Finite Group Databasebeta

← C4×#91249 #14416713

Subgroups — C4×#91249 #14416713

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×#91249C211yesmaximal, characteristic
2C4×D5×D12C211yesmaximal, characteristic, complemented
3C4×#6773C211yesmaximal, characteristic, complemented
4C4×D120C211yesmaximal, characteristic, complemented
5C4×C5×#204C211yesmaximal, characteristic, complemented
6C3×C4×#676C211yesmaximal, characteristic, complemented
7#11748105C211yesmaximal, characteristic, complemented
8#11747772C211yesmaximal, characteristic, complemented
9#11747769C211yesmaximal, characteristic, complemented
10#11747748C211yesmaximal, characteristic, complemented
11#11747746C211yesmaximal, characteristic, complemented
12#11747618C211yesmaximal, characteristic, complemented
13#11747606C211yesmaximal, characteristic, complemented
14C4×#6660C211yesmaximal, characteristic, complemented
15C4×#6654C211yesmaximal, characteristic, complemented
16C4×#4060—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18C2×C4×D3×D5—21no—
19C2×#6773C2211yescharacteristic
20C2×D120C2211yescharacteristic
21C4×D60C2211yescharacteristic
22C4×D60C2211yescharacteristic, complemented
23C2×C5×#204C2211yescharacteristic
24C4×C5×D12C2211yescharacteristic
25C4×C5×Dic6C2211yescharacteristic, complemented
26C2×C3×#676C2211yescharacteristic
27C2×C3×#676C2211yescharacteristic
28C3×C42×D5C2211yescharacteristic
29D5×(C2×D3)⋊C4—21no—
30C4×#1203—21no—
31#91444—21no—
32C4×#1202—21no—
33#91418C2211yescharacteristic
34#91418C2211yescharacteristic, complemented
35Dic5×D12C2211yescharacteristic
36D5×C4⋊Dic3C2211yescharacteristic
37#91405—21no—
38#91402—21no—
39C4×#1200—21no—
40#91358C2211yescharacteristic
41Dic5×Dic6C2211yescharacteristic, complemented
42C2×#6660C2211yescharacteristic
43C2×#6654C2211yescharacteristic
44#91249C418yesdirect product factor
45C3×C4×C5×C8C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91105C2211yescharacteristic, complemented
48#91102C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×#817C2211yescharacteristic, complemented
51C5×#816C2211yescharacteristic, complemented
52C3×#3947C2211yescharacteristic, complemented
53C3×#3947C2211yescharacteristic, complemented
54C3×C4×#168C2211yescharacteristic, complemented
55#90988C2211yescharacteristic, complemented
56#90985C2211yescharacteristic, complemented
57#90973C2211yescharacteristic, complemented
58#90969C2211yescharacteristic
59#90969C2211yescharacteristic, complemented
60#90967C2211yescharacteristic
61C4×#908—51nomaximal, Hall
62C2×#4060—31no—
63C4×#713—31no—
64C4×D4×D5—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67C4×#688—31no—
68C4×#686—31no—
69#65158—31no—
70#65150—31no—
71#65106—31no—
72#65092—31no—
73#65074—31no—
74#65059—31no—
75C4×D40—31no—
76C4×#676D311yescharacteristic, complemented
77C22×D3×D5—21no—
78C2×D60C2311yescharacteristic
79C2×D60C2311yescharacteristic
80C2×C4×D15—21no—
81C2×C4×D15—21no—
82C2×C5×D12C2311yescharacteristic
83C2×C4×C5×D3—21no—
