Finite Group Databasebeta

← #14416799

Subgroups — #14416799

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×#6819C211yesmaximal, characteristic, complemented
2C2×#91482C211yesmaximal, characteristic
3C4×#6777C211yesmaximal, characteristic, complemented
4C5×#5014C211yesmaximal, characteristic, complemented
5C3×#65303C211yesmaximal, characteristic, complemented
6#11748994C211yesmaximal, characteristic, complemented
7#11748993C211yesmaximal, characteristic, complemented
8#11748959C211yesmaximal, characteristic, complemented
9#11747479C211yesmaximal, characteristic, complemented
10#11747459C211yesmaximal, characteristic, complemented
11#11747234C211yesmaximal, characteristic, complemented
12#11747227C211yesmaximal, characteristic, complemented
13#11747056C211yesmaximal, characteristic, complemented
14#11747052C211yesmaximal, characteristic, complemented
15#11746844C211yesmaximal, characteristic, complemented
16#10611596—31nomaximal, Hall
17C2×#6819C2211yescharacteristic
18C2×#6777C2211yescharacteristic
19C2×C4×D3×D5—21no—
20C3×C4×C5×D4C2211yescharacteristic, complemented
21D4×Dic15C2211yescharacteristic, complemented
22C4×#1220—21no—
23C2×C4×Dic15—21no—
24#91781C2211yescharacteristic
25#91776C2211yescharacteristic, complemented
26#91770—21no—
27#91766—21no—
28C42×D15C2211yescharacteristic
29C4×Dic30C2211yescharacteristic, complemented
30C2×C5×#213C2211yescharacteristic
31C4×C5×D12C2211yescharacteristic
32C2×C3×#686C2211yescharacteristic
33C3×C4×D20C2211yescharacteristic
34#91482C418yescomplemented
35#91473—21no—
36#91442—21no—
37C4×#1201—21no—
38#91437C2211yescharacteristic
39#91435C2211yescharacteristic
40#91434C2211yescharacteristic
41C2×#6659C2211yescharacteristic
42C2×#6657C2211yescharacteristic
43C2×#6651C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45C5×#832C2211yescharacteristic, complemented
46C5×#809C2211yescharacteristic
47C5×#808C2211yescharacteristic, complemented
48C5×#803C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic, complemented
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic, complemented
52C3×#3935C2211yescharacteristic, complemented
53#90990C2211yescharacteristic, complemented
54#90988C2211yescharacteristic, complemented
55#90975C2211yescharacteristic, complemented
56#90974C2211yescharacteristic, complemented
57#90967C2211yescharacteristic
58#90965C2211yescharacteristic
59#90951C2211yescharacteristic, complemented
60#90951C2211yescharacteristic, complemented
61#79865—51nomaximal, Hall
62C2×#4057—31no—
63C4×D4×D5—31no—
64C4×#711—31no—
65C5×#442—31no—
66D8×Dic5—31no—
67#65307—31no—
68#65303D311yescharacteristic, complemented
69#65150—31no—
70#65141—31no—
71#65060—31no—
72#65059—31no—
73#65047—31no—
74#65045—31no—
75#64999—31no—
76#64996—31no—
77C22×D3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×#1220—21no—
81C22×Dic15—21no—
82C22×Dic15—21no—
83#6819—22no—
84#6819C2×C414yescomplemented
85C2×C4×D15D411yescharacteristic
86C2×C4×D15D411yescharacteristic
87C2×C4×D15C2311yescharacteristic
88C2×Dic30C2311yescharacteristic
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⋊C4C2311yescharacteristic
101C3×C5×C22⋊C4—21no—
102C3×C42×C5C2311yescharacteristic
103#6719—21no—
