Finite Group Databasebeta

← #13007686

Subgroups — #13007686

Order 1280.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3498C211yesmaximal, characteristic, complemented
2#10619186C212yesmaximal, complemented
3Dic5×H(5,𝔽2)C212yesmaximal, complemented
4#10618677C212yesmaximal, complemented
5#10618674C212yesmaximal, complemented
6#10618669C212yesmaximal, complemented
7#10618668C212yesmaximal, complemented
8#10618513C216yesmaximal, complemented
9#10618511C216yesmaximal, complemented
10#10618507C216yesmaximal, complemented
11D4×#711C216yesmaximal, complemented
12#10618233C216yesmaximal, complemented
13#10618215C216yesmaximal, complemented
14#10618126C213yesmaximal, complemented
15#10618120C213yesmaximal, complemented
16#10618091C213yesmaximal, complemented
17C2×#66050C213yesmaximal, complemented
18C4×D5×#41C211yesmaximal, characteristic, complemented
19#10617729C211yesmaximal, characteristic, complemented
20C2×C5×H(5,𝔽2)C2212yes—
21C2×D5×#41C2211yescharacteristic
22C22×#711C2216yescomplemented
23C5×#550C2212yescomplemented
24C5×#550C2212yescomplemented
25C5×D42C2216yescomplemented
26C5×D42C2216yescomplemented
27C5×#535C2216yescomplemented
28C5×#532C2213yescomplemented
29C2×C5×#127C2213yescomplemented
30C4×C5×#41C2211yescharacteristic
31#66168C2214yescomplemented
32#66167C2216yescomplemented
33#66165C2214yescomplemented
34#66162C2216yescomplemented
35#66161C2212yes—
36#66161C2216yescomplemented
37#66161C2214yescomplemented
38#41×Dic5C2211yescharacteristic
39#41×Dic5C2216yescomplemented
40#41×Dic5C2214yescomplemented
41#66140C22112yescomplemented
42#66140C22112yescomplemented
43#66140C22112yescomplemented
44#66139C2216yescomplemented
45D4×C22⋊D5C22112yescomplemented
46C2×#4084C2216yescomplemented
47C2×#4084C2216yescomplemented
48#66132C2216yescomplemented
49#66132C22112yescomplemented
50C2×#4082C2216yescomplemented
51C2×D4×Dic5C2216yescomplemented
52C2×D4×Dic5C22112yescomplemented
53C2×D4×Dic5C2216yescomplemented
54#66062C2211yescharacteristic, complemented
55#66062C2213yescomplemented
56#66053C22112yescomplemented
57#66052C2216yescomplemented
58#66052C2216yescomplemented
59#66050C2213yescomplemented
60#66050C2213yescomplemented
61#66050C2216yescomplemented
62#66050C2216yescomplemented
63#66050C2216yescomplemented
64#66050C2216yescomplemented
65#66050C2216yescomplemented
66#66050C2216yescomplemented
67#66050C2216yescomplemented
68#66047C2216yescomplemented
69#66047C2216yescomplemented
70#66016C22112yescomplemented
71#66014C2216yescomplemented
72#66014C2216yescomplemented
73#65953C22112yescomplemented
74#65952C22112yescomplemented
75#65952C22112yescomplemented
76#65950C22112yescomplemented
77#65948C22112yescomplemented
78#65945C22112yescomplemented
79#65940C2216yescomplemented
80#65940C2216yescomplemented
81#65937C22112yescomplemented
82#65934C2216yescomplemented
83#65934C2216yescomplemented
84#65934C22112yescomplemented
85#65932C22112yescomplemented
86#65930C22112yescomplemented
87#65927C22124yescomplemented
88#65925C22124yescomplemented
89#65921C22124yescomplemented
90#65920C22124yescomplemented