84C2×C5×Dic6C2311yescharacteristic
85C2×C3×C4×D5D411yescharacteristic
86C2×C3×C4×D5D411yescharacteristic
87C2×C3×C4×D5C2311yescharacteristic
88C2×#1203—21no—
89C2×#1202—21no—
90C2×#1200—21no—
91C2×#1200—21no—
92C2×#1200—21no—
93C2×D3×Dic5—21no—
94C2×D5×Dic3—21no—
95D5×D12—22no—
96D5×D12C2×C414yescomplemented
97C4×D3×D5—44no—
98#6773—22no—
99#6773C2×C414yescomplemented
100C2×C3×C5×C8C2311yescharacteristic
101C2×C3×C5×C8C2311yescharacteristic
102C3×C42×C5C2311yescharacteristic
103#6714—21no—
104#6714—21no—
105C4⋊Dic15C2311yescharacteristic
106C4⋊Dic15C2311yescharacteristic
107D120C2×C414yescomplemented
108C5×(C2×D3)⋊C4—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C5×C4⋊Dic3C2311yescharacteristic
111C5×Dic3⋊C4—21no—
112C4×C5×Dic3—21no—
113C5×#204C2×C414yescomplemented
114C3×C4×Dic5D411yescharacteristic
115C3×C4×Dic5D411yescharacteristic
116C3×C4×Dic5C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119C3×#676—22no—
120C3×#676C2×C414yescomplemented
121Dic3⋊Dic5—21no—
122#6668—21no—
123#6667—21no—
124#6667—21no—
125(C2×D3)⋊Dic5—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128Dic3×Dic5—21no—
129#6660C2×C414yescomplemented
130#6654C2×C414yescomplemented
131C2×#908—51no—
132C4×#235—51no—
133C2×C4×D12—51no—
134C3×C4×M16—51no—
135#5133—51no—
136#5131—51no—
137#5121—51no—
138#4711—51no—
139#4711—51no—
140#4710—51no—
141#4710—51no—
142C4×D24—51no—
143C4×D24—51no—
144C4×#204—51no—
145C4×#204D511yescharacteristic, complemented
146C2×#713—31no—
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×SD16—31no—
150C4×C5×Q8—31no—
151C4×C5×D4—31no—
152Q8×Dic5—31no—
153C2×#688—31no—
154D4×Dic5—31no—
155C2×#686—31no—
156C4×C22⋊D5—61no—
157#4060—38no—
158C2×D40—31no—
159C2×#676C2×D311yescharacteristic
160C2×#676C2×D311yescharacteristic
161#4039—31no—
162#4039—31no—
163#4039—61no—
164#4038—31no—
165#4038—61no—
166D5×C4⋊C4—31no—
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C4×D20—31no—
171C4×D20—61no—
172C42×D5—61no—
173C42×D5C2×D311yescharacteristic
174C5×#106—31no—
175C5×#103—31no—
176C5×#102—31no—
177C4×C5×C8C2×D311yescharacteristic, complemented
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3953—31no—
182#3950—31no—
183#3947C2×D311yescharacteristic, complemented
184#3947C2×D311yescharacteristic, complemented
185#3941—31no—
186#3941—31no—
187#3940—31no—
188#3939—31no—
189C4×#168C2×D311yescharacteristic, complemented
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×D15—21no—
193C22×C5×D3—21no—
194C22×C3×D5C2×D411yescharacteristic
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—
203D60—21no—
204D60—21no—
205D60C22×C412yes—
206D60C22×C412yescomplemented
207C4×D15—42no—
208C4×D15—42no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—21no—
212C5×D12—21no—
213C5×D12C22×C412yes—
214C4×C5×D3—42no—
215C5×Dic6—21no—
216C5×Dic6C22×C412yescomplemented
217C2×C3×Dic5C2×D411yescharacteristic
218C2×C3×Dic5C2×D411yescharacteristic
219C2×C3×Dic5C2×D411yescharacteristic
220C3×C4×D5—22no—
221C3×C4×D5—41no—
