Finite Group Databasebeta

← #14416666

Subgroups — #14416666

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
2C4×D4×D15C211yesmaximal, characteristic, complemented
3C4×#6819C211yesmaximal, characteristic, complemented
4C3×C5×#442C211yesmaximal, characteristic, complemented
5D8×Dic15C211yesmaximal, characteristic, complemented
6#11751119C211yesmaximal, characteristic, complemented
7#11751115C211yesmaximal, characteristic, complemented
8#11750962C211yesmaximal, characteristic, complemented
9#11750953C211yesmaximal, characteristic, complemented
10#11750872C211yesmaximal, characteristic, complemented
11#11750871C211yesmaximal, characteristic, complemented
12#11750859C211yesmaximal, characteristic, complemented
13#11750857C211yesmaximal, characteristic, complemented
14#11750811C211yesmaximal, characteristic, complemented
15#11750808C211yesmaximal, characteristic, complemented
16#10611596—31nomaximal, Hall
17C2×#6819C2211yescharacteristic
18C2×D4×D15C2211yescharacteristic
19C22×C4×D15—21no—
20C2×C3×C5×D8C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C3×C4×C5×D4C2211yescharacteristic, complemented
23D4×Dic15C2211yescharacteristic
24D4×Dic15C2211yescharacteristic, complemented
25C2×#6716C2211yescharacteristic
26C2×#6715C2211yescharacteristic
27C4×#1220—21no—
28C4×#1220—21no—
29C2×C4×Dic15—21no—
30#91800C418yescomplemented
31C2×#6706C2211yescharacteristic
32C2×#6705C2211yescharacteristic
33C2×#6705C2211yescharacteristic
34#91782C2211yescharacteristic
35#91781C2211yescharacteristic
36C4⋊C4×D15C2211yescharacteristic
37#91776C2211yescharacteristic, complemented
38#91770—21no—
39#91770—21no—
40C22⋊C4×D15—21no—
41#91766—21no—
42C4×D60C2211yescharacteristic
43C42×D15C2211yescharacteristic
44C4×Dic30C2211yescharacteristic, complemented
45C3×C5×#106C2211yescharacteristic, complemented
46C3×C5×#102C2211yescharacteristic
47C3×C5×#102C2211yescharacteristic, complemented
48C3×C5×#97C2211yescharacteristic, complemented
49#91116C2211yescharacteristic
50#91116C2211yescharacteristic, complemented
51#91105C2211yescharacteristic
52#91102C2211yescharacteristic, complemented
53#91100C2211yescharacteristic, complemented
54C8×Dic15C2211yescharacteristic, complemented
55C8×Dic15C2211yescharacteristic, complemented
56#91094C2211yescharacteristic, complemented
57#91093C2211yescharacteristic
58#91092C2211yescharacteristic, complemented
59#91091C2211yescharacteristic, complemented
60#91087C2211yescharacteristic, complemented
61#79865—51nomaximal, Hall
62C2×#4057—31no—
63C4×D4×D5—31no—
64C4×#711—31no—
65C5×#442D311yescharacteristic, complemented
66D8×Dic5—31no—
67#65307—31no—
68#65303—31no—
69#65150—31no—
70#65141—31no—
71#65060—31no—
72#65059—31no—
73#65047—31no—
74#65045—31no—
75#64999—31no—
76#64996—31no—
77C23×D15—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×C3×C4×C5—21no—
81C22×C3×C4×C5—21no—
82C2×#1220—21no—
83C2×#1220—21no—
84C22×Dic15—21no—
85C22×Dic15—21no—
86C22×Dic15—21no—
87#6819—22no—
88#6819C2×C414yescomplemented
89D4×D15—22no—
90D4×D15C2×C414yescomplemented
91C2×D60C2311yescharacteristic
92C2×C4×D15—21no—
93C2×C4×D15—21no—
94C2×C4×D15—21no—
95C2×C4×D15—44no—
96C2×C4×D15D411yescharacteristic
97C2×C4×D15D411yescharacteristic
98C2×C4×D15C2311yescharacteristic
99C2×Dic30C2311yescharacteristic
100C3×C5×D8C2×C414yescomplemented
101C2×C3×C5×C8C2311yescharacteristic
102C2×C3×C5×C8C2311yescharacteristic
103C3×C5×C4⋊C4C2311yescharacteristic
104C3×C5×C4⋊C4C2311yescharacteristic
105C3×C5×C22⋊C4—21no—
106C3×C5×C22⋊C4—21no—
107C3×C42×C5C2311yescharacteristic
108#6719—21no—
109#6719—21no—
110#6716C2×C414yescomplemented
111#6715C2×C414yescomplemented
112#6714—21no—
113#6714—21no—
114#6714—21no—
115C4⋊Dic15C2311yescharacteristic
