Finite Group Databasebeta

← #14418187

Subgroups — #14418187

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#11756842C211yesmaximal, characteristic, complemented
2#11756841C211yesmaximal, characteristic, complemented
3#11754052C211yesmaximal, characteristic
4#11752392C211yesmaximal, characteristic, complemented
5C3×#65732C211yesmaximal, characteristic, complemented
6#11751957C211yesmaximal, characteristic, complemented
7#11751955C211yesmaximal, characteristic, complemented
8#11751954C211yesmaximal, characteristic, complemented
9#11751952C211yesmaximal, characteristic, complemented
10D3×#4008C211yesmaximal, characteristic, complemented
11#11751935C211yesmaximal, characteristic, complemented
12#11751688C211yesmaximal, characteristic, complemented
13#11751679C211yesmaximal, characteristic, complemented
14#11751676C211yesmaximal, characteristic, complemented
15AGL(1,𝔽5)×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16#10617449—31nomaximal, Hall
17#92024C2211yescharacteristic
18D3×#711C2211yescharacteristic
19#91990C2211yescharacteristic, complemented
20#91990C2211yescharacteristic, complemented
21C3×#4131C2211yescharacteristic, complemented
22C3×#4131C2211yescharacteristic, complemented
23C2×#6740—21no—
24C2×#6739—21no—
25#91931—21no—
26#91929—21no—
27#91929—21no—
28D3×#704—21no—
29#91927—21no—
30#91927—21no—
31C4×D3×AGL(1,𝔽5)C2211yescharacteristic
32D5⋊ΓL(1,𝔽25)C2211yescharacteristic
33#91916C2211yescharacteristic, complemented
34#91915C2211yescharacteristic
35#91914C2211yescharacteristic, complemented
36#91913C2211yescharacteristic, complemented
37D3×#700C2211yescharacteristic
38#91911C2211yescharacteristic, complemented
39#91800C411yescharacteristic, complemented
40C5×#911C411yescharacteristic, complemented
41C3×#4058C2211yescharacteristic
42#91500C411yescharacteristic, complemented
43#91496C411yescharacteristic, complemented
44#91492C2211yescharacteristic
45#91490C2211yescharacteristic
46#91488C411yescharacteristic, complemented
47#91486C411yescharacteristic, complemented
48#91280C411yescharacteristic, complemented
49#91269C2211yescharacteristic
50#91263C411yescharacteristic, complemented
51D5×ΓL(1,𝔽25)C2211yescharacteristic
52#91237C2211yescharacteristic, complemented
53#91237C2211yescharacteristic, complemented
54#91224C2211yescharacteristic, complemented
55#91221C2211yescharacteristic, complemented
56C3×#4008C2211yescharacteristic, complemented
57C3×#4008C2211yescharacteristic, complemented
58C3×#3996C2211yescharacteristic, complemented
59C3×C8×AGL(1,𝔽5)C2211yescharacteristic, complemented
60#91162C2211yescharacteristic, complemented
61#91161C2211yescharacteristic, complemented
62#91158C2211yescharacteristic, complemented
63#91157C2211yescharacteristic, complemented
64#91156C2211yescharacteristic, complemented
65#91155C2211yescharacteristic, complemented
66#91150C2211yescharacteristic, complemented
67AGL(1,𝔽5)×C3⋊C8C2211yescharacteristic, complemented
68#79889—51nomaximal, Hall
69#66264—31no—
70#66256—31no—
71#66107—31no—
