Finite Group Databasebeta

← D3×#65348 #14438846

Subgroups — D3×#65348 #14438846

Order 1920.

1184 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×#124C211yesmaximal, characteristic, complemented
2C2×D3×#689C211yesmaximal, characteristic, complemented
3C2×D3×#688C211yesmaximal, characteristic, complemented
4C2×D3×#687C211yesmaximal, characteristic, complemented
5C2×D3×#686C211yesmaximal, characteristic
6D3×#4021C211yesmaximal, characteristic, complemented
7#11751160C211yesmaximal, characteristic, complemented
8C3×#65348C211yesmaximal, characteristic, complemented
9#11749323C211yesmaximal, characteristic, complemented
10#11749317C211yesmaximal, characteristic, complemented
11#11749078C211yesmaximal, characteristic, complemented
12#11749074C211yesmaximal, characteristic, complemented
13#11747040C211yesmaximal, characteristic, complemented
14#11747030C211yesmaximal, characteristic, complemented
15C4×D3×#168C211yesmaximal, characteristic, complemented
16C2×#65348—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×C5×D3×D4C2211yescharacteristic
19C2×D3×D20C2211yescharacteristic
20C2×D3×Dic10C2211yescharacteristic
21C3×C5×#124C2211yescharacteristic, complemented
22C2×#6718C2211yescharacteristic, complemented
23C2×#6717C2211yescharacteristic, complemented
24C2×#6716C2211yescharacteristic, complemented
25C2×#6715C2211yescharacteristic
26#91764C2211yescharacteristic, complemented
27C5×#947C2211yescharacteristic, complemented
28C5×#936C2211yescharacteristic, complemented
29C5×#885—22no—
30C5×D3×C22⋊C4—22no—
31C5×#875C2211yescharacteristic, complemented
32C42×C5×D3C2211yescharacteristic
33C2×C3×#689C2211yescharacteristic, complemented
34C2×C3×#688C2211yescharacteristic, complemented
35C2×C3×#687C2211yescharacteristic, complemented
36C2×C3×#686C2211yescharacteristic
37C3×#4021C2211yescharacteristic, complemented
38D3×#689—24no—
39D3×#688—24no—
40D3×#687—24no—
41D3×#686—24no—
42D3×#685—22no—
43#91374C2211yescharacteristic, complemented
44#91364C2211yescharacteristic, complemented
45#91353—22no—
46C2×#6663C2211yescharacteristic, complemented
47C2×#6661C2211yescharacteristic, complemented
48C2×#6660C2211yescharacteristic, complemented
49C2×#6659C2211yescharacteristic, complemented
50C2×#6656C2211yescharacteristic, complemented
51C2×#6655C2211yescharacteristic, complemented
52C2×#6654C2211yescharacteristic
53C2×#6652C2211yescharacteristic
54C2×D3×#168C2211yescharacteristic
55C2×D3×#168C2211yescharacteristic
56C4×C3⋊#168C2211yescharacteristic, complemented
57C3×C4×#168C2211yescharacteristic, complemented