104#6714—21no—
105C4⋊Dic15C2311yescharacteristic
106#6712—21no—
107#6712—21no—
108C4×Dic15—21no—
109C4×Dic15—21no—
110C4×Dic15—21no—
111C4×Dic15D411yescharacteristic
112C4×Dic15D411yescharacteristic
113C4×Dic15C2311yescharacteristic
114C5×#213C2×C414yescomplemented
115C5×(C2×D3)⋊C4—21no—
116C5×C4⋊Dic3C2311yescharacteristic
117C2×C5×C3⋊C8C2311yescharacteristic
118C2×C5×C3⋊C8C2311yescharacteristic
119C3×#686C2×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#6659C2×C414yescomplemented
128#6657C2×C414yescomplemented
129#6651—22no—
130#6651C2×C414yescomplemented
131C2×#911—51no—
132C4×D3×D4—51no—
133C4×#237—51no—
134C3×#442—51no—
135Dic3×D8—51no—
136#5018—51no—
137#5014D511yescharacteristic, complemented
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×D8—31no—
150C4×C5×D4—31no—
151C4×C5×D4C2×D311yescharacteristic, complemented
152D4×Dic5—31no—
153D4×Dic5—31no—
154C2×#687—31no—
155C2×#686C2×D311yescharacteristic
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×D20C2×D311yescharacteristic
172C42×D5—31no—
173C4×Dic10—31no—
174C5×#106—31no—
175C5×#102—31no—
176C5×#102—31no—
177C5×#97—31no—
178#3964—31no—
179#3964C2×D311yescharacteristic, complemented
180#3953—31no—
181#3950—31no—
182#3948—31no—
183C8×Dic5—31no—
184C8×Dic5—31no—
185#3942—31no—
186#3941C2×D311yescharacteristic
187#3940C2×D311yescharacteristic, complemented
188#3939—31no—
189#3935C2×D311yescharacteristic, complemented
190C4×AGL(1,ℤ/8)—151noSylow
191C23×C3×C5—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×D4—21no—
199C3×C5×D4C22×C412yescomplemented
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—42no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2×D411yescharacteristic
204C2×C3×C4×C5C2411yescharacteristic
205#1220—24no—
206C2×Dic15—21no—
207C2×Dic15—24no—
208C2×Dic15—21no—
209C2×Dic15—42no—
210C2×Dic15C2×D411yescharacteristic
211C2×Dic15C2×D411yescharacteristic
212C2×Dic15C2×D411yescharacteristic
213C4×D15—22no—
214C4×D15—41no—
215C4×D15C22×C412yes—
216C4×D15#4112yes—
217Dic30—21no—
218Dic30C22×C412yescomplemented
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×#237—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×D8—51no—
239C3×C4×D4—51no—
240C3×C4×D4C2×D511yescharacteristic, complemented
241D4×Dic3—51no—
242D4×Dic3—51no—
243C2×#214—51no—
244C2×#213C2×D511yescharacteristic
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×D12C2×D511yescharacteristic
261C42×D3—51no—
262C4×Dic6—51no—
263C3×#106—51no—
264C3×#102—51no—
265C3×#102—51no—
266C3×#97—51no—
267#832—51no—
268#832C2×D511yescharacteristic, complemented
269#821—51no—
270#818—51no—
271#816—51no—
272C8×Dic3—51no—
273C8×Dic3—51no—
274#810—51no—
275#809C2×D511yescharacteristic
276#808C2×D511yescharacteristic, complemented
277#807—51no—
278#803C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C2×C5×D4—31no—
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—21no—
283C22×C4×C5—61no—
284C2×C22⋊D5—61no—
285C2×C22⋊D5—61no—
286C22×Dic5—61no—
287C22×Dic5—61no—
288C22×Dic5—61no—
289#711—34no—
290#711—62no—
291D4×D5—34no—
292D4×D5—62no—
293C2×D20C22×D311yescharacteristic
294C2×C4×D5—21no—
295C2×C4×D5—31no—
296C2×C4×D5—31no—
297C2×C4×D5—31no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—124no—
