Finite Group Databasebeta

← D3×#65107 #14425916

Subgroups — D3×#65107 #14425916

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4090C211yesmaximal, characteristic, complemented
2C2×D3×#688C211yesmaximal, characteristic
3C2×D3×#677C211yesmaximal, characteristic
4D3×#4039C211yesmaximal, characteristic
5#11750919C211yesmaximal, characteristic, complemented
6C5×D3×#103C211yesmaximal, characteristic, complemented
7C3×#65107C211yesmaximal, characteristic, complemented
8#11749229C211yesmaximal, characteristic, complemented
9#11749222C211yesmaximal, characteristic, complemented
10#11747761C211yesmaximal, characteristic, complemented
11#11747749C211yesmaximal, characteristic, complemented
12D3×#3946C211yesmaximal, characteristic, complemented
13D3×#3942C211yesmaximal, characteristic, complemented
14#11747426C211yesmaximal, characteristic, complemented
15#11747414C211yesmaximal, characteristic, complemented
16C2×#65107—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C2×D3×D20C2211yescharacteristic
19C2×C4×D3×D5—21no—
20C2×D3×Dic10C2211yescharacteristic
21#91833C2211yescharacteristic, complemented
22C2×#6717C2211yescharacteristic
23C2×#6706C2211yescharacteristic
24#91782C2211yescharacteristic
25C2×C5×D3×C8C2211yescharacteristic
26C5×D3×C4⋊C4C2211yescharacteristic
27C3×#4090C2211yescharacteristic, complemented
28C2×C3×#688C2211yescharacteristic
29C2×C3×#677C2211yescharacteristic
30C3×#4039C2211yescharacteristic
31D3×#688—24no—
32D3×#685—21no—
33#91444—21no—
34#91434C2211yescharacteristic
35#91418C2211yescharacteristic
36D3×#683—21no—
37D3×#683—21no—
38C4×D3×Dic5C2211yescharacteristic
39#91396—21no—
40#91385C2211yescharacteristic, complemented
41#91376C2211yescharacteristic, complemented
42#91329—21no—
43#91329—21no—
44C2×#6660C2211yescharacteristic
45C2×#6658C2211yescharacteristic
46C2×#6657C2211yescharacteristic
47C2×#6655C2211yescharacteristic
48C2×D3×#168C2211yescharacteristic
49D3×#677—24no—
50C3×C5×#103C2211yescharacteristic, complemented
51#91098C2211yescharacteristic, complemented
52#91094C2211yescharacteristic, complemented
53C5×#835C2211yescharacteristic, complemented
54C5×#816C2211yescharacteristic, complemented
55C5×#810C2211yescharacteristic, complemented
56C3×#3946C2211yescharacteristic, complemented
57C3×#3942C2211yescharacteristic, complemented
58#90983C2211yescharacteristic, complemented
59#90982C2211yescharacteristic, complemented
60#90975C2211yescharacteristic, complemented
61#90970C2211yescharacteristic, complemented
62D3×#461—51nomaximal, Hall
63C2×#4090—31no—
64C22×#688—31no—
65C22×#677—31no—
66C2×#4039—31no—
67C2×C5×#103—31no—
68C2×#3946—31no—
