Finite Group Databasebeta

← Dic3×#4060 #14416693

Subgroups — Dic3×#4060 #14416693

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×C3×#4060C211yesmaximal, characteristic
2Dic3×#713C211yesmaximal, characteristic, complemented
3D4×D5×Dic3C211yesmaximal, characteristic, complemented
4#11751265C211yesmaximal, characteristic, complemented
5C5×Dic3×SD16C211yesmaximal, characteristic, complemented
6#11749241C211yesmaximal, characteristic, complemented
7Dic3×#688C211yesmaximal, characteristic, complemented
8#11749198C211yesmaximal, characteristic, complemented
9#11748995C211yesmaximal, characteristic, complemented
10Dic3×#686C211yesmaximal, characteristic, complemented
11#11748962C211yesmaximal, characteristic, complemented
12#11747815C211yesmaximal, characteristic, complemented
13Dic3×D40C211yesmaximal, characteristic, complemented
14#11747618C211yesmaximal, characteristic, complemented
15Dic3×#676C211yesmaximal, characteristic, complemented
16C4×#4060—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×D4×D5C2211yescharacteristic
19C22×D5×Dic3—21no—
20C2×C3×C5×SD16C2211yescharacteristic
21Q8×Dic15C2211yescharacteristic, complemented
22D4×Dic15C2211yescharacteristic
23C5×Q8×Dic3C2211yescharacteristic, complemented
24C5×D4×Dic3C2211yescharacteristic
25C2×C3×#688C2211yescharacteristic
26C2×C3×#686C2211yescharacteristic
27C3×#4060C418yescomplemented
28C2×C3×D40C2211yescharacteristic
29C2×C3×#676C2211yescharacteristic
30#91559—21no—
31Dic3×C22⋊D5—21no—
32D5×#217—21no—
33#91434—21no—
34#91434C2211yescharacteristic
35#91434C2211yescharacteristic, complemented
36Dic3×D20—21no—
37Dic3×D20C2211yescharacteristic
38Dic3×D20C2211yescharacteristic, complemented
39D5×C4⋊Dic3C2211yescharacteristic
40C4×D5×Dic3—21no—
41C4×D5×Dic3C2211yescharacteristic
42#91358—21no—
43#91358C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45#91119C2211yescharacteristic, complemented
46#91116C2211yescharacteristic
47#91102C2211yescharacteristic, complemented
48#91099C2211yescharacteristic, complemented
49C5×#835C2211yescharacteristic, complemented
50C5×#832C2211yescharacteristic
51C5×#817C2211yescharacteristic, complemented
52C5×C8×Dic3C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90985C2211yescharacteristic, complemented
55#90965C2211yescharacteristic
56#90965C2211yescharacteristic, complemented
57#90964C2211yescharacteristic
58#90964C2211yescharacteristic, complemented
59#90954C2211yescharacteristic, complemented
60Dic3×#168C2211yescharacteristic, complemented
61Dic3×AGL(1,ℤ/8)—51nomaximal, Hall
62C2×#4060D311yescharacteristic
63C4×#713—31no—
64C4×D4×D5—31no—
65C4×C5×SD16—31no—
66#65453—31no—
67C4×#688—31no—
68C4×#686—31no—
69#65158—31no—
70#65150—31no—
71#65106—31no—
72#65092—31no—
73#65074—31no—
74#65059—31no—
75C4×D40—31no—
76C4×#676—31no—
77C23×C3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C22×Dic15—21no—
81C22×C5×Dic3—21no—
82C2×C3×C22⋊D5—21no—
83C3×#713—22no—
84C3×#713C2×C414yescomplemented
85C3×D4×D5—22no—
86C3×D4×D5C2×C414yescomplemented
