Finite Group Databasebeta

← #14416682

Subgroups — #14416682

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×#91800C211yesmaximal, characteristic
2#11754853C211yesmaximal, characteristic, complemented
3D4×#1200C211yesmaximal, characteristic, complemented
4C5×Dic3×D8C211yesmaximal, characteristic, complemented
5C3×#65441C211yesmaximal, characteristic, complemented
6#11749011C211yesmaximal, characteristic, complemented
7#11749004C211yesmaximal, characteristic, complemented
8#11748986C211yesmaximal, characteristic, complemented
9#11748979C211yesmaximal, characteristic, complemented
10#11748972C211yesmaximal, characteristic, complemented
11#11748959C211yesmaximal, characteristic, complemented
12#11747789C211yesmaximal, characteristic, complemented
13#11747778C211yesmaximal, characteristic, complemented
14#11747638C211yesmaximal, characteristic, complemented
15#11747599C211yesmaximal, characteristic, complemented
16C4×#4057—31nomaximal, Hall
17C2×#6819C2211yescharacteristic
18C2×D4×D15C2211yescharacteristic
19C22×#1200—21no—
20C2×C3×C5×D8C2211yescharacteristic
21C2×#6716C2211yescharacteristic
22C2×#6715C2211yescharacteristic
23#91800C418yescomplemented
24C2×#6706C2211yescharacteristic
25C2×#6705C2211yescharacteristic
26C5×D4×Dic3C2211yescharacteristic
27C5×D4×Dic3C2211yescharacteristic, complemented
28C3×D4×Dic5C2211yescharacteristic
29C3×D4×Dic5C2211yescharacteristic, complemented
30#91561—21no—
31#91556—21no—
32#91556—21no—
33#91552—21no—
34#91552—21no—
35#91532—21no—
36C2×Dic3×Dic5—21no—
37#91437C2211yescharacteristic
38#91428C2211yescharacteristic
39#91418C2211yescharacteristic
40C4×#1200C2211yescharacteristic
41#91347C2211yescharacteristic
42#91340C2211yescharacteristic, complemented
43#91333C2211yescharacteristic, complemented
44C2×#6651C2211yescharacteristic
45C5×#832C2211yescharacteristic
46C5×#832C2211yescharacteristic, complemented
47C5×#818C2211yescharacteristic, complemented
48C5×C8×Dic3C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic
50C3×#3964C2211yescharacteristic, complemented
51C3×#3949C2211yescharacteristic, complemented
52C3×#3947C2211yescharacteristic, complemented
53#90989C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90975C2211yescharacteristic, complemented
56#90974C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90968C2211yescharacteristic
59#90952C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#79865—51nomaximal, Hall
62C2×#4057—31no—
63C4×D4×D5—31no—
64C4×#711—31no—
65C4×C5×D8—31no—
66#65441D311yescharacteristic, complemented
67C4×#687—31no—
68C4×#686—31no—
69#65178—31no—
70#65170—31no—
71#65074—31no—
72#65060—31no—
73#65059—31no—
74#65046—31no—
75C4×#677—31no—
76C4×#676—31no—
77C23×D15—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C2×#1220—21no—
81C2×#1220—21no—
82C22×Dic15—21no—
83#6819—22no—
84#6819C2×C414yescomplemented
85D4×D15—22no—
86D4×D15C2×C414yescomplemented
87C2×D60C2311yescharacteristic
88C2×C4×D15C2311yescharacteristic
89C2×Dic30C2311yescharacteristic
90C22×C5×Dic3—21no—
91C22×C5×Dic3—21no—
92C22×C3×Dic5—21no—
93C22×C3×Dic5—21no—
94C2×#1200—21no—
95C2×#1200—21no—
96C2×#1200—21no—
97C2×#1200—44no—
98C2×#1200D411yescharacteristic
99C2×#1200D411yescharacteristic
100C3×C5×D8C2×C414yescomplemented
101C2×C3×C5×C8C2311yescharacteristic
102#6716C2×C414yescomplemented
103#6715C2×C414yescomplemented
104C2×C3⋊#168C2311yescharacteristic
105#6706C2×C414yescomplemented
106#6705C2×C414yescomplemented
107C5×#217—21no—
108C5×#217—21no—
109C5×C4⋊Dic3C2311yescharacteristic