58Dic3×#168C2211yescharacteristic, complemented
59Dic3×#168C2211yescharacteristic, complemented
60D3×#495—51nomaximal, Hall
61C2×C5×#124—31no—
62C22×#689—31no—
63C22×#688—31no—
64C22×#687—31no—
65C22×#686—31no—
66C2×#4021—31no—
67#65348—31no—
68#65348—31no—
69#65348—31no—
70#65348—31no—
71#65348—31no—
72#65348—31no—
73#65348—31no—
74#65348D311yescharacteristic, direct product factor
75C2×C4×#168—31no—
76C23×C5×D3—21no—
77C22×D3×D5—21no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4C2311yescharacteristic
80C2×D60C2311yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×C5×#67—21no—
83C5×D3×Q8—22no—
84C5×D3×Q8—22no—
85C5×D3×D4—22no—
86C5×D3×D4—22no—
87C2×C5×D12C2311yescharacteristic
88C2×C4×C5×D3—21no—
89C2×C4×C5×D3D412yes—
90C2×C4×C5×D3C2311yescharacteristic
91C2×C5×Dic6—21no—
92C2×C5×Dic6C2311yescharacteristic
93C2×C3×D20C2311yescharacteristic
94C2×C3×Dic10C2311yescharacteristic
95C2×#1204—21no—
96C2×#1202—21no—
97C2×D3×Dic5—21no—
98D3×D20—22no—
99D3×D20—22no—
100D3×Dic10—22no—
101D3×Dic10—22no—
102C3×C5×C22⋊C4—22no—
103C3×C42×C5C2311yescharacteristic
104#6718—22no—
105#6717—22no—
106#6716—22no—
107#6715—22no—
108#6714—22no—
109C2×C3⋊#168C2311yescharacteristic
110C2×C3⋊#168C2311yescharacteristic
111C5×#217—22no—
112C5×(C2×D3)⋊C4—22no—
113C5×(C2×D3)⋊C4—22no—
114C4×C5×Dic3D412yes—
115C4×C5×Dic3C2311yescharacteristic
116C3×#689—22no—
117C3×#688—22no—
118C3×#687—22no—
119C3×#686—22no—
120C3×#685—22no—
121C2×C3×#168C2311yescharacteristic
122C2×C3×#168C2311yescharacteristic
123#6667—22no—
124#6665—22no—
125#6663—22no—
126#6661—22no—
127#6660—22no—
128#6659—22no—
129#6656—22no—
130#6655—22no—
131#6654—22no—
132#6652—22no—
133D3×#168D414yes—
134D3×#168D414yes—
135C2×D3×Q16—51no—
136C2×D3×SD16—51no—
137C2×D3×SD16—51no—
138C2×D3×D8—51no—
139D3×#124—51no—
140D3×#124D511yescharacteristic, complemented
141C3×#495—51no—
142#5191—51no—
143#5168—51no—
144#5168—51no—
145#5155—51no—
146#5059—51no—
147#5059—51no—
148#4696—51no—
149C4×D3×C8—51no—
150C22×C5×Q8—31no—
151C22×C5×D4—31no—
152C22×D20—31no—
153C22×Dic10—31no—
154C5×#124—31no—
155C5×#124—31no—
156C5×#124—31no—
157C5×#124—62no—
158C5×#124C2×D311yescharacteristic, complemented
159C2×C5×C22⋊C4—62no—
160C2×C42×C5—31no—
161C2×#689—31no—
162C2×#689—31no—
163C2×#689—31no—
164C2×#689—64no—
165C2×#689C2×D311yescharacteristic, complemented
166C2×#688—31no—
167C2×#688—31no—
168C2×#688—31no—
169C2×#688—64no—
170C2×#688C2×D311yescharacteristic, complemented
171C2×#687—31no—
172C2×#687—31no—
173C2×#687—31no—
174C2×#687—64no—
175C2×#687C2×D311yescharacteristic, complemented
176C2×#686—31no—