87C2×C3×D20—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5C2311yescharacteristic
92C2×D5×Dic3—21no—
93C2×D5×Dic3—21no—
94C2×D5×Dic3—21no—
95C2×D5×Dic3—21no—
96C2×D5×Dic3—21no—
97C2×D5×Dic3—44no—
98C2×D5×Dic3D411yescharacteristic
99C2×D5×Dic3D411yescharacteristic
100C3×C5×SD16C2×C414yescomplemented
101C2×C3×C5×C8C2311yescharacteristic
102#6719—21no—
103C4⋊Dic15—21no—
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106C4×Dic15—21no—
107C4×Dic15C2311yescharacteristic
108C2×C3⋊#168C2311yescharacteristic
109C5×#217—21no—
110C5×C4⋊Dic3—21no—
111C5×C4⋊Dic3C2311yescharacteristic
112C5×C4⋊Dic3C2311yescharacteristic
113C4×C5×Dic3—21no—
114C4×C5×Dic3C2311yescharacteristic
115C2×C5×C3⋊C8C2311yescharacteristic
116C3×#688C2×C414yescomplemented
117C3×#686C2×C414yescomplemented
118C2×C3×#168C2311yescharacteristic
119C3×D40C2×C414yescomplemented
120C3×#676C2×C414yescomplemented
121#6668—21no—
122#6665—21no—
123#6665—21no—
124#6665—21no—
125#6665—21no—
126#6665—21no—
127Dic3×Dic5—21no—
128Dic3×Dic5D411yescharacteristic
129Dic3×Dic5D411yescharacteristic
130#6649—22no—
131C2×C3×AGL(1,ℤ/8)—51no—
132Dic3×#41—51no—
133C2×D4×Dic3—51no—
134#5232—51no—
135#5215—51no—
136#5164—51no—
137#5164—51no—
138Dic3×SD16—51no—
139Dic3×SD16D511yescharacteristic, complemented
140#5152—51no—
141#5152—51no—
142Dic3×D8—51no—
143Dic3×D8—51no—
144#5121—51no—
145Dic3×M16—51no—
146C2×#713C2×D311yescharacteristic
147C2×D4×D5C2×D311yescharacteristic
148C22×C4×D5—61no—
149C2×C5×SD16C2×D311yescharacteristic
150C4×C5×Q8—31no—
151C4×C5×D4—31no—
152Q8×Dic5—31no—
153C2×#688C2×D311yescharacteristic
154D4×Dic5—31no—
155C2×#686C2×D311yescharacteristic
156C4×C22⋊D5—61no—
157#4060Dic318yesdirect product factor
158C2×D40C2×D311yescharacteristic
159C2×#676—31no—
160C2×#676C2×D311yescharacteristic
161#4039—31no—
162#4039—31no—
163#4039—61no—
164#4038—31no—
165#4038—61no—
166D5×C4⋊C4—31no—
167#4027—61no—
168D5×C22⋊C4—61no—
169C4×D20—31no—
170C4×D20—31no—
171C4×D20—61no—
172C42×D5—31no—
173C42×D5—61no—
174C5×#106—31no—
175C5×#103—31no—
176C5×#102—31no—
177C4×C5×C8—31no—
178#3967—31no—
179#3964—31no—
180#3953—31no—
181#3953—31no—
182#3950—31no—
183#3947—31no—
184#3947—31no—
185#3941—31no—
186#3941—31no—
187#3940—31no—
188#3939—31no—
189C4×#168—31no—
190C4×AGL(1,ℤ/8)—151noSylow
191C23×C3×C5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—24no—
195C22×C3×D5—42no—
196C22×C3×D5—42no—
197C22×C3×D5C2×D411yescharacteristic
198C3×C5×Q8—21no—
199C3×C5×Q8C22×C412yescomplemented
200C3×C5×D4—21no—
201C3×C5×D4C22×C412yes—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5C2411yescharacteristic
204C2×Dic15—21no—
205C2×Dic15—21no—
206C2×Dic15—42no—
207C2×Dic15C2×D411yescharacteristic
208C2×Dic15C2×D411yescharacteristic
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3—42no—
212C2×C5×Dic3C2×D411yescharacteristic
213C2×C5×Dic3C2×D411yescharacteristic
214C3×C22⋊D5—24no—
215C2×C3×Dic5C2×D411yescharacteristic
216C3×D20—24no—
217C3×D20—21no—
218C3×D20—21no—
219C3×D20C22×C412yes—
220C3×D20C22×C412yescomplemented
221C3×C4×D5—24no—
222C3×C4×D5C22×C412yes—
223C3×C4×D5#4112yes—