69C2×#3942—31no—
70#65107—31no—
71#65107—31no—
72#65107—31no—
73#65107—31no—
74#65107—31no—
75#65107—31no—
76#65107—31no—
77#65107D311yescharacteristic, direct product factor
78C22×D3×D5—21no—
79C2×C3×C5×Q8C2311yescharacteristic
80C2×D60C2311yescharacteristic
81C2×C4×D15—21no—
82C2×Dic30C2311yescharacteristic
83C5×D3×Q8—22no—
84C5×D3×Q8—22no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3—21no—
87C2×C4×C5×D3C2311yescharacteristic
88C2×C5×Dic6—21no—
89C2×C5×Dic6C2311yescharacteristic
90C2×C3×D20C2311yescharacteristic
91C2×C3×C4×D5—21no—
92C2×C3×Dic10C2311yescharacteristic
93C2×#1204—21no—
94C2×#1202—21no—
95C2×#1200—21no—
96C2×D3×Dic5—21no—
97C2×D3×Dic5D411yescharacteristic
98C2×D3×Dic5D411yescharacteristic
99C2×D5×Dic3—21no—
100D3×D20—22no—
101D3×D20D414yes—
102C4×D3×D5—44no—
103D3×Dic10—22no—
104D3×Dic10—22no—
105C2×C3×C5×C8C2311yescharacteristic
106C3×C5×C4⋊C4C2311yescharacteristic
107#6717—22no—
108#6714—21no—
109#6712—21no—
110#6712—21no—
111C4×Dic15C2311yescharacteristic
112C2×C3⋊#168C2311yescharacteristic
113#6706—22no—
114C5×C4⋊Dic3C2311yescharacteristic
115C5×Dic3⋊C4—21no—
116C2×C5×C3⋊C8C2311yescharacteristic
117C5×D3×C8—22no—
118C3×#688—22no—
119C3×#685—21no—
120C3×#683—21no—
121C3×#683—21no—
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C3×#677—22no—
125#6669—21no—
126#6669—21no—
127#6668—21no—
128#6668—21no—
129#6667—21no—
130#6665—21no—
131Dic3×Dic5D411yescharacteristic
132Dic3×Dic5D411yescharacteristic
133#6660—22no—
134#6658—22no—
135#6657—22no—
136#6655—22no—
137D3×#168—22no—
138C2×D3×SD16—51no—
139C2×D3×SD16—51no—
140D3×C4⋊Q8—51no—
141C4×D3×D4—51no—
142C3×#461—51no—
143#5162—51no—
144#5162—51no—
145#5083—51no—
146#5019—51no—
147#4841—51no—
148D3×C4⋊C8—51no—
149#4818—51no—
150#4818—51no—
151D3×#103—51no—
152D3×#103D511yescharacteristic, complemented
153C22×C5×Q8—31no—
154C22×D20—31no—
155C22×C4×D5—61no—
156C22×Dic10—31no—
157C22×C5×C8—31no—
158C2×C5×C4⋊C4—31no—
159#4090—31no—
160#4090—31no—
161#4090—31no—
162#4090—61no—
163#4090—61no—
164#4090C2×D311yescharacteristic, complemented
165C2×#688—31no—
166C2×#688—31no—
167C2×#688—31no—
168C2×#688—64no—
169C2×#688C2×D311yescharacteristic
170C2×#685—61no—
171C2×#683—61no—
172C2×#683—61no—
173C2×C4×Dic5—31no—
174C22×#168—31no—
175C2×#677—31no—
176C2×#677—31no—
177C2×#677—31no—
178C2×#677—64no—
179C2×#677C2×D311yescharacteristic
180#4039—31no—
181#4039—31no—
182#4039—31no—
183#4039—61no—
184#4039—61no—
185#4039C2×D311yescharacteristic
186C5×#103—31no—
187C5×#103—31no—
188C5×#103—31no—
189C5×#103C2×D311yescharacteristic, complemented
190#3946—31no—
191#3946—31no—
192#3946—31no—
193#3946C2×D311yescharacteristic, complemented