91C4×#713C2211yescharacteristic, complemented
92C4×#713C2211yescharacteristic, complemented
93C4×Q8×D5C2211yescharacteristic, complemented
94C4×Q8×D5C2211yescharacteristic, complemented
95#65904C2212yescomplemented
96Q8×Dic10C2212yescomplemented
97#65897C2216yescomplemented
98#65891C2216yescomplemented
99#65891C2216yescomplemented
100#65889C2216yescomplemented
101C4×D4×D5C2213yescomplemented
102C4×D4×D5C2213yescomplemented
103#65877C2216yescomplemented
104#65877C2216yescomplemented
105#65876C2216yescomplemented
106D4×Dic10C2216yescomplemented
107C4×#711C2216yescomplemented
108C4×#711C2216yescomplemented
109C4×#711C2213yescomplemented
110C4×#711C2213yescomplemented
111#65856C2213yescomplemented
112D5×#117C2213yescomplemented
113#65853C2216yescomplemented
114C4×#709C2213yescomplemented
115C2×C42×D5C2213yescomplemented
116#65804C2213yescomplemented
117C2×#4015C2213yescomplemented
118#62800—51nomaximal, Sylow
119C5×H(5,𝔽2)—216no—
120C2×C5×#41C2316yes—
121C2×C5×#41C2314yes—
122C2×C5×#41C2311yescharacteristic
123C22×C5×D4C2316yes—
124C22×C5×D4C23112yes—
125C22×C5×D4C2316yes—
126C22×C5×D4C2316yes—
127C22×C22⋊D5C23112yes—
128C23×Dic5C23112yes—
129D5×#41—28no—
130C2×#713C2311yescharacteristic
131C2×Q8×D5C2311yescharacteristic
132C2×#711—424no—
133C2×#711C2316yes—
134C2×#711C2313yes—
135C2×#711C23112yes—
136C2×#711C23112yes—
137C2×#711C23112yes—
138C2×#711C2316yes—
139C2×D4×D5C2313yes—
140C2×#709C2313yes—
141C22×C4×D5C2313yes—
142C22×C4×D5C2313yes—
143C22×C4×D5C2313yes—
144C22×Dic10C2316yes—
145C5×C4⋊Q8C2311yescharacteristic
146C5×#127C2313yes—
147C5×#127C2316yes—
148C5×#127C2316yes—
149C5×#127C2316yes—
150C5×#124C2316yes—
151C5×#121C23112yes—
152C5×#121C2316yes—
153C5×#121C2316yes—
154C5×#121C23112yes—
155C5×#120C23124yes—
156C4×C5×Q8C2311yescharacteristic
157C4×C5×Q8C2311yescharacteristic
158C4×C5×D4C2313yes—
159C4×C5×D4C2316yes—
160C4×C5×D4C2313yes—
161C4×C5×D4C2316yes—
162C5×#117C2313yes—
163C2×C42×C5C2313yes—
164#4099C23124yes—
165C2×C22⋊Dic5C23112yes—
166C2×C22⋊Dic5C23112yes—
167C2×C22⋊Dic5C23124yes—
168#4092C2312yes—
169#4092C2316yes—
170Q8×Dic5C2312yes—
171Q8×Dic5C2316yes—
172Q8×Dic5C2314yes—
173Q8×Dic5C2311yescharacteristic
174Q8×Dic5C2311yescharacteristic
175#4086C23112yes—
176#4085C23124yes—
177#4085C23124yes—
178#4085C23124yes—
179#4084C2316yes—
180#4084C2316yes—
181#4084C23112yes—
182#4084C23112yes—
183#4084C23112yes—
184#4084C23112yes—
185#4084C23112yes—
186#4084C23112yes—
187#4084C2316yes—
188#4084C2316yes—
189#4083C23112yes—
190#4082C2316yes—
191#4082C23112yes—
192#4082C23112yes—
193#4082C23112yes—
194#4082C2316yes—
195#4082C23112yes—
196#4081C23124yes—
197#4081C23124yes—
198#4081C23112yes—
199D4×Dic5C2316yes—
200D4×Dic5C2316yes—
201D4×Dic5C23112yes—
202D4×Dic5C23112yes—
203D4×Dic5C23112yes—
204D4×Dic5C23112yes—
205D4×Dic5C23112yes—
206D4×Dic5C23112yes—
207D4×Dic5C2316yes—
208D4×Dic5C2316yes—
209D4×Dic5C23112yes—
210D4×Dic5C23112yes—
211D4×Dic5C2313yes—
212D4×Dic5C2313yes—
213D4×Dic5C23112yes—
214D4×Dic5C23112yes—
215D4×Dic5C23124yes—
216D4×Dic5C23112yes—
217#4076C23112yes—
218C4×C22⋊D5C2316yes—
219C4×C22⋊D5C2316yes—
