Finite Group Databasebeta

← #14418186

Subgroups — #14418186

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756851C211yesmaximal, characteristic, complemented
2#11756842C211yesmaximal, characteristic, complemented
3#11754078C211yesmaximal, characteristic
4#11752395C211yesmaximal, characteristic, complemented
5C3×#65737C211yesmaximal, characteristic, complemented
6#11751982C211yesmaximal, characteristic, complemented
7#11751977C211yesmaximal, characteristic, complemented
8D3×#4010C211yesmaximal, characteristic, complemented
9#11751958C211yesmaximal, characteristic, complemented
10#11751953C211yesmaximal, characteristic, complemented
11#11751935C211yesmaximal, characteristic, complemented
12#11751689C211yesmaximal, characteristic, complemented
13#11751684C211yesmaximal, characteristic, complemented
14#11751676C211yesmaximal, characteristic, complemented
15#11751650C211yesmaximal, characteristic, complemented
16#10617453—31nomaximal, Hall
17D3×#713C2211yescharacteristic
18#92024C2211yescharacteristic
19#91992C2211yescharacteristic, complemented
20#91990C2211yescharacteristic, complemented
21C3×#4133C2211yescharacteristic, complemented
22C3×#4131C2211yescharacteristic, complemented
23C2×#6740—21no—
24#91931—21no—
25#91929—21no—
26#91927—21no—
27C4×D3×AGL(1,𝔽5)C2211yescharacteristic
28D5⋊ΓL(1,𝔽25)—21no—
29D5⋊ΓL(1,𝔽25)C2211yescharacteristic
30#91916—21no—
31#91916C2211yescharacteristic, complemented
32#91916C2211yescharacteristic, complemented
33#91915—21no—
34#91915C2211yescharacteristic
35#91914—21no—
36#91914C2211yescharacteristic, complemented
37#91914C2211yescharacteristic, complemented
38D3×#700C2211yescharacteristic
39#91803C411yescharacteristic, complemented
40C5×#915C411yescharacteristic, complemented
41C3×#4062C2211yescharacteristic
42#91520C411yescharacteristic, complemented
43#91516C2211yescharacteristic
44#91512C411yescharacteristic, complemented
45#91498C411yescharacteristic, complemented
46#91492C2211yescharacteristic
47#91480C411yescharacteristic, complemented
48#91278C411yescharacteristic, complemented
49#91271C2211yescharacteristic
50#91253C411yescharacteristic, complemented
51D5×ΓL(1,𝔽25)C2211yescharacteristic
52#91239C2211yescharacteristic, complemented
53#91237C2211yescharacteristic, complemented
54#91224C2211yescharacteristic, complemented
55C8×ΓL(1,𝔽16)C2211yescharacteristic, complemented
56C3×#4010C2211yescharacteristic, complemented
57C3×#4008C2211yescharacteristic, complemented
58C3×#3996C2211yescharacteristic, complemented
59C3×#3992C2211yescharacteristic, complemented
60#91162C2211yescharacteristic, complemented
61#91161C2211yescharacteristic, complemented
62#91158C2211yescharacteristic, complemented
63#91158C2211yescharacteristic, complemented