116C4⋊Dic15C2311yescharacteristic
117#6712—21no—
118#6712—21no—
119#6712—21no—
120C4×Dic15—21no—
121C4×Dic15—21no—
122C4×Dic15—21no—
123C4×Dic15D411yescharacteristic
124C4×Dic15D411yescharacteristic
125C4×Dic15C2311yescharacteristic
126C2×C3⋊#168C2311yescharacteristic
127C2×C3⋊#168C2311yescharacteristic
128#6706C2×C414yescomplemented
129#6705—22no—
130#6705C2×C414yescomplemented
131C2×#911—51no—
132C4×D3×D4—51no—
133C4×#237—51no—
134C3×#442D511yescharacteristic, complemented
135Dic3×D8—51no—
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×D4C2×D311yescharacteristic
151C4×C5×D4C2×D311yescharacteristic, complemented
152D4×Dic5—31no—
153D4×Dic5—31no—
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×#106C2×D311yescharacteristic, complemented
175C5×#102C2×D311yescharacteristic
176C5×#102C2×D311yescharacteristic, complemented
177C5×#97C2×D311yescharacteristic, complemented
178#3964—31no—
179#3964—31no—
180#3953—31no—
181#3950—31no—
182#3948—31no—
183C8×Dic5—31no—
184C8×Dic5—31no—
185#3942—31no—
186#3941—31no—
187#3940—31no—
188#3939—31no—
189#3935—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×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—42no—
205C2×C3×C4×C5—42no—
206C2×C3×C4×C5C2×D411yescharacteristic
207C2×C3×C4×C5C2×D411yescharacteristic
208C2×C3×C4×C5C2411yescharacteristic
209#1220—24no—
210#1220—24no—
211C2×Dic15—21no—
212C2×Dic15—24no—
213C2×Dic15—21no—
214C2×Dic15—21no—
215C2×Dic15—42no—
216C2×Dic15—42no—
217C2×Dic15C2×D411yescharacteristic
218C2×Dic15C2×D411yescharacteristic
219C2×Dic15C2×D411yescharacteristic
220D60—21no—
221D60C22×C412yes—
222C4×D15—22no—
223C4×D15—41no—
224C4×D15—42no—
225C4×D15—42no—
226C4×D15—42no—
227C4×D15C22×C412yes—
228C4×D15#4112yes—
229Dic30—21no—
230Dic30C22×C412yescomplemented
231C3×C5×C8—21no—
232C3×C5×C8C22×C412yescomplemented
233C3⋊#168—21no—
234C3⋊#168C22×C412yescomplemented
235C2×#237—51no—
236C2×D3×D4—51no—
237C22×C4×D3—101no—
238C2×C3×D8C2×D511yescharacteristic
239C3×C4×D4C2×D511yescharacteristic
240C3×C4×D4C2×D511yescharacteristic, complemented
241D4×Dic3—51no—
242D4×Dic3—51no—
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×#106C2×D511yescharacteristic, complemented
264C3×#102C2×D511yescharacteristic
265C3×#102C2×D511yescharacteristic, complemented
266C3×#97C2×D511yescharacteristic, complemented
267#832—51no—
268#832—51no—
269#821—51no—
270#818—51no—
271#816—51no—
272C8×Dic3—51no—
273C8×Dic3—51no—
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—21no—
283C22×C4×C5—21no—
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×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×C8C22×D311yescharacteristic
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4C22×D311yescharacteristic
306C5×C4⋊C4C22×D311yescharacteristic
307C5×C22⋊C4—21no—
308C5×C22⋊C4—21no—
309C42×C5C22×D311yescharacteristic
310C22⋊Dic5—61no—
311C22⋊Dic5—61no—
312#687—34no—
313#686—34no—
314#685—61no—
315#685—61no—
316#685—61no—
317C4⋊Dic5—31no—
318C4⋊Dic5—31no—
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×#168—31no—
329C2×#168—31no—
330#677—34no—
331#676—34no—
332#676—62no—
333C2×AGL(1,ℤ/8)—151no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—151no—
337#442D1511yescharacteristic, complemented
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—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×C5—21no—
363C3×C4×C5—21no—
364C3×C4×C5—41no—
365C3×C4×C5—41no—
366C3×C4×C5C23×C411yescharacteristic
367C3×C4×C5C2×#4111yescharacteristic
368Dic15—22no—
369Dic15—21no—
370Dic15—41no—
371Dic15—41no—
372Dic15C4×D412yes—
373Dic15AGL(1,ℤ/8)12yescomplemented
374C23×D3—101no—
375C2×C3×D4C22×D511yescharacteristic
376C2×C3×D4C22×D511yescharacteristic
377C22×C3×C4—21no—