194#3942—31no—
195#3942—31no—
196#3942—31no—
197#3942C2×D311yescharacteristic, complemented
198C2×#461—151noSylow
199C22×D15—21no—
200C22×C5×D3C2×D411yescharacteristic
201C22×C3×D5—21no—
202C2×D3×D5—24no—
203C2×D3×D5—42no—
204C2×D3×D5—42no—
205C3×C5×Q8—21no—
206C3×C5×Q8—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5C2411yescharacteristic
210C2×Dic15—21no—
211C2×Dic15C2×D411yescharacteristic
212C2×Dic15C2×D411yescharacteristic
213D60—21no—
214D60C2×D412yes—
215C4×D15—42no—
216Dic30—21no—
217Dic30—21no—
218C2×C5×Dic3—21no—
219C2×C5×Dic3—21no—
220C2×C5×Dic3C2×D411yescharacteristic
221C4×C5×D3—42no—
222C4×C5×D3—42no—
223C4×C5×D3C2×D412yes—
224C4×C5×D3#4112yes—
225C5×Dic6—21no—
226C5×Dic6—21no—
227C5×Dic6—42no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5C2×D411yescharacteristic
230C2×C3×Dic5C2×D411yescharacteristic
231C3×D20—21no—
232C3×D20C2×D412yes—
233C3×C4×D5—42no—
234C3×Dic10—21no—
235C3×Dic10—21no—
236#1204—42no—
237#1202—24no—
238#1200—42no—
239D3×Dic5—22no—
240D3×Dic5—42no—
241D3×Dic5SD1614yescomplemented
242D5×Dic3—42no—
243C3×C5×C8—21no—
244C3⋊#168—21no—
245C3×#168—21no—
246C5×C3⋊C8—21no—
247C2×D3×Q8—51no—
248C2×D3×Q8C2×D511yescharacteristic
249C2×D3×D4—51no—
250C22×C4×D3—101no—
251C2×C3×SD16—51no—
252C2×C3×SD16—51no—
253C3×C4⋊Q8—51no—
254C3×C4×D4—51no—
255#944—51no—
256#944—51no—
257C2×#215—51no—
258C2×#215—51no—
259D4×Dic3—51no—
260C2×#214—51no—
261C2×#214—51no—
262C4×#67—101no—
263D3×SD16—104no—
264D3×SD16—104no—
265C2×#204—51no—
266C2×#204—51no—
267C2×D3×C8—51no—
268C2×D3×C8C2×D511yescharacteristic
269#893—51no—
270D3×C4⋊C4—101no—
271D3×C4⋊C4—101no—
272D3×C4⋊C4C2×D511yescharacteristic
273#888—101no—
274#888—101no—
275#67⋊C4—101no—
276D3×C22⋊C4—101no—
277C4×D12—51no—
278C42×D3—51no—
279#869—51no—
280C3×C4⋊C8—51no—
281C3×#103—51no—
282C3×#103C2×D511yescharacteristic, complemented
283#835—51no—
284#835C2×D511yescharacteristic, complemented
285#816—51no—
286#816C2×D511yescharacteristic, complemented
287Dic3⋊C8—51no—
288Dic3⋊C8—51no—
289#810—51no—
290#810C2×D511yescharacteristic, complemented
291C4⋊(C3⋊C8)—51no—
292C23×D5—61no—
293C2×C5×Q8—31no—
294C2×C5×Q8—61no—
295C2×C5×Q8—62no—
296C2×C5×Q8—62no—
297C2×C5×Q8C22×D311yescharacteristic
298C22×C4×C5—31no—
299C22×C4×C5—61no—
300C22×C4×C5—61no—
301C22×Dic5—31no—
302C22×Dic5—31no—
303C22×Dic5—61no—
304C2×D20—31no—
305C2×D20—34no—
306C2×D20—62no—
307C2×D20—61no—
308C2×D20C22×D311yescharacteristic
309C2×C4×D5—21no—
310C2×C4×D5—61no—
311C2×C4×D5—61no—
312C2×C4×D5—61no—
313C2×C4×D5—124no—
314C2×Dic10—31no—
315C2×Dic10—62no—
316C2×Dic10—62no—
317C2×Dic10—61no—
318C2×Dic10C22×D311yescharacteristic
