Finite Group Databasebeta

← #14416761

Subgroups — #14416761

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91254C211yesmaximal, characteristic
2D3×#4039C211yesmaximal, characteristic, complemented
3#11753398C211yesmaximal, characteristic, complemented
4#11750990C211yesmaximal, characteristic, complemented
5C5×#4881C211yesmaximal, characteristic, complemented
6C3×#65161C211yesmaximal, characteristic, complemented
7#11747815C211yesmaximal, characteristic, complemented
8#11747760C211yesmaximal, characteristic, complemented
9Dic5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
10#11747503C211yesmaximal, characteristic, complemented
11#11747477C211yesmaximal, characteristic, complemented
12#11747268C211yesmaximal, characteristic, complemented
13#11747229C211yesmaximal, characteristic, complemented
14#11747228C211yesmaximal, characteristic, complemented
15#11747223C211yesmaximal, characteristic, complemented
16#10610930—31nomaximal, Hall
17C2×D3×D20C2211yescharacteristic
18C2×C4×D3×D5—21no—
19C2×#6765C2211yescharacteristic
20C2×#6706C2211yescharacteristic
21#91782C2211yescharacteristic
22#91776C2211yescharacteristic, complemented
23C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
24C5×#892C2211yescharacteristic
25C5×D3×C4⋊C4C2211yescharacteristic
26C2×C3×D40C2211yescharacteristic
27C3×#4039C2211yescharacteristic
28C3×#4039C2211yescharacteristic, complemented
29D3×#685—21no—
30#91444—21no—
31#91442—21no—
32#91440—21no—
33#91434C2211yescharacteristic
34#91434C2211yescharacteristic, complemented
35#91418C2211yescharacteristic
36C4×D3×Dic5C2211yescharacteristic
37#91396—21no—
38#91393—21no—
39C4×D5×Dic3—21no—
40#91333C2211yescharacteristic, complemented
41C2×#6657C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44#91254C418yescomplemented
45C3×C5×#107C2211yescharacteristic, complemented
46#91099C2211yescharacteristic, complemented
47#91094C2211yescharacteristic, complemented
48#91093C2211yescharacteristic
49C5×#817C2211yescharacteristic, complemented
50C5×#808C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C3×C8×Dic5C2211yescharacteristic, complemented
53C3×#3941C2211yescharacteristic
54C3×#3941C2211yescharacteristic, complemented
55#90975C2211yescharacteristic, complemented
56#90969C2211yescharacteristic
57#90964C2211yescharacteristic
58#90964C2211yescharacteristic, complemented
59#90954C2211yescharacteristic, complemented
60Dic5×C3⋊C8C2211yescharacteristic, complemented
61C4×#911—51nomaximal, Hall
62C2×#4054—31no—
63#65856—31no—
64C2×#4039—31no—
65C5×#428—31no—
66M16×Dic5—31no—
67#65290—31no—
68#65255—31no—
69#65178—31no—
70#65178—31no—
71#65161—31no—
72#65161D311yescharacteristic, complemented
73#65158—31no—
74#65158—31no—
75#65141—31no—
76#65141—31no—
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30C2311yescharacteristic
81C2×C4×C5×D3—21no—
82C2×C4×C5×D3C2311yescharacteristic
83C2×C3×D20C2311yescharacteristic
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×#1202—21no—
88C2×#1201—21no—
89C2×#1200—21no—
90C2×D3×Dic5D411yescharacteristic
91C2×D3×Dic5D411yescharacteristic
92C2×D5×Dic3—21no—
93C2×D5×Dic3—21no—
94C2×D5×Dic3—21no—
95D3×D20—22no—
96D3×D20C2×C414yescomplemented
97C4×D3×D5—44no—
98#6765—22no—
99#6765C2×C414yescomplemented
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C4⋊C4C2311yescharacteristic
103#6714—21no—
104#6712—21no—
105C4×Dic15—21no—
106C4×Dic15C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108#6706C2×C414yescomplemented
109C5×(C2×D3)⋊C4—21no—