177C2×#686—31no—
178C2×#686—31no—
179C2×#686—64no—
180C2×#686C2×D311yescharacteristic
181C2×#685—62no—
182C22×#168—31no—
183C22×#168—31no—
184#4021—31no—
185#4021—31no—
186#4021—31no—
187#4021—62no—
188#4021C2×D311yescharacteristic, complemented
189C4×#168—31no—
190C4×#168—31no—
191C4×#168—31no—
192C4×#168C2×D311yescharacteristic, complemented
193C2×#495—151noSylow
194C23×C3×C5—21no—
195C22×D15—21no—
196C22×C5×D3—21no—
197C22×C5×D3—42no—
198C22×C5×D3—44no—
199C22×C5×D3C2×D411yescharacteristic
200C22×C3×D5—21no—
201C2×D3×D5—42no—
202C2×D3×D5—44no—
203C3×C5×Q8—21no—
204C3×C5×Q8—21no—
205C3×C5×D4—21no—
206C3×C5×D4—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5C2×D412yes—
209C2×C3×C4×C5C2411yescharacteristic
210C2×Dic15—21no—
211D60—21no—
212D60—21no—
213Dic30—21no—
214Dic30—21no—
215C5×#67—42no—
216C2×C5×Dic3—21no—
217C2×C5×Dic3C2×D412yes—
218C2×C5×Dic3C2×D411yescharacteristic
219C5×D12—21no—
220C5×D12—21no—
221C4×C5×D3—24no—
222C4×C5×D3—42no—
223C4×C5×D3C2×D412yes—
224C4×C5×D3C2×D412yes—
225C5×Dic6—21no—
226C5×Dic6—21no—
227C5×Dic6—42no—
228C2×C3×Dic5—21no—
229C3×D20—21no—
230C3×D20—21no—
231C3×Dic10—21no—
232C3×Dic10—21no—
233#1204—42no—
234#1202—42no—
235D3×Dic5—42no—
236C3⋊#168C2×D412yes—
237C3⋊#168C2×D412yes—
238C3×#168C2×D412yes—
239C3×#168C2×D412yes—
240C2×D3×Q8—51no—
241C2×D3×Q8C2×D511yescharacteristic
242C2×D3×D4—51no—
243C2×D3×D4C2×D511yescharacteristic
244C2×C3×Q16—51no—
245C2×C3×SD16—51no—
246C2×C3×SD16—51no—
247C2×C3×D8—51no—
248C3×#124—51no—
249C3×#124C2×D511yescharacteristic, complemented
250#947—51no—
251#947C2×D511yescharacteristic, complemented
252C2×#216—51no—
253C2×#216—51no—
254C2×#215—51no—
255C2×#215—51no—
256#936—51no—
257#936C2×D511yescharacteristic, complemented
258C2×#214—51no—
259C2×#214—51no—
260C2×#213—51no—
261C2×#213—51no—
262D3×Q16—104no—
263D3×SD16—104no—
264D3×SD16—104no—
265D3×D8—104no—
266C2×Dic12—51no—
267C2×D24—51no—
268C2×#204—51no—
269C2×#204—51no—
270C2×D3×C8—51no—
271C2×D3×C8—51no—
272#885—22no—
273#885—102no—
274D3×C22⋊C4—22no—
275D3×C22⋊C4—102no—
276#875—51no—
277#875C2×D511yescharacteristic, complemented
278C42×D3C2×D511yescharacteristic
279C3×C4×C8—51no—
280C8×Dic3—51no—
281C8×Dic3—51no—
282C4×C3⋊C8—51no—
283C24×C5—61no—
284C23×D5—61no—
285C2×C5×Q8—31no—
286C2×C5×Q8—61no—
287C2×C5×Q8—62no—
288C2×C5×Q8—62no—
289C2×C5×Q8C22×D311yescharacteristic
290C2×C5×D4—31no—
291C2×C5×D4—62no—
292C2×C5×D4—62no—
293C2×C5×D4—61no—
294C2×C5×D4C22×D311yescharacteristic
295C22×C4×C5—31no—
296C22×C4×C5—32no—
297C22×C4×C5—61no—
298C22×Dic5—61no—
299C2×D20—31no—
300C2×D20—62no—
301C2×D20—62no—