220C4×C22⋊D5C23112yes—
221C4×C22⋊D5C23112yes—
222#4072C2316yes—
223#4072C2313yes—
224#4072C23112yes—
225#4072C23112yes—
226C2×C4⋊Dic5C2316yes—
227C2×C4⋊Dic5C2316yes—
228C2×C4⋊Dic5C23112yes—
229#4070C2316yes—
230#4070C2316yes—
231#4070C23112yes—
232C2×C4×Dic5C2313yes—
233C2×C4×Dic5C2313yes—
234C2×C4×Dic5C2313yes—
235C2×C4×Dic5C23112yes—
236#4043C2316yes—
237#4043C2312yes—
238#4039C2313yes—
239#4039C2313yes—
240#4038C2312yes—
241#4038C2316yes—
242#4038C2313yes—
243#4038C2313yes—
244D5×C4⋊C4C2313yes—
245D5×C4⋊C4C2313yes—
246#4036C2316yes—
247#4036C2312yes—
248#4036C23112yes—
249#4034C23112yes—
250#4033C2312yes—
251#4033C2316yes—
252#4033C2313yes—
253#4033C2313yes—
254#4032C23124yes—
255#4031C23124yes—
256#4029C23112yes—
257#4029C23112yes—
258#4027C2316yes—
259#4027C2316yes—
260#4027C23112yes—
261#4027C23112yes—
262D5×C22⋊C4C2316yes—
263#4025C23124yes—
264#4025C23112yes—
265#4025C23112yes—
266#4024C23124yes—
267#4024C23124yes—
268#4023C2316yes—
269#4023C23112yes—
270#4023C23112yes—
271C4×D20C2313yes—
272C4×D20C2313yes—
273#4018C2316yes—
274C42×D5C2311yescharacteristic
275C42×D5C2313yes—
276C42×D5C2313yes—
277C42×D5C2313yes—
278C42×D5C2313yes—
279C42×D5C2313yes—
280C42×D5C2313yes—
281C42×D5C2313yes—
282#4016C2316yes—
283#4015C2313yes—
284#4015C2311yescharacteristic
285#4015C2316yes—
286#4015C2316yes—
287#4015C2316yes—
288C4×Dic10C2316yes—
289C4×Dic10C2316yes—
290C4×Dic10C2313yes—
291C4×Dic10C2313yes—
292#3522—52no—
293#3519—56no—
294#3517—52no—
295#3514—56no—
296#3511—53no—
297#3508—53no—
298#3503—51no—
299#3498D511yescharacteristic, complemented
300#3494—56no—
301#3488—52no—
302#3483—52no—
303#3481—56no—
304#3480—52no—
305D4×#41—56no—
306#3460—56no—
307#3444—53no—
308C2×#532—53no—
309C4×H(5,𝔽2)—52no—
310C2×C4×#41—51no—
311C24×C5C24112yes—
312C23×D5C2413yes—
313C5×#41—216no—
314C5×#41—224no—
315C5×#41#4118yescomplemented
316C2×C5×Q8C2412yes—
317C2×C5×Q8C2411yescharacteristic
318C2×C5×D4—248no—
319C2×C5×D4—224no—
320C2×C5×D4—412no—
321C2×C5×D4—412no—
322C2×C5×D4C2416yes—
323C2×C5×D4C2416yes—
324C2×C5×D4C24112yes—
325C2×C5×D4C24112yes—
326C2×C5×D4C2416yes—
327C2×C5×D4C24112yes—
328C2×C5×D4C24112yes—
329C2×C5×D4C2413yes—
330C22×C4×C5C2413yes—
331C22×C4×C5C2413yes—
332C22×C4×C5C24112yes—
333C22×C4×C5C2413yes—
334C2×C22⋊D5—424no—
335C2×C22⋊D5C2416yes—
336C2×C22⋊D5C24112yes—
337C2×C22⋊D5C24112yes—
338C2×C22⋊D5C24124yes—
339C22×Dic5—424no—
340C22×Dic5C2413yes—
341C22×Dic5C2413yes—
342C22×Dic5C24112yes—
343C22×Dic5C2413yes—
344C22×Dic5C24112yes—
345C22×Dic5C24112yes—
346C22×Dic5C24124yes—
347#713—24no—
348Q8×D5—24no—
349#711—212no—
350#711—224no—
351#711—424no—
352#711—412no—
353#711—424no—
354#711—424no—
355D4×D5—212no—
356#709—212no—
357C2×D20C2413yes—
358C2×C4×D5—212no—
359C2×C4×D5—212no—
360C2×C4×D5—46no—
361C2×C4×D5C2411yescharacteristic
362C2×C4×D5C2411yescharacteristic
363C2×C4×D5C2413yes—
364C2×C4×D5C2413yes—
365C2×C4×D5C2413yes—
366C2×C4×D5C2413yes—
367C2×C4×D5C2413yes—
368C2×C4×D5C2413yes—
369C2×C4×D5C2413yes—
370C2×C4×D5C2413yes—
371C2×C4×D5C2413yes—
372C2×C4×D5C2411yescharacteristic
373C2×Dic10—412no—