319C2×C5×C8—31no—
320C2×C5×C8—62no—
321C2×C5×C8C22×D311yescharacteristic
322C5×C4⋊C4—31no—
323C5×C4⋊C4—61no—
324C5×C4⋊C4C22×D311yescharacteristic
325#688—22no—
326#688—62no—
327#688—62no—
328#688—62no—
329#685—21no—
330#685—61no—
331#685—61no—
332#685—61no—
333#683—21no—
334#683—21no—
335#683—61no—
336#683—61no—
337#683—61no—
338#683—61no—
339#683—61no—
340#683—61no—
341C4×Dic5—31no—
342C4×Dic5—31no—
343C4×Dic5—31no—
344C4×Dic5C22×D311yescharacteristic
345C2×#168—31no—
346C2×#168—62no—
347C2×#168C22×D311yescharacteristic
348#677—22no—
349#677—62no—
350#677—62no—
351#677—62no—
352C22×SD16—151no—
353C22×SD16—151no—
354C2×C4⋊Q8—151no—
355C2×C4×D4—151no—
356#461—51no—
357#461—151no—
358#461—151no—
359#461—151no—
360#461—151no—
361#461—151no—
362#461—151no—
363#461—151no—
364C2×C4⋊C8—151no—
365C2×#103—31no—
366C2×#103—151no—
367C22×C3×C5C22×D411yescharacteristic
368C2×D15—22no—
369C2×D15—41no—
370C2×D15—41no—
371C2×C5×D3#12112yes—
372C2×C5×D3C2×SD1612yes—
373C2×C5×D3#13712yes—
374C2×C3×D5—22no—
375C2×C3×D5—41no—
376C2×C3×D5—41no—
377D3×D5—48no—
378C3×C4×C5—41no—
379C3×C4×C5—41no—
380C3×C4×C5C22×D411yescharacteristic
381C3×C4×C5C2×#4111yescharacteristic
382Dic15—21no—
383Dic15—41no—
384Dic15C2×SD1612yescomplemented
385C3×Dic5—21no—
386C3×Dic5—41no—
387C3×Dic5C2×SD1612yescomplemented
388C5×Dic3—41no—
389C5×Dic3—41no—
390C5×Dic3#12112yes—
391C23×D3—101no—
392C2×C3×Q8—51no—
393C2×C3×Q8C22×D511yescharacteristic
394C2×C3×D4—51no—
395C22×C3×C4—101no—
396C2×#67—101no—
397C22×Dic3—101no—
398D3×Q8—22no—
399D3×Q8—22no—
400D3×Q8—102no—
401D3×Q8—102no—
402D3×D4—54no—
403D3×D4—102no—
404C2×D12—51no—
405C2×C4×D3—21no—
406C2×C4×D3—21no—
407C2×C4×D3—51no—
408C2×C4×D3—51no—
409C2×C4×D3—101no—
410C2×C4×D3—101no—
411C2×C4×D3—101no—
412C2×C4×D3—204no—
413C2×C4×D3C22×D511yescharacteristic
414C2×Dic6—21no—
415C2×Dic6—51no—
416C2×Dic6—101no—
417C2×Dic6C22×D511yescharacteristic
418C3×SD16—102no—
419C3×SD16—102no—
420C2×C3×C8—51no—
421C2×C3×C8C22×D511yescharacteristic
422C3×C4⋊C4—101no—
423C3×C4⋊C4—101no—
424C3×C4⋊C4C22×D511yescharacteristic
425C3×C22⋊C4—101no—
426C3×C42—51no—
427#217—101no—
428#215—102no—
429#215—102no—
430#214—102no—
431#214—102no—
432(C2×D3)⋊C4—101no—
433(C2×D3)⋊C4—101no—
434C4⋊Dic3—101no—
435C4⋊Dic3—101no—
436C4⋊Dic3C22×D511yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—101no—
439Dic3⋊C4—101no—
440Dic3⋊C4—101no—
441Dic3⋊C4—101no—
442C4×Dic3—51no—
443C4×Dic3—51no—
444C4×Dic3—51no—
445C2×C3⋊C8—51no—
446C2×C3⋊C8C22×D511yescharacteristic
447#204—102no—
448#204—102no—
449D3×C8—22no—
450D3×C8—102no—
451C23×C5—31no—
452C22×D5—21no—
453C22×D5—64no—
454C22×D5—61no—
455C22×D5—122no—
456C22×D5—122no—
