Finite Group Databasebeta

← C4×#91254 #14416710

Subgroups — C4×#91254 #14416710

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
2C4×D3×D20C211yesmaximal, characteristic, complemented
3C4×#6765C211yesmaximal, characteristic, complemented
4C4×#6706C211yesmaximal, characteristic, complemented
5C4×C5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
6C3×C4×D40C211yesmaximal, characteristic, complemented
7#11748138C211yesmaximal, characteristic, complemented
8#11748107C211yesmaximal, characteristic, complemented
9#11747800C211yesmaximal, characteristic, complemented
10#11747799C211yesmaximal, characteristic, complemented
11#11747742C211yesmaximal, characteristic, complemented
12#11747741C211yesmaximal, characteristic, complemented
13#11747630C211yesmaximal, characteristic, complemented
14C4×#6657C211yesmaximal, characteristic, complemented
15C4×#6653C211yesmaximal, characteristic, complemented
16C4×#4054—31nomaximal, Hall
17C2×D3×D20C2211yescharacteristic
18C2×C4×D3×D5—21no—
19C2×#6765C2211yescharacteristic
20C2×#6706C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C4×Dic30C2211yescharacteristic, complemented
23C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
25C42×C5×D3C2211yescharacteristic
26C2×C3×D40C2211yescharacteristic
27C3×C4×D20C2211yescharacteristic
28C3×C4×D20C2211yescharacteristic, complemented
29D3×#685—21no—
30C4×#1202—21no—
31#91441—21no—
32C4×#1201—21no—
33#91428C2211yescharacteristic
34D3×C4⋊Dic5C2211yescharacteristic
35Dic3×D20C2211yescharacteristic
36Dic3×D20C2211yescharacteristic, complemented
37#91395—21no—
38#91393—21no—
39C4×D5×Dic3—21no—
40#91340C2211yescharacteristic, complemented
41#91338C2211yescharacteristic
42C2×#6657C2211yescharacteristic
43C2×#6653C2211yescharacteristic
44#91254C418yesdirect product factor
45C3×C4×C5×C8C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91101C2211yescharacteristic, complemented
48#91100C2211yescharacteristic, complemented
49C5×#815C2211yescharacteristic, complemented
50C5×#815C2211yescharacteristic, complemented
51C4×C5×C3⋊C8C2211yescharacteristic, complemented
52C3×#3953C2211yescharacteristic
53C3×#3953C2211yescharacteristic, complemented
54C3×#3950C2211yescharacteristic, complemented
55#90990C2211yescharacteristic, complemented
56#90987C2211yescharacteristic, complemented
57#90974C2211yescharacteristic, complemented
58#90968C2211yescharacteristic
59#90965C2211yescharacteristic
60#90965C2211yescharacteristic, complemented
61C4×#911—51nomaximal, Hall
62C2×#4054—31no—
63C4×#709—31no—
64C2×C4×D20—31no—
65C4×C5×M16—31no—
66#65422—31no—
67#65420—31no—
68#65410—31no—
69#65000—31no—
70#65000—31no—
71#64999—31no—
72#64999—31no—
73C4×D40—31no—
74C4×D40D311yescharacteristic, complemented
75C4×#677—31no—
76C4×#677—31no—
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30C2311yescharacteristic
81C2×C4×C5×D3D411yescharacteristic
82C2×C4×C5×D3D411yescharacteristic
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×D20C2311yescharacteristic
85C2×C3×D20C2311yescharacteristic
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5—21no—
88C2×#1202—21no—
89C2×#1201—21no—
90C2×#1200—21no—
91C2×D3×Dic5—21no—
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
101C2×C3×C5×C8C2311yescharacteristic
102C3×C42×C5C2311yescharacteristic
103#6714—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106#6712—21no—
107C4×Dic15—21no—
108#6706C2×C414yescomplemented
109C4×C5×Dic3D411yescharacteristic
110C4×C5×Dic3D411yescharacteristic
111C4×C5×Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C5×ΓL(1,𝔽25)—22no—
115C5×ΓL(1,𝔽25)C2×C414yescomplemented
116C3×#685—21no—
117C3×#685—21no—
118C3×C4⋊Dic5C2311yescharacteristic
119C3×C4⋊Dic5C2311yescharacteristic