64#91157C2211yescharacteristic, complemented
65#91157C2211yescharacteristic, complemented
66#91149C2211yescharacteristic, complemented
67ΓL(1,𝔽16)⋊C8C2211yescharacteristic, complemented
68#79898—51nomaximal, Hall
69#66264—31no—
70#66260—31no—
71#66111—31no—
72D5⋊#104—31no—
73C2×#4010—31no—
74#65741—31no—
75#65741—31no—
76#65740—31no—
77#65740—31no—
78#65737—31no—
79#65737D311yescharacteristic, complemented
80#65736—31no—
81#65736—31no—
82#65729—31no—
83M16×AGL(1,𝔽5)—31no—
84C2×D3×AGL(1,𝔽5)—21no—
85#6821C2×C411yescharacteristic
86D4×D15C2×C411yescharacteristic
87C5×D3×Q8C2×C411yescharacteristic
88C5×#237C2×C411yescharacteristic
89C3×#713C2311yescharacteristic
90C3×#711C2311yescharacteristic
91#6790—21no—
92C2×#1200—21no—
93#6782—21no—
94#6779—21no—
95D3×D20—21no—
96D3×D20C2×C411yescharacteristic
97C4×D3×D5—21no—
98C4×D3×D5C2311yescharacteristic
99#6773—21no—
100#6773C2311yescharacteristic
101#6773C2311yescharacteristic
102D15⋊Q8C2×C411yescharacteristic
103#6769C2×C411yescharacteristic
104#6766—21no—
105#6766C2×C411yescharacteristic
106#6762—21no—
107C2×C3⋊#170—21no—
108C4×ΓL(1,𝔽16)C2311yescharacteristic
109#6758—21no—
110#6758C2311yescharacteristic
111#6758C2311yescharacteristic
112D5⋊(C3⋊C8)—21no—
113D5⋊(C3⋊C8)C2311yescharacteristic
114C3×#704—21no—
115C2×C3×#170—21no—
116C3×C4×AGL(1,𝔽5)C2311yescharacteristic
117C3×#700—21no—
118C3×#700C2311yescharacteristic
119C3×#700C2311yescharacteristic
120C3×D5⋊C8—21no—
121C3×D5⋊C8C2311yescharacteristic
122#6740—21no—
123#6740—21no—
124#6740—21no—
125#6740—21no—
126#6740—21no—
127#6740D411yescharacteristic
128#6740D411yescharacteristic
129#6739—21no—
130#6739D411yescharacteristic
131#6739D411yescharacteristic
132#6738—21no—
133#6738—21no—
134#6738—21no—
135#6738—21no—
136#6738—21no—
137D3×#170—21no—
138Dic3×AGL(1,𝔽5)—21no—
139C3×C5×SD16C2×C411yescharacteristic, complemented
140#6717C2×C411yescharacteristic, complemented
141#6715C2×C411yescharacteristic, complemented
142D120C2×C411yescharacteristic, complemented
143#6705C2×C411yescharacteristic
144C5×#216C2×C411yescharacteristic, complemented
145C5×#214C2×C411yescharacteristic, complemented
146C5×Dic12C2×C411yescharacteristic, complemented
147C5×ΓL(1,𝔽25)C2×C411yescharacteristic
148C3×#689C2×C411yescharacteristic, complemented
149C3×#686C2×C411yescharacteristic, complemented
150C3×#677C2×C411yescharacteristic, complemented
151C3×C8×D5C2311yescharacteristic
152#6661C2×C411yescharacteristic, complemented
153#6660C2×C411yescharacteristic, complemented
154#6660C2×C411yescharacteristic, complemented
155#6658C2×C411yescharacteristic, complemented
156#6655C2×C411yescharacteristic, complemented
157#6653C2×C411yescharacteristic, complemented
158#6651C2×C411yescharacteristic