374C2×Dic10C2416yes—
375C2×Dic10C2413yes—
376C2×Dic10C2412yes—
377C2×Dic10C24112yes—
378C5×C4⋊C4C2413yes—
379C5×C4⋊C4C2413yes—
380C5×C4⋊C4C2412yes—
381C5×C4⋊C4C2412yes—
382C5×C22⋊C4C2416yes—
383C5×C22⋊C4C24112yes—
384C5×C22⋊C4C24112yes—
385C42×C5C2411yescharacteristic
386C42×C5C2413yes—
387C42×C5C2413yes—
388C42×C5C2413yes—
389C22⋊Dic5C2416yes—
390C22⋊Dic5C24112yes—
391C22⋊Dic5C24112yes—
392C22⋊Dic5C24112yes—
393C22⋊Dic5C24112yes—
394C22⋊Dic5C24124yes—
395C22⋊Dic5C24124yes—
396C22⋊Dic5C24112yes—
397#685C2416yes—
398#685C2416yes—
399#685C2414yes—
400#685C24112yes—
401C4⋊Dic5C2412yes—
402C4⋊Dic5C2416yes—
403C4⋊Dic5C2413yes—
404C4⋊Dic5C2413yes—
405C4⋊Dic5C2416yes—
406C4⋊Dic5C24112yes—
407C4⋊Dic5C24112yes—
408C4⋊Dic5C2412yes—
409C4⋊Dic5C24112yes—
410C4⋊Dic5C2414yes—
411#683C24112yes—
412#683C24112yes—
413#683C2416yes—
414#683C2416yes—
415#683C2414yes—
416#683C24112yes—
417C4×Dic5C2413yes—
418C4×Dic5C2413yes—
419C4×Dic5C24112yes—
420C4×Dic5C2411yescharacteristic
421C4×Dic5C2411yescharacteristic
422C4×Dic5C2411yescharacteristic
423C4×Dic5C2413yes—
424C4×Dic5C2413yes—
425C4×Dic5C2413yes—
426C4×Dic5C2413yes—
427C4×Dic5C2413yes—
428C4×Dic5C2413yes—
429C4×Dic5C2413yes—
430C4×Dic5C2414yes—
431C4×Dic5C24112yes—
432C2×H(5,𝔽2)C2×D512yes—
433C22×#41—51no—
434C22×#41—56no—
435#559—56no—
436#559—56no—
437Q82—52no—
438#557—52no—
439#556—56no—
440#555—512no—
441#555—56no—
442#554—56no—
443#554—56no—
444#553—512no—
445#553—512no—
446#553—512no—
447#551—524no—
448#550—54no—
449#550—56no—
450#550—56no—
451#550C2×D512yescomplemented
452#550C2×D512yescomplemented
453D4×Q8—56no—
454#548—54no—
455#548—512no—
456#547—512no—
457#547—56no—
458#546—512no—
459#546—512no—
460#546—512no—
461#546—524no—
462D42—512no—
463D42C2×D516yescomplemented
464D42C2×D516yescomplemented
465#544—56no—
466#542—512no—
467#542—512no—
468#540—512no—
469#540—512no—
470#538—524no—
471#537—56no—
472#535—56no—
473#535C2×D516yescomplemented
474#533—51no—
475#533—53no—
476#533—53no—
477#532—53no—
478#532—56no—
479#532—56no—
480#532—56no—
481#532—56no—
482#532—56no—
483#532—56no—
484#532—56no—
485#532—53no—
486#532—512no—
487#532C2×D513yescomplemented
488C2×C4⋊Q8—53no—
489C2×#127C2×D513yescomplemented
490#529—56no—
491#529—56no—
492#529—56no—
493#529—56no—
494#529—512no—
495#529—56no—
496#529—56no—
497C2×#124—56no—
498#525—56no—
499#525—56no—
500#525—56no—
501#525—524no—
502C2×#121—56no—
503C2×#121—56no—
504#520—52no—
505#520—56no—
506#520—54no—
507#518—56no—
508#518—512no—
509C4×#41—51no—
510C4×#41—56no—
511C4×#41—54no—
512C4×#41—51no—
513C4×#41—51no—
514C4×#41—53no—
515C4×#41—53no—
516C4×#41—56no—
517C4×#41—56no—
518C4×#41—53no—
519C4×#41—53no—
520C4×#41C2×D511yescharacteristic
521C2×C4×Q8—51no—
522C2×C4×Q8—51no—
523C2×C4×D4—56no—
524C2×C4×D4—512no—
525C2×C4×D4—56no—
526C2×C4×D4—53no—
527C2×C4×D4—53no—
528C2×#117—53no—
529C22×C42—53no—
530C23×C5—224no—
531C23×C5—412no—
532C23×C5—412no—
533C23×C5C25112yes—
534C23×C5C2513yes—
535C22×D5—26no—
536C22×D5—26no—
537C22×D5—43no—
538C22×D5C2513yes—
539C22×D5C2511yescharacteristic
540C5×Q8—24no—
541C5×Q8C2×#4114yescomplemented
