Finite Group Databasebeta

← #14416765

Subgroups — #14416765

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
1Dic3×#711C211yesmaximal, characteristic, complemented
2C2×#91478C211yesmaximal, characteristic
3D5×#893C211yesmaximal, characteristic, complemented
4#11750886C211yesmaximal, characteristic, complemented
5C5×#4756C211yesmaximal, characteristic, complemented
6C3×#65060C211yesmaximal, characteristic, complemented
7#11748996C211yesmaximal, characteristic, complemented
8#11748986C211yesmaximal, characteristic, complemented
9#11748105C211yesmaximal, characteristic, complemented
10#11747830C211yesmaximal, characteristic, complemented
11#11747738C211yesmaximal, characteristic, complemented
12Dic3×#676C211yesmaximal, characteristic, complemented
13#11747452C211yesmaximal, characteristic, complemented
14#11747273C211yesmaximal, characteristic, complemented
15#11747264C211yesmaximal, characteristic, complemented
16C4×#4057—31nomaximal, Hall
17C2×C3×#711C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C2×C4×D3×D5—21no—
20D4×Dic15C2211yescharacteristic, complemented
21C2×#6715C2211yescharacteristic
22#91782C2211yescharacteristic
23C5×D4×Dic3C2211yescharacteristic, complemented
24C2×C5×#213C2211yescharacteristic
25C5×#893C2211yescharacteristic
26C2×C3×#676C2211yescharacteristic
27C3×D5×C4⋊C4C2211yescharacteristic
28#91559—21no—
29Dic3×C22⋊D5—21no—
30#91528—21no—
31C2×Dic3×Dic5—21no—
32#91478C418yescomplemented
33D5×(C2×D3)⋊C4—21no—
34#91446—21no—
35#91435C2211yescharacteristic
36#91428C2211yescharacteristic
37#91406—21no—
38C4×D5×Dic3C2211yescharacteristic
39#91358C2211yescharacteristic
40#91331C2211yescharacteristic, complemented
41Dic3×Dic10C2211yescharacteristic, complemented
42C2×#6658C2211yescharacteristic
43C2×#6656C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic, complemented
46#91105C2211yescharacteristic
47#91099C2211yescharacteristic, complemented
48#91092C2211yescharacteristic, complemented
49C5×#821C2211yescharacteristic
50C5×C8×Dic3C2211yescharacteristic, complemented
51C5×#807C2211yescharacteristic, complemented
52C3×#3964C2211yescharacteristic, complemented
53C3×#3948C2211yescharacteristic, complemented
54C3×#3942C2211yescharacteristic, complemented
55#90989C2211yescharacteristic, complemented
56#90987C2211yescharacteristic, complemented
57#90969C2211yescharacteristic
58#90967C2211yescharacteristic
59#90954C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61#78866—51nomaximal, Hall
62C2×#4057—31no—
63C4×D4×D5—31no—
64C4×#711—31no—
65C4×C5×D8—31no—
66#65441—31no—
67C4×#687—31no—
68C4×#686—31no—
69#65178—31no—
70#65170—31no—
71#65074—31no—
72#65060D311yescharacteristic, complemented
73#65059—31no—
74#65046—31no—
75C4×#677—31no—
76C4×#676—31no—
77C22×D3×D5—21no—
78C2×C3×C5×D4C2311yescharacteristic
79C22×Dic15—21no—
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C22×C5×Dic3—21no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C3×C22⋊D5—21no—
86C22×C3×Dic5—21no—
87C3×#711—22no—
88C3×#711C2×C414yescomplemented
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×Dic10C2311yescharacteristic
92C2×#1203—21no—
93C2×#1200—21no—
94C2×D3×Dic5—21no—
95C2×D5×Dic3D411yescharacteristic
96C2×D5×Dic3D411yescharacteristic
97D5×D12—22no—
98D5×D12C2×C414yescomplemented
99C4×D3×D5—44no—
100C2×C3×C5×C8C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102#6719—21no—
103#6715C2×C414yescomplemented
104#6714—21no—
105C4⋊Dic15C2311yescharacteristic
