊C4C22×D5112yes—
1021C2×C42—53no—
1022C2×C42—56no—
1023C2×C42—53no—
1024C2×C42—53no—
1025C2×C42—53no—
1026C2×C42—53no—
1027C2×C42—53no—
1028C2×C42—56no—
1029C2×C42—53no—
1030C2×C42—53no—
1031C2×C42—53no—
1032C2×C42—53no—
1033C2×C42—51no—
1034C2×C42C22×D513yes—
1035C2×C42C22×D516yes—
1036C22×C5—23no—
1037C22×C5—23no—
1038C22×C5—26no—
1039C22×C5—26no—
1040C22×C5—26no—
1041C22×C5—812no—
1042C22×C5C22×#4116yes—
1043C22×C5C2611yescharacteristic
1044C2×D5—21no—
1045C2×D5—21no—
1046C2×D5—22no—
1047C2×D5—23no—
1048C2×D5—23no—
1049C2×D5—22no—
1050C2×D5—22no—
1051C2×D5—23no—
1052C2×D5—412no—
1053C2×D5#58512yes—
1054C4×C5—22no—
1055C4×C5—22no—
1056C4×C5—26no—
1057C4×C5—21no—
1058C4×C5—23no—
1059C4×C5—23no—
1060C4×C5C22×#4116yes—
1061C4×C5C22×#4112yes—
1062C4×C5#58512yes—
1063Dic5—26no—
1064Dic5—23no—
1065Dic5—21no—
1066Dic5—22no—
1067Dic5—23no—
1068Dic5—23no—
1069Dic5—26no—
1070Dic5—21no—
1071Dic5—21no—
1072C24—53no—
1073C24C23×D516yes—
1074#41—28no—
1075#41—212no—
1076#41—104no—
1077#41—1012no—
1078#41—1024no—
1079#41—1012no—
1080#41—1012no—
1081#41—2012no—
1082#41—2012no—
1083#41#70918yescomplemented
1084C2×Q8—56no—
1085C2×Q8—53no—
1086C2×Q8—53no—
1087C2×Q8—56no—
1088C2×Q8—56no—
1089C2×Q8—104no—
1090C2×Q8—108no—
1091C2×Q8—1012no—
1092C2×Q8C23×D511yescharacteristic
1093C2×Q8C23×D511yescharacteristic
1094C2×D4—224no—
1095C2×D4—212no—
1096C2×D4—56no—
1097C2×D4—56no—
1098C2×D4—56no—
1099C2×D4—56no—
1100C2×D4—56no—
1101C2×D4—56no—
1102C2×D4—512no—
1103C2×D4—52no—
1104C2×D4—53no—
1105C2×D4—51no—
1106C2×D4—56no—
1107C2×D4—1012no—
1108C2×D4—2012no—
1109C2×D4C23×D516yes—
1110C2×D4C23×D513yes—
1111C2×D4C23×D516yes—
1112C2×D4C23×D513yes—
1113C22×C4—412no—
1114C22×C4—53no—
1115C22×C4—56no—
1116C22×C4—53no—
1117C22×C4—53no—
1118C22×C4—56no—
1119C22×C4—51no—
1120C22×C4—51no—
1121C22×C4—53no—
1122C22×C4—53no—
1123C22×C4—53no—
1124C22×C4—53no—
1125C22×C4—56no—
1126C22×C4—51no—
1127C22×C4—52no—
1128C22×C4—53no—
1129C22×C4—53no—
1130C22×C4—53no—
1131C22×C4—53no—
1132C22×C4—53no—
1133C22×C4—56no—
1134C22×C4—1012no—
1135C22×C4—206no—
1136C22×C4—206no—
1137C22×C4C23×D516yes—
1138C22×C4C23×D513yes—
1139C22×C4C23×D516yes—
1140C22×C4C23×D513yes—
1141C22×C4C23×D516yes—
1142C22×C4C23×D516yes—
1143C22×C4C23×D5112yes—
1144C22×C4C23×D513yes—
1145C4⋊C4—56no—
1146C4⋊C4—56no—
1147C4⋊C4—56no—
1148C4⋊C4—53no—
1149C4⋊C4—56no—
1150C4⋊C4—56no—
1151C4⋊C4—512no—
1152C4⋊C4—53no—
1153C4⋊C4—53no—
1154C4⋊C4—56no—
1155C4⋊C4—56no—
1156C4⋊C4—512no—
1157C4⋊C4—512no—
1158C4⋊C4—512no—
1159C4⋊C4—51no—
1160C4⋊C4—56no—
1161C4⋊C4—52no—
1162C4⋊C4—52no—
1163C4⋊C4—52no—
1164C4⋊C4—56no—
1165C4⋊C4—56no—
1166C4⋊C4—56no—
1167C4⋊C4—56no—