222C3×C4×D5C22×C412yes—
223C3×C4×D5#4112yes—
224#1203—24no—
225#1202—24no—
226#1200—24no—
227#1200—42no—
228#1200—42no—
229D3×Dic5—42no—
230D5×Dic3—42no—
231C3×C5×C8—21no—
232C3×C5×C8C22×C412yescomplemented
233C3×#168—21no—
234C3×#168C22×C412yescomplemented
235C2×#235—51no—
236C22×D12—51no—
237C22×C4×D3—101no—
238C2×C3×M16—51no—
239C2×C3×M16—51no—
240C2×C3×C42—51no—
241C4×#67—101no—
242C4×#67—101no—
243C2×(C2×D3)⋊C4—101no—
244#926—51no—
245C2×C4⋊Dic3—51no—
246#908—58no—
247C2×D24—51no—
248C2×D24—51no—
249C2×#204—51no—
250C2×#204C2×D511yescharacteristic
251C4×D12—51no—
252C4×D12—51no—
253C4×D12—51no—
254C4×D12—51no—
255C4×D12—51no—
256C4×D12—101no—
257C4×D12—101no—
258C4×D12C2×D511yescharacteristic
259#872—101no—
260C42×D3—101no—
261C4×Dic6—51no—
262C4×Dic6C2×D511yescharacteristic, complemented
263C3×#97—51no—
264C3×#97—51no—
265C3×C4×C8—51no—
266C3×C4×C8C2×D511yescharacteristic, complemented
267#821—51no—
268#821—51no—
269#821—51no—
270#821—51no—
271#821—51no—
272#821C2×D511yescharacteristic
273#818—51no—
274#818—51no—
275#817—51no—
276#817C2×D511yescharacteristic, complemented
277#816—51no—
278#816C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C2×C5×Q8—31no—
281C2×C5×D4—31no—
282C22×C4×C5—61no—
283C2×C22⋊D5—61no—
284C22×Dic5—61no—
285#713—34no—
286#713—62no—
287D4×D5—34no—
288D4×D5—62no—
289C2×D20—31no—
290C2×D20—31no—
291C2×D20—61no—
292C2×C4×D5—61no—
293C2×C4×D5—61no—
294C2×C4×D5—61no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—124no—
299C2×C4×D5D1211yescharacteristic
300C2×C4×D5D1211yescharacteristic
301C2×C4×D5C22×D311yescharacteristic
302C5×SD16—34no—
303C2×C5×C8C22×D311yescharacteristic
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—31no—
307C5×C4⋊C4—61no—
308C5×C22⋊C4—61no—
309C42×C5—61no—
310C42×C5C22×D311yescharacteristic
311C22⋊Dic5—61no—
312#688—34no—
313#686—34no—
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—31no—
321C4⋊Dic5—61no—
322#683—61no—
323C4×Dic5—61no—
324C4×Dic5—61no—
325C4×Dic5D1211yescharacteristic
326C4×Dic5D1211yescharacteristic
327C4×Dic5C22×D311yescharacteristic
328C2×#168C22×D311yescharacteristic
329C2×#168C22×D311yescharacteristic
330D40—34no—
331#676—22no—
332#676C4×D314yescomplemented
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—31no—
341C4×SD16—151no—
342C4×D8—151no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—151no—
347C4×M16—51no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—22no—
350C2×D15—22no—
351C2×D15—41no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15—41no—
355C2×C5×D3—22no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C3×D5—21no—
359C2×C3×D5—21no—
360C2×C3×D5C4×D412yes—
361D3×D5—48no—
362C3×C4×C5—21no—
363C3×C4×C5AGL(1,ℤ/8)12yescomplemented
364C3×C4×C5C23×C411yescharacteristic
365C3×C4×C5C2×#4111yescharacteristic
366Dic15—41no—
367Dic15—41no—
368C3×Dic5—21no—
369C3×Dic5—21no—
370C3×Dic5C4×D412yes—
371C5×Dic3—22no—
372C5×Dic3—41no—
373C5×Dic3—41no—
374C23×D3—101no—
375C22×C3×C4—51no—
376C22×C3×C4—51no—