72D5⋊#104—31no—
73C2×#4008—31no—
74#65737—31no—
75#65737—31no—
76#65736—31no—
77#65736—31no—
78#65733—31no—
79#65733—31no—
80#65732—31no—
81#65732D311yescharacteristic, complemented
82#65729—31no—
83M16×AGL(1,𝔽5)—31no—
84C2×D3×AGL(1,𝔽5)—21no—
85#6819C2×C411yescharacteristic
86D4×D15C2×C411yescharacteristic
87C5×#237C2×C411yescharacteristic
88C5×D3×D4C2×C411yescharacteristic
89C3×#711C2311yescharacteristic
90C3×#711C2311yescharacteristic
91#6790—21no—
92D3×C22⋊D5—21no—
93C2×#1200—21no—
94#6782—21no—
95#6782—21no—
96C2×D3×Dic5—21no—
97#6780—21no—
98#6779—21no—
99C4×D3×D5C2311yescharacteristic
100#6773C2311yescharacteristic
101#6772C2311yescharacteristic
102D15⋊Q8C2×C411yescharacteristic
103#6769C2×C411yescharacteristic
104#6768C2×C411yescharacteristic
105D3×Dic10C2×C411yescharacteristic
106#6762—21no—
107#6762—21no—
108C2×C3⋊#170—21no—
109C2×C3⋊#170—21no—
110C4×ΓL(1,𝔽16)C2311yescharacteristic
111#6758C2311yescharacteristic
112#6758C2311yescharacteristic
113D5⋊(C3⋊C8)C2311yescharacteristic
114C3×#704—21no—
115C3×#704—21no—
116C2×C3×#170—21no—
117C2×C3×#170—21no—
118C3×C4×AGL(1,𝔽5)C2311yescharacteristic
119C3×#700C2311yescharacteristic
120C3×#700C2311yescharacteristic
121C3×D5⋊C8C2311yescharacteristic
122#6740—21no—
123#6740—21no—
124#6740—21no—
125#6740D411yescharacteristic
126#6740D411yescharacteristic
127#6739—21no—
128#6739—21no—
129#6739—21no—
130#6739D411yescharacteristic
131#6739D411yescharacteristic
132#6738—21no—
133#6738—21no—
134#6738—21no—
135D3×#170—21no—
136D3×#170—21no—
137D3×#170—21no—
138Dic3×AGL(1,𝔽5)—21no—
139C3×C5×D8C2×C411yescharacteristic, complemented
140#6716C2×C411yescharacteristic, complemented
141#6715C2×C411yescharacteristic, complemented
142#6706C2×C411yescharacteristic, complemented
143#6705C2×C411yescharacteristic
144C5×#214C2×C411yescharacteristic, complemented
145C5×#213C2×C411yescharacteristic, complemented
146C5×#204C2×C411yescharacteristic, complemented
147C5×ΓL(1,𝔽25)C2×C411yescharacteristic
148C3×#687C2×C411yescharacteristic, complemented
149C3×#687C2×C411yescharacteristic, complemented
150C3×Dic20C2×C411yescharacteristic, complemented
151C3×C8×D5C2311yescharacteristic
152#6663C2×C411yescharacteristic, complemented
153#6662C2×C411yescharacteristic, complemented
154#6661C2×C411yescharacteristic, complemented
155#6658C2×C411yescharacteristic, complemented
156#6656C2×C411yescharacteristic, complemented
157#6654C2×C411yescharacteristic, complemented
158#6651C2×C411yescharacteristic
159#6650C2×C411yescharacteristic
160D5×C3⋊C8C2311yescharacteristic
161#5768—51no—
162#5750—51no—
163#5750—51no—
164C3×#443—51no—
165#5197—51no—
166#5145—51no—
167#5145—51no—
168#4894—51no—
169#4893—51no—
170#4824—51no—
171#4824—51no—
172D3×#104—51no—
173D3×#104—51no—
174#4700—51no—
175C4×ΓL(1,𝔽25)—51no—
176D5×#41—31no—
177C2×#711—31no—
178C2×#704—61no—
179C2×#704—61no—
180#4133—31no—
181#4133—31no—
182#4131—31no—
183#4131—31no—
184#4131—31no—
185#4131—31no—
186#4131—61no—
187#4131—61no—
188#4131—61no—
189#4131—61no—