106C4×Dic15C2311yescharacteristic
107C2×C3⋊#168C2311yescharacteristic
108C5×#217—21no—
109C5×#213C2×C414yescomplemented
110C5×(C2×D3)⋊C4—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C4×C5×Dic3C2311yescharacteristic
113C2×C5×C3⋊C8C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
116C2×C3×#168C2311yescharacteristic
117C3×#676—22no—
118#6668—21no—
119#6668—21no—
120#6667—21no—
121(C2×D3)⋊Dic5—21no—
122#6665—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5D411yescharacteristic
127Dic3×Dic5D411yescharacteristic
128#6658C2×C414yescomplemented
129#6656C2×C414yescomplemented
130#6649C2×C414yescomplemented
131Dic3×#41—51no—
132C2×#949—51no—
133C2×#893—51no—
134C3×#417—51no—
135#5131—51no—
136Dic3×M16—51no—
137#4964—51no—
138#4817—51no—
139#4817—51no—
140#4788—51no—
141#4788—51no—
142#4785—51no—
143#4785—51no—
144#4756—51no—
145#4756D511yescharacteristic, complemented
146C2×#711C2×D311yescharacteristic
147C2×D4×D5—31no—
148C22×C4×D5—61no—
149C2×C5×D8—31no—
150C4×C5×D4—31no—
151C4×C5×D4—31no—
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×#676C2×D311yescharacteristic
163#4039—31no—
164#4038—31no—
165D5×C4⋊C4C2×D311yescharacteristic
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×#102C2×D311yescharacteristic, complemented
177C4×C5×C8—31no—
178#3964—31no—
179#3964C2×D311yescharacteristic, complemented
180#3953—31no—
181#3949—31no—
182#3948C2×D311yescharacteristic, complemented
183#3947—31no—
184#3947—31no—
185#3942C2×D311yescharacteristic, complemented
186#3941—31no—
187#3940—31no—
188#3939—31no—
189C4×#168—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C23×C3×C5—21no—
192C22×D15—21no—
193C22×C5×D3—21no—
194C22×C3×D5C2×D411yescharacteristic
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×C5C2411yescharacteristic
202C2×Dic15—21no—
203C2×Dic15—42no—
204C2×Dic15C2×D411yescharacteristic
205C2×Dic15C2×D411yescharacteristic
206D60—21no—
207D60C22×C412yes—
208C4×D15—42no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—42no—
211C2×C5×Dic3C2×D411yescharacteristic
212C2×C5×Dic3C2×D411yescharacteristic
213C5×D12—21no—
214C5×D12C22×C412yes—
215C4×C5×D3—42no—
216C3×C22⋊D5—24no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—24no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5C2×D411yescharacteristic
221C3×C4×D5—42no—
222C3×C4×D5C22×C412yes—
223C3×C4×D5#4112yes—
224C3×Dic10—21no—
225C3×Dic10C22×C412yescomplemented
226#1203—24no—
227#1200—42no—
228D3×Dic5—42no—
229D5×Dic3—22no—
230D5×Dic3—41no—
231C3×C5×C8—21no—
232C3⋊#168C22×C412yescomplemented
233C3×#168—21no—
234C5×C3⋊C8C22×C412yescomplemented
235C2×C3×#41—51no—
236C22×D12—51no—
237C22×C4×D3—101no—
238C2×C3×M16—51no—
239C2×C3×C4⋊C4—51no—
240#949—58no—
241Q8×Dic3—51no—
242Q8×Dic3—51no—
243C2×#215—51no—
244C2×#215—51no—
245D4×Dic3—51no—
246D4×Dic3—101no—
247D4×Dic3—101no—
248D4×Dic3C2×D511yescharacteristic, complemented
249C2×#213—51no—
250C2×#213C2×D511yescharacteristic
251C2×(C2×D3)⋊C4—101no—
252#926—51no—
253#926—101no—
254C2×C4×Dic3—51no—
255C2×C4×Dic3—101no—
256C2×#208—51no—
257#893—51no—
258#893—51no—
259#893—51no—
260#893—101no—
261#893—101no—
262#893C2×D511yescharacteristic
263C3×#103—51no—
264C3×#103—51no—
265C3×#102—51no—
266C3×#102C2×D511yescharacteristic, complemented
267#821—51no—
268#821—51no—
269#821—51no—
270#821C2×D511yescharacteristic
271#815—51no—
272#815—51no—
273C8×Dic3—51no—
274C8×Dic3C2×D511yescharacteristic, complemented
275#808—51no—