377C22×C3×C4—51no—
378C2×#67—101no—
379C22×Dic3—101no—
380#235—54no—
381#235—102no—
382C2×D12—51no—
383C2×D12—51no—
384C2×D12—54no—
385C2×D12—102no—
386C2×D12—101no—
387C2×D12C22×D511yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3—101no—
390C2×C4×D3—101no—
391C2×C4×D3—101no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—204no—
396C2×Dic6C22×D511yescharacteristic
397C3×M16—54no—
398C3×M16—102no—
399C2×C3×C8—51no—
400C2×C3×C8—51no—
401C2×C3×C8C22×D511yescharacteristic
402C2×C3×C8C22×D511yescharacteristic
403C3×C42—51no—
404C3×C42—51no—
405C3×C42—51no—
406C3×C42C22×D511yescharacteristic
407#217—101no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412(C2×D3)⋊C4—101no—
413(C2×D3)⋊C4—101no—
414C4⋊Dic3—51no—
415C4⋊Dic3—51no—
416C4⋊Dic3—101no—
417C4⋊Dic3C22×D511yescharacteristic
418C4⋊Dic3C22×D511yescharacteristic
419Dic3⋊C4—21no—
420Dic3⋊C4—101no—
421C4×Dic3—21no—
422C4×Dic3—101no—
423C4×Dic3—101no—
424D24—54no—
425D24—54no—
426#204—54no—
427#204C4×D514yescomplemented
428C23×C5—61no—
429C22×D5—61no—
430C22×D5—61no—
431C22×D5—64no—
432C22×D5—122no—
433C22×D5—122no—
434C22×D5C2×D1211yescharacteristic
435C5×Q8—32no—
436C5×Q8—61no—
437C5×D4—32no—
438C5×D4—61no—
439C2×C4×C5—61no—
440C2×C4×C5—61no—
441C2×C4×C5—61no—
442C2×C4×C5—122no—
443C2×C4×C5C2×D1211yescharacteristic
444C2×C4×C5C2×D1211yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—122no—
450C2×Dic5C2×D1211yescharacteristic
451C2×Dic5C2×D1211yescharacteristic
452C2×Dic5C2×D1211yescharacteristic
453D20—32no—
454D20—32no—
455D20—64no—
456D20—61no—
457D20—61no—
458C4×D5—22no—
459C4×D5—41no—
460C4×D5—64no—
461C4×D5—122no—
462C4×D5—122no—
463C4×D5—122no—
464C4×D5—122no—
465C4×D5—122no—
466C4×D5C2×C4×D312yes—
467C4×D5#23512yes—
468C5×C8—21no—
469C5×C8C2×C4×D312yescomplemented
470#168—21no—
471#168C2×C4×D312yescomplemented
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—31no—
477C2×SD16—151no—
478C2×D8—151no—
479C2×D8—151no—
480C2×M16—51no—
481C2×M16—51no—
482C4×Q8—31no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—151no—
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—51no—
499C2×C42—301no—
500#107—151no—
501#107—151no—
502#106—31no—
503#106—151no—
504#103—31no—
505#103—151no—
506#102—31no—
507#102—151no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—51no—
513#97—51no—
514C4×C8—51no—
515C4×C8D3×D511yescharacteristic, complemented
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—42no—
520D15—42no—
521C3×D5—22no—
522C5×D3—42no—
523C23×C3—51no—
524C22×D3—21no—
525C22×D3—104no—
526C22×D3—101no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C2×C3×C4—51no—
531C2×C3×C4—52no—
532C2×C3×C4—52no—
533C2×C3×C4—51no—
534C2×C3×C4—51no—
535C2×C3×C4—102no—
536C2×C3×C4—201no—
537C2×C3×C4D4×D511yescharacteristic
538C2×C3×C4D4×D511yescharacteristic
539C2×C3×C4C23×D511yescharacteristic
540#67—104no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—101no—
545C2×Dic3—101no—
546C2×Dic3—202no—
547D12—21no—
548D12—52no—
549D12—52no—
