Finite Group Databasebeta

← #14435507

Subgroups — #14435507

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×D3×Q8C211yesmaximal, characteristic, complemented
2#11752695C211yesmaximal, characteristic
3#11751131C211yesmaximal, characteristic, complemented
4C3×#65315C211yesmaximal, characteristic, complemented
5#11749333C211yesmaximal, characteristic, complemented
6#11749325C211yesmaximal, characteristic, complemented
7#11749302C211yesmaximal, characteristic, complemented
8#11749278C211yesmaximal, characteristic
9#11747393C211yesmaximal, characteristic, complemented
10#11747373C211yesmaximal, characteristic, complemented
11#11747320C211yesmaximal, characteristic
12#11747178C211yesmaximal, characteristic, complemented
13#11747093C211yesmaximal, characteristic, complemented
14#11747048C211yesmaximal, characteristic, complemented
15#11746878C211yesmaximal, characteristic, complemented
16#10614176—31nomaximal, Hall
17C2×C5×D3×Q8C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×Q8×Dic3C2211yescharacteristic
22C5×D3×C4⋊C4—21no—
23C5×D3×C4⋊C4C2211yescharacteristic
24C5×#887—21no—
25C5×#887C2211yescharacteristic
26C42×C5×D3—21no—
27C42×C5×D3C2211yescharacteristic
28C4×C5×Dic6—21no—
29C4×C5×Dic6C2211yescharacteristic
30C2×C3×#688C2211yescharacteristic
31C3×C4×D20C2211yescharacteristic
32#91456C2211yescharacteristic
33#91452—21no—
34C4×#1201—21no—
35#91381C2211yescharacteristic
36#91365C2211yescharacteristic
37#91364C2211yescharacteristic
38#91363—21no—
39#91357—21no—
40C2×#6663C2211yescharacteristic
41C2×#6655C2211yescharacteristic
42#91119C2211yescharacteristic
43#91094C2211yescharacteristic
44#91092C2211yescharacteristic
45#91087C2211yescharacteristic
46C3×#3967C2211yescharacteristic
47C3×#3941C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×#3935C2211yescharacteristic
50#90989C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90973C2211yescharacteristic
56#90972C2211yescharacteristic
57#90964C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic
60#79784—51nomaximal, Hall
61C2×C4×C5×Q8—31no—
62#65813—31no—
63#65517—31no—
64#65516—31no—
65#65319—31no—
66#65319—31no—
67#65317—31no—
68#65317—31no—
69#65315—31no—
70#65315D311yescharacteristic, complemented
71#65311—31no—
72#65311—31no—
73#65259—31no—
74#65257—31no—
75#65215—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C5×D3×Q8—22no—
79C5×D3×Q8—22no—
80C2×C4×C5×D3—21no—
81C2×C4×C5×D3—21no—
82C2×C4×C5×D3D411yescharacteristic
83C2×C4×C5×D3D411yescharacteristic
84C2×C4×C5×D3C2311yescharacteristic
85C2×C5×Dic6—21no—
86C2×C5×Dic6C2311yescharacteristic
87C2×C3×D20C2311yescharacteristic
88C2×C3×C4×D5—21no—
89C2×#1201—21no—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C42×C5—21no—
93C3×C42×C5C2311yescharacteristic
94#6718—22no—
95C4⋊Dic15C2311yescharacteristic
96#6712—21no—
97C4×Dic15—21no—
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C5×C4⋊Dic3—21no—
101C5×C4⋊Dic3C2311yescharacteristic
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C5×Dic3⋊C4—21no—
105C4×C5×Dic3—21no—
106C4×C5×Dic3—21no—
107C4×C5×Dic3—21no—
108C4×C5×Dic3D411yescharacteristic
109C4×C5×Dic3D411yescharacteristic
110C4×C5×Dic3C2311yescharacteristic
111C3×#688—22no—
112C3×#685—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116#6669—21no—
117#6668—21no—
118#6668—21no—
119(C2×D3)⋊Dic5—21no—
120#6665—21no—
121#6665—21no—
122#6665—21no—
123#6663—22no—
124#6655—22no—
125C4×D3×Q8D511yescharacteristic, complemented
126#5557—51no—
127C3×#440—51no—
128#5170—51no—
129#5166—51no—
130#5030—51no—
131#5018—51no—
132#4884—51no—
133#4877—51no—
134#4809—51no—
135#4799—51no—
136#4777—51no—
137#4767—51no—