1168C4⋊C4—56no—
1169C4⋊C4—56no—
1170C4⋊C4C23×D513yes—
1171C4⋊C4C23×D513yes—
1172C4⋊C4C23×D513yes—
1173C4⋊C4C23×D516yes—
1174C4⋊C4C23×D516yes—
1175C4⋊C4C23×D511yescharacteristic
1176C4⋊C4C23×D512yes—
1177C22⋊C4—56no—
1178C22⋊C4—56no—
1179C22⋊C4—56no—
1180C22⋊C4—56no—
1181C22⋊C4—512no—
1182C22⋊C4—512no—
1183C22⋊C4—512no—
1184C22⋊C4—56no—
1185C22⋊C4—56no—
1186C22⋊C4—56no—
1187C22⋊C4—56no—
1188C22⋊C4—56no—
1189C22⋊C4—512no—
1190C22⋊C4—52no—
1191C22⋊C4—52no—
1192C22⋊C4—56no—
1193C22⋊C4—52no—
1194C22⋊C4—52no—
1195C22⋊C4—52no—
1196C22⋊C4—56no—
1197C22⋊C4—56no—
1198C22⋊C4—56no—
1199C22⋊C4C23×D516yes—
1200C22⋊C4C23×D516yes—
1201C22⋊C4C23×D516yes—
1202C22⋊C4C23×D5112yes—
1203C22⋊C4C23×D516yes—
1204C42—51no—
1205C42—51no—
1206C42—53no—
1207C42—53no—
1208C42—53no—
1209C42—53no—
1210C42—53no—
1211C42—53no—
1212C42—53no—
1213C42—53no—
1214C42—512no—
1215C42—56no—
1216C42—56no—
1217C42—51no—
1218C42—56no—
1219C42—53no—
1220C42C23×D513yes—
1221C42C23×D513yes—
1222C42C23×D516yes—
1223C42C23×D516yes—
1224C42C23×D513yes—
1225C42C23×D511yescharacteristic
1226C42C23×D512yes—
1227C2×C5—26no—
1228C2×C5—46no—
1229C2×C5C23×#4111yescharacteristic
1230C2×C5C2×#58511yescharacteristic
1231C2×C5C2×#58511yescharacteristic
1232D5—22no—
1233D5—42no—
1234D5—43no—
1235C23—212no—
1236C23—46no—
1237C23—46no—
1238C23—51no—
1239C23—53no—
1240C23—52no—
1241C23—106no—
1242C23—106no—
1243C23—203no—
1244C23C24×D516yes—
1245C23C24×D513yes—
1246Q8—22no—
1247Q8—1012no—
1248Q8—106no—
1249Q8—106no—
1250Q8—206no—
1251Q8—206no—
1252Q8C2×#70914yes—
1253D4—212no—
1254D4—212no—
1255D4—26no—
1256D4—104no—
1257D4—1012no—
1258D4—1012no—
1259D4—1012no—
1260D4—106no—
1261D4—102no—
1262D4—206no—
1263D4—2012no—
1264D4—206no—
1265D4—206no—
1266D4—206no—
1267D4C2×#709112yes—
1268C2×C4—212no—
1269C2×C4—26no—
1270C2×C4—212no—
1271C2×C4—412no—
1272C2×C4—46no—
1273C2×C4—43no—
1274C2×C4—46no—
1275C2×C4—51no—
1276C2×C4—51no—
1277C2×C4—51no—
1278C2×C4—52no—
1279C2×C4—56no—
1280C2×C4—53no—
1281C2×C4—53no—
1282C2×C4—53no—
1283C2×C4—56no—
1284C2×C4—102no—
1285C2×C4—106no—
1286C2×C4—106no—
1287C2×C4—1012no—
1288C2×C4—102no—
1289C2×C4—106no—
1290C2×C4—106no—
1291C2×C4—106no—
1292C2×C4—1012no—
1293C2×C4—102no—
1294C2×C4—106no—
1295C2×C4—104no—
1296C2×C4—203no—
1297C2×C4—203no—
1298C2×C4—203no—
1299C2×C4—203no—
1300C2×C4—206no—
1301C2×C4—203no—
1302C2×C4—203no—
1303C2×C4—206no—
1304C2×C4C2×#709112yes—
1305C2×C4C24×D513yes—
1306C2×C4C24×D511yescharacteristic
1307C2×C4C24×D513yes—
1308C2×C4C24×D512yes—
1309C2×C4C24×D512yes—
1310C2×C4C24×D516yes—
1311C2×C4C24×D513yes—
1312C2×C4C24×D511yescharacteristic
1313C2×C4C24×D511yescharacteristic
