Finite Group Databasebeta

← C4×#91506 #14416715

Subgroups — C4×#91506 #14416715

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
1C4×#6821C211yesmaximal, characteristic, complemented
2C2×#91506C211yesmaximal, characteristic
3C4×#6777C211yesmaximal, characteristic, complemented
4C4×C5×#215C211yesmaximal, characteristic, complemented
5C3×C4×#688C211yesmaximal, characteristic, complemented
6#11749242C211yesmaximal, characteristic, complemented
7#11749241C211yesmaximal, characteristic, complemented
8#11749205C211yesmaximal, characteristic, complemented
9#11747479C211yesmaximal, characteristic, complemented
10#11747459C211yesmaximal, characteristic, complemented
11#11747236C211yesmaximal, characteristic, complemented
12#11747229C211yesmaximal, characteristic, complemented
13C4×#6654C211yesmaximal, characteristic, complemented
14C4×#6653C211yesmaximal, characteristic, complemented
15C4×#6651C211yesmaximal, characteristic, complemented
16C4×#4060—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×#6777C2211yescharacteristic
19C2×C4×D3×D5—21no—
20C3×C4×C5×Q8C2211yescharacteristic, complemented
21Q8×Dic15C2211yescharacteristic, complemented
22#91782—21no—
23#91782C2211yescharacteristic, complemented
24#91781—21no—
25#91781C2211yescharacteristic
26C4×D60—21no—
27C4×D60C2211yescharacteristic, complemented
28C42×D15—21no—
29C42×D15C2211yescharacteristic
30C2×C5×#215C2211yescharacteristic
31C4×C5×D12C2211yescharacteristic
32C2×C3×#688C2211yescharacteristic
33C3×C4×D20C2211yescharacteristic
34#91506C418yesdirect product factor
35#91473—21no—
36#91442—21no—
37C4×#1201—21no—
38#91437C2211yescharacteristic
39#91435C2211yescharacteristic
40#91434C2211yescharacteristic
41C2×#6654C2211yescharacteristic
42C2×#6653C2211yescharacteristic
43C2×#6651C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45C5×#835C2211yescharacteristic, complemented
46C5×#809C2211yescharacteristic
47C5×#808C2211yescharacteristic, complemented
48C4×C5×C3⋊C8C2211yescharacteristic, complemented
49C3×#3967C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic, complemented
52C3×C4×#168C2211yescharacteristic, complemented
53#90990C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55#90969C2211yescharacteristic, complemented
56#90968C2211yescharacteristic, complemented
57#90967C2211yescharacteristic
58#90965C2211yescharacteristic
59#90954C2211yescharacteristic, complemented
60#90954C2211yescharacteristic, complemented
61C4×#914—51nomaximal, Hall
62C2×#4060—31no—
63C4×#713—31no—
64C4×D4×D5—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67C4×#688D311yescharacteristic, complemented
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×#676—31no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79#6821—22no—
80#6821C2×C414yescomplemented
81C2×D60—21no—
82C2×D60C2311yescharacteristic
83C2×C4×D15—21no—
84C2×C4×D15—21no—
85C2×C4×D15—21no—
86C2×C4×D15D411yescharacteristic
87C2×C4×D15D411yescharacteristic
88C2×C4×D15C2311yescharacteristic
89C2×C5×D12C2311yescharacteristic
90C2×C4×C5×D3—21no—
91C2×C3×D20C2311yescharacteristic
92C2×C3×C4×D5—21no—
93C2×#1201—21no—
94C2×#1200—21no—
95C2×D3×Dic5—21no—
96C2×D5×Dic3—21no—
97#6777—22no—
98#6777C2×C414yescomplemented
99C4×D3×D5—44no—
100C3×C5×C4⋊C4—21no—
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C42×C5—21no—
103C3×C42×C5C2311yescharacteristic
104#6714—21no—
105#6714—21no—
106#6714—21no—
107C4⋊Dic15—21no—
108C4⋊Dic15C2311yescharacteristic
109C4×Dic15—21no—
110C4×Dic15—21no—
