Finite Group Databasebeta

← C4×#91496 #14416705

Subgroups — C4×#91496 #14416705

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×C5×D3×D4C211yesmaximal, characteristic, complemented
2C2×#91496C211yesmaximal, characteristic
3C4×#6769C211yesmaximal, characteristic, complemented
4C4×#6715C211yesmaximal, characteristic, complemented
5C3×C4×#687C211yesmaximal, characteristic, complemented
6#11749010C211yesmaximal, characteristic, complemented
7#11748989C211yesmaximal, characteristic, complemented
8#11748967C211yesmaximal, characteristic, complemented
9#11747505C211yesmaximal, characteristic, complemented
10#11747470C211yesmaximal, characteristic, complemented
11#11747455C211yesmaximal, characteristic, complemented
12#11747265C211yesmaximal, characteristic, complemented
13C4×#6656C211yesmaximal, characteristic, complemented
14C4×#6654C211yesmaximal, characteristic, complemented
15C4×#6650C211yesmaximal, characteristic, complemented
16C4×#4078—31nomaximal, Hall
17C2×C5×D3×D4C2211yescharacteristic
18C22×C4×C5×D3—21no—
19C2×#6769C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C2×#6715C2211yescharacteristic
22C4×D60C2211yescharacteristic, complemented
23C5×D4×Dic3C2211yescharacteristic
24C4×C5×#67—21no—
25C5×#893C2211yescharacteristic
26C5×D3×C4⋊C4C2211yescharacteristic
27C5×#67⋊C4—21no—
28C5×D3×C22⋊C4—21no—
29C4×C5×D12C2211yescharacteristic
30C42×C5×D3C2211yescharacteristic
31C2×C3×#687C2211yescharacteristic
32C3×C4×Dic10C2211yescharacteristic, complemented
33#91496C418yesdirect product factor
34#91446—21no—
35C4×#1203—21no—
36#91428C2211yescharacteristic, complemented
37#91403—21no—
38C4×#1200—21no—
39#91338C2211yescharacteristic
40Dic3×Dic10C2211yescharacteristic, complemented
41C2×#6656C2211yescharacteristic
42C2×#6654C2211yescharacteristic
43C2×#6650C2211yescharacteristic
44C2×#6650C2211yescharacteristic
45#91116C2211yescharacteristic
46#91093C2211yescharacteristic, complemented
47#91091C2211yescharacteristic, complemented
48C4×C3⋊#168C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic
50C3×#3942C2211yescharacteristic, complemented
51C3×#3940C2211yescharacteristic, complemented
52C3×C4×#168C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90970C2211yescharacteristic, complemented
56#90969C2211yescharacteristic, complemented
57#90967C2211yescharacteristic
58#90966C2211yescharacteristic
59#90953C2211yescharacteristic, complemented
60#90953C2211yescharacteristic, complemented
61C4×#914—51nomaximal, Hall
62C2×C4×C5×D4—31no—
63C2×#4078—31no—
64C4×#709—31no—
65#65504—31no—
66#65307—31no—
67#65307—31no—
68C4×#687—31no—
69C4×#687D311yescharacteristic, complemented
70#65303—31no—
71#65303—31no—
72C4×#686—31no—
73C4×#686—31no—
74#65255—31no—
75#65253—31no—
76C4×#681—31no—
77C23×C5×D3—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×C5×#67—21no—
83C22×C5×Dic3—21no—
84C5×D3×D4—22no—
85C5×D3×D4C2×C414yescomplemented
86C2×C5×D12C2311yescharacteristic
87C2×C4×C5×D3—21no—
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3—21no—
90C2×C4×C5×D3—44no—