302C2×D20—61no—
303C2×D20C22×D311yescharacteristic
304C2×Dic10—31no—
305C2×Dic10—62no—
306C2×Dic10—62no—
307C2×Dic10—61no—
308C2×Dic10C22×D311yescharacteristic
309C5×C22⋊C4—22no—
310C5×C22⋊C4—62no—
311C5×C22⋊C4—62no—
312C5×C22⋊C4—62no—
313C42×C5—32no—
314C42×C5—31no—
315C42×C5C22×D311yescharacteristic
316#689—22no—
317#689—62no—
318#689—62no—
319#689—62no—
320#688—22no—
321#688—62no—
322#688—62no—
323#688—62no—
324#687—22no—
325#687—62no—
326#687—62no—
327#687—62no—
328#686—22no—
329#686—62no—
330#686—62no—
331#686—62no—
332#685—22no—
333#685—62no—
334#685—62no—
335#685—62no—
336C2×#168—31no—
337C2×#168—31no—
338C2×#168—34no—
339C2×#168—34no—
340C2×#168C22×D311yescharacteristic
341C2×#168C22×D311yescharacteristic
342C22×Q16—151no—
343C22×SD16—151no—
344C22×SD16—151no—
345C22×D8—151no—
346C2×#124—31no—
347C2×#124—151no—
348#495—51no—
349#495—151no—
350#495—151no—
351#495—151no—
352#495—151no—
353#495—151no—
354#495—151no—
355#495—151no—
356C2×C4×C8—151no—
357C22×C3×C5—41no—
358C22×C3×C5—42no—
359C22×C3×C5C22×D411yescharacteristic
360C2×D15—41no—
361C2×D15—42no—
362C2×C5×D3—41no—
363C2×C5×D3—42no—
364C2×C5×D3—84no—
365C2×C5×D3#12712yes—
366C2×C5×D3#13514yes—
367C2×C3×D5—41no—
368C2×C3×D5—42no—
369D3×D5—84no—
370C3×C4×C5—22no—
371C3×C4×C5—41no—
372C3×C4×C5C22×D411yescharacteristic
373C3×C4×C5C22×D411yescharacteristic
374Dic15—41no—
375C3×Dic5—41no—
376C5×Dic3—22no—
377C5×Dic3—41no—
378C5×Dic3#12712yes—
379C23×D3—21no—
380C23×D3—101no—
381C2×C3×Q8—51no—
382C2×C3×Q8C22×D511yescharacteristic
383C2×C3×D4—51no—
384C2×C3×D4C22×D511yescharacteristic
385C2×#67—21no—
386C2×#67—101no—
387D3×Q8—22no—
388D3×Q8—22no—
389D3×Q8—102no—
390D3×Q8—102no—
391D3×D4—22no—
392D3×D4—22no—
393D3×D4—102no—
394D3×D4—102no—
395C2×D12—51no—
396C2×D12C22×D511yescharacteristic
397C2×C4×D3—21no—
398C2×C4×D3—101no—
399C2×C4×D3C22⋊D512yes—
400C2×C4×D3C22×D511yescharacteristic
401C2×Dic6—21no—
402C2×Dic6—51no—
403C2×Dic6—101no—
404C2×Dic6C22×D511yescharacteristic
405C3×Q16—102no—
406C3×SD16—102no—
407C3×SD16—102no—
408C3×D8—102no—
409C2×C3×C8—51no—
410C2×C3×C8—51no—
411C3×C22⋊C4—22no—
412C3×C22⋊C4—102no—
413C3×C42C22×D511yescharacteristic
414#217—22no—
415#217—102no—
416#216—102no—
417#216—102no—
418#215—102no—
419#215—102no—
420#214—102no—
421#214—102no—
422#213—102no—
423#213—102no—
424(C2×D3)⋊C4—22no—
425(C2×D3)⋊C4—22no—
426(C2×D3)⋊C4—102no—
427(C2×D3)⋊C4—102no—
428C4×Dic3C22⋊D512yes—
429C4×Dic3C22×D511yescharacteristic
430C2×C3⋊C8—51no—
431C2×C3⋊C8—51no—
432Dic12—102no—
433D24—102no—
434#204—102no—
435#204—102no—
436D3×C8—54no—
437D3×C8—54no—