224D5×Dic3—22no—
225D5×Dic3—41no—
226D5×Dic3—42no—
227D5×Dic3—42no—
228D5×Dic3—42no—
229D5×Dic3—42no—
230D5×Dic3—42no—
231C3×C5×C8C22×C412yescomplemented
232C3⋊#168—21no—
233C3×#168C22×C412yescomplemented
234C5×C3⋊C8—21no—
235C2×C3×#41—51no—
236C22×C3×D4—51no—
237C23×Dic3—101no—
238C3×AGL(1,ℤ/8)—58no—
239C2×C3×SD16—51no—
240C2×C3×SD16C2×D511yescharacteristic
241C2×C3×D8—51no—
242C2×C3×D8—51no—
243C2×C3×M16—51no—
244C2×#217—101no—
245Q8×Dic3—51no—
246Q8×Dic3C2×D511yescharacteristic, complemented
247D4×Dic3—51no—
248D4×Dic3—51no—
249D4×Dic3—51no—
250D4×Dic3—51no—
251D4×Dic3—51no—
252D4×Dic3—101no—
253D4×Dic3—101no—
254D4×Dic3—101no—
255D4×Dic3—101no—
256D4×Dic3C2×D511yescharacteristic
257#926—51no—
258#926—101no—
259C2×C4⋊Dic3—51no—
260C2×C4×Dic3—51no—
261C2×C4×Dic3—101no—
262C2×#208—51no—
263#835—51no—
264#835C2×D511yescharacteristic, complemented
265#832—51no—
266#832—51no—
267#832—51no—
268#832—51no—
269#832—51no—
270#832C2×D511yescharacteristic
271#818—51no—
272#818—51no—
273#817—51no—
274#817C2×D511yescharacteristic, complemented
275#815—51no—
276#815—51no—
277C8×Dic3—51no—
278C8×Dic3C2×D511yescharacteristic, complemented
279C23×D5—21no—
280C2×C5×Q8C22×D311yescharacteristic
281C2×C5×D4C22×D311yescharacteristic
282C22×C4×C5—61no—
283C2×C22⋊D5—21no—
284C22×Dic5—61no—
285#713—22no—
286#713C2×Dic314yescomplemented
287D4×D5—22no—
288D4×D5C2×Dic314yescomplemented
289C2×D20—21no—
290C2×D20C22×D311yescharacteristic
291C2×D20C22×D311yescharacteristic
292C2×C4×D5—21no—
293C2×C4×D5—31no—
294C2×C4×D5—31no—
295C2×C4×D5—61no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—61no—
299C2×C4×D5—61no—
300C2×C4×D5—124no—
301C2×C4×D5C22×D311yescharacteristic
302C5×SD16C2×Dic314yescomplemented
303C2×C5×C8—31no—
304C2×C5×C8C22×D311yescharacteristic
305C5×C4⋊C4—31no—
306C5×C4⋊C4—31no—
307C5×C4⋊C4—61no—
308C5×C22⋊C4—61no—
309C42×C5—31no—
310C42×C5—61no—
311C22⋊Dic5—61no—
312#688C2×Dic314yescomplemented
313#686C2×Dic314yescomplemented
314#685—61no—
315#685—61no—
316#685—61no—
317#685—61no—
318#685—61no—
319C4⋊Dic5—31no—
320C4⋊Dic5—31no—
321C4⋊Dic5—61no—
322#683—61no—
323C4×Dic5—31no—
324C4×Dic5—31no—
325C4×Dic5—31no—
326C4×Dic5—61no—
327C4×Dic5—61no—
328C2×#168—31no—
329C2×#168C22×D311yescharacteristic
330D40C2×Dic314yescomplemented
331#676—62no—
332#676C2×Dic314yescomplemented
333C2×AGL(1,ℤ/8)—51no—
334C4×#41—151no—
335C2×C4×D4—151no—
336#442—151no—
337#442—151no—
338#440—151no—
339#440—151no—
340C4×SD16—31no—
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×C3×D5—21no—
353C2×C3×D5—21no—
354C2×C3×D5—22no—
355C2×C3×D5—22no—
356C2×C3×D5—48no—
357C2×C3×D5—41no—
358C2×C3×D5—41no—
359C2×C3×D5—41no—
360C2×C3×D5—41no—
361C2×C3×D5C4×D412yes—
362C3×C4×C5—22no—
363C3×C4×C5C23×C411yescharacteristic
364C3×C4×C5C2×#4111yescharacteristic
365Dic15—21no—
366Dic15—21no—
367Dic15—41no—
368Dic15—41no—
369C3×Dic5C4×D412yes—
370C5×Dic3—21no—
371C5×Dic3—41no—
372C5×Dic3—41no—
373C5×Dic3AGL(1,ℤ/8)12yescomplemented
374C24×C3—101no—
375C3×#41—54no—
376C3×#41—102no—
377C2×C3×Q8C22×D511yescharacteristic