91C2×C4×C5×D3D411yescharacteristic
92C2×C4×C5×D3D411yescharacteristic
93C2×C4×C5×D3C2311yescharacteristic
94C2×C3×Dic10C2311yescharacteristic
95C2×#1203—21no—
96C2×#1200—21no—
97C2×#1200—21no—
98#6769—22no—
99#6769C2×C414yescomplemented
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C22⋊C4—21no—
102C3×C42×C5C2311yescharacteristic
103#6715C2×C414yescomplemented
104#6714—21no—
105C4⋊Dic15C2311yescharacteristic
106C2×C3⋊#168C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C5×#217—21no—
109C5×(C2×D3)⋊C4—21no—
110C5×(C2×D3)⋊C4—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×Dic3⋊C4—21no—
113C4×C5×Dic3D411yescharacteristic
114C4×C5×Dic3D411yescharacteristic
115C4×C5×Dic3C2311yescharacteristic
116C3×#687C2×C414yescomplemented
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C2×C3×#168C2311yescharacteristic
121C2×C3×#168C2311yescharacteristic
122#6668—21no—
123#6667—21no—
124(C2×D3)⋊Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6656C2×C414yescomplemented
128#6654C2×C414yescomplemented
129#6650—22no—
130#6650C2×C414yescomplemented
131C2×#914—51no—
132C4×#239—51no—
133C4×D3×D4D511yescharacteristic, complemented
134C3×C4×SD16—51no—
135#5164—51no—
136C4×#215—51no—
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—
146C22×C5×D4—31no—
147C23×C4×C5—61no—
148C2×#709—31no—
149C4×C5×D4—31no—
150C4×C5×D4—31no—
151C4×C5×D4—31no—
152C4×C5×D4—61no—
153C4×C5×D4—61no—
154C4×C5×D4C2×D311yescharacteristic
155C2×C5×C4⋊C4—31no—
156C2×C5×C22⋊C4—61no—
157C2×C42×C5—31no—
158C2×#687—31no—
159C2×#687C2×D311yescharacteristic
160#4078—38no—
161C2×#686—31no—
162C2×#686—31no—
163C4×C22⋊D5—61no—
164C4×C22⋊D5—61no—
165#4072—31no—
166C2×#681—31no—
167C2×#681—31no—
168C4×D20—31no—
169C4×D20—31no—
170#4018—61no—
171C42×D5—61no—
172C4×Dic10—31no—
173C4×Dic10C2×D311yescharacteristic, complemented
174#3964—31no—
175#3964—31no—
176#3964—31no—
177#3964C2×D311yescharacteristic
178#3942—31no—
179#3942C2×D311yescharacteristic, complemented
180#3941—31no—
181#3941—31no—
182#3940—31no—
183#3940C2×D311yescharacteristic, complemented
184#3939—31no—
185#3939—31no—
186#3935—31no—
187#3935—31no—
188C4×#168—31no—
189C4×#168C2×D311yescharacteristic, complemented
190C4×AGL(1,ℤ/8)—151noSylow
191C23×C3×C5—21no—
192C22×D15—21no—
193C22×C5×D3—21no—
194C22×C5×D3—24no—
195C22×C5×D3—42no—
196C22×C5×D3—42no—
197C22×C5×D3C2×D411yescharacteristic
198C3×C5×D4—21no—
199C3×C5×D4C22×C412yes—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—42no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205C2×Dic15—21no—
206D60—21no—
207D60C22×C412yescomplemented
208C4×D15—42no—
209C5×#67—24no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—42no—
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C2×C5×Dic3C2×D411yescharacteristic
215C5×D12—21no—
216C5×D12C22×C412yes—
217C4×C5×D3—22no—
218C4×C5×D3—41no—
219C4×C5×D3—42no—
220C4×C5×D3—42no—
221C4×C5×D3—42no—
222C4×C5×D3C22×C412yes—
223C4×C5×D3#4112yes—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C3×Dic10—21no—