111C4×Dic15D411yescharacteristic
112C4×Dic15D411yescharacteristic
113C4×Dic15C2311yescharacteristic
114C5×#215C2×C414yescomplemented
115C5×(C2×D3)⋊C4—21no—
116C5×C4⋊Dic3C2311yescharacteristic
117C2×C5×C3⋊C8C2311yescharacteristic
118C2×C5×C3⋊C8C2311yescharacteristic
119C3×#688C2×C414yescomplemented
120C3×#685—21no—
121C3×C4⋊Dic5C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124#6669—21no—
125(C2×D3)⋊Dic5—21no—
126#6665—21no—
127#6654C2×C414yescomplemented
128#6653C2×C414yescomplemented
129#6651—22no—
130#6651C2×C414yescomplemented
131C2×#914—51no—
132C4×#239—51no—
133C4×D3×D4—51no—
134C3×C4×SD16—51no—
135#5164—51no—
136C4×#215D511yescharacteristic, complemented
137C4×#213—51no—
138#4869—51no—
139#4861—51no—
140#4817—51no—
141#4803—51no—
142#4785—51no—
143#4770—51no—
144C4×D24—51no—
145C4×ΓL(1,𝔽25)—51no—
146C2×#713—31no—
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×SD16—31no—
150C4×C5×Q8C2×D311yescharacteristic, complemented
151C4×C5×D4—31no—
152Q8×Dic5—31no—
153C2×#688C2×D311yescharacteristic
154D4×Dic5—31no—
155C2×#686—31no—
156C4×C22⋊D5—61no—
157#4060—38no—
158C2×D40—31no—
159C2×#676—31no—
160C2×#676—31no—
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—61no—
171C4×D20C2×D311yescharacteristic
172C42×D5—31no—
173C42×D5—61no—
174C5×#106—31no—
175C5×#103—31no—
176C5×#102—31no—
177C4×C5×C8—31no—
178#3967C2×D311yescharacteristic, complemented
179#3964—31no—
180#3953—31no—
181#3953—31no—
182#3950—31no—
183#3947—31no—
184#3947—31no—
185#3941—31no—
186#3941C2×D311yescharacteristic
187#3940C2×D311yescharacteristic, complemented
188#3939—31no—
189C4×#168C2×D311yescharacteristic, complemented
190C4×AGL(1,ℤ/8)—151noSylow
191C22×D15—21no—
192C22×D15C2×D411yescharacteristic
193C22×C5×D3—21no—
194C22×C3×D5—21no—
195C2×D3×D5—24no—
196C2×D3×D5—42no—
197C2×D3×D5—42no—
198C3×C5×Q8—21no—
199C3×C5×Q8C22×C412yescomplemented
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205C2×Dic15—21no—
206C2×Dic15C2×D411yescharacteristic
207C2×Dic15C2×D411yescharacteristic
208C2×Dic15C2×D411yescharacteristic
209D60—24no—
210D60—21no—
211D60C22×C412yescomplemented
212C4×D15—22no—
213C4×D15—24no—
214C4×D15—41no—
215C4×D15—42no—
216C4×D15—42no—
217C4×D15C22×C412yes—
218C4×D15#4112yes—
219C2×C5×Dic3—21no—
220C5×D12—21no—
221C5×D12C22×C412yes—
222C4×C5×D3—42no—
223C2×C3×Dic5—21no—
224C3×D20—21no—
225C3×D20C22×C412yes—
226C3×C4×D5—42no—
227#1201—24no—
228#1200—42no—
229D3×Dic5—42no—
230D5×Dic3—42no—
231C3×#168—21no—
232C3×#168C22×C412yescomplemented
233C5×C3⋊C8—21no—
234C5×C3⋊C8C22×C412yescomplemented
235C2×#239—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×SD16—51no—
239C3×C4×Q8C2×D511yescharacteristic, complemented
240C3×C4×D4—51no—
241Q8×Dic3—51no—
242C2×#215C2×D511yescharacteristic
243D4×Dic3—51no—
244C2×#213—51no—
245C4×#67—101no—
246#914—58no—
247C2×D24—51no—
248C2×ΓL(1,𝔽25)—51no—
249C2×ΓL(1,𝔽25)—51no—
250#893—51no—
251#893—51no—
252#893—101no—
253#892—51no—
254#892—101no—
255D3×C4⋊C4—51no—
256#67⋊C4—101no—
257D3×C22⋊C4—101no—
258C4×D12—51no—
259C4×D12—101no—
260C4×D12C2×D511yescharacteristic
261C42×D3—51no—
262C42×D3—101no—
263C3×#106—51no—
264C3×#103—51no—
265C3×#102—51no—
266C3×C4×C8—51no—
267#835C2×D511yescharacteristic, complemented
268#832—51no—
269#821—51no—
270#821—51no—
271#818—51no—
272#815—51no—
273#815—51no—
274#809—51no—
275#809C2×D511yescharacteristic
276#808C2×D511yescharacteristic, complemented
277#807—51no—
278C4×C3⋊C8C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C2×C5×Q8C22×D311yescharacteristic