276#808—51no—
277#807—51no—
278#807C2×D511yescharacteristic, complemented
279C23×D5—61no—
280C2×C5×D4—31no—
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—61no—
283C22×C4×C5—61no—
284C2×C22⋊D5—21no—
285C2×C22⋊D5—61no—
286C22×Dic5—21no—
287C22×Dic5—61no—
288C22×Dic5—61no—
289#711—22no—
290#711C4×D314yescomplemented
291D4×D5—34no—
292D4×D5—62no—
293C2×D20—31no—
294C2×C4×D5—21no—
295C2×C4×D5—31no—
296C2×C4×D5—31no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—124no—
300C2×C4×D5C22×D311yescharacteristic
301C2×Dic10C22×D311yescharacteristic
302C5×D8—34no—
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4C22×D311yescharacteristic
307C5×C22⋊C4—61no—
308C5×C22⋊C4—61no—
309C42×C5—31no—
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⋊Dic5C22×D311yescharacteristic
319#683—21no—
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×#168C22×D311yescharacteristic
330#677—34no—
331#676—22no—
332#676—34no—
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—151no—
341C4×SD16—151no—
342C4×D8—31no—
343C4×D8—151no—
344#428—151no—
345#418—151no—
346#417—51no—
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—22no—
356C2×C5×D3—41no—
357C2×C5×D3—41no—
358C2×C3×D5—21no—
359C2×C3×D5—21no—
360C2×C3×D5C4×D412yes—
361D3×D5—48no—
362C3×C4×C5—41no—
363C3×C4×C5C23×C411yescharacteristic
364C3×C4×C5C2×#4111yescharacteristic
365Dic15—21no—
366Dic15—21no—
367Dic15—41no—
368C3×Dic5—22no—
369C3×Dic5—41no—
370C3×Dic5C4×D412yes—
371C5×Dic3—21no—
372C5×Dic3—41no—
373C5×Dic3AGL(1,ℤ/8)12yescomplemented
374C23×D3—101no—
375C3×#41—54no—
376C3×#41—102no—
377C2×C3×Q8—51no—
378C2×C3×D4—101no—
379C2×C3×D4C22×D511yescharacteristic
380C22×C3×C4—51no—
381C22×C3×C4—101no—
382C22×C3×C4—101no—
383C22×Dic3—21no—
384C22×Dic3—51no—
385C22×Dic3—51no—
386C22×Dic3—101no—
387C2×D12—51no—
388C2×D12—54no—
389C2×D12—102no—
390C2×D12—101no—
391C2×D12C22×D511yescharacteristic
392C2×C4×D3—21no—
393C2×C4×D3—101no—
394C2×C4×D3—101no—
395C2×C4×D3—101no—
396C2×C4×D3—204no—
397C3×M16—102no—
398C2×C3×C8—51no—
399C2×C3×C8C22×D511yescharacteristic
400C3×C4⋊C4—51no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4C22×D511yescharacteristic
403#217—21no—
404#217—101no—
405#217—101no—
406#215—54no—
407#215—54no—
408#213—54no—
409#213C4×D514yescomplemented
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⋊Dic3—101no—
417C4⋊Dic3C22×D511yescharacteristic
418C4×Dic3—51no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—101no—
422C4×Dic3—101no—
423C4×Dic3—101no—
424C4×Dic3C22×D511yescharacteristic
425#208—54no—
426C2×C3⋊C8—51no—
427C2×C3⋊C8C22×D511yescharacteristic
428C23×C5—21no—
429C23×C5—61no—
430C22×D5—61no—
431C22×D5—64no—
432C22×D5—122no—
433C22×D5—122no—
434C22×D5D3×D411yescharacteristic
435C5×D4—21no—
436C5×D4—32no—
437C5×D4—61no—
438C5×D4C2×C4×D312yescomplemented
439C2×C4×C5—21no—
440C2×C4×C5—31no—
441C2×C4×C5—31no—
442C2×C4×C5—61no—
443C2×C4×C5—122no—
444C2×C4×C5—122no—
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—24no—
447C22⋊D5—64no—
448C2×Dic5—21no—
449C2×Dic5—24no—
450C2×Dic5—21no—
451C2×Dic5—31no—
452C2×Dic5—31no—
453C2×Dic5—61no—
454C2×Dic5—122no—
455C2×Dic5—122no—
456C2×Dic5D3×D411yescharacteristic
457D20—32no—
458D20—61no—
459C4×D5—42no—
460C4×D5—62no—
461C4×D5—122no—
462C4×D5—122no—
463C4×D5—121no—
464C4×D5C2×C4×D312yes—
465C4×D5#23712yes—
466Dic10—21no—
467Dic10C2×C4×D312yescomplemented
468C5×C8—21no—
469C5×C8—32no—
470#168—21no—
471#168—32no—
472C2×#41—51no—
473C22×D4—151no—