438C23×C5—21no—
439C23×C5—31no—
440C23×C5—61no—
441C23×C5—122no—
442C23×C5—124no—
443C22×D5—21no—
444C22×D5—61no—
445C22×D5—122no—
446C22×D5—124no—
447C5×Q8—21no—
448C5×Q8—21no—
449C5×Q8—61no—
450C5×Q8—61no—
451C5×Q8—122no—
452C5×D4—21no—
453C5×D4—21no—
454C5×D4—61no—
455C5×D4—61no—
456C5×D4—122no—
457C2×C4×C5—21no—
458C2×C4×C5—31no—
459C2×C4×C5—32no—
460C2×C4×C5—32no—
461C2×C4×C5—32no—
462C2×C4×C5—64no—
463C2×C4×C5—61no—
464C2×C4×C5—122no—
465C2×C4×C5D3×D412yes—
466C2×C4×C5C23×D311yescharacteristic
467C2×Dic5—21no—
468C2×Dic5—61no—
469C2×Dic5—122no—
470D20—21no—
471D20—21no—
472D20—61no—
473D20—61no—
474D20—122no—
475Dic10—21no—
476Dic10—21no—
477Dic10—61no—
478Dic10—61no—
479Dic10—122no—
480#168—32no—
481#168—32no—
482#168D3×D412yes—
483#168D3×D412yes—
484C22×Q8—31no—
485C22×Q8—151no—
486C22×D4—31no—
487C22×D4—151no—
488C2×Q16—51no—
489C2×Q16—151no—
490C2×Q16—151no—
491C2×Q16—151no—
492C2×Q16—304no—
493C2×SD16—51no—
494C2×SD16—51no—
495C2×SD16—151no—
496C2×SD16—151no—
497C2×SD16—151no—
498C2×SD16—151no—
499C2×SD16—151no—
500C2×SD16—151no—
501C2×SD16—304no—
502C2×SD16—304no—
503C2×D8—51no—
504C2×D8—151no—
505C2×D8—151no—
506C2×D8—151no—
507C2×D8—304no—
508C22×C8—151no—
509C22×C8—151no—
510#124—31no—
511#124—31no—
512#124—31no—
513#124—51no—
514#124—62no—
515#124—151no—
516#124—151no—
517#124—151no—
518#124—302no—
519#124D3×D511yescharacteristic, complemented
520C2×C22⋊C4—62no—
521C2×C22⋊C4—302no—
522C2×C42—31no—
523C4×C8—51no—
524C4×C8—151no—
525C4×C8—151no—
526C4×C8—151no—
527C2×C3×C5—81no—
528C2×C3×C5C2×#12711yescharacteristic
529C2×C3×C5C2×#13512yes—
530D15—81no—
531C3×D5—81no—
532C5×D3—81no—
533C5×D3#49514yescomplemented
534C23×C3—21no—
535C23×C3—101no—
536C22×D3—21no—
537C22×D3—44no—
538C22×D3—42no—
539C22×D3—101no—
540C22×D3—204no—
541C22×D3—202no—
542C22×D3C2×C22⋊D511yescharacteristic
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—101no—
546C3×Q8—101no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—101no—
550C3×D4—101no—
551C2×C3×C4—21no—
552C2×C3×C4—101no—
553C2×C3×C4C2×C22⋊D512yes—
554C2×C3×C4C23×D511yescharacteristic
555#67—42no—
556#67—202no—
557C2×Dic3—21no—
558C2×Dic3—101no—
559C2×Dic3C2×C22⋊D512yes—
560C2×Dic3C2×C22⋊D511yescharacteristic
561D12—21no—
562D12—21no—
563D12—101no—
564D12—101no—
565C4×D3—24no—
566C4×D3—42no—
567C4×D3—202no—
568C4×D3D4×D512yes—
569C4×D3D4×D512yes—
570Dic6—21no—
571Dic6—21no—
572Dic6—42no—
573Dic6—101no—
574Dic6—101no—
575Dic6—202no—
576C3×C8—52no—
577C3×C8—52no—
578C3⋊C8—52no—
579C3⋊C8—52no—
580C22×C5—32no—
581C22×C5—34no—
582C22×C5—41no—
583C22×C5—42no—