190#4131C2×D311yescharacteristic, complemented
191#4131C2×D311yescharacteristic, complemented
192C2×C4×AGL(1,𝔽5)—31no—
193D5⋊M16—31no—
194D5⋊M16—31no—
195D5⋊M16—61no—
196C2×#700—31no—
197C2×#700—61no—
198C5×AGL(1,ℤ/8)—31no—
199#4097—31no—
200#4078—31no—
201#4062—31no—
202#4062—31no—
203#4061—31no—
204#4061—31no—
205#4058—31no—
206#4058C2×D311yescharacteristic
207#4057—31no—
208#4057—31no—
209#4055—31no—
210D5×M16—31no—
211#4010—31no—
212#4010—31no—
213#4008—31no—
214#4008—31no—
215#4008—31no—
216#4008—31no—
217#4008C2×D311yescharacteristic, complemented
218#4008C2×D311yescharacteristic, complemented
219#3996—31no—
220#3996C2×D311yescharacteristic, complemented
221#3995—31no—
222#3995—31no—
223#3992—31no—
224#3992—31no—
225C8×AGL(1,𝔽5)—31no—
226C8×AGL(1,𝔽5)C2×D311yescharacteristic, complemented
227#2956—151noSylow
228C22×D15—21no—
229C22×C5×D3—21no—
230C2×D3×D5#4111yescharacteristic
231C2×ΓL(1,𝔽16)—21no—
232C2×C3×AGL(1,𝔽5)—21no—
233D3×AGL(1,𝔽5)—42no—
234C3×C5×D4C22×C411yescharacteristic
235C3×C5×D4C22×C411yescharacteristic
236#1220—21no—
237#1220—21no—
238C2×Dic15—21no—
239D60C22×C411yescharacteristic
240C4×D15C22×C411yescharacteristic
241Dic30C22×C411yescharacteristic
242C5×#67—21no—
243C5×#67—21no—
244C2×C5×Dic3—21no—
245C5×D12C22×C411yescharacteristic
246C4×C5×D3C22×C411yescharacteristic
247C5×Dic6C22×C411yescharacteristic
248C3×C22⋊D5—21no—
249C3×C22⋊D5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C3×C4×D5C2411yescharacteristic
253C3×Dic10C22×C411yescharacteristic
254C3×Dic10C22×C411yescharacteristic
255#1204—21no—
256#1204—21no—
257#1203—21no—
258#1203—21no—
259#1202—21no—
260#1201—21no—
261#1200—21no—
262#1200—21no—
263#1200—21no—
264#1200C2×D411yescharacteristic
265D3×Dic5—21no—
266D3×Dic5—21no—
267D3×Dic5—21no—
268D3×Dic5C2×D411yescharacteristic
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#915—51no—
295#914—51no—
296#914—51no—
297#911—51no—
298#911AGL(1,𝔽5)11yescharacteristic, complemented
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×C4×C8—51no—
321#837—51no—
322#837—51no—
323#825—51no—
324#825—51no—
325#822—51no—
326#822—51no—
327#819—51no—
328#815—51no—
329#815—51no—
330#805—51no—
331#805—51no—
332C4×C3⋊C8—51no—
333C22×AGL(1,𝔽5)—61no—
334C5×#41—31no—
335C2×C5×D4—31no—
336C2×C22⋊D5—61no—
337C22×Dic5—61no—
338#713—31no—
339Q8×D5—31no—
340#711—31no—
341#711—31no—
342#711—31no—
343#711—61no—
344#711—61no—
345#711—61no—
346#711C22×D311yescharacteristic
347#711C22×D311yescharacteristic
348D4×D5—31no—
349D4×D5—61no—
350#709—31no—
351#709—61no—
352C2×C4×D5—31no—
353C2×C4×D5—61no—
354C2×Dic10—31no—
355#704—21no—
356#704—21no—
357#704—31no—
358#704—31no—
359#704—61no—
360#704—61no—
361#704—61no—
362#704—61no—
363#704—61no—
364C2×#170—21no—
365C2×#170—21no—
366C2×#170—61no—
367C2×#170—61no—
368C2×#170—61no—
369C2×#170—61no—
370C2×#170—61no—
371C4×AGL(1,𝔽5)—31no—
372C4×AGL(1,𝔽5)—61no—
373C4×AGL(1,𝔽5)C22×D311yescharacteristic
374#700—31no—
375#700—31no—
376#700—31no—
377#700—31no—
378#700—61no—
379#700—61no—
380#700—61no—