110C5×C4⋊Dic3C2311yescharacteristic
111C4×C5×Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C3×C22⋊Dic5—21no—
114C3×C22⋊Dic5—21no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4×Dic5C2311yescharacteristic
118C2×C3×#168C2311yescharacteristic
119#6669—21no—
120#6669—21no—
121#6669—21no—
122#6667—21no—
123#6667—21no—
124#6667—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127Dic3×Dic5—21no—
128Dic3×Dic5D411yescharacteristic
129Dic3×Dic5D411yescharacteristic
130#6651—22no—
131C2×#911—51no—
132C4×D3×D4—51no—
133C4×#237—51no—
134C3×#442—51no—
135Dic3×D8D511yescharacteristic, complemented
136#5018—51no—
137#5014—51no—
138#4861—51no—
139#4852—51no—
140#4771—51no—
141#4770—51no—
142#4758—51no—
143#4756—51no—
144#4710—51no—
145#4707—51no—
146C2×#711—31no—
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×D8C2×D311yescharacteristic
150C4×C5×D4—31no—
151C4×C5×D4—31no—
152D4×Dic5C2×D311yescharacteristic
153D4×Dic5C2×D311yescharacteristic, complemented
154C2×#687—31no—
155C2×#686—31no—
156C4×C22⋊D5—61no—
157C4×C22⋊D5—61no—
158C2×C4×Dic5—61no—
159#4057—38no—
160C2×#677—31no—
161C2×#676—31no—
162C2×#676—31no—
163#4039—31no—
164#4038—31no—
165D5×C4⋊C4—31no—
166#4033—31no—
167#4027—61no—
168#4027—61no—
169D5×C22⋊C4—61no—
170#4023—61no—
171C4×D20—31no—
172C42×D5—31no—
173C4×Dic10—31no—
174C5×#107—31no—
175C5×#102—31no—
176C5×#102—31no—
177C4×C5×C8—31no—
178#3964C2×D311yescharacteristic
179#3964C2×D311yescharacteristic, complemented
180#3953—31no—
181#3949C2×D311yescharacteristic, complemented
182#3948—31no—
183#3947—31no—
184#3947C2×D311yescharacteristic, complemented
185#3942—31no—
186#3941—31no—
187#3940—31no—
188#3939—31no—
189C4×#168—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C22×D15—21no—
194C22×D15—24no—
195C22×D15—42no—
196C22×D15—42no—
197C22×D15C2×D411yescharacteristic
198C3×C5×D4—21no—
199C3×C5×D4—21no—
200C3×C5×D4C22×C412yes—
201C3×C5×D4C22×C412yescomplemented
202C2×C3×C4×C5C2411yescharacteristic
203#1220—24no—
204#1220—24no—
205C2×Dic15—21no—
206C2×Dic15—24no—
207C2×Dic15C2×D411yescharacteristic
208D60—21no—
209D60C22×C412yes—
210C4×D15C22×C412yes—
211C4×D15#4112yes—
212Dic30—21no—
213Dic30C22×C412yescomplemented
214C2×C5×Dic3—21no—
215C2×C5×Dic3—21no—
216C2×C5×Dic3—42no—
217C2×C5×Dic3—42no—
218C2×C5×Dic3C2×D411yescharacteristic
219C2×C5×Dic3C2×D411yescharacteristic
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—42no—
223C2×C3×Dic5—42no—
224C2×C3×Dic5C2×D411yescharacteristic
225C2×C3×Dic5C2×D411yescharacteristic
226#1200—22no—
227#1200—41no—
228#1200—42no—
229#1200—42no—
230#1200—42no—
231C3×C5×C8C22×C412yescomplemented
232C3⋊#168C22×C412yescomplemented
233C3×#168—21no—
234C5×C3⋊C8—21no—
235C2×#237—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×D8C2×D511yescharacteristic
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241D4×Dic3C2×D511yescharacteristic
242D4×Dic3C2×D511yescharacteristic, complemented
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)—51no—
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×D3—51no—
262C4×Dic6—51no—
263C3×#106—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#97—51no—
267#832C2×D511yescharacteristic
268#832C2×D511yescharacteristic, complemented
269#821—51no—
270#818C2×D511yescharacteristic, complemented
271#816—51no—
272C8×Dic3—51no—
273C8×Dic3C2×D511yescharacteristic, complemented
274#810—51no—
275#809—51no—
276#808—51no—
277#807—51no—
278#803—51no—
279C23×D5—61no—
280C2×C5×D4C22×D311yescharacteristic
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—61no—