457C5×Q8—21no—
458C5×Q8—21no—
459C5×Q8—61no—
460C5×Q8—61no—
461C5×Q8—122no—
462C2×C4×C5—21no—
463C2×C4×C5—21no—
464C2×C4×C5—31no—
465C2×C4×C5—32no—
466C2×C4×C5—32no—
467C2×C4×C5—61no—
468C2×C4×C5—61no—
469C2×C4×C5—122no—
470C2×C4×C5—122no—
471C2×C4×C5C23×D311yescharacteristic
472C2×Dic5—21no—
473C2×Dic5—31no—
474C2×Dic5—34no—
475C2×Dic5—31no—
476C2×Dic5—62no—
477C2×Dic5—61no—
478C2×Dic5—122no—
479C2×Dic5D3×D411yescharacteristic
480C2×Dic5D3×D411yescharacteristic
481D20—21no—
482D20—32no—
483D20—64no—
484D20—61no—
485D20D3×D412yes—
486C4×D5—42no—
487C4×D5—122no—
488C4×D5—122no—
489C4×D5—122no—
490Dic10—21no—
491Dic10—21no—
492Dic10—61no—
493Dic10—61no—
494Dic10—122no—
495C5×C8—21no—
496C5×C8—61no—
497#168—21no—
498#168—61no—
499C22×Q8—31no—
500C22×Q8—151no—
501C22×D4—151no—
502C23×C4—301no—
503C2×SD16—51no—
504C2×SD16—51no—
505C2×SD16—151no—
506C2×SD16—151no—
507C2×SD16—151no—
508C2×SD16—151no—
509C2×SD16—151no—
510C2×SD16—151no—
511C2×SD16—304no—
512C2×SD16—304no—
513C22×C8—31no—
514C22×C8—151no—
515C4⋊Q8—51no—
516C4⋊Q8—151no—
517C4⋊Q8—151no—
518C4⋊Q8—151no—
519C4⋊Q8—301no—
520C4⋊Q8—301no—
521C4×D4—51no—
522C4×D4—151no—
523C4×D4—151no—
524C4×D4—151no—
525C4×D4—301no—
526C4×D4—301no—
527C2×C4⋊C4—31no—
528C2×C4⋊C4—301no—
529C2×C4⋊C4—301no—
530C2×C22⋊C4—301no—
531C2×C42—151no—
532C4⋊C8—51no—
533C4⋊C8—151no—
534C4⋊C8—151no—
535C4⋊C8—151no—
536#103—31no—
537#103—31no—
538#103—31no—
539#103—51no—
540#103—151no—
541#103—151no—
542#103—151no—
543#103D3×D511yescharacteristic, complemented
544C2×C3×C5C2×#12111yescharacteristic
545C2×C3×C5C22×SD1611yescharacteristic
546C2×C3×C5C2×#13711yescharacteristic
547D15—42no—
548C3×D5—42no—
549C5×D3#46114yescomplemented
550C23×C3—101no—
551C22×D3—101no—
552C22×D3—104no—
553C22×D3—202no—
554C22×D3—202no—
555C22×D3D4×D511yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—101no—
559C3×Q8—101no—
560C3×D4—52no—
561C3×D4—101no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—51no—
565C2×C3×C4—51no—
566C2×C3×C4—101no—
567C2×C3×C4—202no—
568C2×C3×C4C23×D511yescharacteristic
569#67—104no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—51no—
573C2×Dic3—51no—
574C2×Dic3—101no—
575C2×Dic3—202no—
576C2×Dic3D4×D511yescharacteristic
577D12—52no—
578D12—101no—
579C4×D3—42no—
580C4×D3—42no—
581C4×D3—54no—
582C4×D3—102no—
583C4×D3—202no—
584C4×D3—202no—
585C4×D3—202no—
586C4×D3#70912yes—
587C4×D3D4×D512yes—
588Dic6—21no—
589Dic6—21no—
590Dic6—42no—
591Dic6—101no—
592Dic6—101no—
593Dic6—202no—
594C3×C8—21no—
595C3×C8—101no—
596C3⋊C8—21no—
597C3⋊C8—101no—
598C22×C5—32no—
599C22×C5—32no—
600C22×C5—32no—
601C22×C5C2×D3×D411yescharacteristic