381#700C22×D311yescharacteristic
382#700C22×D311yescharacteristic
383D5⋊C8—31no—
384D5⋊C8—61no—
385D5⋊C8—61no—
386D5⋊C8—61no—
387D5⋊C8C22×D311yescharacteristic
388C5×SD16—31no—
389C5×SD16—31no—
390C5×D8—31no—
391C5×D8C4×D311yescharacteristic, complemented
392C5×M16—31no—
393#689—31no—
394#689—31no—
395#687—31no—
396#687—31no—
397#687C4×D311yescharacteristic, complemented
398#687C4×D311yescharacteristic, complemented
399#686—31no—
400#686—31no—
401#681—31no—
402Dic20—31no—
403Dic20C4×D311yescharacteristic, complemented
404#677—31no—
405#677—31no—
406#676—31no—
407#676—31no—
408C8×D5—31no—
409C8×D5C22×D311yescharacteristic
410#575—151no—
411#568—151no—
412#568—151no—
413#444—151no—
414#444—151no—
415#444—151no—
416#444—151no—
417#443—51no—
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—
426C22×C3×C5—21no—
427C2×D15—21no—
428C2×D15—81no—
429C2×D15C4×D411yescharacteristic
430C2×C5×D3—21no—
431C2×C5×D3—81no—
432C2×C5×D3C4×D411yescharacteristic
433C2×C3×D5C2×#4111yescharacteristic
434D3×D5—41no—
435ΓL(1,𝔽16)—41no—
436C3×AGL(1,𝔽5)—22no—
437C3×C4×C5C23×C411yescharacteristic
438Dic15—21no—
439Dic15C4×D411yescharacteristic
440C3×Dic5—21no—
441C3×Dic5—21no—
442C3×Dic5C22×D411yescharacteristic
443C5×Dic3—21no—
444C5×Dic3C4×D411yescharacteristic
445C3×#41—51no—
446C3×#41—51no—
447#239—51no—
448#239—51no—
449D3×Q8—51no—
450D3×Q8—51no—
451#237—51no—
452#237—101no—
453#237—101no—
454#237C2×AGL(1,𝔽5)11yescharacteristic
455D3×D4—51no—
456D3×D4—101no—
457D3×D4—101no—
458D3×D4C2×AGL(1,𝔽5)11yescharacteristic
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×SD16—51no—
470C3×D8C2×AGL(1,𝔽5)11yescharacteristic, complemented
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#216—51no—
482#215—51no—
483#215—51no—
484#214—51no—
485#214C2×AGL(1,𝔽5)11yescharacteristic, complemented
486#213—51no—
487#213C2×AGL(1,𝔽5)11yescharacteristic, complemented
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—
498Dic12—51no—
499D24—51no—
500#204—51no—
501#204C2×AGL(1,𝔽5)11yescharacteristic, complemented
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—
522C23×C5—61no—
523C22×D5—31no—
524C22×D5—61no—
525C2×AGL(1,𝔽5)—21no—
526C2×AGL(1,𝔽5)—61no—
527C2×AGL(1,𝔽5)—122no—
528C5×Q8—31no—
529C5×D4—31no—
530C5×D4—61no—
531C5×D4—61no—
532C5×D4C2×C4×D311yescharacteristic
533C5×D4C2×C4×D311yescharacteristic
534C2×C4×C5—31no—
535C2×C4×C5—61no—
536C22⋊D5—21no—
537C22⋊D5—21no—
538C22⋊D5—61no—
539C22⋊D5—61no—
540C22⋊D5—61no—
541C22⋊D5—61no—
542C22⋊D5—61no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—31no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—61no—
550D20—31no—
551D20—61no—
552C4×D5—31no—
553C4×D5—31no—
554C4×D5—31no—
555C4×D5—61no—
556C4×D5—61no—
557C4×D5—61no—
558C4×D5C23×D311yescharacteristic
559Dic10—31no—
560Dic10—61no—
561Dic10—61no—
562Dic10C2×C4×D311yescharacteristic
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—151no—
579#137—151no—
580#137—151no—
581#137—151no—
582AGL(1,ℤ/8)—31no—
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—151no—