159#6650C2×C411yescharacteristic
160D5×C3⋊C8C2311yescharacteristic
161#5768—51no—
162#5750—51no—
163#5750—51no—
164C3×#444—51no—
165#5196—51no—
166#5144—51no—
167#5144—51no—
168#4895—51no—
169#4893—51no—
170#4823—51no—
171#4823—51no—
172D3×#104—51no—
173D3×#104—51no—
174#4717—51no—
175#4707—51no—
176D5×#41—31no—
177C2×#713—31no—
178#4133—31no—
179#4133—31no—
180#4133—31no—
181#4133—31no—
182#4133—31no—
183#4133—61no—
184#4133—61no—
185#4133C2×D311yescharacteristic, complemented
186#4131—31no—
187#4131—61no—
188#4131—61no—
189#4131C2×D311yescharacteristic, complemented
190C2×C4×AGL(1,𝔽5)—31no—
191D5⋊M16—31no—
192D5⋊M16—31no—
193D5⋊M16—61no—
194D5⋊M16—61no—
195D5⋊M16—61no—
196C2×#700—31no—
197C2×#700—61no—
198C5×#137—31no—
199#4095—31no—
200#4088—31no—
201#4065—31no—
202#4065—31no—
203#4064—31no—
204#4064—31no—
205#4062—31no—
206#4062C2×D311yescharacteristic
207#4060—31no—
208#4060—31no—
209#4054—31no—
210D5×M16—31no—
211#4010—31no—
212#4010—31no—
213#4010—31no—
214#4010—31no—
215#4010—31no—
216#4010C2×D311yescharacteristic, complemented
217#4008—31no—
218#4008C2×D311yescharacteristic, complemented
219#3996—31no—
220#3996C2×D311yescharacteristic, complemented
221#3995—31no—
222#3995—31no—
223#3992—31no—
224#3992C2×D311yescharacteristic, complemented
225C8×AGL(1,𝔽5)—31no—
226C8×AGL(1,𝔽5)—31no—
227#2956—151noSylow
228C22×D15—21no—
229C2×D3×D5—21no—
230C2×D3×D5#4111yescharacteristic
231C2×ΓL(1,𝔽16)—21no—
232C2×C3×AGL(1,𝔽5)—21no—
233D3×AGL(1,𝔽5)—42no—
234C3×C5×Q8C22×C411yescharacteristic
235C3×C5×D4C22×C411yescharacteristic
236#1220—21no—
237D60—21no—
238D60C22×C411yescharacteristic
239D60C22×C411yescharacteristic
240C4×D15—21no—
241C4×D15C22×C411yescharacteristic
242C5×#67—21no—
243C2×C5×Dic3—21no—
244C4×C5×D3—21no—
245C4×C5×D3C22×C411yescharacteristic
246C5×Dic6—21no—
247C5×Dic6C22×C411yescharacteristic
248C5×Dic6C22×C411yescharacteristic
249C3×C22⋊D5—21no—
250C2×C3×Dic5—21no—
251C3×D20—21no—
252C3×D20C22×C411yescharacteristic
253C3×C4×D5—21no—
254C3×C4×D5C2411yescharacteristic
255C3×Dic10C22×C411yescharacteristic
256#1204—21no—
257#1203—21no—
258#1202—21no—
259#1202—21no—
260#1202—21no—
261#1202—21no—
262#1200—21no—
263#1200—21no—
264#1200—21no—
265#1200—21no—
266#1200C2×D411yescharacteristic
267D3×Dic5C2×D411yescharacteristic
268D5×Dic3—21no—
269D5×Dic3#4111yescharacteristic
270C3⋊#170—21no—
271C3⋊#170—21no—
272C3⋊#170C2×D411yescharacteristic
273C3⋊#170C2×D411yescharacteristic
274C3×#170—21no—
275C3×#170—21no—
276C3×#170C2×D411yescharacteristic
277C3×#170C2×D411yescharacteristic
278C3×C5×C8C22×C411yescharacteristic
279C3⋊#168C22×C411yescharacteristic
280C3×#168C22×C411yescharacteristic
281C5×C3⋊C8C22×C411yescharacteristic
282D3×#41—51no—
283D3×#41—51no—
284C3×#135—51no—
285C3×#131—51no—