542C5×D4—224no—
543C5×D4—224no—
544C5×D4—212no—
545C5×D4—212no—
546C5×D4—212no—
547C5×D4—412no—
548C5×D4—412no—
549C5×D4C2×#41112yescomplemented
550C2×C4×C5—224no—
551C2×C4×C5—26no—
552C2×C4×C5—26no—
553C2×C4×C5C2×#41112yescomplemented
554C2×C4×C5C2514yes—
555C2×C4×C5C2513yes—
556C2×C4×C5C2513yes—
557C2×C4×C5C2513yes—
558C2×C4×C5C2511yescharacteristic
559C2×C4×C5C2511yescharacteristic
560C2×C4×C5C2511yescharacteristic
561C22⋊D5—212no—
562C22⋊D5—224no—
563C22⋊D5—424no—
564C22⋊D5—412no—
565C2×Dic5—26no—
566C2×Dic5—26no—
567C2×Dic5—224no—
568C2×Dic5—412no—
569C2×Dic5—43no—
570C2×Dic5—424no—
571C2×Dic5—412no—
572C2×Dic5C2511yescharacteristic
573C2×Dic5C2513yes—
574C2×Dic5C2511yescharacteristic
575C2×Dic5C2513yes—
576C2×Dic5C2514yes—
577C2×Dic5C2513yes—
578C2×Dic5C25112yes—
579C2×Dic5C2511yescharacteristic
580D20—26no—
581C4×D5—26no—
582C4×D5—22no—
583C4×D5—26no—
584C4×D5—26no—
585C4×D5—26no—
586C4×D5—26no—
587C4×D5—22no—
588C4×D5—26no—
589C4×D5—26no—
590C4×D5—43no—
591C4×D5—43no—
592C4×D5H(5,𝔽2)14yescomplemented
593Dic10—26no—
594Dic10—212no—
595Dic10—24no—
596Dic10—412no—
597H(5,𝔽2)—216no—
598C2×#41—51no—
599C2×#41—53no—
600C2×#41—56no—
601C2×#41—56no—
602C2×#41—512no—
603C2×#41—512no—
604C2×#41—512no—
605C2×#41—53no—
606C2×#41—108no—
607C2×#41—2024no—
608C2×#41C22×D516yes—
609C2×#41C22×D514yes—
610C2×#41C22×D511yescharacteristic
611C22×Q8—51no—
612C22×Q8—56no—
613C22×D4—512no—
614C22×D4—53no—
615C22×D4C22×D516yes—
616C22×D4C22×D5112yes—
617C22×D4C22×D516yes—
618C22×D4C22×D516yes—
619C23×C4—512no—
620C23×C4—53no—
621C23×C4—53no—
622C23×C4—53no—
623C4⋊Q8—512no—
624C4⋊Q8—53no—
625C4⋊Q8—56no—
626C4⋊Q8—56no—
627C4⋊Q8—56no—
628C4⋊Q8—51no—
629C4⋊Q8C22×D511yescharacteristic
630#127—512no—
631#127C22×D513yes—
632#127C22×D516yes—
633#127C22×D516yes—
634#127C22×D516yes—
635#126—512no—
636#126—512no—
637#126—524no—
638#125—52no—
639#125—56no—
640#125—512no—
641#125—56no—
642#124—56no—
643#124—512no—
644#124—512no—
645#124—512no—
646#124—56no—
647#124—512no—
648#124—524no—
649#124C22×D516yes—
650#123—512no—
651#123—524no—
652#123—524no—
653#123—512no—
654#123—512no—
655#123—524no—
656C22⋊Q8—52no—
657C22⋊Q8—56no—
658C22⋊Q8—56no—
659C22⋊Q8—56no—
660C22⋊Q8—512no—
661C22⋊Q8—52no—
662C22⋊Q8—56no—
663C22⋊Q8—524no—
664C22⋊Q8—524no—
665#121—56no—
666#121—56no—
667#121—512no—
668#121—512no—
669#121—512no—
670#121—512no—
671#121—512no—
672#121—512no—
673#121—56no—
674#121—56no—
675#121—524no—
676#121—524no—
677#121—524no—
678#121—512no—
679#121C22×D516yes—
680#121C22×D516yes—
681#121C22×D5112yes—
682#121C22×D5112yes—
683#120—524no—
684#120—512no—
685#120C22×D5124yes—
686C4×Q8—51no—
687C4×Q8—51no—
688C4×Q8—52no—
689C4×Q8—56no—
690C4×Q8—54no—
691C4×Q8—53no—
692C4×Q8—53no—
693C4×Q8—52no—
694C4×Q8—56no—
695C4×Q8—53no—
696C4×Q8—53no—
697C4×Q8—56no—
698C4×Q8—56no—
699C4×Q8C22×D511yescharacteristic
700C4×Q8C22×D511yescharacteristic
701C4×D4—53no—
702C4×D4—512no—
703C4×D4—56no—
704C4×D4—512no—
705C4×D4—56no—
706C4×D4—53no—
707C4×D4—512no—
708C4×D4—512no—
709C4×D4—512no—
710C4×D4—524no—
711C4×D4—512no—
712C4×D4—512no—
713C4×D4—512no—