301C2×Dic10—31no—
302C5×D8—34no—
303C2×C5×C8—31no—
304C2×C5×C8—31no—
305C5×C4⋊C4—31no—
306C5×C4⋊C4C22×D311yescharacteristic
307C5×C22⋊C4—21no—
308C5×C22⋊C4—61no—
309C42×C5C22×D311yescharacteristic
310C22⋊Dic5—61no—
311C22⋊Dic5—61no—
312#687—34no—
313#686C4×D314yescomplemented
314#685—21no—
315#685—61no—
316#685—61no—
317C4⋊Dic5—31no—
318C4⋊Dic5C22×D311yescharacteristic
319#683—61no—
320#683—61no—
321#683—61no—
322C4×Dic5—31no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—61no—
326C4×Dic5—61no—
327C4×Dic5—61no—
328C2×#168C22×D311yescharacteristic
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—31no—
337#442—51no—
338#440—151no—
339#440—151no—
340C4×SD16—151no—
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—21no—
353C2×D15—21no—
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—21no—
363C3×C4×C5—21no—
364C3×C4×C5—41no—
365C3×C4×C5C23×C411yescharacteristic
366C3×C4×C5C2×#4111yescharacteristic
367Dic15—22no—
368Dic15—21no—
369Dic15—41no—
370Dic15C4×D412yes—
371Dic15AGL(1,ℤ/8)12yescomplemented
372C3×Dic5—41no—
373C5×Dic3—41no—
374C23×D3—101no—
375C2×C3×D4—51no—
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—21no—
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×D12C22×D511yescharacteristic
389C2×C4×D3—21no—
390C2×C4×D3—51no—
391C2×C4×D3—51no—
392C2×C4×D3—51no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—204no—
396C2×Dic6—51no—
397C3×D8—54no—
398C2×C3×C8—51no—
399C2×C3×C8—51no—
400C3×C4⋊C4—51no—
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—101no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#217—101no—
407#214—54no—
408#213C4×D514yescomplemented
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412C4⋊Dic3—51no—
413C4⋊Dic3C22×D511yescharacteristic
414Dic3⋊C4—101no—
415Dic3⋊C4—101no—
416Dic3⋊C4—101no—
417C4×Dic3—51no—
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—101no—
421C4×Dic3—101no—
422C4×Dic3—101no—
423C2×C3⋊C8C22×D511yescharacteristic
424C2×C3⋊C8C22×D511yescharacteristic
425#204—54no—
426ΓL(1,𝔽25)—54no—
427ΓL(1,𝔽25)—102no—
428C23×C5—21no—
429C23×C5—61no—
430C22×D5—21no—
431C22×D5—31no—
432C22×D5—64no—
433C22×D5—122no—
434C22×D5—122no—
435C5×D4—21no—
436C5×D4—32no—
437C5×D4—61no—
438C5×D4C2×C4×D312yescomplemented
439C2×C4×C5—21no—
440C2×C4×C5—42no—
441C2×C4×C5—61no—
442C2×C4×C5—122no—
443C2×C4×C5D3×D411yescharacteristic
444C2×C4×C5D3×D411yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C22⋊D5—64no—
448C2×Dic5—21no—
449C2×Dic5—31no—
450C2×Dic5—31no—
451C2×Dic5—31no—
452C2×Dic5—64no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—122no—
456C2×Dic5—122no—
457D20—21no—
458D20C2×C4×D312yes—
459C4×D5—32no—
460C4×D5—32no—
461C4×D5—42no—
462C4×D5—62no—
463C4×D5—122no—
464C4×D5—122no—
465C4×D5—121no—
466Dic10—32no—
467Dic10—61no—
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—151no—
477C2×SD16—151no—
478C2×D8—31no—
479C2×D8—51no—
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—151no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—51no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—151no—
489C4×D4—301no—
490C4×D4—301no—
491C4×D4—301no—
492C4×D4—301no—
493C4×D4D3×D511yescharacteristic, complemented