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—61no—
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—31no—
294C2×C4×D5—31no—
295C2×C4×D5—31no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—61no—
301C2×C4×D5—124no—
302C5×SD16—34no—
303C2×C5×C8—31no—
304C2×C5×C8—31no—
305C5×C4⋊C4—21no—
306C5×C4⋊C4—31no—
307C5×C4⋊C4C22×D311yescharacteristic
308C5×C22⋊C4—61no—
309C42×C5—21no—
310C42×C5C22×D311yescharacteristic
311C22⋊Dic5—61no—
312#688C4×D314yescomplemented
313#686—34no—
314#685—21no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—61no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—61no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C4×Dic5—61no—
327C4×Dic5—61no—
328C2×#168C22×D311yescharacteristic
329C2×#168C22×D311yescharacteristic
330D40—34no—
331#676—34no—
332#676—62no—
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—51no—
342C4×D8—151no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5C22×D411yescharacteristic
349C2×D15—21no—
350C2×D15—21no—
351C2×D15—22no—
352C2×D15—41no—
353C2×D15—41no—
354C2×D15C4×D412yes—
355C2×C5×D3—22no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C3×D5—22no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361D3×D5—48no—
362C3×C4×C5—22no—
363C3×C4×C5—21no—
364C3×C4×C5—41no—
365C3×C4×C5AGL(1,ℤ/8)12yescomplemented
366C3×C4×C5C23×C411yescharacteristic
367C3×C4×C5C2×#4111yescharacteristic
368Dic15—21no—
369Dic15—21no—
370Dic15—41no—
371Dic15C4×D412yes—
372C3×Dic5—41no—
373C5×Dic3—41no—
374C23×D3—101no—
375C2×C3×Q8C22×D511yescharacteristic
376C2×C3×D4—51no—
377C22×C3×C4—101no—
378C2×#67—101no—
379C22×Dic3—101no—
380#239—54no—
381#239—102no—
382D3×D4—54no—
383D3×D4—102no—
384C2×D12—51no—
385C2×D12—101no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—51no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—101no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—204no—
397C3×SD16—54no—
398C2×C3×C8—51no—
399C2×C3×C8—51no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—51no—
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—101no—
404C3×C42—21no—
405C3×C42C22×D511yescharacteristic
406#217—101no—
407#215C4×D514yescomplemented
408#213—54no—
409(C2×D3)⋊C4—21no—
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—101no—
416C4⋊Dic3C22×D511yescharacteristic
417Dic3⋊C4—101no—
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—101no—
422C4×Dic3—101no—
423C2×C3⋊C8C22×D511yescharacteristic
424C2×C3⋊C8C22×D511yescharacteristic
425D24—54no—
426ΓL(1,𝔽25)—54no—
427ΓL(1,𝔽25)—102no—
428C23×C5—61no—
429C22×D5—21no—
430C22×D5—31no—
431C22×D5—64no—
432C22×D5—61no—
433C22×D5—122no—
434C22×D5—122no—
435C5×Q8—21no—
436C5×Q8C2×C4×D312yescomplemented
437C5×D4—32no—
438C5×D4—61no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—61no—
442C2×C4×C5—122no—
443C2×C4×C5D3×D411yescharacteristic
444C2×C4×C5D3×D411yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C2×Dic5—21no—
448C2×Dic5—31no—
449C2×Dic5—31no—
450C2×Dic5—31no—
451C2×Dic5—61no—
452C2×Dic5—122no—
453D20—21no—
454D20—32no—
455D20—64no—
456D20—61no—
457D20C2×C4×D312yes—
458C4×D5—32no—
459C4×D5—32no—
460C4×D5—42no—
461C4×D5—64no—
462C4×D5—62no—
463C4×D5—122no—
464C4×D5—121no—
465C4×D5—122no—
466C4×D5—122no—
467C4×D5—122no—
468C5×C8—32no—
469C5×C8—61no—
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—51no—
478C2×D8—151no—
479C2×D8—151no—
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—151no—
483C4×Q8D3×D511yescharacteristic, complemented
484C4×D4—31no—