474C23×C4—301no—
475AGL(1,ℤ/8)—158no—
476C2×SD16—151no—
477C2×SD16—151no—
478C2×D8—31no—
479C2×D8—151no—
480C2×M16—51no—
481C2×M16—151no—
482C4×Q8—151no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—31no—
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—51no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—31no—
501#107—151no—
502#106—151no—
503#106—151no—
504#103—51no—
505#103—51no—
506#102—31no—
507#102—51no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102D3×D511yescharacteristic, complemented
512#97—151no—
513#97—151no—
514C4×C8—31no—
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—
521C3×D5—22no—
522C5×D3—42no—
523C23×C3—21no—
524C23×C3—51no—
525C22×D3—21no—
526C22×D3—104no—
527C22×D3—101no—
528C22×D3—202no—
529C22×D3—202no—
530C3×Q8—52no—
531C3×Q8—101no—
532C3×D4—21no—
533C3×D4—104no—
534C3×D4C2×C4×D512yescomplemented
535C2×C3×C4—21no—
536C2×C3×C4—51no—
537C2×C3×C4—52no—
538C2×C3×C4—52no—
539C2×C3×C4—104no—
540C2×C3×C4—101no—
541C2×C3×C4—101no—
542C2×C3×C4—202no—
543C2×C3×C4C23×D511yescharacteristic
544C2×Dic3—21no—
545C2×Dic3—42no—
546C2×Dic3—51no—
547C2×Dic3—51no—
548C2×Dic3—102no—
549C2×Dic3—101no—
550C2×Dic3—201no—
551C2×Dic3—202no—
552C2×Dic3D4×D511yescharacteristic
553C2×Dic3D4×D511yescharacteristic
554D12—21no—
555D12—52no—
556D12—104no—
557D12—101no—
558D12C2×C4×D512yes—
559C4×D3—42no—
560C4×D3—202no—
561C4×D3—202no—
562C4×D3—202no—
563C3×C8—21no—
564C3×C8—101no—
565C3⋊C8—52no—
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—21no—
575C2×D5—21no—
576C2×D5—62no—
577C2×D5—128no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5#67⋊C412yes—
581C4×C5—32no—
582C4×C5—41no—
583C4×C5—61no—
584C4×C5—121no—
585C4×C5C22×C4×D311yescharacteristic
586C4×C5C2×#23711yescharacteristic
587Dic5—22no—
588Dic5—41no—
589Dic5—61no—
590Dic5—61no—
591Dic5—121no—
592Dic5#67⋊C412yes—
593C24—301no—
594#41—54no—
595#41—102no—
596C2×Q8—51no—
597C2×D4—31no—
598C2×D4—101no—
599C2×D4—154no—
600C2×D4—151no—
601C2×D4—302no—
602C2×D4—301no—
603C2×D4C2×D3×D511yescharacteristic
604C22×C4—51no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—101no—
608C22×C4—101no—
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—34no—
619D8—154no—
620M16—102no—
621M16—154no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—51no—
628C4⋊C4—101no—
629C4⋊C4—151no—
630C4⋊C4—301no—
631C4⋊C4—301no—
632C4⋊C4C2×D3×D511yescharacteristic
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—151no—
642C42—151no—
643C42—151no—
644C42—301no—
645C42—301no—
646C42—301no—
647C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
648C22×C3—22no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—52no—
652C22×C3—101no—
653C22×C3—101no—
654C22×C3C2×D4×D511yescharacteristic
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—102no—
659C2×D3—208no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—41no—
663C3×C4—52no—
664C3×C4—102no—
665C3×C4—201no—
666C3×C4C22×C4×D511yescharacteristic
667C3×C4D5×#4111yescharacteristic
668Dic3—21no—
669Dic3—41no—
670Dic3—101no—
671Dic3—101no—
672Dic3—201no—
673Dic3#405712yescomplemented
674C2×C5—42no—
675C2×C5—122no—
676C2×C5C2×#67⋊C411yescharacteristic
677C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
678C2×C5#577711yescharacteristic
679D5—22no—
680D5—122no—
681C23—21no—
682C23—51no—
683C23—61no—
684C23—304no—
685C23—301no—
686C23—602no—
687C23—602no—
688Q8—52no—
689Q8—101no—
690D4—21no—
691D4—32no—
692D4—61no—
693D4—104no—