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—151no—
505#103—151no—
506#102—31no—
507#102—31no—
508#102—51no—
509#102—51no—
510#102—151no—
511#102—151no—
512#97—31no—
513#97—51no—
514C4×C8—151no—
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—22no—
521C3×D5—42no—
522C5×D3—42no—
523C23×C3—21no—
524C23×C3—101no—
525C22×D3—21no—
526C22×D3—51no—
527C22×D3—104no—
528C22×D3—202no—
529C22×D3—202no—
530C3×D4—21no—
531C3×D4—52no—
532C3×D4—101no—
533C3×D4C2×C4×D512yescomplemented
534C2×C3×C4—21no—
535C2×C3×C4—42no—
536C2×C3×C4—101no—
537C2×C3×C4—202no—
538C2×C3×C4D4×D511yescharacteristic
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542#67—104no—
543C2×Dic3—21no—
544C2×Dic3—51no—
545C2×Dic3—51no—
546C2×Dic3—51no—
547C2×Dic3—104no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—202no—
551C2×Dic3—202no—
552D12—21no—
553D12C2×C4×D512yes—
554C4×D3—42no—
555C4×D3—52no—
556C4×D3—52no—
557C4×D3—102no—
558C4×D3—202no—
559C4×D3—202no—
560C4×D3—201no—
561Dic6—52no—
562Dic6—101no—
563C3×C8—52no—
564C3×C8—101no—
565C3⋊C8—21no—
566C3⋊C8C2×C4×D512yescomplemented
567C22×C5—22no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5—62no—
571C22×C5—121no—
572C22×C5—121no—
573C22×C5C2×D3×D411yescharacteristic
574C2×D5—22no—
575C2×D5—32no—
576C2×D5—41no—
577C2×D5—41no—
578C2×D5—61no—
579C2×D5—61no—
580C2×D5—128no—
581C4×C5—21no—
582C4×C5—21no—
583C4×C5—41no—
584C4×C5—121no—
585C4×C5C22×C4×D311yescharacteristic
586C4×C5D3×#4111yescharacteristic
587Dic5—32no—
588Dic5—32no—
589Dic5—41no—
590Dic5—61no—
591Dic5—62no—
592Dic5—121no—
593C24—301no—
594#41—154no—
595#41—302no—
596C2×Q8—151no—
597C2×D4—31no—
598C2×D4—51no—
599C2×D4—154no—
600C2×D4—302no—
601C2×D4—301no—
602C2×D4—301no—
603C2×D4C2×D3×D511yescharacteristic
604C22×C4—21no—
605C22×C4—61no—
606C22×C4—101no—
607C22×C4—151no—
608C22×C4—151no—
609C22×C4—151no—
610C22×C4—301no—
611C22×C4—301no—
612C22×C4—301no—
613C22×C4—301no—
614C22×C4—301no—
615C22×C4—604no—
616SD16—154no—
617SD16—154no—
618D8—34no—
619D8—54no—
620M16—154no—
621M16—302no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—51no—
625C2×C8—51no—
626C4⋊C4—31no—
627C4⋊C4—51no—
628C4⋊C4—151no—
629C4⋊C4—301no—
630C4⋊C4—301no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—21no—
634C22⋊C4—61no—
635C22⋊C4—101no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—151no—
641C42—151no—
642C42—151no—
643C42—301no—
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×C3—102no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—52no—
659C2×D3—101no—
660C2×D3—101no—
661C2×D3—208no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—41no—
665C3×C4—201no—
666C3×C4C22×C4×D511yescharacteristic
667C3×C4D5×#4111yescharacteristic
668Dic3—41no—
669Dic3—52no—
670Dic3—52no—
671Dic3—101no—
672Dic3—102no—
673Dic3—201no—
674C2×C5—42no—
675C2×C5—122no—
676C2×C5C4×D3×D411yescharacteristic
677C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
678C2×C5#577311yescharacteristic
679D5—42no—
680D5—62no—
681C23—21no—
682C23—61no—
683C23—101no—
684C23—151no—
685C23—304no—
686C23—602no—
687C23—602no—
688Q8—152no—
689Q8—301no—
690D4—21no—
691D4—32no—
692D4—52no—
693D4—61no—
694D4—101no—
695D4—304no—
696D4—304no—
697D4C4×D3×D512yescomplemented
698C2×C4—21no—