378C22×C3×C4—21no—
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×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×C8C22×D511yescharacteristic
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4C22×D511yescharacteristic
401C3×C4⋊C4C22×D511yescharacteristic
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C42C22×D511yescharacteristic
405#217—101no—
406#217—101no—
407#214—54no—
408#213—54no—
409(C2×D3)⋊C4—101no—
410(C2×D3)⋊C4—101no—
411(C2×D3)⋊C4—101no—
412C4⋊Dic3—51no—
413C4⋊Dic3—51no—
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⋊C8—51no—
424C2×C3⋊C8—51no—
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—21no—
440C2×C4×C5—21no—
441C2×C4×C5—42no—
442C2×C4×C5—42no—
443C2×C4×C5D3×D411yescharacteristic
444C2×C4×C5D3×D411yescharacteristic
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—64no—
447C22⋊D5—64no—
448C2×Dic5—31no—
449C2×Dic5—31no—
450C2×Dic5—31no—
451C2×Dic5—64no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—122no—
456C2×Dic5—122no—
457D20—32no—
458D20—61no—
459C4×D5—32no—
460C4×D5—32no—
461C4×D5—62no—
462C4×D5—122no—
463C4×D5—121no—
464C4×D5—122no—
465C4×D5—122no—
466Dic10—32no—
467Dic10—61no—
468C5×C8—21no—
469C5×C8C2×C4×D312yescomplemented
470#168—32no—
471#168—61no—
472C2×#41—151no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—151no—
477C2×SD16—151no—
478C2×D8—151no—
479C2×D8C2×D1511yescharacteristic
480C2×M16—151no—
481C2×M16—151no—
482C4×Q8—151no—
483C4×Q8—151no—
484C4×D4—151no—
485C4×D4—151no—
486C4×D4—151no—
487C4×D4—151no—
488C4×D4—301no—
489C4×D4—301no—
490C4×D4—301no—
491C4×D4—301no—
492C4×D4C2×D1511yescharacteristic
493C4×D4C2×D1511yescharacteristic, 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—151no—
503#106C2×D1511yescharacteristic, complemented
504#103—151no—
505#103—151no—
506#102—151no—
507#102—151no—
508#102—151no—
509#102—151no—
510#102C2×D1511yescharacteristic
511#102C2×D1511yescharacteristic, complemented
512#97—151no—
513#97C2×D1511yescharacteristic, complemented
514C4×C8—151no—
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—21no—
535C2×C3×C4—21no—
536C2×C3×C4—42no—
537C2×C3×C4—42no—
538C2×C3×C4D4×D511yescharacteristic
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4C23×D511yescharacteristic
541#67—104no—
542#67—104no—
543C2×Dic3—51no—
544C2×Dic3—51no—
545C2×Dic3—51no—
546C2×Dic3—104no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—202no—
551C2×Dic3—202no—
552D12—52no—
553D12—101no—
554C4×D3—52no—
555C4×D3—52no—
556C4×D3—102no—
557C4×D3—202no—
558C4×D3—201no—
559C4×D3—202no—
560C4×D3—202no—
561Dic6—52no—
562Dic6—101no—
563C3×C8—21no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—52no—
566C3⋊C8—101no—
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—21no—
582C4×C5—21no—
583C4×C5—41no—
584C4×C5—41no—
585C4×C5C22×C4×D311yescharacteristic
586C4×C5D3×#4111yescharacteristic
587Dic5—32no—
588Dic5—32no—
589Dic5—61no—
590Dic5—62no—
591Dic5—121no—
592Dic5—121no—
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×D4C22×D1511yescharacteristic
603C2×D4C22×D1511yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
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—154no—
617SD16—154no—
618D8—154no—
619D8C4×D1514yescomplemented
620M16—154no—
621M16—302no—
622C2×C8—151no—
623C2×C8—151no—
624C2×C8C22×D1511yescharacteristic
625C2×C8C22×D1511yescharacteristic
626C4⋊C4—151no—
627C4⋊C4—151no—
628C4⋊C4—301no—
629C4⋊C4—301no—
630C4⋊C4—301no—
631C4⋊C4C22×D1511yescharacteristic
632C4⋊C4C22×D1511yescharacteristic
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—151no—
641C42—151no—
642C42—151no—
643C42—301no—
644C42—301no—
645C42—301no—
646C42C22×D1511yescharacteristic
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—21no—