286C3×#131—51no—
287#950—51no—
288#950—51no—
289#948—51no—
290#948—51no—
291#918—51no—
292#918—51no—
293#915—51no—
294#915AGL(1,𝔽5)11yescharacteristic, complemented
295#914—51no—
296#914—51no—
297#911—51no—
298#911—51no—
299#907—51no—
300#907—51no—
301#907—101no—
302#907—101no—
303D3×M16—51no—
304D3×M16—51no—
305D3×M16—101no—
306D3×M16—101no—
307#904—51no—
308#901—51no—
309#901—51no—
310#901—101no—
311#901—101no—
312C2×ΓL(1,𝔽25)—51no—
313C2×ΓL(1,𝔽25)—51no—
314C2×ΓL(1,𝔽25)—101no—
315C2×ΓL(1,𝔽25)—101no—
316C42×D3—51no—
317C3×#108—51no—
318C3×#104—51no—
319C3×#104—51no—
320C3×#97—51no—
321#837—51no—
322#837—51no—
323#825—51no—
324#825—51no—
325#822—51no—
326#822—51no—
327#819—51no—
328C8×Dic3—51no—
329C8×Dic3—51no—
330#805—51no—
331#805—51no—
332#803—51no—
333C22×AGL(1,𝔽5)—61no—
334C5×#41—31no—
335C2×C5×Q8—31no—
336#713—31no—
337#713—31no—
338#713—31no—
339#713—31no—
340#713—61no—
341#713—61no—
342#713C22×D311yescharacteristic
343Q8×D5—31no—
344#711—61no—
345#711C22×D311yescharacteristic
346D4×D5—31no—
347D4×D5—61no—
348#709—31no—
349#709—61no—
350C2×D20—31no—
351C2×D20—61no—
352C2×C4×D5—31no—
353C2×C4×D5—61no—
354C2×C4×D5—61no—
355#704—21no—
356#704—31no—
357#704—31no—
358#704—61no—
359#704—61no—
360C2×#170—21no—
361C2×#170—61no—
362C2×#170—61no—
363C4×AGL(1,𝔽5)—31no—
364C4×AGL(1,𝔽5)—61no—
365C4×AGL(1,𝔽5)C22×D311yescharacteristic
366#700—21no—
367#700—31no—
368#700—31no—
369#700—31no—
370#700—31no—
371#700—61no—
372#700—61no—
373#700—61no—
374#700—61no—
375#700—61no—
376#700—61no—
377#700C22×D311yescharacteristic
378#700C22×D311yescharacteristic
379D5⋊C8—21no—
380D5⋊C8—31no—
381D5⋊C8—61no—
382D5⋊C8—61no—
383D5⋊C8—61no—
384D5⋊C8—61no—
385D5⋊C8—61no—
386D5⋊C8—61no—
387D5⋊C8C22×D311yescharacteristic
388C5×Q16—31no—
389C5×Q16—31no—
390C5×SD16—31no—
391C5×SD16C4×D311yescharacteristic, complemented
392C5×M16—31no—
393#689—31no—
394#689C4×D311yescharacteristic, complemented
395#688—31no—
396#688—31no—
397#688—31no—
398#688—31no—
399#686—31no—
400#686C4×D311yescharacteristic, complemented
401#681—31no—
402D40—31no—
403D40—31no—
404#677—31no—
405#677C4×D311yescharacteristic, complemented
406#676—31no—
407#676—31no—
408C8×D5—31no—
409C8×D5C22×D311yescharacteristic
410#575—151no—
411#568—151no—
412#568—151no—
413#444—51no—
414#444—151no—
415#444—151no—
416#444—151no—
417#443—151no—
418#443—151no—
419#443—151no—
420#443—151no—
421#430—151no—
422C2×#104—151no—
423C2×#104—151no—
424C4×M16—151no—
425C22×C3×C5—21no—
426C2×D15—21no—
427C2×D15—21no—
428C2×D15—81no—
429C2×D15C4×D411yescharacteristic
430C2×C5×D3C4×D411yescharacteristic
431C2×C3×D5—21no—
432C2×C3×D5C2×#4111yescharacteristic
433D3×D5—41no—
434D3×D5—81no—
435ΓL(1,𝔽16)—22no—
436C3×AGL(1,𝔽5)—41no—
437C3×C4×C5—21no—