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—151no—
499C2×C42—301no—
500#107—151no—
501#107—151no—
502#106—31no—
503#106—51no—
504#103—31no—
505#103—51no—
506#102—31no—
507#102—51no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
512#97—151no—
513#97—151no—
514C4×C8—31no—
515C4×C8—51no—
516C2×C3×C5C2×C4×D411yescharacteristic
517C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
518C2×C3×C5#57511yescharacteristic
519D15—22no—
520D15—42no—
521C3×D5—42no—
522C5×D3—42no—
523C23×C3—101no—
524C22×D3—21no—
525C22×D3—51no—
526C22×D3—104no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C3×Q8—21no—
531C3×Q8C2×C4×D512yescomplemented
532C3×D4—52no—
533C3×D4—101no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—101no—
537C2×C3×C4—202no—
538C2×C3×C4D4×D511yescharacteristic
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542C2×Dic3—21no—
543C2×Dic3—51no—
544C2×Dic3—51no—
545C2×Dic3—51no—
546C2×Dic3—101no—
547C2×Dic3—202no—
548D12—21no—
549D12—52no—
550D12—104no—
551D12—101no—
552D12C2×C4×D512yes—
553C4×D3—42no—
554C4×D3—52no—
555C4×D3—52no—
556C4×D3—104no—
557C4×D3—102no—
558C4×D3—202no—
559C4×D3—201no—
560C4×D3—202no—
561C4×D3—202no—
562C4×D3—202no—
563C3×C8—52no—
564C3×C8—101no—
565C3⋊C8—21no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—62no—
568C22×C5—121no—
569C22×C5—121no—
570C22×C5C2×D3×D411yescharacteristic
571C2×D5—22no—
572C2×D5—32no—
573C2×D5—41no—
574C2×D5—41no—
575C2×D5—61no—
576C2×D5—61no—
577C2×D5—62no—
578C2×D5—128no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—21no—
582C4×C5—22no—
583C4×C5—41no—
584C4×C5—121no—
585C4×C5#91412yescomplemented
586C4×C5C22×C4×D311yescharacteristic
587C4×C5D3×#4111yescharacteristic
588Dic5—32no—
589Dic5—41no—
590Dic5—61no—
591Dic5—61no—
592Dic5—121no—
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8C2×D3×D511yescharacteristic
597C2×D4—31no—
598C2×D4—51no—
599C2×D4—154no—
600C2×D4—151no—
601C2×D4—301no—
602C2×D4—302no—
603C2×D4—301no—
604C22×C4—61no—
605C22×C4—101no—
606C22×C4—151no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—301no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—34no—
617SD16—54no—
618D8—154no—
619D8—154no—
620M16—154no—
621M16—302no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—51no—
625C2×C8—51no—
626C4⋊C4—21no—
627C4⋊C4—31no—
628C4⋊C4—51no—
629C4⋊C4—151no—
630C4⋊C4—301no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—61no—
634C22⋊C4—101no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—21no—
641C42—151no—
642C42—151no—
643C42—151no—
644C42—301no—
645C42—301no—
646C42C2×D3×D511yescharacteristic
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—102no—
649C22×C3—201no—
650C22×C3—201no—
651C22×C3C2×D4×D511yescharacteristic
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—52no—
656C2×D3—101no—
657C2×D3—101no—
658C2×D3—102no—
659C2×D3—208no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—21no—
663C3×C4—22no—
664C3×C4—41no—
665C3×C4—201no—
666C3×C4#406012yescomplemented
667C3×C4C22×C4×D511yescharacteristic
668C3×C4D5×#4111yescharacteristic
669Dic3—41no—
670Dic3—52no—
671Dic3—101no—
672Dic3—101no—
673Dic3—201no—
674C2×C5—122no—
675C2×C5C4×D3×D411yescharacteristic
676C2×C5C2×#91411yescharacteristic
677C2×C5#576811yescharacteristic
678D5—42no—
679D5—62no—
680D5—122no—
681C23—61no—
682C23—101no—
683C23—151no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—21no—
689Q8C4×D3×D512yescomplemented
690D4—32no—
691D4—52no—
692D4—61no—
693D4—101no—
694D4—152no—
695D4—304no—