663C3×C4—21no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4C22×C4×D511yescharacteristic
667C3×C4D5×#4111yescharacteristic
668Dic3—52no—
669Dic3—52no—
670Dic3—101no—
671Dic3—102no—
672Dic3—201no—
673Dic3—201no—
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×C4×D1512yes—
697D4C2×C4×D1512yescomplemented
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—151no—
703C2×C4—151no—
704C2×C4—152no—
705C2×C4—152no—
706C2×C4—151no—
707C2×C4—302no—
708C2×C4—304no—
709C2×C4—301no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—601no—
713C2×C4—602no—
714C2×C4—602no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4D4×D1511yescharacteristic
719C2×C4D4×D1511yescharacteristic
720C2×C4C23×D1511yescharacteristic
721C8—21no—
722C8—152no—
723C8—301no—
724C8C2×C4×D1512yescomplemented
725C2×C3—42no—
726C2×C3—42no—
727C2×C3C4×D4×D511yescharacteristic
728C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
729C2×C3#6610711yescharacteristic
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—
746C22C2×D4×D1511yescharacteristic
747C4—21no—
748C4—21no—
749C4—41no—
750C4—41no—
751C4—152no—
752C4—152no—
753C4—302no—
754C4—301no—
755C4—601no—
756C4—601no—
757C4C22×C4×D1511yescharacteristic
758C4#41×D1511yescharacteristic
759C3#1061159611yescharacteristic, complemented, Sylow
760C2—42no—
761C2—42no—
762C2—302no—
763C2—602no—
764C2C4×D4×D1511yescharacteristic
765C2D15×AGL(1,ℤ/8)11yescharacteristic
766C2#1175653211yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#442C2
socleC22×C3×C5C22×D4
prime radicalC2×#91800C2
cosocleC2×C3×C4×C5C24
hypercenter#442D15
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D15C2semidirect
3. C4×#6819C2semidirect
4. C3×C5×#442C2semidirect
5. D8×Dic15C2semidirect
6. #11751119C2semidirect
7. #11751115C2semidirect
8. #11750962C2semidirect
9. #11750953C2semidirect
10. #11750872C2semidirect
11. #11750871C2semidirect
12. #11750859C2semidirect
13. #11750857C2semidirect
14. #11750811C2semidirect
15. #11750808C2semidirect
22. C3×C4×C5×D4C22semidirect
24. D4×Dic15C22semidirect
30. #91800C4semidirect
37. #91776C22semidirect
44. C4×Dic30C22semidirect
45. C3×C5×#106C22semidirect
47. C3×C5×#102C22semidirect
48. C3×C5×#97C22semidirect
50. #91116C22semidirect
52. #91102C22semidirect
53. #91100C22semidirect
54. C8×Dic15C22semidirect
55. C8×Dic15C22semidirect
56. #91094C22semidirect
58. #91092C22semidirect
59. #91091C22semidirect
60. #91087C22semidirect
65. C5×#442D3semidirect
88. #6819C2×C4semidirect
90. D4×D15C2×C4semidirect
100. C3×C5×D8C2×C4semidirect
110. #6716C2×C4semidirect
111. #6715C2×C4semidirect
128. #6706C2×C4semidirect
130. #6705C2×C4semidirect
134. C3×#442D5semidirect
151. C4×C5×D4C2×D3semidirect
174. C5×#106C2×D3semidirect
176. C5×#102C2×D3semidirect
177. C5×#97C2×D3semidirect
201. C3×C5×D4C22×C4semidirect
230. Dic30C22×C4semidirect
232. C3×C5×C8C22×C4semidirect
234. C3⋊#168C22×C4semidirect
240. C3×C4×D4C2×D5semidirect
263. C3×#106C2×D5semidirect
265. C3×#102C2×D5semidirect
266. C3×#97C2×D5semidirect
302. C5×D8C4×D3semidirect
337. #442D15semidirect
373. Dic15AGL(1,ℤ/8)semidirect
397. C3×D8C4×D5semidirect
438. C5×D4C2×C4×D3semidirect
469. C5×C8C2×C4×D3semidirect
493. C4×D4C2×D15semidirect
503. #106C2×D15semidirect
511. #102C2×D15semidirect
513. #97C2×D15semidirect
533. C3×D4C2×C4×D5semidirect
564. C3×C8C2×C4×D5semidirect
619. D8C4×D15semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
697. D4C2×C4×D15semidirect
724. C8C2×C4×D15semidirect
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
C2×#918002
C4×D4×D152
C4×#68192
C3×C5×#4422
D8×Dic152
#117511192
#117511152
#117509622
#117509532
#117508722
#117508712
#117508592
#117508572
#117508112
#117508082
#106115963
#798655