227C3×Dic10C22×C412yescomplemented
228#1203—24no—
229#1200—24no—
230#1200—42no—
231C3⋊#168—21no—
232C3⋊#168C22×C412yescomplemented
233C3×#168—21no—
234C3×#168C22×C412yescomplemented
235C2×#239—51no—
236C2×D3×D4C2×D511yescharacteristic
237C22×C4×D3—21no—
238C2×C3×SD16—51no—
239C3×C4×Q8—51no—
240C3×C4×D4C2×D511yescharacteristic
241Q8×Dic3—51no—
242C2×#215—51no—
243D4×Dic3C2×D511yescharacteristic
244C2×#213—51no—
245C4×#67—21no—
246#914—58no—
247C2×D24—51no—
248C2×ΓL(1,𝔽25)—51no—
249C2×ΓL(1,𝔽25)—51no—
250#893—51no—
251#893—101no—
252#893C2×D511yescharacteristic
253#892—51no—
254#892—101no—
255D3×C4⋊C4C2×D511yescharacteristic
256#67⋊C4—21no—
257D3×C22⋊C4—21no—
258C4×D12—51no—
259C4×D12—101no—
260C4×D12C2×D511yescharacteristic
261C42×D3—101no—
262C42×D3C2×D511yescharacteristic
263C3×#106—51no—
264C3×#103—51no—
265C3×#102—51no—
266C3×C4×C8—51no—
267#835—51no—
268#832—51no—
269#821—51no—
270#821—51no—
271#818—51no—
272#815—51no—
273#815—51no—
274#809—51no—
275#809—51no—
276#808—51no—
277#807—51no—
278C4×C3⋊C8—51no—
279C24×C5—61no—
280C2×C5×D4—34no—
281C2×C5×D4—31no—
282C2×C5×D4—62no—
283C2×C5×D4—61no—
284C2×C5×D4C22×D311yescharacteristic
285C22×C4×C5—21no—
286C22×C4×C5—31no—
287C22×C4×C5—31no—
288C22×C4×C5—31no—
289C22×C4×C5—61no—
290C22×C4×C5—61no—
291C22×C4×C5—61no—
292C22×C4×C5—61no—
293C22×C4×C5—124no—
294C2×C22⋊D5—61no—
295#709—34no—
296#709—62no—
297C2×D20—31no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—61no—
301C2×Dic10C22×D311yescharacteristic
302C5×C4⋊C4—31no—
303C5×C4⋊C4—61no—
304C5×C4⋊C4C22×D311yescharacteristic
305C5×C22⋊C4—21no—
306C5×C22⋊C4—61no—
307C5×C22⋊C4—61no—
308C5×C22⋊C4—61no—
309C42×C5—31no—
310C42×C5—31no—
311C42×C5—31no—
312C42×C5C22×D311yescharacteristic
313C22⋊Dic5—61no—
314#687—34no—
315#687C4×D314yescomplemented
316#686—34no—
317#686—34no—
318#685—61no—
319#685—61no—
320C4⋊Dic5—31no—
321C4⋊Dic5C22×D311yescharacteristic
322#683—21no—
323#683—61no—
324C4×Dic5—21no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327#681—34no—
328#681—62no—
329C2×#168—31no—
330C2×#168—31no—
331C2×#168C22×D311yescharacteristic
332C2×#168C22×D311yescharacteristic
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—31no—
336#442—151no—
337#442—151no—
338#440—151no—
339#440—151no—
340C4×SD16—51no—
341C4×SD16—151no—
342C4×D8—151no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5—22no—
349C22×C3×C5—41no—
350C22×C3×C5—41no—
351C22×C3×C5C22×D411yescharacteristic
352C2×D15—22no—
353C2×D15—41no—
354C2×D15—41no—
355C2×C5×D3—21no—
356C2×C5×D3—21no—
357C2×C5×D3—22no—
358C2×C5×D3—48no—
359C2×C5×D3—41no—
360C2×C5×D3—41no—
361C2×C5×D3C4×D412yes—
362C3×C4×C5—21no—
363C3×C4×C5—41no—
364C3×C4×C5AGL(1,ℤ/8)12yescomplemented
365C3×C4×C5C23×C411yescharacteristic
366C3×C4×C5C2×#4111yescharacteristic
367Dic15—41no—
368C3×Dic5—22no—
369C3×Dic5—41no—
370C5×Dic3—21no—
371C5×Dic3—21no—
372C5×Dic3—41no—
373C5×Dic3C4×D412yes—
374C23×D3—21no—
375C2×C3×Q8—51no—
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—21no—
378C2×#67—21no—
379C22×Dic3—21no—
380#239—54no—