550D12—104no—
551D12—101no—
552D12—101no—
553D12C2×C4×D512yes—
554C4×D3—42no—
555C4×D3—104no—
556C4×D3—202no—
557C4×D3—202no—
558C4×D3—202no—
559C4×D3—202no—
560C4×D3—202no—
561Dic6—21no—
562Dic6C2×C4×D512yescomplemented
563C3×C8—21no—
564C3×C8—52no—
565C3×C8—101no—
566C3×C8C2×C4×D512yescomplemented
567C22×C5—62no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5C22×D1211yescharacteristic
571C2×D5—21no—
572C2×D5—21no—
573C2×D5—62no—
574C2×D5—62no—
575C2×D5—128no—
576C2×D5—121no—
577C2×D5—121no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5C4×D1212yes—
581C4×C5—21no—
582C4×C5—62no—
583C4×C5—121no—
584C4×C5—121no—
585C4×C5#90812yescomplemented
586C4×C5C22×C4×D311yescharacteristic
587C4×C5C2×#23511yescharacteristic
588Dic5—21no—
589Dic5—21no—
590Dic5—121no—
591Dic5—121no—
592Dic5C4×D1212yes—
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—31no—
597C2×D4—31no—
598C2×D4—154no—
599C2×D4—151no—
600C2×D4—151no—
601C2×D4—302no—
602C2×D4—301no—
603C2×D4—301no—
604C22×C4—51no—
605C22×C4—51no—
606C22×C4—51no—
607C22×C4—61no—
608C22×C4—301no—
609C22×C4—301no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—34no—
617SD16—154no—
618D8—154no—
619D8—154no—
620M16—54no—
621M16—102no—
622C2×C8—51no—
623C2×C8—51no—
624C2×C8C2×D3×D511yescharacteristic
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—151no—
630C4⋊C4—151no—
631C4⋊C4—301no—
632C4⋊C4—301no—
633C22⋊C4—61no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—51no—
641C42—51no—
642C42—51no—
643C42—61no—
644C42—301no—
645C42—301no—
646C42C2×D3×D511yescharacteristic
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—52no—
649C22×C3—101no—
650C22×C3—101no—
651C22×C3C2×D4×D511yescharacteristic
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—102no—
656C2×D3—102no—
657C2×D3—208no—
658C2×D3—201no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—21no—
663C3×C4—52no—
664C3×C4—101no—
665C3×C4—101no—
666C3×C4#406012yescomplemented
667C3×C4C22×C4×D511yescharacteristic
668C3×C4D5×#4111yescharacteristic
669Dic3—22no—
670Dic3—41no—
671Dic3—41no—
672Dic3—201no—
673Dic3—201no—
674C2×C5—122no—
675C2×C5C2×C4×D1211yescharacteristic
676C2×C5C2×#90811yescharacteristic
677C2×C5#574811yescharacteristic
678D5—22no—
679D5—122no—
680D5—122no—
681C23—51no—
682C23—61no—
683C23—304no—
684C23—301no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—32no—
689Q8—61no—
690D4—32no—
691D4—61no—
692D4—152no—
693D4—152no—
694D4—304no—
695D4—304no—
696D4—301no—
697D4—301no—
698C2×C4—51no—
699C2×C4—52no—
700C2×C4—52no—
701C2×C4—51no—
702C2×C4—51no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—102no—
707C2×C4—122no—
708C2×C4—201no—
709C2×C4—304no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—602no—
713C2×C4—602no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4D5×D1211yescharacteristic
719C2×C4D5×D1211yescharacteristic
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—52no—
723C8—101no—
724C8C4×D3×D512yescomplemented
725C2×C3—102no—
726C2×C3C4×D4×D511yescharacteristic