283C22×C4×C5—61no—
284C2×C22⋊D5—61no—
285C2×C22⋊D5—61no—
286C22×Dic5—21no—
287C22×Dic5—21no—
288C22×Dic5—61no—
289#711—34no—
290#711—62no—
291D4×D5—34no—
292D4×D5—62no—
293C2×D20—31no—
294C2×C4×D5—31no—
295C2×C4×D5—31no—
296C2×C4×D5—31no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—124no—
301C2×Dic10—31no—
302C5×D8C4×D314yescomplemented
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—31no—
307C5×C22⋊C4—61no—
308C5×C22⋊C4—61no—
309C42×C5—31no—
310C22⋊Dic5—21no—
311C22⋊Dic5—21no—
312#687—34no—
313#686—34no—
314#685—61no—
315#685—61no—
316#685—61no—
317C4⋊Dic5C22×D311yescharacteristic
318C4⋊Dic5C22×D311yescharacteristic
319#683—61no—
320#683—61no—
321#683—61no—
322C4×Dic5—31no—
323C4×Dic5—31no—
324C4×Dic5—61no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327C4×Dic5C22×D311yescharacteristic
328C2×#168—31no—
329C2×#168C22×D311yescharacteristic
330#677—34no—
331#676—34no—
332#676—62no—
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—51no—
337#442—151no—
338#440—151no—
339#440—151no—
340C4×SD16—151no—
341C4×SD16—151no—
342C4×D8—31no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—151no—
347C4×M16—151no—
348C22×C3×C5—22no—
349C22×C3×C5—22no—
350C22×C3×C5—41no—
351C22×C3×C5—41no—
352C22×C3×C5—41no—
353C22×C3×C5—41no—
354C22×C3×C5C22×D411yescharacteristic
355C2×D15—21no—
356C2×D15—21no—
357C2×D15—22no—
358C2×D15—48no—
359C2×D15—41no—
360C2×D15—41no—
361C2×D15C4×D412yes—
362C3×C4×C5C23×C411yescharacteristic
363C3×C4×C5C2×#4111yescharacteristic
364Dic15—22no—
365Dic15C4×D412yes—
366C3×Dic5—21no—
367C3×Dic5—21no—
368C3×Dic5—41no—
369C3×Dic5—41no—
370C5×Dic3—21no—
371C5×Dic3—41no—
372C5×Dic3—41no—
373C5×Dic3AGL(1,ℤ/8)12yescomplemented
374C23×D3—101no—
375C2×C3×D4C22×D511yescharacteristic
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—101no—
378C22×C3×C4—101no—
379C2×#67—101no—
380C2×#67—101no—
381C22×Dic3—21no—
382C22×Dic3—21no—
383C22×Dic3—101no—
384#237—54no—
385#237—102no—
386D3×D4—54no—
387D3×D4—102no—
388C2×D12—51no—
389C2×C4×D3—51no—
390C2×C4×D3—51no—
391C2×C4×D3—51no—
392C2×C4×D3—101no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—204no—
396C2×Dic6—51no—
397C3×D8C4×D514yescomplemented
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—51no—
402C3×C22⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C42—51no—
405#217—21no—
406#217—21no—
407#214—54no—
408#213—54no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412C4⋊Dic3C22×D511yescharacteristic
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—101no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—51no—
418C4×Dic3—51no—
419C4×Dic3—101no—
420C4×Dic3—101no—
421C4×Dic3—101no—
422C4×Dic3C22×D511yescharacteristic
423C2×C3⋊C8—51no—
424C2×C3⋊C8C22×D511yescharacteristic
425#204—54no—
426ΓL(1,𝔽25)—54no—
427ΓL(1,𝔽25)—102no—
428C23×C5—21no—
429C23×C5—21no—
430C22×D5—31no—
431C22×D5—64no—
432C22×D5—61no—
433C22×D5—122no—
434C22×D5—122no—
435C5×D4—21no—
436C5×D4—21no—
437C5×D4C2×C4×D312yes—
438C5×D4C2×C4×D312yescomplemented
439C2×C4×C5—31no—
440C2×C4×C5—31no—
441C2×C4×C5—61no—
442C2×C4×C5—61no—
443C2×C4×C5—122no—
444C2×C4×C5—122no—
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C22⋊D5—64no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—31no—
451C2×Dic5—42no—
452C2×Dic5—42no—
453C2×Dic5—64no—
454C2×Dic5—61no—
455C2×Dic5D3×D411yescharacteristic
456C2×Dic5D3×D411yescharacteristic
457D20—32no—
458D20—61no—
459C4×D5—32no—
460C4×D5—32no—
461C4×D5—62no—
462C4×D5—121no—
463C4×D5—122no—
464C4×D5—122no—
465C4×D5—122no—
466Dic10—32no—