1314C5#6281011yescharacteristic, complemented, Sylow
1315C22—23no—
1316C22—23no—
1317C22—26no—
1318C22—26no—
1319C22—26no—
1320C22—52no—
1321C22—812no—
1322C22—101no—
1323C22—101no—
1324C22—102no—
1325C22—103no—
1326C22—103no—
1327C22—102no—
1328C22—102no—
1329C22—103no—
1330C22—2012no—
1331C22C22×#70916yes—
1332C22C25×D511yescharacteristic
1333C4—22no—
1334C4—23no—
1335C4—26no—
1336C4—21no—
1337C4—23no—
1338C4—22no—
1339C4—101no—
1340C4—103no—
1341C4—106no—
1342C4—101no—
1343C4—103no—
1344C4—102no—
1345C4—101no—
1346C4—103no—
1347C4—106no—
1348C4C22×#70916yes—
1349C4C22×#70912yes—
1350C4#6628512yes—
1351C2—26no—
1352C2—46no—
1353C2—102no—
1354C2—203no—
1355C2—202no—
1356C2C23×#70911yescharacteristic
1357C2C2×#6628511yescharacteristic
1358C2D5×#58511yescharacteristic
subgroupG/H
centerC2×C4C24×D5
commutator, socle, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC4×C5×H(5,𝔽2)C2
hypercenterC4×H(5,𝔽2)D5
hypocenterC5#62810
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C4×C5×H(5,𝔽2)C2semidirect
2. #10619186C2semidirect
3. #10619184C2semidirect
4. #10617807C2semidirect
5. #10617805C2semidirect
6. #10617802C2semidirect
7. #10617799C2semidirect
8. #10617795C2semidirect
9. #10617791C2semidirect
10. #10617771C2semidirect
11. #10617770C2semidirect
12. #10617766C2semidirect
13. #10617764C2semidirect
14. #10617745C2semidirect
15. #10617743C2semidirect
16. #10617737C2semidirect
17. C4×D5×#41C2semidirect
18. #10617724C2semidirect
19. C4×#4150C2semidirect
20. #10617686C2semidirect
21. #10617678C2semidirect
22. C2×#65891C2semidirect
23. #10617665C2semidirect
28. C5×#520C22semidirect
29. C5×#520C22semidirect
30. C5×#518C22semidirect
31. C5×#518C22semidirect
33. C4×C5×#41C22semidirect
34. C4×C5×#41C22semidirect
35. C2×C4×C5×D4C22semidirect
36. C2×C4×C5×D4C22semidirect
39. #66166C22semidirect
41. #66165C22semidirect
42. #66165C22semidirect
46. #66159C22semidirect
48. #66140C22semidirect
49. #66140C22semidirect
51. #66139C22semidirect
54. C2×#4082C22semidirect
55. #66125C22semidirect
56. C2×C4×C22⋊D5C22semidirect
57. C2×#4072C22semidirect
58. #65917C22semidirect
59. #65914C22semidirect
60. #65914C22semidirect
61. #65912C22semidirect
62. #65912C22semidirect
63. #65910C22semidirect
64. Q8×D20C22semidirect
65. C4×#713C22semidirect
66. C4×#713C22semidirect
67. #65906C22semidirect
68. C4×Q8×D5C22semidirect
69. C4×Q8×D5C22semidirect
70. C4×Q8×D5C22semidirect
71. #65904C22semidirect
72. #65903C22semidirect
73. #65899C22semidirect
74. #65898C22semidirect
75. #65897C22semidirect
76. #65896C22semidirect
77. #65896C22semidirect
78. #65895C22semidirect
79. #65895C22semidirect