138#4716—51no—
139#4705—51no—
140C22×C5×Q8—31no—
141C4×C5×Q8—31no—
142C4×C5×Q8—31no—
143C4×C5×Q8—31no—
144C4×C5×Q8—61no—
145C4×C5×Q8—61no—
146C4×C5×Q8C2×D311yescharacteristic
147C2×C5×C4⋊C4—31no—
148C2×C5×C4⋊C4—61no—
149C2×C42×C5—31no—
150C2×C42×C5—61no—
151C2×#689—31no—
152C2×#689—31no—
153C2×#688—31no—
154C2×#688C2×D311yescharacteristic
155#4076—31no—
156#4075—61no—
157C4×C22⋊D5—61no—
158#4070—31no—
159#4022—61no—
160#4021—31no—
161C4×D20C2×D311yescharacteristic
162#4018—61no—
163#4016—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967—31no—
167#3967—31no—
168#3967C2×D311yescharacteristic
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3941—31no—
174#3941C2×D311yescharacteristic
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939C2×D311yescharacteristic
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3935—31no—
182#3935C2×D311yescharacteristic
183#3117—151noSylow
184C22×C5×D3C2×D411yescharacteristic
185C22×C3×D5—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8#4112yes—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195Dic30—21no—
196Dic30—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C4×C5×D3—24no—
203C4×C5×D3—22no—
204C4×C5×D3—21no—
205C4×C5×D3—21no—
206C4×C5×D3—41no—
207C4×C5×D3—42no—
208C5×Dic6—24no—
209C5×Dic6—21no—
210C5×Dic6#4112yes—
211C2×C3×Dic5—21no—
212C3×D20—21no—
213C3×D20—21no—
214C3×C4×D5—42no—
215#1201—42no—
216C3⋊#168—21no—
217C3⋊#168—21no—
218C3×#168—21no—
219C3×#168—21no—
220C2×D3×Q8C2×D511yescharacteristic
221C2×C3×SD16—51no—
222C3×C4×Q8C2×D511yescharacteristic
223C3×C4×D4—51no—
224Q8×Dic3C2×D511yescharacteristic
225C2×#216—51no—
226#938—51no—
227#936—51no—
228C2×#214—51no—
229C4×#67—101no—
230#926—101no—
231C2×Dic12—51no—
232#897—51no—
233D3×C4⋊C4—21no—
234D3×C4⋊C4C2×D511yescharacteristic
235#890—51no—
236#887—21no—
237#887C2×D511yescharacteristic
238#883—101no—
239#879—101no—
240C42×D3—21no—
241C42×D3C2×D511yescharacteristic
242C4×Dic6—21no—
243C4×Dic6—51no—
244C4×Dic6C2×D511yescharacteristic
245C3×#107—51no—
246C3×#103—51no—
247C3×#102—51no—
248C3×#97—51no—
249#835—51no—
250#832—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8—51no—
253#817—51no—
254#816—51no—
255#816—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258#810—51no—
259#810—51no—
260#808—51no—
261#807—51no—
262#803—51no—
263C2×C5×Q8—31no—
264C2×C5×Q8—61no—
265C2×C5×Q8—62no—
266C2×C5×Q8—62no—
267C2×C5×Q8C22×D311yescharacteristic
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×C4×C5—31no—
271C22×C4×C5—61no—
272C22×C4×C5—61no—
273C2×C22⋊D5—61no—
274C2×D20C22×D311yescharacteristic
275C2×C4×D5—21no—
276C2×Dic10—31no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—31no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4C22×D311yescharacteristic
284C42×C5—21no—
285C42×C5—31no—
286C42×C5—31no—
287C42×C5—31no—
288C42×C5—61no—
289C42×C5—61no—
290C42×C5—61no—
291C42×C5C22×D311yescharacteristic
292C22⋊Dic5—61no—
293#689—62no—
294#689—62no—
295#688—22no—
296#688—62no—
297#685—21no—
298#685—61no—
299#685—61no—
300#685—61no—
301C4⋊Dic5—31no—
302C4⋊Dic5C22×D311yescharacteristic
303#683—61no—
304#683—61no—
305#683—61no—
306#683—61no—
307C4×Dic5—61no—
308C2×#168—31no—
309C2×#168—31no—
310C2×#168C22×D311yescharacteristic
311C2×#168C22×D311yescharacteristic
312#529—151no—
313C2×C4×Q8—31no—
314#484—151no—
315#481—151no—
316#479—151no—
317#479—151no—
318#464—151no—
319#464—151no—
320#451—151no—
321#448—151no—
322#441—151no—
323#441—151no—
324#440—51no—
325#440—151no—
326#432—151no—
327C22×C3×C5C22×D411yescharacteristic
328C2×C5×D3—21no—
329C2×C5×D3—21no—
330C2×C5×D3#13712yes—
331C2×C3×D5—41no—
332C2×C3×D5—41no—