624#97—151no—
625C4×C8—51no—
626C4×C8—151no—
627C2×C3×C5—41no—
628C2×C3×C5—41no—
629C2×C3×C5C2×C4×D411yescharacteristic
630D15—21no—
631D15—41no—
632C3×D5—21no—
633C5×D3—21no—
634C5×D3—41no—
635C22×D3—21no—
636C22×D3—51no—
637C22×D3—101no—
638C3×Q8—51no—
639C3×Q8—51no—
640C3×D4—101no—
641C3×D4—101no—
642C3×D4C22×AGL(1,𝔽5)11yescharacteristic
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—21no—
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—101no—
660D12—101no—
661D12C22×AGL(1,𝔽5)11yescharacteristic
662C4×D3—51no—
663C4×D3—51no—
664C4×D3—51no—
665C4×D3—101no—
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—51no—
674Dic6—101no—
675Dic6—101no—
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—21no—
691C22×C5—31no—
692C22×C5—61no—
693C22×C5—241no—
694C2×D5—31no—
695C2×D5—61no—
696C2×D5—121no—
697C2×D5—241no—
698C2×D5D3×#4111yescharacteristic
699AGL(1,𝔽5)—22no—
700AGL(1,𝔽5)—121no—
701C4×C5—31no—
702C4×C5—61no—
703C4×C5C22×C4×D311yescharacteristic
704Dic5—21no—
705Dic5—21no—
706Dic5—31no—
707Dic5—61no—
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—151no—
722C2×Q8—151no—
723C2×D4—31no—
724C2×D4—151no—
725C2×D4—301no—
726C2×D4—301no—
727C22×C4—151no—
728C22×C4—301no—
729C22×C4—301no—
730C22×C4—301no—
731Q16—51no—
732Q16—151no—
733Q16—151no—
734Q16—151no—
735SD16—31no—
736SD16—31no—
737SD16—51no—
738SD16—51no—
739SD16—151no—
740SD16—151no—
741SD16—151no—
742SD16—151no—
743D8—31no—
744D8—151no—
745D8—151no—
746D8D3×AGL(1,𝔽5)11yescharacteristic, complemented
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—21no—
789C22×C3—51no—
790C2×D3—21no—
791C2×D3—51no—
792C2×D3—81no—
793C2×D3—101no—
794C2×D3—201no—
795C2×D3—401no—
796C2×D3D4×AGL(1,𝔽5)11yescharacteristic
797C3×C4—51no—
798C3×C4—102no—
799C3×C4—101no—
800C3×C4—101no—
801C3×C4C23×AGL(1,𝔽5)11yescharacteristic
802Dic3—21no—
803Dic3—51no—
804Dic3—101no—
805Dic3—201no—
806Dic3D4×AGL(1,𝔽5)11yescharacteristic
807C2×C5—41no—
808C2×C5—41no—
809C2×C5—61no—
810C2×C5—121no—
811C2×C5C4×D3×D411yescharacteristic
812D5—21no—
813D5—61no—
814D5—121no—
815C23—61no—
816C23—151no—
817C23—301no—
818Q8—31no—
819Q8—51no—
820Q8—51no—
821Q8—151no—
822Q8—301no—
823Q8—301no—
824D4—31no—
825D4—61no—
826D4—61no—
827D4—101no—
828D4—101no—
829D4—151no—
830D4—301no—
831D4—301no—
832D4—301no—
833D4—301no—
834D4—301no—
835D4—301no—
836D4C2×D3×AGL(1,𝔽5)11yescharacteristic
837D4C2×D3×AGL(1,𝔽5)11yescharacteristic
838C2×C4—31no—
839C2×C4—51no—
840C2×C4—61no—
841C2×C4—101no—
842C2×C4—101no—
843C2×C4—101no—
844C2×C4—151no—
845C2×C4—151no—
846C2×C4—151no—
847C2×C4—151no—
848C2×C4—301no—
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—41no—
871C2×C3—101no—
872C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
873D3—21no—
874D3—41no—
875D3—101no—
876D3—201no—
877C5#7988911yescharacteristic, complemented, Sylow
878C22—21no—
879C22—21no—
880C22—31no—
881C22—51no—
882C22—61no—
883C22—151no—
884C22—241no—
885C22—301no—
886C22—601no—
887C22—1201no—
888C4—31no—
889C4—51no—
890C4—61no—