120C3×D40C2×C414yescomplemented
121Dic3⋊Dic5—21no—
122#6669—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125#6665—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128Dic3×Dic5—21no—
129#6657C2×C414yescomplemented
130#6653C2×C414yescomplemented
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#4881—51no—
140#4785—51no—
141#4771—51no—
142#4770—51no—
143#4757—51no—
144C4×#204—51no—
145C4×ΓL(1,𝔽25)D511yescharacteristic, complemented
146C2×#709—31no—
147C22×D20—31no—
148C22×C4×D5—61no—
149C2×C5×M16—31no—
150C2×C5×M16—31no—
151C2×C42×C5—31no—
152C4×C22⋊D5—61no—
153C4×C22⋊D5—61no—
154C2×#685—61no—
155#4072—31no—
156C2×C4⋊Dic5—31no—
157#4054—38no—
158C2×D40—31no—
159C2×D40C2×D311yescharacteristic
160C2×#677—31no—
161C2×#677—31no—
162C4×D20—31no—
163C4×D20—31no—
164C4×D20—31no—
165C4×D20—31no—
166C4×D20—61no—
167C4×D20—61no—
168C4×D20C2×D311yescharacteristic
169C4×D20C2×D311yescharacteristic, complemented
170#4018—61no—
171C42×D5—61no—
172C4×Dic10—31no—
173C4×Dic10—31no—
174C5×#97—31no—
175C5×#97—31no—
176C4×C5×C8—31no—
177C4×C5×C8C2×D311yescharacteristic, complemented
178#3953—31no—
179#3953—31no—
180#3953—31no—
181#3953—31no—
182#3953C2×D311yescharacteristic
183#3953C2×D311yescharacteristic, complemented
184#3950—31no—
185#3950C2×D311yescharacteristic, complemented
186#3949—31no—
187#3949—31no—
188#3948—31no—
189#3948—31no—
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×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2411yescharacteristic
201C2×Dic15—21no—
202C2×Dic15—21no—
203C2×Dic15—21no—
204D60—21no—
205D60C22×C412yes—
206C4×D15—42no—
207Dic30—21no—
208Dic30C22×C412yescomplemented
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C5×Dic3C2×D411yescharacteristic
211C2×C5×Dic3C2×D411yescharacteristic
212C4×C5×D3—22no—
213C4×C5×D3—41no—
214C4×C5×D3C22×C412yes—
215C4×C5×D3#4112yes—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C3×D20—21no—
219C3×D20—21no—
220C3×D20C22×C412yes—
221C3×D20C22×C412yescomplemented
222C3×C4×D5—42no—
223C3×C4×D5—42no—
224#1202—24no—
225#1201—24no—
226#1200—42no—
227D3×Dic5—42no—
228D5×Dic3—24no—
229D5×Dic3—42no—
230D5×Dic3—42no—
231C3×C5×C8—21no—
232C3×C5×C8C22×C412yescomplemented
233C5×C3⋊C8—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)C2×D511yescharacteristic
251C2×ΓL(1,𝔽25)C2×D511yescharacteristic
252#893—51no—
253#892—51no—
254D3×C4⋊C4—51no—
255#887—51no—
256#67⋊C4—101no—
257#67⋊C4—101no—
258D3×C22⋊C4—101no—
259#877—101no—
260C4×D12—51no—
261C42×D3C2×D511yescharacteristic
262C4×Dic6—51no—
263C3×#107—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×C4×C8C2×D511yescharacteristic, complemented
267#832—51no—
268#832—51no—
269#821—51no—
270#817—51no—
271#816—51no—
272#815C2×D511yescharacteristic, complemented
273#815C2×D511yescharacteristic, complemented
274#810—51no—
275#809—51no—
276#808—51no—
277#807—51no—
278C4×C3⋊C8C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C22×C4×C5—31no—
281C22×C4×C5—31no—
282C22×C4×C5—31no—
283C2×C22⋊D5—61no—
284C22×Dic5—61no—
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—
303C5×M16—62no—
304C2×C5×C8—31no—
305C2×C5×C8—31no—
306C2×C5×C8C22×D311yescharacteristic
307C2×C5×C8C22×D311yescharacteristic
308C42×C5—31no—
309C42×C5—31no—
310C42×C5—31no—
311C42×C5C22×D311yescharacteristic
312C22⋊Dic5—61no—
313#685—21no—
314#685—21no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—31no—
321C4⋊Dic5—61no—
322C4⋊Dic5C22×D311yescharacteristic
323C4⋊Dic5C22×D311yescharacteristic
324#683—61no—
325#683—61no—
326C4×Dic5—61no—
327C4×Dic5—61no—
328C4×Dic5—61no—
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—151no—
345#418—151no—
346#417—151no—
347C4×M16—31no—
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—21no—