727C2×C3C2×#406011yescharacteristic
728C2×C3#6610211yescharacteristic
729D3—42no—
730D3—202no—
731D3—202no—
732C5C4×#90811yescharacteristic, complemented, Sylow
733C22—52no—
734C22—62no—
735C22—101no—
736C22—101no—
737C22—121no—
738C22—121no—
739C22—302no—
740C22—302no—
741C22—608no—
742C22—601no—
743C22—601no—
744C22—601no—
745C22—601no—
746C22C2×D5×D1211yescharacteristic
747C4—21no—
748C4—52no—
749C4—62no—
750C4—101no—
751C4—101no—
752C4—121no—
753C4—121no—
754C4—601no—
755C4—601no—
756C4#9124912yesdirect product factor
757C4C2×C4×D3×D511yescharacteristic
758C4D5×#23511yescharacteristic
759C3C4×#406011yescharacteristic, complemented, Sylow
760C2—102no—
761C2—122no—
762C2—602no—
763C2—602no—
764C2C4×D5×D1211yescharacteristic
765C2C2×#9124911yescharacteristic
766C2#1175395911yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91249C2
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×D5×D12C2semidirect
3. C4×#6773C2semidirect
4. C4×D120C2semidirect
5. C4×C5×#204C2semidirect
6. C3×C4×#676C2semidirect
7. #11748105C2semidirect
8. #11747772C2semidirect
9. #11747769C2semidirect
10. #11747748C2semidirect
11. #11747746C2semidirect
12. #11747618C2semidirect
13. #11747606C2semidirect
14. C4×#6660C2semidirect
15. C4×#6654C2semidirect
22. C4×D60C22semidirect
25. C4×C5×Dic6C22semidirect
34. #91418C22semidirect
41. Dic5×Dic6C22semidirect
44. #91249C4direct (N × H)
45. C3×C4×C5×C8C22semidirect
47. #91105C22semidirect
48. #91102C22semidirect
50. C5×#817C22semidirect
51. C5×#816C22semidirect
52. C3×#3947C22semidirect
53. C3×#3947C22semidirect
54. C3×C4×#168C22semidirect
55. #90988C22semidirect
56. #90985C22semidirect
57. #90973C22semidirect
59. #90969C22semidirect
76. C4×#676D3semidirect
96. D5×D12C2×C4semidirect
99. #6773C2×C4semidirect
107. D120C2×C4semidirect
113. C5×#204C2×C4semidirect
120. C3×#676C2×C4semidirect
129. #6660C2×C4semidirect
130. #6654C2×C4semidirect
145. C4×#204D5semidirect
177. C4×C5×C8C2×D3semidirect
183. #3947C2×D3semidirect
184. #3947C2×D3semidirect
189. C4×#168C2×D3semidirect
206. D60C22×C4semidirect
216. C5×Dic6C22×C4semidirect
232. C3×C5×C8C22×C4semidirect
234. C3×#168C22×C4semidirect
262. C4×Dic6C2×D5semidirect
266. C3×C4×C8C2×D5semidirect
276. #817C2×D5semidirect
278. #816C2×D5semidirect
332. #676C4×D3semidirect
363. C3×C4×C5AGL(1,ℤ/8)semidirect
427. #204C4×D5semidirect
469. C5×C8C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
515. C4×C8D3×D5semidirect
562. Dic6C2×C4×D5semidirect
566. C3×C8C2×C4×D5semidirect
585. C4×C5#908semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
666. C3×C4#4060semidirect
724. C8C4×D3×D5semidirect
732. C5C4×#908semidirect
756. C4#91249direct (N × H)
759. C3C4×#4060semidirect

Maximal subgroups

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

subgroupindex
C2×#912492
C4×D5×D122
C4×#67732
C4×D1202
C4×C5×#2042
C3×C4×#6762
#117481052
#117477722
#117477692
#117477482
#117477462
#117476182
#117476062
C4×#66602
C4×#66542
C4×#40603
C4×#9085