714C4×D4—512no—
715C4×D4—512no—
716C4×D4—56no—
717C4×D4—512no—
718C4×D4—56no—
719C4×D4—56no—
720C4×D4—56no—
721C4×D4—512no—
722C4×D4—512no—
723C4×D4—53no—
724C4×D4—53no—
725C4×D4—56no—
726C4×D4—56no—
727C4×D4—512no—
728C4×D4—512no—
729C4×D4—53no—
730C4×D4—53no—
731C4×D4C22×D513yes—
732C4×D4C22×D513yes—
733C4×D4C22×D516yes—
734C4×D4C22×D516yes—
735#117—53no—
736#117—56no—
737#117—512no—
738#117—512no—
739#117—53no—
740#117—53no—
741#117—52no—
742#117—56no—
743#117—56no—
744#117—512no—
745#117—512no—
746#117—56no—
747#117C22×D513yes—
748C2×C4⋊C4—56no—
749C2×C4⋊C4—512no—
750C2×C4⋊C4—56no—
751C2×C4⋊C4—53no—
752C2×C4⋊C4—53no—
753C2×C22⋊C4—512no—
754C2×C22⋊C4—524no—
755C2×C22⋊C4—512no—
756C2×C22⋊C4—56no—
757C2×C42—53no—
758C2×C42—53no—
759C2×C42—512no—
760C2×C42—53no—
761C2×C42—53no—
762C2×C42—53no—
763C2×C42—53no—
764C2×C42—53no—
765C2×C42—53no—
766C2×C42—53no—
767C2×C42—53no—
768C2×C42—51no—
769C2×C42C22×D513yes—
770C22×C5—23no—
771C22×C5—23no—
772C22×C5—212no—
773C22×C5—212no—
774C22×C5—212no—
775C22×C5—824no—
776C22×C5C22×#4116yes—
777C22×C5C2611yescharacteristic
778C2×D5—21no—
779C2×D5—21no—
780C2×D5—23no—
781C2×D5—23no—
782C2×D5—23no—
783C2×D5—412no—
784C2×D5C2×H(5,𝔽2)12yes—
785C4×C5—24no—
786C4×C5—23no—
787C4×C5—23no—
788C4×C5C22×#4116yes—
789C4×C5C22×#4112yes—
790C4×C5C2×H(5,𝔽2)12yes—
791C4×C5#58512yes—
792Dic5—23no—
793Dic5—21no—
794Dic5—212no—
795Dic5—23no—
796Dic5—24no—
797Dic5—21no—
798Dic5—23no—
799Dic5C2×H(5,𝔽2)12yes—
800C24—53no—
801C24C23×D5112yes—
802#41—216no—
803#41—224no—
804#41—1024no—
805#41—104no—
806#41—1012no—
807#41—1012no—
808#41—2024no—
809#41—2024no—
810#41—2012no—
811#41—2024no—
812#41#71118yescomplemented
813C2×Q8—53no—
814C2×Q8—52no—
815C2×Q8—56no—
816C2×Q8—512no—
817C2×Q8—104no—
818C2×Q8—2012no—
819C2×Q8C23×D512yes—
820C2×Q8C23×D511yescharacteristic
821C2×D4—248no—
822C2×D4—224no—
823C2×D4—412no—
824C2×D4—412no—
825C2×D4—56no—
826C2×D4—512no—
827C2×D4—512no—
828C2×D4—524no—
829C2×D4—53no—
830C2×D4—1012no—
831C2×D4—2024no—
832C2×D4C23×D5112yes—
833C2×D4C23×D516yes—
834C2×D4C23×D5112yes—
835C2×D4C23×D516yes—
836C2×D4C23×D516yes—
837C2×D4C23×D5112yes—
838C2×D4C23×D5112yes—
839C2×D4C23×D513yes—
840C22×C4—51no—
841C22×C4—53no—
842C22×C4—53no—
843C22×C4—512no—
844C22×C4—53no—
845C22×C4—512no—
846C22×C4—512no—
847C22×C4—524no—
848C22×C4—51no—
849C22×C4—51no—
850C22×C4—53no—
851C22×C4—53no—
852C22×C4—53no—
853C22×C4—53no—
854C22×C4—53no—
855C22×C4—53no—
856C22×C4—53no—
857C22×C4—53no—
858C22×C4—53no—
859C22×C4—1012no—
860C22×C4—1012no—
861C22×C4—206no—
862C22×C4—2024no—
863C22×C4C23×D513yes—
864C22×C4C23×D513yes—
865C22×C4C23×D5112yes—
866C22×C4C23×D513yes—
867C4⋊C4—53no—
868C4⋊C4—512no—
869C4⋊C4—56no—
870C4⋊C4—56no—
871C4⋊C4—512no—
872C4⋊C4—53no—
873C4⋊C4—56no—
874C4⋊C4—56no—
875C4⋊C4—512no—
876C4⋊C4—52no—
877C4⋊C4—54no—
878C4⋊C4—54no—
879C4⋊C4—52no—
880C4⋊C4—512no—
881C4⋊C4—512no—
882C4⋊C4—512no—
883C4⋊C4C23×D513yes—
884C4⋊C4C23×D513yes—
885C4⋊C4C23×D512yes—
886C4⋊C4C23×D512yes—
887C22⋊C4—56no—
888C22⋊C4—512no—
889C22⋊C4—512no—
890C22⋊C4—512no—
891C22⋊C4—524no—
892C22⋊C4—512no—