378C2×C3×D4—54no—
379C2×C3×D4—51no—
380C2×C3×D4—51no—
381C2×C3×D4—101no—
382C2×C3×D4—102no—
383C2×C3×D4—101no—
384C2×C3×D4C22×D511yescharacteristic
385C22×C3×C4—51no—
386C22×C3×C4—101no—
387C22×Dic3—21no—
388C22×Dic3—51no—
389C22×Dic3—51no—
390C22×Dic3—101no—
391C22×Dic3—101no—
392C22×Dic3—101no—
393C22×Dic3—101no—
394C22×Dic3—101no—
395C22×Dic3—101no—
396C22×Dic3—204no—
397C3×SD16—54no—
398C3×SD16C4×D514yescomplemented
399C3×D8—54no—
400C3×D8—54no—
401C3×M16—54no—
402C2×C3×C8—51no—
403C2×C3×C8C22×D511yescharacteristic
404#217—21no—
405#217—101no—
406#217—101no—
407#217—101no—
408#217—101no—
409#217—101no—
410#217—101no—
411C4⋊Dic3—21no—
412C4⋊Dic3—51no—
413C4⋊Dic3—51no—
414C4⋊Dic3—101no—
415C4⋊Dic3—101no—
416C4⋊Dic3C22×D511yescharacteristic
417C4⋊Dic3C22×D511yescharacteristic
418C4×Dic3—21no—
419C4×Dic3—51no—
420C4×Dic3—51no—
421C4×Dic3—51no—
422C4×Dic3—101no—
423C4×Dic3—101no—
424C4×Dic3C22×D511yescharacteristic
425#208—102no—
426C2×C3⋊C8—51no—
427C2×C3⋊C8C22×D511yescharacteristic
428C23×C5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—24no—
432C22×D5—42no—
433C22×D5—42no—
434C22×D5D3×D411yescharacteristic
435C5×Q8—21no—
436C5×Q8C22×Dic312yescomplemented
437C5×D4—21no—
438C5×D4C22×Dic312yes—
439C2×C4×C5—21no—
440C2×C4×C5—31no—
441C2×C4×C5—31no—
442C2×C4×C5—61no—
443C2×C4×C5—61no—
444C2×C4×C5—122no—
445C2×C4×C5C23×D311yescharacteristic
446C22⋊D5—24no—
447C2×Dic5—31no—
448C2×Dic5—31no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—122no—
452C2×Dic5D3×D411yescharacteristic
453D20—24no—
454D20—21no—
455D20—21no—
456D20C22×Dic312yes—
457D20C22×Dic312yescomplemented
458C4×D5—24no—
459C4×D5—62no—
460C4×D5—121no—
461C4×D5—122no—
462C4×D5—122no—
463C4×D5—122no—
464C4×D5—122no—
465C4×D5—122no—
466C4×D5#23712yes—
467C4×D5C22×Dic312yes—
468C5×C8—61no—
469C5×C8C22×Dic312yescomplemented
470#168—61no—
471#168C22×Dic312yescomplemented
472C2×#41—51no—
473C22×D4—51no—
474C23×C4—301no—
475AGL(1,ℤ/8)—58no—
476C2×SD16—51no—
477C2×SD16D3×D511yescharacteristic
478C2×D8—51no—
479C2×D8—51no—
480C2×M16—51no—
481C2×M16—151no—
482C4×Q8—31no—
483C4×Q8—151no—
484C4×D4—31no—
485C4×D4—151no—
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—151no—
497C2×C22⋊C4—301no—
498C2×C42—151no—
499C2×C42—301no—
500#107—151no—
501#107—151no—
502#106—31no—
503#106—151no—
504#103—31no—
505#103—151no—
506#102—31no—
507#102—151no—
508#102—151no—
509#102—151no—
510#102—151no—
511#102—151no—
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
520C3×D5—22no—
521C3×D5—42no—
522C3×D5—42no—
523C23×C3—21no—
524C23×C3—51no—
525C23×C3—104no—
526C23×C3—101no—
527C23×C3—101no—
528C23×C3—202no—
529C23×C3—202no—
530C3×Q8—21no—
531C3×Q8C2×C4×D512yescomplemented
532C3×D4—21no—
533C3×D4—52no—
534C3×D4—52no—
535C3×D4—104no—
536C3×D4—104no—
537C3×D4—101no—
538C3×D4—101no—
539C3×D4C2×C4×D512yes—
540C2×C3×C4—21no—
541C2×C3×C4—51no—
542C2×C3×C4—52no—
543C2×C3×C4—52no—
544C2×C3×C4—104no—
545C2×C3×C4C23×D511yescharacteristic
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—42no—
549C2×Dic3—51no—
550C2×Dic3—51no—