467Dic10—61no—
468C5×C8—61no—
469C5×C8C2×C4×D312yescomplemented
470#168—21no—
471#168—32no—
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—151no—
477C2×SD16—151no—
478C2×D8—151no—
479C2×D8D3×D511yescharacteristic
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—151no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—31no—
486C4×D4—51no—
487C4×D4—51no—
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—31no—
501#107—151no—
502#106—51no—
503#106—151no—
504#103—151no—
505#103—151no—
506#102—31no—
507#102—31no—
508#102—51no—
509#102—51no—
510#102—151no—
511#102—151no—
512#97—51no—
513#97—151no—
514C4×C8—31no—
515C4×C8—151no—
516C2×C3×C5—42no—
517C2×C3×C5—42no—
518C2×C3×C5C2×C4×D411yescharacteristic
519C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
520C2×C3×C5#57511yescharacteristic
521D15—22no—
522D15—42no—
523C23×C3—21no—
524C23×C3—21no—
525C22×D3—51no—
526C22×D3—104no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4C2×C4×D512yes—
533C3×D4C2×C4×D512yescomplemented
534C2×C3×C4—51no—
535C2×C3×C4—51no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
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—42no—
546C2×Dic3—42no—
547C2×Dic3—51no—
548C2×Dic3—104no—
549C2×Dic3—101no—
550C2×Dic3D4×D511yescharacteristic
551C2×Dic3D4×D511yescharacteristic
552D12—52no—
553D12—101no—
554C4×D3—52no—
555C4×D3—52no—
556C4×D3—102no—
557C4×D3—201no—
558C4×D3—202no—
559C4×D3—202no—
560C4×D3—202no—
561Dic6—52no—
562Dic6—101no—
563C3×C8—101no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—21no—
566C3⋊C8—52no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—41no—
570C22×C5—41no—
571C22×C5—41no—
572C22×C5—41no—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—32no—
575C2×D5—61no—
576C2×D5—61no—
577C2×D5—62no—
578C2×D5—128no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—32no—
582C4×C5—61no—
583C4×C5—121no—
584C4×C5—121no—
585C4×C5C22×C4×D311yescharacteristic
586C4×C5D3×#4111yescharacteristic
587Dic5—21no—
588Dic5—21no—
589Dic5—32no—
590Dic5—41no—
591Dic5—41no—
592Dic5—62no—
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—151no—
597C2×D4—154no—
598C2×D4—151no—
599C2×D4—302no—
600C2×D4—301no—
601C2×D4—301no—
602C2×D4C2×D3×D511yescharacteristic
603C2×D4C2×D3×D511yescharacteristic
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—151no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—154no—
617SD16—154no—
618D8—154no—
619D8#120014yescomplemented
620M16—154no—
621M16—302no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—51no—
629C4⋊C4—51no—
630C4⋊C4—301no—
631C4⋊C4—301no—
632C4⋊C4—301no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—101no—
636C22⋊C4—101no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—51no—
642C42—151no—
643C42—151no—
644C42—301no—
645C42—301no—
646C42—301no—
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—52no—
656C2×D3—101no—
657C2×D3—101no—
658C2×D3—102no—
659C2×D3—208no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—101no—
663C3×C4—101no—
664C3×C4—201no—
665C3×C4—201no—
666C3×C4C22×C4×D511yescharacteristic
667C3×C4D5×#4111yescharacteristic
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—52no—
672Dic3—102no—
673Dic3#405712yescomplemented
674C2×C5—42no—
675C2×C5—42no—
676C2×C5C4×D3×D411yescharacteristic
677C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
678C2×C5#577311yescharacteristic
679D5—62no—
680D5—122no—
681C23—21no—
682C23—21no—
683C23—151no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—152no—
689Q8—301no—
690D4—21no—