602C2×D5—22no—
603C2×D5—41no—
604C2×D5—41no—
605C2×D5—62no—
606C2×D5—128no—
607C2×D5—121no—
608C2×D5—121no—
609C4×C5—32no—
610C4×C5—41no—
611C4×C5—41no—
612C4×C5—121no—
613C4×C5—121no—
614C4×C5C2×D3×D411yescharacteristic
615C4×C5D3×#4111yescharacteristic
616Dic5—21no—
617Dic5—32no—
618Dic5—41no—
619Dic5—61no—
620Dic5—121no—
621Dic5D3×SD1612yescomplemented
622C24—301no—
623C2×Q8—31no—
624C2×Q8—51no—
625C2×Q8—61no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—151no—
629C2×Q8—301no—
630C2×Q8—302no—
631C2×Q8—302no—
632C2×Q8C2×D3×D511yescharacteristic
633C2×D4—51no—
634C2×D4—154no—
635C2×D4—151no—
636C2×D4—302no—
637C2×D4—301no—
638C22×C4—31no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—101no—
642C22×C4—151no—
643C22×C4—151no—
644C22×C4—301no—
645C22×C4—301no—
646C22×C4—301no—
647C22×C4—301no—
648C22×C4—604no—
649SD16—102no—
650SD16—102no—
651SD16—302no—
652SD16—302no—
653SD16—302no—
654SD16—302no—
655SD16—302no—
656SD16—302no—
657C2×C8—31no—
658C2×C8—51no—
659C2×C8—62no—
660C2×C8—151no—
661C2×C8—302no—
662C2×C8C2×D3×D511yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—61no—
665C4⋊C4—101no—
666C4⋊C4—101no—
667C4⋊C4—301no—
668C4⋊C4—301no—
669C4⋊C4—301no—
670C4⋊C4—301no—
671C4⋊C4—301no—
672C4⋊C4—301no—
673C4⋊C4C2×D3×D511yescharacteristic
674C22⋊C4—101no—
675C22⋊C4—301no—
676C22⋊C4—301no—
677C22⋊C4—301no—
678C42—51no—
679C42—151no—
680C42—151no—
681C42—151no—
682C3×C5C2×#46111yescharacteristic, complemented, Hall
683C22×C3—102no—
684C22×C3—201no—
685C22×C3—201no—
686C22×C3C2×D4×D511yescharacteristic
687C2×D3—102no—
688C2×D3—201no—
689C2×D3—201no—
690C2×D3—208no—
691C2×D3#403012yes—
692C2×D3D5×SD1612yes—
693C2×D3#406412yes—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—52no—
697C3×C4—101no—
698C3×C4—201no—
699C3×C4C2×#70911yescharacteristic
700C3×C4C2×D4×D511yescharacteristic
701Dic3—41no—
702Dic3—41no—
703Dic3—52no—
704Dic3—101no—
705Dic3—201no—
706Dic3#403012yes—
707C2×C5—34no—
708C2×C5D3×#12111yescharacteristic
709C2×C5C2×D3×SD1611yescharacteristic
710C2×C5D3×#13711yescharacteristic
711D5—42no—
712D5—122no—
713C23—31no—
714C23—101no—
715C23—304no—
716C23—301no—
717C23—602no—
718C23—602no—
719Q8—21no—
720Q8—21no—
721Q8—61no—
722Q8—61no—
723Q8—101no—
724Q8—101no—
725Q8—122no—
726Q8—301no—
727Q8—301no—
728Q8—602no—
729D4—52no—
730D4—101no—
731D4—152no—
732D4—304no—
733D4—301no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—31no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—51no—
740C2×C4—51no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—101no—
744C2×C4—122no—
745C2×C4—122no—
746C2×C4—154no—
747C2×C4—151no—
748C2×C4—151no—
749C2×C4—202no—