696D4—304no—
697D4—301no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—61no—
701C2×C4—101no—
702C2×C4—122no—
703C2×C4—151no—
704C2×C4—152no—
705C2×C4—152no—
706C2×C4—151no—
707C2×C4—151no—
708C2×C4—202no—
709C2×C4—304no—
710C2×C4—302no—
711C2×C4—301no—
712C2×C4—601no—
713C2×C4—602no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4#679011yescharacteristic
719C2×C4#679011yescharacteristic
720C2×C4C22×D3×D511yescharacteristic
721C8—32no—
722C8—52no—
723C8—61no—
724C8—101no—
725C2×C3—202no—
726C2×C3C4×D4×D511yescharacteristic
727C2×C3C2×#406011yescharacteristic
728C2×C3#6610211yescharacteristic
729D3—42no—
730D3—102no—
731D3—202no—
732C5C4×#91411yescharacteristic, complemented, Sylow
733C22—62no—
734C22—102no—
735C22—121no—
736C22—121no—
737C22—152no—
738C22—201no—
739C22—201no—
740C22—301no—
741C22—301no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22C2×#679011yescharacteristic
747C4—21no—
748C4—22no—
749C4—41no—
750C4—121no—
751C4—152no—
752C4—201no—
753C4—301no—
754C4—301no—
755C4—601no—
756C4#9150612yesdirect product factor
757C4C2×C4×D3×D511yescharacteristic
758C4#9201611yescharacteristic
759C3C4×#406011yescharacteristic, complemented, Sylow
760C2—122no—
761C2—202no—
762C2—302no—
763C2—602no—
764C2C4×#679011yescharacteristic
765C2C2×#9150611yescharacteristic
766C2#1175532911yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91506C2
cosocleC2×C3×C4×C5C24
hypercenterC4×Q8D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#6821C2semidirect
3. C4×#6777C2semidirect
4. C4×C5×#215C2semidirect
5. C3×C4×#688C2semidirect
6. #11749242C2semidirect
7. #11749241C2semidirect
8. #11749205C2semidirect
9. #11747479C2semidirect
10. #11747459C2semidirect
11. #11747236C2semidirect
12. #11747229C2semidirect
13. C4×#6654C2semidirect
14. C4×#6653C2semidirect
15. C4×#6651C2semidirect
20. C3×C4×C5×Q8C22semidirect
21. Q8×Dic15C22semidirect
23. #91782C22semidirect
27. C4×D60C22semidirect
34. #91506C4direct (N × H)
45. C5×#835C22semidirect
47. C5×#808C22semidirect
48. C4×C5×C3⋊C8C22semidirect
49. C3×#3967C22semidirect
51. C3×#3940C22semidirect
52. C3×C4×#168C22semidirect
53. #90990C22semidirect
54. #90988C22semidirect
55. #90969C22semidirect
56. #90968C22semidirect
59. #90954C22semidirect
60. #90954C22semidirect
67. C4×#688D3semidirect
80. #6821C2×C4semidirect
98. #6777C2×C4semidirect
114. C5×#215C2×C4semidirect
119. C3×#688C2×C4semidirect
127. #6654C2×C4semidirect
128. #6653C2×C4semidirect
130. #6651C2×C4semidirect
136. C4×#215D5semidirect
150. C4×C5×Q8C2×D3semidirect
178. #3967C2×D3semidirect
187. #3940C2×D3semidirect
189. C4×#168C2×D3semidirect
199. C3×C5×Q8C22×C4semidirect
211. D60C22×C4semidirect
232. C3×#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
239. C3×C4×Q8C2×D5semidirect
267. #835C2×D5semidirect
276. #808C2×D5semidirect
278. C4×C3⋊C8C2×D5semidirect
312. #688C4×D3semidirect
365. C3×C4×C5AGL(1,ℤ/8)semidirect
407. #215C4×D5semidirect
436. C5×Q8C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
483. C4×Q8D3×D5semidirect
531. C3×Q8C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
585. C4×C5#914semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
666. C3×C4#4060semidirect
689. Q8C4×D3×D5semidirect
732. C5C4×#914semidirect
756. C4#91506direct (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
C4×#68212
C2×#915062
C4×#67772
C4×C5×#2152
C3×C4×#6882
#117492422
#117492412
#117492052
#117474792
#117474592
#117472362
#117472292
C4×#66542
C4×#66532
C4×#66512
C4×#40603
C4×#9145