438C3×C4×C5C23×C411yescharacteristic
439Dic15C4×D411yescharacteristic
440C3×Dic5—21no—
441C3×Dic5C22×D411yescharacteristic
442C5×Dic3—21no—
443C5×Dic3—21no—
444C5×Dic3C4×D411yescharacteristic
445C3×#41—51no—
446C3×#41—51no—
447#239—51no—
448#239—51no—
449D3×Q8—51no—
450D3×Q8C2×AGL(1,𝔽5)11yescharacteristic
451#237—51no—
452#237—101no—
453#237—101no—
454#237C2×AGL(1,𝔽5)11yescharacteristic
455D3×D4—51no—
456D3×D4—51no—
457D3×D4—101no—
458D3×D4—101no—
459#235—51no—
460#235—51no—
461#235—101no—
462#235—101no—
463C2×C4×D3—51no—
464C2×C4×D3—101no—
465C2×C4×D3—101no—
466C2×C4×D3—101no—
467C3×Q16—51no—
468C3×SD16—51no—
469C3×SD16C2×AGL(1,𝔽5)11yescharacteristic, complemented
470C3×D8—51no—
471C3×M16—51no—
472C3×M16—51no—
473C3×M16—101no—
474C3×M16—101no—
475C2×C3×C8—51no—
476C2×C3×C8—51no—
477C2×C3×C8—101no—
478C2×C3×C8—101no—
479C3×C42—51no—
480#216—51no—
481#216C2×AGL(1,𝔽5)11yescharacteristic, complemented
482#215—51no—
483#215—51no—
484#214—51no—
485#214C2×AGL(1,𝔽5)11yescharacteristic, complemented
486#213—51no—
487#213—51no—
488C4×Dic3—51no—
489C4×Dic3—101no—
490#208—51no—
491#208—51no—
492#208—101no—
493#208—101no—
494C2×C3⋊C8—51no—
495C2×C3⋊C8—51no—
496C2×C3⋊C8—101no—
497C2×C3⋊C8—101no—
498Dic12C2×AGL(1,𝔽5)11yescharacteristic, complemented
499D24—51no—
500#204—51no—
501#204—51no—
502ΓL(1,𝔽25)—51no—
503ΓL(1,𝔽25)—51no—
504ΓL(1,𝔽25)—51no—
505ΓL(1,𝔽25)—51no—
506ΓL(1,𝔽25)—51no—
507ΓL(1,𝔽25)—51no—
508ΓL(1,𝔽25)—51no—
509ΓL(1,𝔽25)—101no—
510ΓL(1,𝔽25)—101no—
511ΓL(1,𝔽25)—101no—
512ΓL(1,𝔽25)—101no—
513ΓL(1,𝔽25)—101no—
514ΓL(1,𝔽25)—101no—
515ΓL(1,𝔽25)C2×AGL(1,𝔽5)11yescharacteristic
516D3×C8—101no—
517D3×C8—101no—
518D3×C8—101no—
519D3×C8—101no—
520D3×C8—101no—
521D3×C8—101no—
522C22×D5—31no—
523C22×D5—61no—
524C22×D5—61no—
525C2×AGL(1,𝔽5)—21no—
526C2×AGL(1,𝔽5)—61no—
527C2×AGL(1,𝔽5)—122no—
528C5×Q8—31no—
529C5×Q8—31no—
530C5×Q8—61no—
531C5×Q8C2×C4×D311yescharacteristic
532C5×D4—61no—
533C5×D4C2×C4×D311yescharacteristic
534C2×C4×C5—31no—
535C2×C4×C5—61no—
536C2×C4×C5—61no—
537C22⋊D5—21no—
538C22⋊D5—61no—
539C22⋊D5—61no—
540C2×Dic5—21no—
541C2×Dic5—31no—
542D20—21no—
543D20—31no—
544D20—31no—
545D20—61no—
546D20—61no—
547D20—61no—
548D20—61no—
549D20—61no—
550D20C2×C4×D311yescharacteristic
551C4×D5—21no—
552C4×D5—31no—
553C4×D5—31no—
554C4×D5—31no—
555C4×D5—61no—
556C4×D5—61no—
557C4×D5—61no—
558C4×D5—61no—
559C4×D5—61no—
560C4×D5—61no—
561C4×D5C23×D311yescharacteristic
562Dic10—61no—
563Dic10C2×C4×D311yescharacteristic
564#170—21no—
565#170—21no—
566#170—31no—
567#170—31no—
568#170—61no—
569#170—61no—
570#170D3×D411yescharacteristic
571#170D3×D411yescharacteristic
572C5×C8—31no—
573C5×C8C2×C4×D311yescharacteristic
574#168—31no—
575#168C2×C4×D311yescharacteristic
576C2×#41—151no—
577C2×#41—151no—