110C5×C4⋊Dic3C2311yescharacteristic
111C5×C4⋊Dic3C2311yescharacteristic
112C5×Dic3⋊C4—21no—
113C4×C5×Dic3—21no—
114C2×C5×C3⋊C8C2311yescharacteristic
115C5×ΓL(1,𝔽25)C2×C414yescomplemented
116C3×#685—21no—
117C3×#685—21no—
118C3×C4×Dic5C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120C3×D40C2×C414yescomplemented
121#6669—21no—
122#6667—21no—
123#6665—21no—
124#6665—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6657C2×C414yescomplemented
129#6653C2×C414yescomplemented
130#6650—22no—
131C2×#911—51no—
132C4×D3×D4—51no—
133C4×#237—51no—
134C3×C4×D8—51no—
135#5152—51no—
136C4×#214—51no—
137C4×#213—51no—
138#4889—51no—
139#4881D511yescharacteristic, complemented
140#4785—51no—
141#4771—51no—
142#4770—51no—
143#4757—51no—
144C4×#204—51no—
145C4×ΓL(1,𝔽25)—51no—
146C2×#709—31no—
147C22×D20—31no—
148C22×C4×D5—61no—
149C2×C5×M16—31no—
150C5×#117—31no—
151C2×C5×C4⋊C4—31no—
152C2×#685—61no—
153C2×C4×Dic5—31no—
154C2×#681—31no—
155#4054—38no—
156C2×D40—31no—
157C2×D40C2×D311yescharacteristic
158C2×#677—31no—
159C2×#677—31no—
160#4039—31no—
161#4039—31no—
162#4039—31no—
163#4039—31no—
164#4039—61no—
165#4039—61no—
166#4039C2×D311yescharacteristic
167#4039C2×D311yescharacteristic, complemented
168#4033—31no—
169#4033—31no—
170#4027—61no—
171#4027—61no—
172#4018—61no—
173C42×D5—61no—
174C5×#107—31no—
175C5×#107C2×D311yescharacteristic, complemented
176C5×#106—31no—
177C5×#106—31no—
178#3947—31no—
179#3947—31no—
180C8×Dic5—31no—
181C8×Dic5C2×D311yescharacteristic, complemented
182#3942—31no—
183#3942—31no—
184#3941—31no—
185#3941—31no—
186#3941—31no—
187#3941—31no—
188#3941C2×D311yescharacteristic
189#3941C2×D311yescharacteristic, complemented
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×C5×D3C2×D411yescharacteristic
193C22×C3×D5—21no—
194C22×C3×D5—21no—
195C2×D3×D5—24no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5C2411yescharacteristic
201C2×Dic15—21no—
202C2×Dic15C2×D411yescharacteristic
203C2×Dic15C2×D411yescharacteristic
204D60—21no—
205D60C22×C412yes—
206C4×D15—42no—
207Dic30—21no—
208Dic30C22×C412yescomplemented
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3C2×D411yescharacteristic
212C4×C5×D3—42no—
213C4×C5×D3C22×C412yes—
214C4×C5×D3#4112yes—
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×D20—21no—
218C3×D20—21no—
219C3×D20C22×C412yes—
220C3×D20C22×C412yescomplemented
221C3×C4×D5—42no—
222C3×C4×D5—42no—
223#1202—24no—
224#1201—24no—
225#1200—42no—
226D3×Dic5—22no—
227D3×Dic5—41no—
228D5×Dic3—24no—
229D5×Dic3—42no—
230D5×Dic3—42no—
231C3×C5×C8C22×C412yescomplemented
232C3⋊#168—21no—
233C3×#168—21no—
234C5×C3⋊C8C22×C412yescomplemented
235C2×#237—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×D8—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241D4×Dic3—51no—
242D4×Dic3—51no—
243C2×#214—51no—
244C2×#213—51no—
245C4×#67—101no—
246C4×#67—101no—
247C2×C4×Dic3—101no—
248#911—58no—
249C2×#204—51no—
250C2×ΓL(1,𝔽25)—51no—
251C2×ΓL(1,𝔽25)C2×D511yescharacteristic
252#893—51no—
253#892C2×D511yescharacteristic
254D3×C4⋊C4C2×D511yescharacteristic
255#887—51no—
256#67⋊C4—101no—
257#67⋊C4—101no—
258D3×C22⋊C4—101no—
259#877—101no—
260C4×D12—51no—
261C42×D3—51no—
262C4×Dic6—51no—
263C3×#107C2×D511yescharacteristic, complemented
264C3×#102—51no—
265C3×#102—51no—
266C3×C4×C8—51no—
267#832—51no—
268#832—51no—
269#821—51no—
270#817C2×D511yescharacteristic, complemented
271#816—51no—
272#815—51no—
273#815—51no—
274#810—51no—
275#809—51no—
276#808C2×D511yescharacteristic, complemented