333C2×C3×D5—41no—
334C3×C4×C5—22no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5C2×#4111yescharacteristic
339C3×C4×C5C2×#4111yescharacteristic
340Dic15—41no—
341Dic15—41no—
342C3×Dic5—41no—
343C5×Dic3—21no—
344C5×Dic3—22no—
345C5×Dic3—21no—
346C5×Dic3—21no—
347C5×Dic3—41no—
348C2×C3×Q8C22×D511yescharacteristic
349C2×C3×D4—51no—
350C22×C3×C4—101no—
351C2×#67—101no—
352D3×Q8—22no—
353D3×Q8—22no—
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3C22⋊D511yescharacteristic
357C2×C4×D3C22⋊D511yescharacteristic
358C2×C4×D3C22×D511yescharacteristic
359C2×Dic6—21no—
360C2×Dic6—51no—
361C2×Dic6C22×D511yescharacteristic
362C3×SD16—102no—
363C2×C3×C8—51no—
364C2×C3×C8—51no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—51no—
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C22⋊C4—101no—
369C3×C42—21no—
370C3×C42C22×D511yescharacteristic
371#217—101no—
372#217—101no—
373#217—101no—
374#216—102no—
375#214—102no—
376(C2×D3)⋊C4—101no—
377C4⋊Dic3—21no—
378C4⋊Dic3—51no—
379C4⋊Dic3—101no—
380C4⋊Dic3—101no—
381C4⋊Dic3C22×D511yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—101no—
391C4×Dic3C22⋊D511yescharacteristic
392C4×Dic3C22⋊D511yescharacteristic
393C4×Dic3C22×D511yescharacteristic
394C2×C3⋊C8—51no—
395C2×C3⋊C8—51no—
396Dic12—102no—
397C23×C5—31no—
398C22×D5—21no—
399C5×Q8—21no—
400C5×Q8—32no—
401C5×Q8—64no—
402C5×Q8—61no—
403C5×Q8#23512yes—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—31no—
407C2×C4×C5—31no—
408C2×C4×C5—31no—
409C2×C4×C5—62no—
410C2×C4×C5—64no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—121no—
416C2×C4×C5—122no—
417C2×C4×C5D3×D411yescharacteristic
418C2×C4×C5D3×D411yescharacteristic
419C2×C4×C5C23×D311yescharacteristic
420C22⋊D5—122no—
421C2×Dic5—21no—
422C2×Dic5—61no—
423C2×Dic5—61no—
424D20—21no—
425D20—21no—
426C4×D5—42no—
427Dic10—61no—
428Dic10—61no—
429#168—21no—
430#168—21no—
431#168—61no—
432#168—61no—
433C22×Q8—31no—
434C2×Q16—151no—
435C2×Q16—151no—
436C2×SD16—51no—
437C2×SD16—151no—
438#126—301no—
439#125—151no—
440#124—151no—
441#123—301no—
442C22⋊Q8—151no—
443#121—151no—
444C4×Q8—31no—
445C4×Q8—31no—
446C4×Q8—31no—
447C4×Q8—61no—
448C4×Q8—61no—
449C4×Q8—151no—
450C4×Q8D3×D511yescharacteristic
451C4×D4—51no—
452C4×D4—301no—
453#117—301no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—61no—
456C2×C42—31no—
457C2×C42—61no—
458#107—51no—
459#107—151no—
460#106—151no—
461#106—151no—
462C4⋊C8—151no—
463C4⋊C8—151no—
464#103—51no—
465#103—151no—
466#103—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#102—51no—
471#102—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474#97—51no—
475#97—151no—
476C2×C3×C5#52511yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C2×C3×C5#57511yescharacteristic
479C3×D5—81no—
480C5×D3—22no—
481C23×C3—101no—
482C22×D3C2×C22⋊D511yescharacteristic
483C3×Q8—21no—
484C3×Q8#70912yes—
485C3×D4—101no—
486C3×D4—101no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—101no—
490C2×C3×C4—202no—
491C2×C3×C4C2×C22⋊D511yescharacteristic
492C2×C3×C4C2×C22⋊D511yescharacteristic
493C2×C3×C4C23×D511yescharacteristic
494#67—202no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3C2×C22⋊D511yescharacteristic
500C2×Dic3C2×C22⋊D511yescharacteristic
501C2×Dic3C2×C22⋊D511yescharacteristic
502C4×D3—24no—
503C4×D3—22no—
504C4×D3—21no—
505C4×D3—21no—
506C4×D3—41no—
507C4×D3—42no—
508Dic6—24no—
509Dic6—21no—
510Dic6—101no—
511Dic6—101no—
512Dic6#70912yes—
513C3×C8—101no—
514C3×C8—101no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5—32no—
518C22×C5—61no—
519C22×C5—61no—
520C22×C5C2×D3×D411yescharacteristic
521C2×D5—41no—
522C2×D5—41no—
523C2×D5—41no—