584C22×C5—121no—
585C22×C5—122no—
586C22×C5—244no—
587C22×C5C2×D3×D411yescharacteristic
588C2×D5—41no—
589C2×D5—42no—
590C2×D5—121no—
591C2×D5—122no—
592C2×D5—244no—
593C4×C5—22no—
594C4×C5—32no—
595C4×C5—41no—
596C4×C5—62no—
597C4×C5—121no—
598C4×C5C2×D3×D411yescharacteristic
599C4×C5C2×D3×D411yescharacteristic
600Dic5—41no—
601Dic5—121no—
602C24—61no—
603C24—301no—
604C2×Q8—31no—
605C2×Q8—51no—
606C2×Q8—61no—
607C2×Q8—62no—
608C2×Q8—62no—
609C2×Q8—151no—
610C2×Q8—301no—
611C2×Q8—302no—
612C2×Q8—302no—
613C2×Q8C2×D3×D511yescharacteristic
614C2×D4—31no—
615C2×D4—51no—
616C2×D4—62no—
617C2×D4—62no—
618C2×D4—61no—
619C2×D4—151no—
620C2×D4—302no—
621C2×D4—302no—
622C2×D4—301no—
623C2×D4C2×D3×D511yescharacteristic
624C22×C4—31no—
625C22×C4—32no—
626C22×C4—61no—
627C22×C4—301no—
628Q16—102no—
629Q16—302no—
630Q16—302no—
631Q16—302no—
632SD16—102no—
633SD16—102no—
634SD16—302no—
635SD16—302no—
636SD16—302no—
637SD16—302no—
638SD16—302no—
639SD16—302no—
640D8—102no—
641D8—302no—
642D8—302no—
643D8—302no—
644C2×C8—51no—
645C2×C8—51no—
646C2×C8—154no—
647C2×C8—154no—
648C2×C8—151no—
649C2×C8—151no—
650C22⋊C4—22no—
651C22⋊C4—62no—
652C22⋊C4—62no—
653C22⋊C4—62no—
654C22⋊C4—102no—
655C22⋊C4—302no—
656C22⋊C4—302no—
657C22⋊C4—302no—
658C42—32no—
659C42—31no—
660C42C2×D3×D511yescharacteristic
661C3×C5C2×#49511yescharacteristic, complemented, Hall
662C22×C3—41no—
663C22×C3—42no—
664C22×C3—201no—
665C22×C3—202no—
666C22×C3C22×C22⋊D511yescharacteristic
667C2×D3—41no—
668C2×D3—42no—
669C2×D3—84no—
670C2×D3—201no—
671C2×D3—202no—
672C2×D3—404no—
673C2×D3#408612yes—
674C2×D3#409614yes—
675C3×C4—22no—
676C3×C4—41no—
677C3×C4—201no—
678C3×C4C2×D4×D511yescharacteristic
679C3×C4C2×D4×D511yescharacteristic
680Dic3—22no—
681Dic3—41no—
682Dic3—201no—
683Dic3#408612yes—
684C2×C5—34no—
685C2×C5—81no—
686C2×C5—241no—
687C2×C5D3×#12711yescharacteristic
688C2×C5D3×#13512yes—
689D5—81no—
690D5—241no—
691C23—21no—
692C23—31no—
693C23—61no—
694C23—101no—
695C23—122no—
696C23—124no—
697C23—301no—
698C23—602no—
699C23—604no—
700Q8—21no—
701Q8—21no—
702Q8—61no—
703Q8—61no—
704Q8—101no—
705Q8—101no—
706Q8—122no—
707Q8—301no—
708Q8—301no—
709Q8—602no—
710D4—21no—
711D4—21no—
712D4—61no—
713D4—61no—
714D4—101no—
715D4—101no—
716D4—122no—
717D4—301no—
718D4—301no—
719D4—602no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—32no—
725C2×C4—64no—
726C2×C4—61no—
727C2×C4—101no—
728C2×C4—122no—
729C2×C4—301no—
730C2×C4—602no—
731C2×C4D3×C22⋊D512yes—
732C2×C4C22×D3×D511yescharacteristic
733C8—52no—
734C8—52no—
735C8—152no—
736C8—152no—
737C2×C3—81no—
738C2×C3—401no—