80. #65895C22semidirect
81. #65893C22semidirect
82. #65893C22semidirect
83. #65892C22semidirect
84. #65892C22semidirect
85. #65891C22semidirect
86. #65891C22semidirect
87. #65891C22semidirect
88. #65891C22semidirect
89. #65891C22semidirect
90. #65891C22semidirect
91. #65891C22semidirect
92. #65891C22semidirect
93. #65891C22semidirect
94. #65891C22semidirect
95. #65890C22semidirect
96. #65889C22semidirect
97. #65888C22semidirect
98. #65885C22semidirect
99. #65882C22semidirect
100. #65882C22semidirect
101. #65882C22semidirect
102. #65881C22semidirect
103. #65881C22semidirect
104. #65880C22semidirect
105. C4×D4×D5C22semidirect
106. C4×D4×D5C22semidirect
107. #65877C22semidirect
108. #65876C22semidirect
109. #65876C22semidirect
110. #65875C22semidirect
111. #65874C22semidirect
112. #65873C22semidirect
113. #65872C22semidirect
114. #65872C22semidirect
115. #65872C22semidirect
116. C4×#711C22semidirect
117. C4×#711C22semidirect
118. C4×#711C22semidirect
119. #65868C22semidirect
120. #65867C22semidirect
121. #65864C22semidirect
122. #65863C22semidirect
123. #65863C22semidirect
124. #65862C22semidirect
125. #65862C22semidirect
126. #65860C22semidirect
127. #65858C22semidirect
128. #65857C22semidirect
129. #65856C22semidirect
130. D5×#117C22semidirect
131. #65853C22semidirect
132. #65852C22semidirect
133. #65851C22semidirect
134. #65850C22semidirect
135. #65848C22semidirect
136. #65847C22semidirect
137. #65847C22semidirect
138. #65845C22semidirect
139. #65844C22semidirect
140. C2×#4043C22semidirect
141. #65834C22semidirect
142. C2×#4036C22semidirect
143. #65829C22semidirect
144. #65829C22semidirect
145. #65829C22semidirect
146. #65828C22semidirect
147. #65824C22semidirect
148. C2×#4029C22semidirect
149. C2×#4025C22semidirect
150. #65813C22semidirect
151. C4×#709C22semidirect
152. C4×#709C22semidirect
153. C4×#709C22semidirect
154. C4×#709C22semidirect
155. C2×C42×D5C22semidirect
156. #65804C22semidirect
157. C2×C4×Dic10C22semidirect
423. C4×H(5,𝔽2)D5semidirect
429. C5×#41#41semidirect
682. #520C2×D5semidirect
683. #520C2×D5semidirect
686. #518C2×D5semidirect
687. #518C2×D5semidirect
700. C4×#41C2×D5semidirect
701. C4×#41C2×D5semidirect
709. C2×C4×D4C2×D5semidirect
710. C2×C4×D4C2×D5semidirect
1083. #41#709semidirect
1314. C5#62810semidirect

Maximal subgroups

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

subgroupindex
C4×C5×H(5,𝔽2)2
#106191862
#106191842
#106178072
#106178052
#106178022
#106177992
#106177952
#106177912
#106177712
#106177702
#106177662
#106177642
#106177452
#106177432
#106177372
C4×D5×#412
#106177242
C4×#41502
#106176862
#106176782
C2×#658912
#106176652
#628105