694D4—152no—
695D4—304no—
696D4—301no—
697D4C4×D3×D512yescomplemented
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—51no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—61no—
705C2×C4—104no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—122no—
709C2×C4—122no—
710C2×C4—151no—
711C2×C4—151no—
712C2×C4—202no—
713C2×C4—302no—
714C2×C4—301no—
715C2×C4—602no—
716C2×C4—602no—
717C2×C4—601no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—21no—
722C8—32no—
723C8—101no—
724C8—152no—
725C2×C3—42no—
726C2×C3—102no—
727C2×C3C4×D4×D511yescharacteristic
728C2×C3C2×#405711yescharacteristic
729C2×C3#6610211yescharacteristic
730D3—42no—
731D3—202no—
732C5#7886611yescharacteristic, complemented, Sylow
733C22—22no—
734C22—41no—
735C22—41no—
736C22—52no—
737C22—62no—
738C22—101no—
739C22—101no—
740C22—121no—
741C22—121no—
742C22—302no—
743C22—608no—
744C22—601no—
745C22—601no—
746C22D3×D4×D511yescharacteristic
747C4—32no—
748C4—41no—
749C4—52no—
750C4—61no—
751C4—102no—
752C4—121no—
753C4—201no—
754C4—301no—
755C4—301no—
756C4—601no—
757C4C2×C4×D3×D511yescharacteristic
758C4D5×#23711yescharacteristic
759C3C4×#405711yescharacteristic, complemented, Sylow
760C2—42no—
761C2—102no—
762C2—122no—
763C2—602no—
764C2D5×#67⋊C411yescharacteristic
765C2D3×#405711yescharacteristic
766C2#1175407511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#91478C2
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. Dic3×#711C2semidirect
3. D5×#893C2semidirect
4. #11750886C2semidirect
5. C5×#4756C2semidirect
6. C3×#65060C2semidirect
7. #11748996C2semidirect
8. #11748986C2semidirect
9. #11748105C2semidirect
10. #11747830C2semidirect
11. #11747738C2semidirect
12. Dic3×#676C2semidirect
13. #11747452C2semidirect
14. #11747273C2semidirect
15. #11747264C2semidirect
20. D4×Dic15C22semidirect
23. C5×D4×Dic3C22semidirect
32. #91478C4semidirect
40. #91331C22semidirect
41. Dic3×Dic10C22semidirect
45. C3×C5×#102C22semidirect
47. #91099C22semidirect
48. #91092C22semidirect
50. C5×C8×Dic3C22semidirect
51. C5×#807C22semidirect
52. C3×#3964C22semidirect
53. C3×#3948C22semidirect
54. C3×#3942C22semidirect
55. #90989C22semidirect
56. #90987C22semidirect
59. #90954C22semidirect
60. Dic3×#168C22semidirect
72. #65060D3semidirect
88. C3×#711C2×C4semidirect
98. D5×D12C2×C4semidirect
103. #6715C2×C4semidirect
109. C5×#213C2×C4semidirect
128. #6658C2×C4semidirect
129. #6656C2×C4semidirect
130. #6649C2×C4semidirect
145. #4756D5semidirect
176. C5×#102C2×D3semidirect
179. #3964C2×D3semidirect
182. #3948C2×D3semidirect
185. #3942C2×D3semidirect
199. C3×C5×D4C22×C4semidirect
225. C3×Dic10C22×C4semidirect
232. C3⋊#168C22×C4semidirect
234. C5×C3⋊C8C22×C4semidirect
248. D4×Dic3C2×D5semidirect
266. C3×#102C2×D5semidirect
274. C8×Dic3C2×D5semidirect
278. #807C2×D5semidirect
290. #711C4×D3semidirect
373. C5×Dic3AGL(1,ℤ/8)semidirect
409. #213C4×D5semidirect
438. C5×D4C2×C4×D3semidirect
467. Dic10C2×C4×D3semidirect
511. #102D3×D5semidirect
534. C3×D4C2×C4×D5semidirect
566. C3⋊C8C2×C4×D5semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
673. Dic3#4057semidirect
697. D4C4×D3×D5semidirect
732. C5#78866semidirect
759. C3C4×#4057semidirect

Maximal subgroups

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

subgroupindex
Dic3×#7112
C2×#914782
D5×#8932
#117508862
C5×#47562
C3×#650602
#117489962
#117489862
#117481052
#117478302
#117477382
Dic3×#6762
#117474522
#117472732
#117472642
C4×#40573
#788665