739C2×C3C2×#408611yescharacteristic
740C2×C3C2×#409612yes—
741D3—81no—
742D3—401no—
743D3#6534814yesdirect product factor
744C5D3×#49511yescharacteristic, complemented, Sylow
745C22—32no—
746C22—34no—
747C22—41no—
748C22—42no—
749C22—121no—
750C22—122no—
751C22—201no—
752C22—202no—
753C22—244no—
754C22—601no—
755C22—602no—
756C22—1204no—
757C22C2×D3×C22⋊D511yescharacteristic
758C4—22no—
759C4—32no—
760C4—41no—
761C4—62no—
762C4—121no—
763C4—201no—
764C4—601no—
765C4D3×D4×D511yescharacteristic
766C4D3×D4×D511yescharacteristic
767C3C2×#6534811yescharacteristic, complemented, Sylow
768C2—34no—
769C2—81no—
770C2—241no—
771C2—401no—
772C2—1201no—
773C2D3×#408611yescharacteristic
774C2D3×#409612yes—
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×#686C2
hypercenter#124D3×D5
hypocenterC3×C5C2×#495
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C5×D3×#124C2semidirect
2. C2×D3×#689C2semidirect
3. C2×D3×#688C2semidirect
4. C2×D3×#687C2semidirect
6. D3×#4021C2semidirect
7. #11751160C2semidirect
8. C3×#65348C2semidirect
9. #11749323C2semidirect
10. #11749317C2semidirect
11. #11749078C2semidirect
12. #11749074C2semidirect
13. #11747040C2semidirect
14. #11747030C2semidirect
15. C4×D3×#168C2semidirect
21. C3×C5×#124C22semidirect
22. C2×#6718C22semidirect
23. C2×#6717C22semidirect
24. C2×#6716C22semidirect
26. #91764C22semidirect
27. C5×#947C22semidirect
28. C5×#936C22semidirect
31. C5×#875C22semidirect
33. C2×C3×#689C22semidirect
34. C2×C3×#688C22semidirect
35. C2×C3×#687C22semidirect
37. C3×#4021C22semidirect
43. #91374C22semidirect
44. #91364C22semidirect
46. C2×#6663C22semidirect
47. C2×#6661C22semidirect
48. C2×#6660C22semidirect
49. C2×#6659C22semidirect
50. C2×#6656C22semidirect
51. C2×#6655C22semidirect
56. C4×C3⋊#168C22semidirect
57. C3×C4×#168C22semidirect
58. Dic3×#168C22semidirect
59. Dic3×#168C22semidirect
74. #65348D3direct (N × H)
140. D3×#124D5semidirect
158. C5×#124C2×D3semidirect
165. C2×#689C2×D3semidirect
170. C2×#688C2×D3semidirect
175. C2×#687C2×D3semidirect
188. #4021C2×D3semidirect
192. C4×#168C2×D3semidirect
249. C3×#124C2×D5semidirect
251. #947C2×D5semidirect
257. #936C2×D5semidirect
277. #875C2×D5semidirect
519. #124D3×D5semidirect
533. C5×D3#495semidirect
661. C3×C5C2×#495semidirect
743. D3#65348direct (N × H)
744. C5D3×#495semidirect
767. C3C2×#65348semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1242
C2×D3×#6892
C2×D3×#6882
C2×D3×#6872
C2×D3×#6862
D3×#40212
#117511602
C3×#653482
#117493232
#117493172
#117490782
#117490742
#117470402
#117470302
C4×D3×#1682
C2×#653483
D3×#4955