381#239—102no—
382D3×D4—22no—
383D3×D4C4×D514yescomplemented
384C2×D12—51no—
385C2×D12—101no—
386C2×D12C22×D511yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—21no—
389C2×C4×D3—21no—
390C2×C4×D3—44no—
391C2×C4×D3—101no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3C22⋊D511yescharacteristic
395C2×C4×D3C22⋊D511yescharacteristic
396C2×C4×D3C22×D511yescharacteristic
397C3×SD16—54no—
398C2×C3×C8—51no—
399C2×C3×C8—51no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4C22×D511yescharacteristic
403C3×C22⋊C4—21no—
404C3×C42—101no—
405C3×C42C22×D511yescharacteristic
406#217—21no—
407#215—54no—
408#213—54no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
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—21no—
418C4×Dic3—101no—
419C4×Dic3—101no—
420C4×Dic3C22⋊D511yescharacteristic
421C4×Dic3C22⋊D511yescharacteristic
422C4×Dic3C22×D511yescharacteristic
423C2×C3⋊C8—51no—
424C2×C3⋊C8—51no—
425D24—54no—
426ΓL(1,𝔽25)—54no—
427ΓL(1,𝔽25)—102no—
428C23×C5—21no—
429C23×C5—31no—
430C23×C5—64no—
431C23×C5—61no—
432C23×C5—122no—
433C23×C5—122no—
434C22×D5—61no—
435C5×D4—21no—
436C5×D4—32no—
437C5×D4—64no—
438C5×D4—61no—
439C5×D4C2×C4×D312yes—
440C2×C4×C5—21no—
441C2×C4×C5—31no—
442C2×C4×C5—32no—
443C2×C4×C5—32no—
444C2×C4×C5—31no—
445C2×C4×C5—31no—
446C2×C4×C5—42no—
447C2×C4×C5—62no—
448C2×C4×C5—61no—
449C2×C4×C5—121no—
450C2×C4×C5—122no—
451C2×C4×C5—122no—
452C2×C4×C5—122no—
453C2×C4×C5—122no—
454C2×C4×C5D3×D411yescharacteristic
455C2×C4×C5D3×D411yescharacteristic
456C2×C4×C5C23×D311yescharacteristic
457C22⋊D5—64no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—61no—
461D20—32no—
462D20—61no—
463C4×D5—64no—
464C4×D5—122no—
465C4×D5—122no—
466Dic10—21no—
467Dic10C2×C4×D312yescomplemented
468#168—21no—
469#168—32no—
470#168—61no—
471#168C2×C4×D312yescomplemented
472C2×#41—151no—
473C22×D4—31no—
474C23×C4—61no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—51no—
477C2×SD16—151no—
478C2×D8—151no—
479C2×D8—151no—
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—51no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—31no—
487C4×D4—61no—
488C4×D4—61no—
489C4×D4—151no—
490C4×D4—151no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4D3×D511yescharacteristic
494#117—151no—
495#117—301no—
496C2×C4⋊C4—31no—
497C2×C22⋊C4—61no—
498C2×C42—31no—
499C2×C42—301no—
500#107—151no—
501#107—151no—
502#106—51no—
503#106—151no—
504#103—51no—
505#103—151no—
506#102—51no—
507#102—151no—
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×C5—42no—
517C2×C3×C5C2×C4×D411yescharacteristic
518C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
519C2×C3×C5#57511yescharacteristic
520D15—42no—
521C5×D3—22no—
522C5×D3—42no—
523C23×C3—21no—
524C22×D3—21no—
525C22×D3—24no—
526C22×D3—42no—
527C22×D3—42no—
528C22×D3—101no—
529C22×D3C2×C22⋊D511yescharacteristic
530C3×Q8—52no—
531C3×Q8—101no—
532C3×D4—21no—
533C3×D4C2×C4×D512yes—
534C2×C3×C4—21no—
535C2×C3×C4—42no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4C2×C22⋊D511yescharacteristic