578#137—31no—
579#137—151no—
580#137—151no—
581#137—151no—
582AGL(1,ℤ/8)—151no—
583AGL(1,ℤ/8)—151no—
584AGL(1,ℤ/8)—151no—
585AGL(1,ℤ/8)—151no—
586#135—51no—
587#135—151no—
588#135—151no—
589#135—151no—
590#131—51no—
591#131—51no—
592#131—151no—
593#131—151no—
594#131—151no—
595#131—151no—
596#131—151no—
597#131—151no—
598#131—301no—
599#131—301no—
600#131—301no—
601#131—301no—
602C2×M16—151no—
603C2×M16—151no—
604C2×M16—151no—
605C2×M16—151no—
606C2×M16—301no—
607C2×M16—301no—
608C2×M16—301no—
609C2×M16—301no—
610C2×C42—151no—
611#108—51no—
612#108—151no—
613#108—151no—
614#108—151no—
615#104—51no—
616#104—51no—
617#104—151no—
618#104—151no—
619#104—151no—
620#104—151no—
621#104—151no—
622#104—151no—
623#97—51no—
624#97—151no—
625C4×C8—151no—
626C4×C8—151no—
627C2×C3×C5—41no—
628C2×C3×C5C2×C4×D411yescharacteristic
629D15—21no—
630D15—41no—
631D15—41no—
632C3×D5—21no—
633C3×D5—41no—
634C5×D3—21no—
635C22×D3—51no—
636C22×D3—101no—
637C22×D3—101no—
638C3×Q8—51no—
639C3×Q8C22×AGL(1,𝔽5)11yescharacteristic
640C3×D4—51no—
641C3×D4—101no—
642C3×D4—101no—
643C3×D4C22×AGL(1,𝔽5)11yescharacteristic
644C2×C3×C4—51no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—101no—
648#67—21no—
649#67—101no—
650#67—101no—
651#67—101no—
652#67—101no—
653#67—101no—
654C2×Dic3—21no—
655C2×Dic3—51no—
656C2×Dic3—101no—
657C2×Dic3—101no—
658D12—51no—
659D12—51no—
660D12—101no—
661D12—101no—
662C4×D3—21no—
663C4×D3—51no—
664C4×D3—51no—
665C4×D3—51no—
666C4×D3—101no—
667C4×D3—101no—
668C4×D3—101no—
669C4×D3—101no—
670C4×D3—101no—
671C4×D3—202no—
672C4×D3C22×AGL(1,𝔽5)11yescharacteristic
673Dic6—21no—
674Dic6—101no—
675Dic6C22×AGL(1,𝔽5)11yescharacteristic
676Dic6C22×AGL(1,𝔽5)11yescharacteristic
677C3×C8—51no—
678C3×C8—51no—
679C3×C8—51no—
680C3×C8—101no—
681C3×C8—101no—
682C3×C8C22×AGL(1,𝔽5)11yescharacteristic
683C3⋊C8—51no—
684C3⋊C8—51no—
685C3⋊C8—51no—
686C3⋊C8—101no—
687C3⋊C8—101no—
688C3⋊C8C22×AGL(1,𝔽5)11yescharacteristic
689C22×C5—21no—
690C22×C5—31no—
691C2×D5—21no—
692C2×D5—31no—
693C2×D5—61no—
694C2×D5—61no—
695C2×D5—121no—
696C2×D5—241no—
697C2×D5—241no—
698C2×D5D3×#4111yescharacteristic
699AGL(1,𝔽5)—41no—
700AGL(1,𝔽5)—62no—
701C4×C5—21no—
702C4×C5—31no—
703C4×C5—61no—
704C4×C5—61no—
705C4×C5C22×C4×D311yescharacteristic
706Dic5—21no—
707Dic5—31no—
708Dic5C2×D3×D411yescharacteristic
709#41—31no—
710#41—51no—
711#41—51no—
712#41—151no—
713#41—151no—
714#41—151no—
715#41—151no—
716#41—151no—
717#41—301no—
718#41—301no—
719#41—301no—
720#41—301no—
721C2×Q8—31no—
722C2×Q8—151no—
723C2×D4—151no—
724C2×D4—151no—
725C2×D4—301no—
726C2×D4—301no—
727C22×C4—151no—
728C22×C4—301no—
729C22×C4—301no—
730C22×C4—301no—
731Q16—31no—
732Q16—31no—
733Q16—51no—
734Q16—151no—
735SD16—31no—
736SD16—51no—
737SD16—151no—