277#807C2×D511yescharacteristic, complemented
278C4×C3⋊C8—51no—
279C23×D5—61no—
280C22×C4×C5—31no—
281C22×C4×C5—61no—
282C2×C22⋊D5—61no—
283C22×Dic5—31no—
284C22×Dic5—31no—
285#709—34no—
286#709—62no—
287C2×D20—31no—
288C2×D20—34no—
289C2×D20—62no—
290C2×D20—61no—
291C2×D20C22×D311yescharacteristic
292C2×D20C22×D311yescharacteristic
293C2×C4×D5—21no—
294C2×C4×D5—21no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—124no—
301C2×Dic10—31no—
302C5×M16—34no—
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—31no—
307C5×C4⋊C4—61no—
308C5×C4⋊C4C22×D311yescharacteristic
309C5×C4⋊C4C22×D311yescharacteristic
310C5×C22⋊C4—61no—
311C42×C5—61no—
312#685—21no—
313#685—21no—
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318#683—61no—
319#683—61no—
320C4×Dic5—31no—
321C4×Dic5—31no—
322C4×Dic5—31no—
323C4×Dic5—61no—
324C4×Dic5—61no—
325C4×Dic5C22×D311yescharacteristic
326#681—62no—
327C2×#168—31no—
328C2×#168C22×D311yescharacteristic
329D40—34no—
330D40C4×D314yescomplemented
331#677—34no—
332#677—34no—
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—151no—
337#442—151no—
338#440—151no—
339#440—151no—
340C4×SD16—151no—
341C4×SD16—151no—
342C4×D8—51no—
343C4×D8—151no—
344#428—31no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—22no—
350C2×D15—41no—
351C2×D15—41no—
352C2×C5×D3—21no—
353C2×C5×D3—21no—
354C2×C5×D3C4×D412yes—
355C2×C3×D5—22no—
356C2×C3×D5—22no—
357C2×C3×D5—41no—
358C2×C3×D5—41no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361D3×D5—48no—
362C3×C4×C5—41no—
363C3×C4×C5—41no—
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—22no—
367Dic15—21no—
368Dic15—21no—
369C3×Dic5—21no—
370C3×Dic5AGL(1,ℤ/8)12yescomplemented
371C5×Dic3—41no—
372C5×Dic3—41no—
373C5×Dic3C4×D412yes—
374C23×D3—101no—
375C2×C3×D4—51no—
376C2×C3×D4—51no—
377C22×C3×C4—101no—
378C22×C3×C4—101no—
379C2×#67—101no—
380C2×#67—101no—
381C22×Dic3—101no—
382C22×Dic3—101no—
383C22×Dic3—101no—
384#237—54no—
385#237—102no—
386D3×D4—54no—
387D3×D4—102no—
388C2×D12—51no—
389C2×C4×D3—21no—
390C2×C4×D3—51no—
391C2×C4×D3—51no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—204no—
395C2×C4×D3C22×D511yescharacteristic
396C2×Dic6—51no—
397C3×D8—54no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C42—51no—
405#217—101no—
406#217—101no—
407#214—54no—
408#213—54no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412C4⋊Dic3C22×D511yescharacteristic
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—21no—
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—101no—
422C4×Dic3—101no—
423C2×C3⋊C8—51no—
424C2×C3⋊C8C22×D511yescharacteristic
425#204—54no—
426ΓL(1,𝔽25)—102no—
427ΓL(1,𝔽25)C4×D514yescomplemented
428C23×C5—31no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—64no—
432C22×D5—61no—
433C22×D5—122no—
434C22×D5—122no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—31no—
438C2×C4×C5—32no—
439C2×C4×C5—32no—
440C2×C4×C5—61no—
441C2×C4×C5—61no—
442C2×C4×C5—122no—
443C2×C4×C5C23×D311yescharacteristic
444C22⋊D5—64no—
445C2×Dic5—31no—
446C2×Dic5—31no—
447C2×Dic5—61no—
448C2×Dic5—62no—
449C2×Dic5—121no—
450C2×Dic5D3×D411yescharacteristic
451C2×Dic5D3×D411yescharacteristic
452D20—21no—
453D20—21no—
454D20—32no—
455D20—64no—
456D20—61no—
457D20C2×C4×D312yes—
458D20C2×C4×D312yescomplemented
459C4×D5—42no—
460C4×D5—42no—
461C4×D5—64no—
462C4×D5—122no—
463C4×D5—122no—
464C4×D5—122no—
465C4×D5—122no—
466Dic10—32no—
467Dic10—61no—
468C5×C8—32no—
469C5×C8C2×C4×D312yescomplemented
470#168—21no—
471#168—61no—
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—151no—