539C2×C3×C4C2×C22⋊D511yescharacteristic
540C2×C3×C4C23×D511yescharacteristic
541#67—24no—
542C2×Dic3—21no—
543C2×Dic3—42no—
544C2×Dic3—101no—
545C2×Dic3C2×C22⋊D511yescharacteristic
546C2×Dic3C2×C22⋊D511yescharacteristic
547C2×Dic3C2×C22⋊D511yescharacteristic
548D12—21no—
549D12—52no—
550D12—104no—
551D12—101no—
552D12C2×C4×D512yes—
553C4×D3—22no—
554C4×D3—41no—
555C4×D3—42no—
556C4×D3—42no—
557C4×D3—42no—
558C4×D3—104no—
559C4×D3—202no—
560C4×D3—202no—
561C4×D3C2×C4×D512yes—
562C4×D3#70912yes—
563C3×C8—52no—
564C3×C8—101no—
565C3⋊C8—52no—
566C3⋊C8—101no—
567C22×C5—22no—
568C22×C5—32no—
569C22×C5—41no—
570C22×C5—41no—
571C22×C5—61no—
572C22×C5—61no—
573C22×C5—62no—
574C22×C5—128no—
575C22×C5—121no—
576C22×C5—121no—
577C22×C5C2×D3×D411yescharacteristic
578C2×D5—62no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—21no—
582C4×C5—32no—
583C4×C5—41no—
584C4×C5—61no—
585C4×C5—61no—
586C4×C5—121no—
587C4×C5#91412yescomplemented
588C4×C5C22×C4×D311yescharacteristic
589C4×C5D3×#4111yescharacteristic
590Dic5—22no—
591Dic5—41no—
592Dic5—121no—
593C24—61no—
594#41—154no—
595#41—302no—
596C2×Q8—51no—
597C2×D4—34no—
598C2×D4—31no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—151no—
602C2×D4—301no—
603C2×D4C2×D3×D511yescharacteristic
604C22×C4—21no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—124no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—301no—
616SD16—54no—
617SD16—154no—
618D8—154no—
619D8—154no—
620M16—154no—
621M16—302no—
622C2×C8—51no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8—151no—
626C4⋊C4—31no—
627C4⋊C4—51no—
628C4⋊C4—61no—
629C4⋊C4—101no—
630C4⋊C4—151no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—21no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—31no—
642C42—31no—
643C42—101no—
644C42—301no—
645C42—301no—
646C42C2×D3×D511yescharacteristic
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—22no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3C22×C22⋊D511yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—48no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—102no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3C4×C22⋊D512yes—
662C3×C4—21no—
663C3×C4—41no—
664C3×C4—102no—
665C3×C4—201no—
666C3×C4#407812yescomplemented
667C3×C4C22×C4×D511yescharacteristic
668C3×C4C2×#70911yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—201no—
673Dic3C4×C22⋊D512yes—
674C2×C5—42no—
675C2×C5—62no—
676C2×C5—122no—
677C2×C5C4×D3×D411yescharacteristic
678C2×C5C2×#91411yescharacteristic
679C2×C5#576811yescharacteristic
680D5—122no—
681C23—21no—
682C23—31no—
683C23—64no—
684C23—61no—
685C23—122no—
686C23—122no—
687C23—301no—
688Q8—52no—
689Q8—101no—
690D4—21no—
691D4—32no—
692D4—64no—
693D4—61no—
694D4—152no—
695D4—304no—
696D4—301no—
697D4C4×D3×D512yes—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—32no—
701C2×C4—32no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—42no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—121no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—304no—