524C4×C5—21no—
525C4×C5—21no—
526C4×C5—22no—
527C4×C5—41no—
528C4×C5—61no—
529C4×C5—61no—
530C4×C5—61no—
531C4×C5—62no—
532C4×C5—121no—
533C4×C5C2×#23511yescharacteristic
534C4×C5D3×#4111yescharacteristic
535Dic5—41no—
536Dic5—121no—
537Dic5—121no—
538C2×Q8—31no—
539C2×Q8—61no—
540C2×Q8—62no—
541C2×Q8—62no—
542C2×Q8—151no—
543C2×Q8C2×D3×D511yescharacteristic
544C2×D4—51no—
545C2×D4—301no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—101no—
552Q16—302no—
553Q16—302no—
554SD16—102no—
555SD16—302no—
556C2×C8—51no—
557C2×C8—51no—
558C2×C8—151no—
559C2×C8—151no—
560C4⋊C4—21no—
561C4⋊C4—31no—
562C4⋊C4—51no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—151no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4C2×D3×D511yescharacteristic
573C22⋊C4—101no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C22⋊C4—301no—
577C22⋊C4—301no—
578C42—21no—
579C42—31no—
580C42—31no—
581C42—31no—
582C42—61no—
583C42—61no—
584C42—61no—
585C42—301no—
586C42C2×D3×D511yescharacteristic
587C3×C5#311711yescharacteristic, complemented, Hall
588C22×C3—201no—
589C22×C3—201no—
590C22×C3—201no—
591C22×C3C22×C22⋊D511yescharacteristic
592C2×D3—21no—
593C2×D3—21no—
594C2×D3#408812yes—
595C3×C4—22no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—41no—
599C3×C4—201no—
600C3×C4C2×#70911yescharacteristic
601C3×C4C2×#70911yescharacteristic
602Dic3—21no—
603Dic3—22no—
604Dic3—21no—
605Dic3—21no—
606Dic3—41no—
607Dic3—201no—
608Dic3—201no—
609C2×C5—62no—
610C2×C5#554711yescharacteristic
611C2×C5#577311yescharacteristic
612C2×C5D3×#13711yescharacteristic
613D5—81no—
614C23—31no—
615C23—101no—
616Q8—21no—
617Q8—32no—
618Q8—64no—
619Q8—61no—
620Q8—301no—
621Q8—301no—
622Q8#677112yes—
623D4—101no—
624D4—101no—
625D4—602no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—62no—
632C2×C4—64no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—101no—
638C2×C4—121no—
639C2×C4—122no—
640C2×C4—202no—
641C2×C4—301no—
642C2×C4—301no—
643C2×C4D3×C22⋊D511yescharacteristic
644C2×C4D3×C22⋊D511yescharacteristic
645C2×C4C22×D3×D511yescharacteristic
646C8—101no—
647C8—101no—
648C8—301no—
649C8—301no—
650C2×C3—401no—
651C2×C3#6612511yescharacteristic
652C2×C3C2×#408811yescharacteristic
653C2×C3#6615611yescharacteristic
654D3—22no—
655C5#7978411yescharacteristic, complemented, Sylow
656C22—32no—
657C22—61no—
658C22—61no—
659C22—201no—
660C22—201no—
661C22—201no—
662C22C2×D3×C22⋊D511yescharacteristic
663C4—22no—
664C4—21no—
665C4—21no—
666C4—41no—
667C4—61no—
668C4—62no—
669C4—61no—
670C4—61no—
671C4—121no—
672C4—201no—
673C4—601no—
674C4—601no—
675C4C2×#677111yescharacteristic
676C4D3×#70911yescharacteristic
677C3#1061417611yescharacteristic, complemented, Sylow
678C2—62no—
679C2—401no—
680C2#1175453811yescharacteristic
681C2D3×#408811yescharacteristic
682C2#1175534511yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#91456C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×C5×D3×Q8C2semidirect
3. #11751131C2semidirect
4. C3×#65315C2semidirect
5. #11749333C2semidirect
6. #11749325C2semidirect
7. #11749302C2semidirect
9. #11747393C2semidirect
10. #11747373C2semidirect
12. #11747178C2semidirect
13. #11747093C2semidirect
14. #11747048C2semidirect
15. #11746878C2semidirect
70. #65315D3semidirect
125. C4×D3×Q8D5semidirect
587. C3×C5#3117semidirect
655. C5#79784semidirect
677. C3#10614176semidirect

Maximal subgroups

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

subgroupindex
C4×C5×D3×Q82
#117526952
#117511312
C3×#653152
#117493332
#117493252
#117493022
#117492782
#117473932
#117473732
#117473202
#117471782
#117470932
#117470482
#117468782
#106141763
#797845