891C4—102no—
892C4—101no—
893C4—101no—
894C4—151no—
895C4—301no—
896C4—601no—
897C4C22×D3×AGL(1,𝔽5)11yescharacteristic
898C3#1061744911yescharacteristic, complemented, Sylow
899C2—41no—
900C2—41no—
901C2—61no—
902C2—101no—
903C2—121no—
904C2—301no—
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×D8C2×C4
socleC2×C3×C5C2×C4×D4
prime radical#11754052C2
cosocleC3×C4×D5C24
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5#2956
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ D8

Complements

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

NH ≅ G/Ntype
1. #11756842C2semidirect
2. #11756841C2semidirect
4. #11752392C2semidirect
5. C3×#65732C2semidirect
6. #11751957C2semidirect
7. #11751955C2semidirect
8. #11751954C2semidirect
9. #11751952C2semidirect
10. D3×#4008C2semidirect
11. #11751935C2semidirect
12. #11751688C2semidirect
13. #11751679C2semidirect
14. #11751676C2semidirect
15. AGL(1,𝔽5)×ΓL(1,𝔽25)C2semidirect
19. #91990C22semidirect
20. #91990C22semidirect
21. C3×#4131C22semidirect
22. C3×#4131C22semidirect
33. #91916C22semidirect
35. #91914C22semidirect
36. #91913C22semidirect
38. #91911C22semidirect
39. #91800C4semidirect
40. C5×#911C4semidirect
42. #91500C4semidirect
43. #91496C4semidirect
46. #91488C4semidirect
47. #91486C4semidirect
48. #91280C4semidirect
50. #91263C4semidirect
52. #91237C22semidirect
53. #91237C22semidirect
54. #91224C22semidirect
55. #91221C22semidirect
56. C3×#4008C22semidirect
57. C3×#4008C22semidirect
58. C3×#3996C22semidirect
59. C3×C8×AGL(1,𝔽5)C22semidirect
60. #91162C22semidirect
61. #91161C22semidirect
62. #91158C22semidirect
63. #91157C22semidirect
64. #91156C22semidirect
65. #91155C22semidirect
66. #91150C22semidirect
67. AGL(1,𝔽5)×C3⋊C8C22semidirect
81. #65732D3semidirect
139. C3×C5×D8C2×C4semidirect
140. #6716C2×C4semidirect
141. #6715C2×C4semidirect
142. #6706C2×C4semidirect
144. C5×#214C2×C4semidirect
145. C5×#213C2×C4semidirect
146. C5×#204C2×C4semidirect
148. C3×#687C2×C4semidirect
149. C3×#687C2×C4semidirect
150. C3×Dic20C2×C4semidirect
152. #6663C2×C4semidirect
153. #6662C2×C4semidirect
154. #6661C2×C4semidirect
155. #6658C2×C4semidirect
156. #6656C2×C4semidirect
157. #6654C2×C4semidirect
190. #4131C2×D3semidirect
191. #4131C2×D3semidirect
217. #4008C2×D3semidirect
218. #4008C2×D3semidirect
220. #3996C2×D3semidirect
226. C8×AGL(1,𝔽5)C2×D3semidirect
298. #911AGL(1,𝔽5)semidirect
391. C5×D8C4×D3semidirect
397. #687C4×D3semidirect
398. #687C4×D3semidirect
403. Dic20C4×D3semidirect
470. C3×D8C2×AGL(1,𝔽5)semidirect
485. #214C2×AGL(1,𝔽5)semidirect
487. #213C2×AGL(1,𝔽5)semidirect
501. #204C2×AGL(1,𝔽5)semidirect
746. D8D3×AGL(1,𝔽5)semidirect
786. C3×C5#2956semidirect
877. C5#79889semidirect
898. C3#10617449semidirect

Maximal subgroups

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

subgroupindex
#117568422
#117568412
#117540522
#117523922
C3×#657322
#117519572
#117519552
#117519542
#117519522
D3×#40082
#117519352
#117516882
#117516792
#117516762
AGL(1,𝔽5)×ΓL(1,𝔽25)2
#106174493
#798895