477C2×SD16—151no—
478C2×D8—51no—
479C2×D8—151no—
480C2×M16—31no—
481C2×M16—151no—
482C4×Q8—151no—
483C4×Q8—151no—
484C4×D4—51no—
485C4×D4—51no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—151no—
489C4×D4—151no—
490C4×D4—301no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4—301no—
494#117—31no—
495#117—301no—
496C2×C4⋊C4—31no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—31no—
501#107D3×D511yescharacteristic, complemented
502#106—31no—
503#106—31no—
504#103—151no—
505#103—151no—
506#102—51no—
507#102—51no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—151no—
513#97—151no—
514C4×C8—51no—
515C4×C8—151no—
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—42no—
520C3×D5—42no—
521C3×D5—42no—
522C5×D3—22no—
523C23×C3—101no—
524C23×C3—101no—
525C22×D3—101no—
526C22×D3—104no—
527C22×D3—202no—
528C22×D3—202no—
529C22×D3D4×D511yescharacteristic
530C3×D4—52no—
531C3×D4—52no—
532C3×D4—101no—
533C3×D4—101no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—51no—
537C2×C3×C4—51no—
538C2×C3×C4—202no—
539C2×C3×C4—202no—
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542#67—104no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—51no—
546C2×Dic3—51no—
547C2×Dic3—101no—
548C2×Dic3—104no—
549C2×Dic3—202no—
550C2×Dic3—202no—
551C2×Dic3D4×D511yescharacteristic
552D12—52no—
553D12—101no—
554C4×D3—42no—
555C4×D3—102no—
556C4×D3—202no—
557C4×D3—202no—
558C4×D3—201no—
559C4×D3C2×C4×D512yes—
560C4×D3#71312yes—
561Dic6—52no—
562Dic6—101no—
563C3×C8—101no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—101no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—32no—
568C22×C5—61no—
569C22×C5—61no—
570C22×C5C2×D3×D411yescharacteristic
571C2×D5—22no—
572C2×D5—22no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—41no—
576C2×D5—41no—
577C2×D5—62no—
578C2×D5—128no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—32no—
582C4×C5—41no—
583C4×C5—41no—
584C4×C5—121no—
585C4×C5—121no—
586C4×C5C22×C4×D311yescharacteristic
587C4×C5D3×#4111yescharacteristic
588Dic5—21no—
589Dic5—61no—
590Dic5—61no—
591Dic5—62no—
592Dic5#91112yescomplemented
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—151no—
597C2×D4—51no—
598C2×D4—51no—
599C2×D4—154no—
600C2×D4—151no—
601C2×D4—302no—
602C2×D4—301no—
603C2×D4—301no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—154no—
617SD16—154no—
618D8—54no—
619D8—154no—
620M16—34no—
621M16—302no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—301no—
630C4⋊C4—301no—
631C4⋊C4C2×D3×D511yescharacteristic
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—61no—
634C22⋊C4—101no—
635C22⋊C4—101no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—51no—
641C42—61no—
642C42—151no—
643C42—151no—
644C42—151no—
645C42—301no—
646C42—301no—
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—102no—
649C22×C3—102no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—102no—
658C2×D3—208no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3#403912yes—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—52no—
665C3×C4—101no—
666C3×C4C22×C4×D511yescharacteristic
667C3×C4C2×#71311yescharacteristic
668Dic3—41no—
669Dic3—41no—
670Dic3—102no—
671Dic3—101no—
672Dic3—101no—
673Dic3#403912yes—
674C2×C5—62no—
675C2×C5C4×D3×D411yescharacteristic
676C2×C5C2×#91111yescharacteristic
677C2×C5#576811yescharacteristic
678D5—42no—
679D5—42no—
680D5—122no—
681C23—31no—
682C23—101no—
683C23—101no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—152no—
689Q8—301no—
690D4—52no—