893C22⋊C4—524no—
894C22⋊C4—512no—
895C22⋊C4—56no—
896C22⋊C4—56no—
897C22⋊C4—54no—
898C22⋊C4—512no—
899C22⋊C4C23×D516yes—
900C22⋊C4C23×D5112yes—
901C22⋊C4C23×D5112yes—
902C42—53no—
903C42—51no—
904C42—51no—
905C42—51no—
906C42—53no—
907C42—53no—
908C42—54no—
909C42—53no—
910C42—53no—
911C42—53no—
912C42—53no—
913C42—53no—
914C42—53no—
915C42—512no—
916C42—512no—
917C42C23×D511yescharacteristic
918C42C23×D513yes—
919C42C23×D513yes—
920C42C23×D513yes—
921C2×C5—26no—
922C2×C5—412no—
923C2×C5C23×#4111yescharacteristic
924C2×C5C22×H(5,𝔽2)11yescharacteristic
925C2×C5C2×#58511yescharacteristic
926D5—22no—
927D5—43no—
928C23—224no—
929C23—412no—
930C23—412no—
931C23—51no—
932C23—53no—
933C23—106no—
934C23—106no—
935C23—203no—
936C23C24×D5112yes—
937C23C24×D513yes—
938Q8—24no—
939Q8—106no—
940Q8—1012no—
941Q8—104no—
942Q8—2012no—
943Q8C2×#71114yescomplemented
944D4—224no—
945D4—224no—
946D4—212no—
947D4—212no—
948D4—212no—
949D4—412no—
950D4—412no—
951D4—1024no—
952D4—1012no—
953D4—106no—
954D4—2024no—
955D4—2012no—
956D4C2×#711112yescomplemented
957C2×C4—224no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—51no—
961C2×C4—54no—
962C2×C4—51no—
963C2×C4—51no—
964C2×C4—53no—
965C2×C4—53no—
966C2×C4—54no—
967C2×C4—53no—
968C2×C4—512no—
969C2×C4—106no—
970C2×C4—106no—
971C2×C4—106no—
972C2×C4—1024no—
973C2×C4—106no—
974C2×C4—102no—
975C2×C4—106no—
976C2×C4—106no—
977C2×C4—106no—
978C2×C4—106no—
979C2×C4—102no—
980C2×C4—106no—
981C2×C4—203no—
982C2×C4—203no—
983C2×C4—2012no—
984C2×C4—2024no—
985C2×C4—203no—
986C2×C4—2012no—
987C2×C4C2×#711112yescomplemented
988C2×C4C24×D514yes—
989C2×C4C24×D513yes—
990C2×C4C24×D513yes—
991C2×C4C24×D513yes—
992C2×C4C24×D511yescharacteristic
993C2×C4C24×D511yescharacteristic
994C2×C4C24×D511yescharacteristic
995C5#6280011yescharacteristic, complemented, Sylow
996C22—23no—
997C22—23no—
998C22—212no—
999C22—212no—
1000C22—212no—
1001C22—52no—
1002C22—824no—
1003C22—101no—
1004C22—101no—
1005C22—103no—
1006C22—103no—
1007C22—103no—
1008C22—2012no—
1009C22C22×#71116yes—
1010C22C25×D511yescharacteristic
1011C4—24no—
1012C4—23no—
1013C4—23no—
1014C4—52no—
1015C4—101no—
1016C4—103no—
1017C4—101no—
1018C4—103no—
1019C4—104no—
1020C4—103no—
1021C4—1012no—
1022C4C22×#71116yes—
1023C4C22×#71112yes—
1024C4D5×H(5,𝔽2)12yes—
1025C4#6628512yes—
1026C2—26no—
1027C2—412no—
1028C2—102no—
1029C2—203no—
1030C2C23×#71111yescharacteristic
1031C2C2×#6628511yescharacteristic
1032C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3498C2
hypercenter#3498D5
hypocenterC5#62800
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C5×#3498C2semidirect
2. #10619186C2semidirect
3. Dic5×H(5,𝔽2)C2semidirect
4. #10618677C2semidirect
5. #10618674C2semidirect
6. #10618669C2semidirect
7. #10618668C2semidirect
8. #10618513C2semidirect
9. #10618511C2semidirect
10. #10618507C2semidirect
11. D4×#711C2semidirect
12. #10618233C2semidirect
13. #10618215C2semidirect
14. #10618126C2semidirect
15. #10618120C2semidirect
16. #10618091C2semidirect
17. C2×#66050C2semidirect
18. C4×D5×#41C2semidirect
19. #10617729C2semidirect
22. C22×#711C22semidirect