699C2×C4—42no—
700C2×C4—61no—
701C2×C4—101no—
702C2×C4—122no—
703C2×C4—151no—
704C2×C4—151no—
705C2×C4—152no—
706C2×C4—152no—
707C2×C4—151no—
708C2×C4—202no—
709C2×C4—302no—
710C2×C4—304no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—601no—
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—42no—
726C2×C3—202no—
727C2×C3C4×D4×D511yescharacteristic
728C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
729C2×C3#6610711yescharacteristic
730D3—42no—
731D3—102no—
732C5#7986511yescharacteristic, complemented, Sylow
733C22—22no—
734C22—41no—
735C22—41no—
736C22—62no—
737C22—102no—
738C22—121no—
739C22—121no—
740C22—152no—
741C22—201no—
742C22—201no—
743C22—301no—
744C22—301no—
745C22—608no—
746C22C2×#679011yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—121no—
751C4—152no—
752C4—152no—
753C4—201no—
754C4—302no—
755C4—301no—
756C4—601no—
757C4C2×C4×D3×D511yescharacteristic
758C4#9201611yescharacteristic
759C3#1061159611yescharacteristic, complemented, Sylow
760C2—42no—
761C2—122no—
762C2—202no—
763C2—302no—
764C2C4×#679011yescharacteristic
765C2#1175470211yescharacteristic
766C2#1175532711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91482C2
cosocleC2×C3×C4×C5C24
hypercenterC4×D4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#6819C2semidirect
3. C4×#6777C2semidirect
4. C5×#5014C2semidirect
5. C3×#65303C2semidirect
6. #11748994C2semidirect
7. #11748993C2semidirect
8. #11748959C2semidirect
9. #11747479C2semidirect
10. #11747459C2semidirect
11. #11747234C2semidirect
12. #11747227C2semidirect
13. #11747056C2semidirect
14. #11747052C2semidirect
15. #11746844C2semidirect
20. C3×C4×C5×D4C22semidirect
21. D4×Dic15C22semidirect
25. #91776C22semidirect
29. C4×Dic30C22semidirect
34. #91482C4semidirect
45. C5×#832C22semidirect
47. C5×#808C22semidirect
48. C5×#803C22semidirect
49. C3×#3964C22semidirect
51. C3×#3940C22semidirect
52. C3×#3935C22semidirect
53. #90990C22semidirect
54. #90988C22semidirect
55. #90975C22semidirect
56. #90974C22semidirect
59. #90951C22semidirect
60. #90951C22semidirect
68. #65303D3semidirect
84. #6819C2×C4semidirect
98. #6777C2×C4semidirect
114. C5×#213C2×C4semidirect
119. C3×#686C2×C4semidirect
127. #6659C2×C4semidirect
128. #6657C2×C4semidirect
130. #6651C2×C4semidirect
137. #5014D5semidirect
151. C4×C5×D4C2×D3semidirect
179. #3964C2×D3semidirect
187. #3940C2×D3semidirect
189. #3935C2×D3semidirect
199. C3×C5×D4C22×C4semidirect
218. Dic30C22×C4semidirect
232. C3×#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
240. C3×C4×D4C2×D5semidirect
268. #832C2×D5semidirect
276. #808C2×D5semidirect
278. #803C2×D5semidirect
313. #686C4×D3semidirect
371. Dic15AGL(1,ℤ/8)semidirect
408. #213C4×D5semidirect
438. C5×D4C2×C4×D3semidirect
471. #168C2×C4×D3semidirect
493. C4×D4D3×D5semidirect
533. C3×D4C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
697. D4C4×D3×D5semidirect
732. C5#79865semidirect
759. C3#10611596semidirect

Maximal subgroups

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

subgroupindex
C4×#68192
C2×#914822
C4×#67772
C5×#50142
C3×#653032
#117489942
#117489932
#117489592
#117474792
#117474592
#117472342
#117472272
#117470562
#117470522
#117468442
#106115963
#798655