715C2×C4—301no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4D3×C22⋊D511yescharacteristic
719C2×C4D3×C22⋊D511yescharacteristic
720C2×C4C22×D3×D511yescharacteristic
721C8—52no—
722C8—101no—
723C8—152no—
724C8—301no—
725C2×C3—42no—
726C2×C3C2×C4×C22⋊D511yescharacteristic
727C2×C3C2×#407811yescharacteristic
728C2×C3#6615611yescharacteristic
729D3—22no—
730D3—42no—
731D3—202no—
732C5C4×#91411yescharacteristic, complemented, Sylow
733C22—22no—
734C22—32no—
735C22—41no—
736C22—41no—
737C22—61no—
738C22—61no—
739C22—62no—
740C22—128no—
741C22—121no—
742C22—121no—
743C22—302no—
744C22—601no—
745C22—601no—
746C22C2×D3×C22⋊D511yescharacteristic
747C4—21no—
748C4—32no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—102no—
753C4—121no—
754C4—201no—
755C4—601no—
756C4#9149612yesdirect product factor
757C4C2×C4×D3×D511yescharacteristic
758C4D3×#70911yescharacteristic
759C3C4×#407811yescharacteristic, complemented, Sylow
760C2—42no—
761C2—62no—
762C2—122no—
763C2—602no—
764C2C4×D3×C22⋊D511yescharacteristic
765C2C2×#9149611yescharacteristic
766C2#1175532211yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91496C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×C5×D3×D4C2semidirect
3. C4×#6769C2semidirect
4. C4×#6715C2semidirect
5. C3×C4×#687C2semidirect
6. #11749010C2semidirect
7. #11748989C2semidirect
8. #11748967C2semidirect
9. #11747505C2semidirect
10. #11747470C2semidirect
11. #11747455C2semidirect
12. #11747265C2semidirect
13. C4×#6656C2semidirect
14. C4×#6654C2semidirect
15. C4×#6650C2semidirect
22. C4×D60C22semidirect
32. C3×C4×Dic10C22semidirect
33. #91496C4direct (N × H)
36. #91428C22semidirect
40. Dic3×Dic10C22semidirect
46. #91093C22semidirect
47. #91091C22semidirect
48. C4×C3⋊#168C22semidirect
50. C3×#3942C22semidirect
51. C3×#3940C22semidirect
52. C3×C4×#168C22semidirect
53. #90988C22semidirect
54. #90986C22semidirect
55. #90970C22semidirect
56. #90969C22semidirect
59. #90953C22semidirect
60. #90953C22semidirect
69. C4×#687D3semidirect
85. C5×D3×D4C2×C4semidirect
99. #6769C2×C4semidirect
103. #6715C2×C4semidirect
116. C3×#687C2×C4semidirect
127. #6656C2×C4semidirect
128. #6654C2×C4semidirect
130. #6650C2×C4semidirect
133. C4×D3×D4D5semidirect
173. C4×Dic10C2×D3semidirect
179. #3942C2×D3semidirect
183. #3940C2×D3semidirect
189. C4×#168C2×D3semidirect
207. D60C22×C4semidirect
227. C3×Dic10C22×C4semidirect
232. C3⋊#168C22×C4semidirect
234. C3×#168C22×C4semidirect
315. #687C4×D3semidirect
364. C3×C4×C5AGL(1,ℤ/8)semidirect
383. D3×D4C4×D5semidirect
467. Dic10C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
587. C4×C5#914semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
666. C3×C4#4078semidirect
732. C5C4×#914semidirect
756. C4#91496direct (N × H)
759. C3C4×#4078semidirect

Maximal subgroups

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

subgroupindex
C4×C5×D3×D42
C2×#914962
C4×#67692
C4×#67152
C3×C4×#6872
#117490102
#117489892
#117489672
#117475052
#117474702
#117474552
#117472652
C4×#66562
C4×#66542
C4×#66502
C4×#40783
C4×#9145