738SD16—151no—
739SD16—151no—
740SD16—151no—
741SD16—151no—
742SD16D3×AGL(1,𝔽5)11yescharacteristic, complemented
743D8—51no—
744D8—151no—
745D8—151no—
746D8—151no—
747M16—31no—
748M16—51no—
749M16—51no—
750M16—101no—
751M16—101no—
752M16—151no—
753M16—151no—
754M16—151no—
755M16—151no—
756M16—151no—
757M16—151no—
758M16—151no—
759M16—151no—
760M16—151no—
761M16—301no—
762M16—301no—
763M16—301no—
764M16—301no—
765M16—301no—
766M16—301no—
767M16—301no—
768M16—301no—
769C2×C8—51no—
770C2×C8—51no—
771C2×C8—101no—
772C2×C8—101no—
773C2×C8—151no—
774C2×C8—151no—
775C2×C8—301no—
776C2×C8—301no—
777C2×C8—301no—
778C2×C8—301no—
779C2×C8—301no—
780C2×C8—301no—
781C2×C8—301no—
782C2×C8—301no—
783C42—51no—
784C42—151no—
785C42—301no—
786C3×C5#295611yescharacteristic, complemented, Hall
787C22×C3—21no—
788C22×C3—51no—
789C22×C3—101no—
790C2×D3—51no—
791C2×D3—101no—
792C2×D3—101no—
793C2×D3—201no—
794C2×D3—401no—
795C2×D3—401no—
796C2×D3D4×AGL(1,𝔽5)11yescharacteristic
797C3×C4—21no—
798C3×C4—51no—
799C3×C4—101no—
800C3×C4—201no—
801C3×C4C23×AGL(1,𝔽5)11yescharacteristic
802Dic3—21no—
803Dic3—21no—
804Dic3—51no—
805Dic3—102no—
806Dic3D4×AGL(1,𝔽5)11yescharacteristic
807C2×C5—41no—
808C2×C5—61no—
809C2×C5C4×D3×D411yescharacteristic
810D5—21no—
811D5—41no—
812D5—61no—
813D5—121no—
814D5—121no—
815C23—151no—
816C23—301no—
817C23—301no—
818Q8—31no—
819Q8—31no—
820Q8—51no—
821Q8—61no—
822Q8—301no—
823Q8C2×D3×AGL(1,𝔽5)11yescharacteristic
824D4—51no—
825D4—61no—
826D4—101no—
827D4—101no—
828D4—151no—
829D4—151no—
830D4—301no—
831D4—301no—
832D4—301no—
833D4—301no—
834D4—301no—
835D4—301no—
836D4—301no—
837D4C2×D3×AGL(1,𝔽5)11yescharacteristic
838C2×C4—31no—
839C2×C4—51no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—101no—
845C2×C4—151no—
846C2×C4—151no—
847C2×C4—151no—
848C2×C4—151no—
849C2×C4—301no—
850C2×C4—301no—
851C2×C4—301no—
852C2×C4—301no—
853C2×C4—301no—
854C2×C4—301no—
855C2×C4—301no—
856C2×C4—602no—
857C8—31no—
858C8—51no—
859C8—51no—
860C8—51no—
861C8—101no—
862C8—101no—
863C8—151no—
864C8—151no—
865C8—151no—
866C8—301no—
867C8—301no—
868C8C2×D3×AGL(1,𝔽5)11yescharacteristic
869C2×C3—41no—
870C2×C3—101no—
871C2×C3—201no—
872C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
873D3—21no—
874D3—101no—
875D3—201no—
876D3—201no—
877C5#7989811yescharacteristic, complemented, Sylow
878C22—21no—
879C22—31no—
880C22—51no—
881C22—101no—
882C22—151no—
883C22—301no—
884C22—301no—
885C22—601no—
886C22—1201no—
887C22—1201no—
888C4—21no—
889C4—31no—
890C4—51no—
891C4—61no—
892C4—61no—
893C4—101no—
894C4—151no—
895C4—201no—
896C4—302no—
897C4C22×D3×AGL(1,𝔽5)11yescharacteristic
898C3#1061745311yescharacteristic, complemented, Sylow
899C2—41no—
900C2—61no—
901C2—101no—
902C2—201no—