551C2×Dic3—102no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—201no—
555C2×Dic3—202no—
556C2×Dic3—202no—
557C2×Dic3—202no—
558C2×Dic3—202no—
559C2×Dic3—202no—
560C2×Dic3—202no—
561C2×Dic3D4×D511yescharacteristic
562C2×Dic3D4×D511yescharacteristic
563C3×C8—52no—
564C3×C8C2×C4×D512yescomplemented
565C3⋊C8—21no—
566C3⋊C8—101no—
567C22×C5—22no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5C2×D3×D411yescharacteristic
571C2×D5—21no—
572C2×D5—21no—
573C2×D5—22no—
574C2×D5—22no—
575C2×D5—48no—
576C2×D5—41no—
577C2×D5—41no—
578C2×D5—41no—
579C2×D5—41no—
580C2×D5D4×Dic312yes—
581C4×C5—22no—
582C4×C5—32no—
583C4×C5—61no—
584C4×C5—121no—
585C4×C5—121no—
586C4×C5C2×#23711yescharacteristic
587C4×C5C23×Dic311yescharacteristic
588Dic5—61no—
589Dic5—61no—
590Dic5—121no—
591Dic5—121no—
592Dic5D4×Dic312yes—
593C24—101no—
594#41—54no—
595#41—102no—
596C2×Q8C2×D3×D511yescharacteristic
597C2×D4—54no—
598C2×D4—51no—
599C2×D4—51no—
600C2×D4—101no—
601C2×D4—102no—
602C2×D4—101no—
603C2×D4C2×D3×D511yescharacteristic
604C22×C4—51no—
605C22×C4—61no—
606C22×C4—101no—
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—54no—
617SD16D5×Dic314yescomplemented
618D8—54no—
619D8—54no—
620M16—54no—
621M16—302no—
622C2×C8—31no—
623C2×C8—51no—
624C2×C8—151no—
625C2×C8C2×D3×D511yescharacteristic
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—151no—
630C4⋊C4—151no—
631C4⋊C4—301no—
632C4⋊C4—301no—
633C22⋊C4—61no—
634C22⋊C4—301no—
635C22⋊C4—301no—
636C22⋊C4—301no—
637C22⋊C4—301no—
638C22⋊C4—301no—
639C22⋊C4—301no—
640C42—31no—
641C42—61no—
642C42—151no—
643C42—151no—
644C42—151no—
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×C3—102no—
655C22×C3—102no—
656C22×C3—208no—
657C22×C3—201no—
658C22×C3—201no—
659C22×C3—201no—
660C22×C3—201no—
661C22×C3C2×D4×D511yescharacteristic
662C3×C4—22no—
663C3×C4—52no—
664C3×C4C22×C4×D511yescharacteristic
665C3×C4D5×#4111yescharacteristic
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—101no—
670Dic3—101no—
671Dic3—201no—
672Dic3—201no—
673Dic3#406012yesdirect product factor
674C2×C5—42no—
675C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
676C2×C5#577311yescharacteristic
677C2×C5C2×D4×Dic311yescharacteristic
678D5—22no—
679D5—42no—
680D5—42no—
681C23—21no—
682C23—51no—
683C23—104no—
684C23—101no—
685C23—101no—
686C23—202no—
687C23—202no—
688Q8—21no—
689Q8C2×D5×Dic312yescomplemented
690D4—21no—
691D4—52no—
692D4—52no—
693D4—104no—
694D4—104no—
695D4—101no—
696D4—101no—
697D4C2×D5×Dic312yes—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—51no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—104no—
707C2×C4—122no—
708C2×C4—151no—
709C2×C4—151no—
710C2×C4—302no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4—602no—
714C2×C4—602no—
715C2×C4—601no—
716C2×C4—602no—
717C2×C4—602no—
718C2×C4—602no—
719C2×C4—602no—
720C2×C4C22×D3×D511yescharacteristic
721C8—52no—
722C8—61no—
723C8—301no—
724C8C2×D5×Dic312yescomplemented
725C2×C3—42no—
726C2×C3—102no—
727C2×C3—202no—
728C2×C3—202no—
729C2×C3C4×D4×D511yescharacteristic
730C2×C3C2×#406011yescharacteristic