23. C5×#550C22semidirect
24. C5×#550C22semidirect
25. C5×D42C22semidirect
26. C5×D42C22semidirect
27. C5×#535C22semidirect
28. C5×#532C22semidirect
29. C2×C5×#127C22semidirect
31. #66168C22semidirect
32. #66167C22semidirect
33. #66165C22semidirect
34. #66162C22semidirect
36. #66161C22semidirect
37. #66161C22semidirect
39. #41×Dic5C22semidirect
40. #41×Dic5C22semidirect
41. #66140C22semidirect
42. #66140C22semidirect
43. #66140C22semidirect
44. #66139C22semidirect
45. D4×C22⋊D5C22semidirect
46. C2×#4084C22semidirect
47. C2×#4084C22semidirect
48. #66132C22semidirect
49. #66132C22semidirect
50. C2×#4082C22semidirect
51. C2×D4×Dic5C22semidirect
52. C2×D4×Dic5C22semidirect
53. C2×D4×Dic5C22semidirect
54. #66062C22semidirect
55. #66062C22semidirect
56. #66053C22semidirect
57. #66052C22semidirect
58. #66052C22semidirect
59. #66050C22semidirect
60. #66050C22semidirect
61. #66050C22semidirect
62. #66050C22semidirect
63. #66050C22semidirect
64. #66050C22semidirect
65. #66050C22semidirect
66. #66050C22semidirect
67. #66050C22semidirect
68. #66047C22semidirect
69. #66047C22semidirect
70. #66016C22semidirect
71. #66014C22semidirect
72. #66014C22semidirect
73. #65953C22semidirect
74. #65952C22semidirect
75. #65952C22semidirect
76. #65950C22semidirect
77. #65948C22semidirect
78. #65945C22semidirect
79. #65940C22semidirect
80. #65940C22semidirect
81. #65937C22semidirect
82. #65934C22semidirect
83. #65934C22semidirect
84. #65934C22semidirect
85. #65932C22semidirect
86. #65930C22semidirect
87. #65927C22semidirect
88. #65925C22semidirect
89. #65921C22semidirect
90. #65920C22semidirect
91. C4×#713C22semidirect
92. C4×#713C22semidirect
93. C4×Q8×D5C22semidirect
94. C4×Q8×D5C22semidirect
95. #65904C22semidirect
96. Q8×Dic10C22semidirect
97. #65897C22semidirect
98. #65891C22semidirect
99. #65891C22semidirect
100. #65889C22semidirect
101. C4×D4×D5C22semidirect
102. C4×D4×D5C22semidirect
103. #65877C22semidirect
104. #65877C22semidirect
105. #65876C22semidirect
106. D4×Dic10C22semidirect
107. C4×#711C22semidirect
108. C4×#711C22semidirect
109. C4×#711C22semidirect
110. C4×#711C22semidirect
111. #65856C22semidirect
112. D5×#117C22semidirect
113. #65853C22semidirect
114. C4×#709C22semidirect
115. C2×C42×D5C22semidirect
116. #65804C22semidirect
117. C2×#4015C22semidirect
299. #3498D5semidirect
315. C5×#41#41semidirect
451. #550C2×D5semidirect
452. #550C2×D5semidirect
463. D42C2×D5semidirect
464. D42C2×D5semidirect
473. #535C2×D5semidirect
487. #532C2×D5semidirect
489. C2×#127C2×D5semidirect
541. C5×Q8C2×#41semidirect
549. C5×D4C2×#41semidirect
553. C2×C4×C5C2×#41semidirect
592. C4×D5H(5,𝔽2)semidirect
812. #41#711semidirect
943. Q8C2×#711semidirect
956. D4C2×#711semidirect
987. C2×C4C2×#711semidirect
995. C5#62800semidirect

Maximal subgroups

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

subgroupindex
C5×#34982
#106191862
Dic5×H(5,𝔽2)2
#106186772
#106186742
#106186692
#106186682
#106185132
#106185112
#106185072
D4×#7112
#106182332
#106182152
#106181262
#106181202
#106180912
C2×#660502
C4×D5×#412
#106177292
#628005