903C2—301no—
904C2—601no—
905C2—601no—
906C2D3×D4×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2D3×D4×AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC3×C5×SD16C2×C4
socleC2×C3×C5C2×C4×D4
prime radical#11754078C2
cosocleC3×C4×D5C24
hypercenterSD16D3×AGL(1,𝔽5)
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #11756851C2semidirect
2. #11756842C2semidirect
4. #11752395C2semidirect
5. C3×#65737C2semidirect
6. #11751982C2semidirect
7. #11751977C2semidirect
8. D3×#4010C2semidirect
9. #11751958C2semidirect
10. #11751953C2semidirect
11. #11751935C2semidirect
12. #11751689C2semidirect
13. #11751684C2semidirect
14. #11751676C2semidirect
15. #11751650C2semidirect
19. #91992C22semidirect
20. #91990C22semidirect
21. C3×#4133C22semidirect
22. C3×#4131C22semidirect
31. #91916C22semidirect
32. #91916C22semidirect
36. #91914C22semidirect
37. #91914C22semidirect
39. #91803C4semidirect
40. C5×#915C4semidirect
42. #91520C4semidirect
44. #91512C4semidirect
45. #91498C4semidirect
47. #91480C4semidirect
48. #91278C4semidirect
50. #91253C4semidirect
52. #91239C22semidirect
53. #91237C22semidirect
54. #91224C22semidirect
55. C8×ΓL(1,𝔽16)C22semidirect
56. C3×#4010C22semidirect
57. C3×#4008C22semidirect
58. C3×#3996C22semidirect
59. C3×#3992C22semidirect
60. #91162C22semidirect
61. #91161C22semidirect
62. #91158C22semidirect
63. #91158C22semidirect
64. #91157C22semidirect
65. #91157C22semidirect
66. #91149C22semidirect
67. ΓL(1,𝔽16)⋊C8C22semidirect
79. #65737D3semidirect
139. C3×C5×SD16C2×C4semidirect
140. #6717C2×C4semidirect
141. #6715C2×C4semidirect
142. D120C2×C4semidirect
144. C5×#216C2×C4semidirect
145. C5×#214C2×C4semidirect
146. C5×Dic12C2×C4semidirect
148. C3×#689C2×C4semidirect
149. C3×#686C2×C4semidirect
150. C3×#677C2×C4semidirect
152. #6661C2×C4semidirect
153. #6660C2×C4semidirect
154. #6660C2×C4semidirect
155. #6658C2×C4semidirect
156. #6655C2×C4semidirect
157. #6653C2×C4semidirect
185. #4133C2×D3semidirect
189. #4131C2×D3semidirect
216. #4010C2×D3semidirect
218. #4008C2×D3semidirect
220. #3996C2×D3semidirect
224. #3992C2×D3semidirect
294. #915AGL(1,𝔽5)semidirect
391. C5×SD16C4×D3semidirect
394. #689C4×D3semidirect
400. #686C4×D3semidirect
405. #677C4×D3semidirect
469. C3×SD16C2×AGL(1,𝔽5)semidirect
481. #216C2×AGL(1,𝔽5)semidirect
485. #214C2×AGL(1,𝔽5)semidirect
498. Dic12C2×AGL(1,𝔽5)semidirect
742. SD16D3×AGL(1,𝔽5)semidirect
786. C3×C5#2956semidirect
877. C5#79898semidirect
898. C3#10617453semidirect

Maximal subgroups

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

subgroupindex
#117568512
#117568422
#117540782
#117523952
C3×#657372
#117519822
#117519772
D3×#40102
#117519582
#117519532
#117519352
#117516892
#117516842
#117516762
#117516502
#106174533
#798985