691D4—52no—
692D4—101no—
693D4—101no—
694D4—152no—
695D4—304no—
696D4—304no—
697D4—301no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—51no—
704C2×C4—51no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—122no—
708C2×C4—151no—
709C2×C4—151no—
710C2×C4—202no—
711C2×C4—202no—
712C2×C4—304no—
713C2×C4—302no—
714C2×C4—301no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—601no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—32no—
722C8—101no—
723C8—301no—
724C8C4×D3×D512yescomplemented
725C2×C3—202no—
726C2×C3—202no—
727C2×C3C2×#403911yescharacteristic
728C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
729C2×C3#6611111yescharacteristic
730D3—22no—
731D3—202no—
732C5C4×#91111yescharacteristic, complemented, Sylow
733C22—32no—
734C22—61no—
735C22—61no—
736C22—102no—
737C22—102no—
738C22—201no—
739C22—201no—
740C22—201no—
741C22—201no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—32no—
748C4—41no—
749C4—41no—
750C4—52no—
751C4—101no—
752C4—121no—
753C4—121no—
754C4—301no—
755C4—302no—
756C4—301no—
757C4C2×C4×D3×D511yescharacteristic
758C4D3×#71311yescharacteristic
759C3#1061093011yescharacteristic, complemented, Sylow
760C2—62no—
761C2—202no—
762C2—202no—
763C2—602no—
764C2D3×#403911yescharacteristic
765C2D5×#91111yescharacteristic
766C2#1175410411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
prime radicalC2×#91254C2
cosocleC2×C3×C4×C5C24
hypercenter#107D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. D3×#4039C2semidirect
3. #11753398C2semidirect
4. #11750990C2semidirect
5. C5×#4881C2semidirect
6. C3×#65161C2semidirect
7. #11747815C2semidirect
8. #11747760C2semidirect
9. Dic5×ΓL(1,𝔽25)C2semidirect
10. #11747503C2semidirect
11. #11747477C2semidirect
12. #11747268C2semidirect
13. #11747229C2semidirect
14. #11747228C2semidirect
15. #11747223C2semidirect
22. #91776C22semidirect
28. C3×#4039C22semidirect
34. #91434C22semidirect
40. #91333C22semidirect
44. #91254C4semidirect
45. C3×C5×#107C22semidirect
46. #91099C22semidirect
47. #91094C22semidirect
49. C5×#817C22semidirect
50. C5×#808C22semidirect
51. C5×#807C22semidirect
52. C3×C8×Dic5C22semidirect
54. C3×#3941C22semidirect
55. #90975C22semidirect
58. #90964C22semidirect
59. #90954C22semidirect
60. Dic5×C3⋊C8C22semidirect
72. #65161D3semidirect
96. D3×D20C2×C4semidirect
99. #6765C2×C4semidirect
108. #6706C2×C4semidirect
115. C5×ΓL(1,𝔽25)C2×C4semidirect
120. C3×D40C2×C4semidirect
128. #6657C2×C4semidirect
129. #6653C2×C4semidirect
139. #4881D5semidirect
167. #4039C2×D3semidirect
175. C5×#107C2×D3semidirect
181. C8×Dic5C2×D3semidirect
189. #3941C2×D3semidirect
208. Dic30C22×C4semidirect
220. C3×D20C22×C4semidirect
231. C3×C5×C8C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
263. C3×#107C2×D5semidirect
270. #817C2×D5semidirect
276. #808C2×D5semidirect
277. #807C2×D5semidirect
330. D40C4×D3semidirect
370. C3×Dic5AGL(1,ℤ/8)semidirect
427. ΓL(1,𝔽25)C4×D5semidirect
458. D20C2×C4×D3semidirect
469. C5×C8C2×C4×D3semidirect
501. #107D3×D5semidirect
564. C3×C8C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
592. Dic5#911semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
724. C8C4×D3×D5semidirect
732. C5C4×#911semidirect
759. C3#10610930semidirect

Maximal subgroups

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

subgroupindex
C2×#912542
D3×#40392
#117533982
#117509902
C5×#48812
C3×#651612
#117478152
#117477602
Dic5×ΓL(1,𝔽25)2
#117475032
#117474772
#117472682
#117472292
#117472282
#117472232
#106109303
C4×#9115