363C3×C4×C5AGL(1,ℤ/8)12yescomplemented
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—22no—
367Dic15—41no—
368Dic15—41no—
369C3×Dic5—41no—
370C3×Dic5—41no—
371C5×Dic3—21no—
372C5×Dic3—21no—
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—101no—
390C2×C4×D3—101no—
391C2×C4×D3—101no—
392C2×C4×D3—204no—
393C2×C4×D3D2011yescharacteristic
394C2×C4×D3D2011yescharacteristic
395C2×C4×D3C22×D511yescharacteristic
396C2×Dic6—51no—
397C3×D8—54no—
398C2×C3×C8C22×D511yescharacteristic
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C22⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#217—101no—
407#214—54no—
408#213—54no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412C4⋊Dic3—51no—
413C4⋊Dic3—51no—
414Dic3⋊C4—101no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—101no—
418C4×Dic3—101no—
419C4×Dic3—101no—
420C4×Dic3D2011yescharacteristic
421C4×Dic3D2011yescharacteristic
422C4×Dic3C22×D511yescharacteristic
423C2×C3⋊C8C22×D511yescharacteristic
424C2×C3⋊C8C22×D511yescharacteristic
425#204—54no—
426ΓL(1,𝔽25)—22no—
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—31no—
436C2×C4×C5—32no—
437C2×C4×C5—32no—
438C2×C4×C5—31no—
439C2×C4×C5—31no—
440C2×C4×C5—62no—
441C2×C4×C5—121no—
442C2×C4×C5D3×D411yescharacteristic
443C2×C4×C5D3×D411yescharacteristic
444C2×C4×C5C23×D311yescharacteristic
445C22⋊D5—64no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—122no—
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—21no—
469C5×C8—32no—
470C5×C8—61no—
471C5×C8C2×C4×D312yescomplemented
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—31no—
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—151no—
495#117—301no—
496C2×C4⋊C4—151no—
497C2×C22⋊C4—301no—
498C2×C42—31no—
499C2×C42—301no—
500#107—51no—
501#107—151no—
502#106—151no—
503#106—151no—
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—31no—
513#97—31no—
514C4×C8—31no—
515C4×C8D3×D511yescharacteristic, complemented
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×D3C2×D2011yescharacteristic
530C3×D4—52no—
531C3×D4—52no—
532C3×D4—101no—
533C3×D4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—202no—
537C2×C3×C4—202no—
538C2×C3×C4C2×D2011yescharacteristic
539C2×C3×C4C2×D2011yescharacteristic
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542#67—104no—
543C2×Dic3—101no—
544C2×Dic3—104no—
545C2×Dic3—101no—
546C2×Dic3—101no—
547C2×Dic3—202no—
548C2×Dic3—202no—
549C2×Dic3C2×D2011yescharacteristic
550C2×Dic3C2×D2011yescharacteristic
551C2×Dic3C2×D2011yescharacteristic
552D12—52no—
553D12—101no—
554C4×D3—22no—
555C4×D3—41no—
556C4×D3—202no—
557C4×D3—202no—
558C4×D3—202no—
559C4×D3C2×C4×D512yes—
560C4×D3#70912yes—
561Dic6—52no—
562Dic6—101no—
563C3×C8—21no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—21no—
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—21no—
582C4×C5—32no—
583C4×C5—61no—
584C4×C5—61no—
585C4×C5#91112yescomplemented
586C4×C5C22×C4×D311yescharacteristic
587C4×C5D3×#4111yescharacteristic
588Dic5—41no—
589Dic5—41no—
590Dic5—62no—
591Dic5—121no—
592Dic5—121no—
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—31no—
606C22×C4—31no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—301no—
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—62no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8C2×D3×D511yescharacteristic
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—51no—
627C4⋊C4—51no—
628C4⋊C4—151no—
629C4⋊C4—151no—
630C4⋊C4—301no—
631C4⋊C4—301no—
632C4⋊C4—301no—
633C22⋊C4—101no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—31no—
642C42—31no—
643C42—301no—
644C42—301no—
645C42—301no—
646C42C2×D3×D511yescharacteristic
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×C3C22×D2011yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—102no—