750C2×C4—302no—
751C2×C4—301no—
752C2×C4—602no—
753C2×C4—602no—
754C2×C4—602no—
755C2×C4—602no—
756C2×C4C22×D3×D511yescharacteristic
757C8—21no—
758C8—61no—
759C8—101no—
760C8—301no—
761C2×C3—202no—
762C2×C3C2×#403011yescharacteristic
763C2×C3C2×D5×SD1611yescharacteristic
764C2×C3C2×#406411yescharacteristic
765D3—202no—
766D3#6510714yesdirect product factor
767C5D3×#46111yescharacteristic, complemented, Sylow
768C22—32no—
769C22—32no—
770C22—32no—
771C22—102no—
772C22—201no—
773C22—201no—
774C22—302no—
775C22—608no—
776C22—601no—
777C22—601no—
778C22D3×D4×D511yescharacteristic
779C4—32no—
780C4—41no—
781C4—41no—
782C4—52no—
783C4—101no—
784C4—121no—
785C4—121no—
786C4—152no—
787C4—201no—
788C4—301no—
789C4—601no—
790C4D3×#70911yescharacteristic
791C4D3×D4×D511yescharacteristic
792C3C2×#6510711yescharacteristic, complemented, Sylow
793C2—34no—
794C2—202no—
795C2—602no—
796C2D3×#403011yescharacteristic
797C2D3×D5×SD1611yescharacteristic
798C2D3×#406411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×D20C22
hypercenter#103D3×D5
hypocenterC3×C5C2×#461
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. D3×#4090C2semidirect
5. #11750919C2semidirect
6. C5×D3×#103C2semidirect
7. C3×#65107C2semidirect
8. #11749229C2semidirect
9. #11749222C2semidirect
10. #11747761C2semidirect
11. #11747749C2semidirect
12. D3×#3946C2semidirect
13. D3×#3942C2semidirect
14. #11747426C2semidirect
15. #11747414C2semidirect
21. #91833C22semidirect
27. C3×#4090C22semidirect
40. #91385C22semidirect
41. #91376C22semidirect
50. C3×C5×#103C22semidirect
51. #91098C22semidirect
52. #91094C22semidirect
53. C5×#835C22semidirect
54. C5×#816C22semidirect
55. C5×#810C22semidirect
56. C3×#3946C22semidirect
57. C3×#3942C22semidirect
58. #90983C22semidirect
59. #90982C22semidirect
60. #90975C22semidirect
61. #90970C22semidirect
77. #65107D3direct (N × H)
152. D3×#103D5semidirect
164. #4090C2×D3semidirect
189. C5×#103C2×D3semidirect
193. #3946C2×D3semidirect
197. #3942C2×D3semidirect
241. D3×Dic5SD16semidirect
282. C3×#103C2×D5semidirect
284. #835C2×D5semidirect
286. #816C2×D5semidirect
290. #810C2×D5semidirect
384. Dic15C2×SD16semidirect
387. C3×Dic5C2×SD16semidirect
543. #103D3×D5semidirect
549. C5×D3#461semidirect
621. Dic5D3×SD16semidirect
682. C3×C5C2×#461semidirect
766. D3#65107direct (N × H)
767. C5D3×#461semidirect
792. C3C2×#65107semidirect

Maximal subgroups

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

subgroupindex
D3×#40902
C2×D3×#6882
C2×D3×#6772
D3×#40392
#117509192
C5×D3×#1032
C3×#651072
#117492292
#117492222
#117477612
#117477492
D3×#39462
D3×#39422
#117474262
#117474142
C2×#651073
D3×#4615