691D4—21no—
692D4—152no—
693D4—304no—
694D4—304no—
695D4—301no—
696D4C2×#120012yes—
697D4C2×#120012yescomplemented
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—51no—
701C2×C4—51no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—101no—
705C2×C4—101no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—151no—
709C2×C4—152no—
710C2×C4—152no—
711C2×C4—202no—
712C2×C4—202no—
713C2×C4—302no—
714C2×C4—304no—
715C2×C4—301no—
716C2×C4—602no—
717C2×C4—601no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—61no—
722C8—101no—
723C8—152no—
724C8C2×#120012yescomplemented
725C2×C3—42no—
726C2×C3—42no—
727C2×C3C4×D4×D511yescharacteristic
728C2×C3C2×#405711yescharacteristic
729C2×C3#6610211yescharacteristic
730D3—102no—
731D3—202no—
732C5#7986511yescharacteristic, complemented, Sylow
733C22—22no—
734C22—22no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—152no—
740C22—301no—
741C22—301no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—32no—
748C4—61no—
749C4—101no—
750C4—101no—
751C4—121no—
752C4—121no—
753C4—152no—
754C4—201no—
755C4—201no—
756C4—302no—
757C4#9202411yescharacteristic
758C4C22×#120011yescharacteristic
759C3C4×#405711yescharacteristic, complemented, Sylow
760C2—42no—
761C2—42no—
762C2—302no—
763C2—602no—
764C2D3×#405711yescharacteristic
765C2#1175405011yescharacteristic
766C2D4×#120011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91800C2
cosocleC2×C3×C4×C5C24
hypercenterC2×D8D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11754853C2semidirect
3. D4×#1200C2semidirect
4. C5×Dic3×D8C2semidirect
5. C3×#65441C2semidirect
6. #11749011C2semidirect
7. #11749004C2semidirect
8. #11748986C2semidirect
9. #11748979C2semidirect
10. #11748972C2semidirect
11. #11748959C2semidirect
12. #11747789C2semidirect
13. #11747778C2semidirect
14. #11747638C2semidirect
15. #11747599C2semidirect
23. #91800C4semidirect
27. C5×D4×Dic3C22semidirect
29. C3×D4×Dic5C22semidirect
42. #91340C22semidirect
43. #91333C22semidirect
46. C5×#832C22semidirect
47. C5×#818C22semidirect
48. C5×C8×Dic3C22semidirect
50. C3×#3964C22semidirect
51. C3×#3949C22semidirect
52. C3×#3947C22semidirect
53. #90989C22semidirect
54. #90986C22semidirect
55. #90975C22semidirect
56. #90974C22semidirect
59. #90952C22semidirect
60. Dic3×#168C22semidirect
66. #65441D3semidirect
84. #6819C2×C4semidirect
86. D4×D15C2×C4semidirect
100. C3×C5×D8C2×C4semidirect
102. #6716C2×C4semidirect
103. #6715C2×C4semidirect
105. #6706C2×C4semidirect
106. #6705C2×C4semidirect
135. Dic3×D8D5semidirect
153. D4×Dic5C2×D3semidirect
179. #3964C2×D3semidirect
181. #3949C2×D3semidirect
184. #3947C2×D3semidirect
201. C3×C5×D4C22×C4semidirect
213. Dic30C22×C4semidirect
231. C3×C5×C8C22×C4semidirect
232. C3⋊#168C22×C4semidirect
242. D4×Dic3C2×D5semidirect
268. #832C2×D5semidirect
270. #818C2×D5semidirect
273. C8×Dic3C2×D5semidirect
302. C5×D8C4×D3semidirect
373. C5×Dic3AGL(1,ℤ/8)semidirect
397. C3×D8C4×D5semidirect
438. C5×D4C2×C4×D3semidirect
469. C5×C8C2×C4×D3semidirect
533. C3×D4C2×C4×D5semidirect
564. C3×C8C2×C4×D5semidirect
619. D8#1200semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
673. Dic3#4057semidirect
697. D4C2×#1200semidirect
724. C8C2×#1200semidirect
732. C5#79865semidirect
759. C3C4×#4057semidirect

Maximal subgroups

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

subgroupindex
C2×#918002
#117548532
D4×#12002
C5×Dic3×D82
C3×#654412
#117490112
#117490042
#117489862
#117489792
#117489722
#117489592
#117477892
#117477782
#117476382
#117475992
C4×#40573
#798655