658C2×D3—208no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3C4×D2012yes—
662C3×C4—21no—
663C3×C4—201no—
664C3×C4—201no—
665C3×C4#405412yescomplemented
666C3×C4C22×C4×D511yescharacteristic
667C3×C4C2×#70911yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—102no—
671Dic3—201no—
672Dic3—201no—
673Dic3C4×D2012yes—
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—31no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—62no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—121no—
707C2×C4—202no—
708C2×C4—202no—
709C2×C4—304no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—602no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4D3×D2011yescharacteristic
719C2×C4D3×D2011yescharacteristic
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—32no—
723C8—61no—
724C8C4×D3×D512yescomplemented
725C2×C3—202no—
726C2×C3—202no—
727C2×C3C2×C4×D2011yescharacteristic
728C2×C3C2×#405411yescharacteristic
729C2×C3#6608211yescharacteristic
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—
746C22C2×D3×D2011yescharacteristic
747C4—21no—
748C4—32no—
749C4—61no—
750C4—61no—
751C4—201no—
752C4—201no—
753C4—302no—
754C4—601no—
755C4—601no—
756C4#9125412yesdirect product factor
757C4C2×C4×D3×D511yescharacteristic
758C4D3×#70911yescharacteristic
759C3C4×#405411yescharacteristic, complemented, Sylow
760C2—62no—
761C2—202no—
762C2—202no—
763C2—602no—
764C2C4×D3×D2011yescharacteristic
765C2C2×#9125411yescharacteristic
766C2#1175396911yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91254C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×D3×D20C2semidirect
3. C4×#6765C2semidirect
4. C4×#6706C2semidirect
5. C4×C5×ΓL(1,𝔽25)C2semidirect
6. C3×C4×D40C2semidirect
7. #11748138C2semidirect
8. #11748107C2semidirect
9. #11747800C2semidirect
10. #11747799C2semidirect
11. #11747742C2semidirect
12. #11747741C2semidirect
13. #11747630C2semidirect
14. C4×#6657C2semidirect
15. C4×#6653C2semidirect
22. C4×Dic30C22semidirect
28. C3×C4×D20C22semidirect
36. Dic3×D20C22semidirect
40. #91340C22semidirect
44. #91254C4direct (N × H)
45. C3×C4×C5×C8C22semidirect
47. #91101C22semidirect
48. #91100C22semidirect
49. C5×#815C22semidirect
50. C5×#815C22semidirect
51. C4×C5×C3⋊C8C22semidirect
53. C3×#3953C22semidirect
54. C3×#3950C22semidirect
55. #90990C22semidirect
56. #90987C22semidirect
57. #90974C22semidirect
60. #90965C22semidirect
74. C4×D40D3semidirect
96. D3×D20C2×C4semidirect
99. #6765C2×C4semidirect
108. #6706C2×C4semidirect
115. C5×ΓL(1,𝔽25)C2×C4semidirect
120. C3×D40C2×C4semidirect
129. #6657C2×C4semidirect
130. #6653C2×C4semidirect
145. C4×ΓL(1,𝔽25)D5semidirect
169. C4×D20C2×D3semidirect
177. C4×C5×C8C2×D3semidirect
183. #3953C2×D3semidirect
185. #3950C2×D3semidirect
208. Dic30C22×C4semidirect
221. C3×D20C22×C4semidirect
232. C3×C5×C8C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
266. C3×C4×C8C2×D5semidirect
272. #815C2×D5semidirect
273. #815C2×D5semidirect
278. C4×C3⋊C8C2×D5semidirect
330. D40C4×D3semidirect
363. C3×C4×C5AGL(1,ℤ/8)semidirect
427. ΓL(1,𝔽25)C4×D5semidirect
458. D20C2×C4×D3semidirect
471. C5×C8C2×C4×D3semidirect
515. C4×C8D3×D5semidirect
564. C3×C8C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
585. C4×C5#911semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
665. C3×C4#4054semidirect
724. C8C4×D3×D5semidirect
732. C5C4×#911semidirect
756. C4#91254direct (N × H)
759. C3C4×#4054semidirect

Maximal subgroups

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

subgroupindex
C2×#912542
C4×D3×D202
C4×#67652
C4×#67062
C4×C5×ΓL(1,𝔽25)2
C3×C4×D402
#117481382
#117481072
#117478002
#117477992
#117477422
#117477412
#117476302
C4×#66572
C4×#66532
C4×#40543
C4×#9115