731C2×C3#6610211yescharacteristic
732C5Dic3×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
733C22—22no—
734C22—41no—
735C22—41no—
736C22—52no—
737C22—101no—
738C22—101no—
739C22—102no—
740C22—102no—
741C22—208no—
742C22—201no—
743C22—201no—
744C22—201no—
745C22—201no—
746C22D3×D4×D511yescharacteristic
747C4—22no—
748C4—32no—
749C4—52no—
750C4—61no—
751C4—121no—
752C4—121no—
753C4—301no—
754C4—301no—
755C4—601no—
756C4—601no—
757C4D5×#23711yescharacteristic
758C4C22×D5×Dic311yescharacteristic
759C3C4×#406011yescharacteristic, complemented, Sylow
760C2—42no—
761C2—102no—
762C2—202no—
763C2—202no—
764C2D3×#406011yescharacteristic
765C2#1175407311yescharacteristic
766C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×SD16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4060C2
cosocleC2×C3×C4×C5C24
hypercenterC2×SD16D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. Dic3×#713C2semidirect
3. D4×D5×Dic3C2semidirect
4. #11751265C2semidirect
5. C5×Dic3×SD16C2semidirect
6. #11749241C2semidirect
7. Dic3×#688C2semidirect
8. #11749198C2semidirect
9. #11748995C2semidirect
10. Dic3×#686C2semidirect
11. #11748962C2semidirect
12. #11747815C2semidirect
13. Dic3×D40C2semidirect
14. #11747618C2semidirect
15. Dic3×#676C2semidirect
21. Q8×Dic15C22semidirect
23. C5×Q8×Dic3C22semidirect
27. C3×#4060C4semidirect
35. #91434C22semidirect
38. Dic3×D20C22semidirect
45. #91119C22semidirect
47. #91102C22semidirect
48. #91099C22semidirect
49. C5×#835C22semidirect
51. C5×#817C22semidirect
52. C5×C8×Dic3C22semidirect
53. #90988C22semidirect
54. #90985C22semidirect
56. #90965C22semidirect
58. #90964C22semidirect
59. #90954C22semidirect
60. Dic3×#168C22semidirect
84. C3×#713C2×C4semidirect
86. C3×D4×D5C2×C4semidirect
100. C3×C5×SD16C2×C4semidirect
116. C3×#688C2×C4semidirect
117. C3×#686C2×C4semidirect
119. C3×D40C2×C4semidirect
120. C3×#676C2×C4semidirect
139. Dic3×SD16D5semidirect
157. #4060Dic3direct (N × H)
199. C3×C5×Q8C22×C4semidirect
220. C3×D20C22×C4semidirect
231. C3×C5×C8C22×C4semidirect
233. C3×#168C22×C4semidirect
246. Q8×Dic3C2×D5semidirect
264. #835C2×D5semidirect
274. #817C2×D5semidirect
278. C8×Dic3C2×D5semidirect
286. #713C2×Dic3semidirect
288. D4×D5C2×Dic3semidirect
302. C5×SD16C2×Dic3semidirect
312. #688C2×Dic3semidirect
313. #686C2×Dic3semidirect
330. D40C2×Dic3semidirect
332. #676C2×Dic3semidirect
373. C5×Dic3AGL(1,ℤ/8)semidirect
398. C3×SD16C4×D5semidirect
436. C5×Q8C22×Dic3semidirect
457. D20C22×Dic3semidirect
469. C5×C8C22×Dic3semidirect
471. #168C22×Dic3semidirect
531. C3×Q8C2×C4×D5semidirect
564. C3×C8C2×C4×D5semidirect
617. SD16D5×Dic3semidirect
647. C3×C5C4×AGL(1,ℤ/8)semidirect
673. Dic3#4060direct (N × H)
689. Q8C2×D5×Dic3semidirect
724. C8C2×D5×Dic3semidirect
732. C5Dic3×AGL(1,ℤ/8)semidirect
759. C3C4×#4060semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40602
Dic3×#7132
D4×D5×Dic32
#117512652
C5×Dic3×SD162
#117492412
Dic3×#6882
#117491982
#117489952
Dic3×#6862
#117489622
#117478152
Dic3×D402
#117476182
Dic3×#6762
C4×#40603
Dic3×AGL(1,ℤ/8)5