Finite Group Databasebeta

← #14430142

Subgroups — #14430142

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×#125C211yesmaximal, characteristic
2C4×D15⋊Q8C211yesmaximal, characteristic
3C5×#5063C211yesmaximal, characteristic, complemented
4C3×#65352C211yesmaximal, characteristic, complemented
5#11747490C211yesmaximal, characteristic
6#11747490C211yesmaximal, characteristic
7#11747441C211yesmaximal, characteristic
8#11747438C211yesmaximal, characteristic
9#11747302C211yesmaximal, characteristic, complemented
10#11747301C211yesmaximal, characteristic, complemented
11#11747299C211yesmaximal, characteristic, complemented
12#11747298C211yesmaximal, characteristic, complemented
13#11747000C211yesmaximal, characteristic
14#11746965C211yesmaximal, characteristic, complemented
15#11746944C211yesmaximal, characteristic, complemented
16D5×#479—31nomaximal, Hall
17C2×D15⋊Q8C2211yescharacteristic
18C3×C5×#125C2211yescharacteristic
19C4⋊C4×D15—21no—
20C4⋊C4×D15—21no—
21C4⋊C4×D15C2211yescharacteristic
22C4⋊C4×D15C2211yescharacteristic
23#91779C2211yescharacteristic
24#91779C2211yescharacteristic
25#91778—21no—
26#91778—21no—
27C42×D15C2211yescharacteristic
28#91759C2211yescharacteristic
29C4×C5×Dic6C2211yescharacteristic
30C3×C4×Dic10C2211yescharacteristic
31C4×#1204—21no—
32#91437C2211yescharacteristic
33#91404—21no—
34C4×#1200—21no—
35#91344C2211yescharacteristic
36#91331C2211yescharacteristic
37#91325—21no—
38C2×#6648C2211yescharacteristic
39C2×#6648C2211yescharacteristic
40C5×#810C2211yescharacteristic
41C5×#810C2211yescharacteristic
42C5×#808C2211yescharacteristic
43C5×#807C2211yescharacteristic
44C5×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#3942C2211yescharacteristic
46C3×#3942C2211yescharacteristic
47C3×#3940C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×C4⋊#168C2211yescharacteristic
50#90990C2211yescharacteristic
51#90988C2211yescharacteristic
52#90987C2211yescharacteristic
53#90985C2211yescharacteristic
54#90983C2211yescharacteristic
55#90983C2211yescharacteristic
56#90973C2211yescharacteristic
57#90973C2211yescharacteristic
58#90971C2211yescharacteristic
59#90971C2211yescharacteristic
60D3×#479—51nomaximal, Hall
61D5×#125—31no—
62C4×Q8×D5—31no—
63C5×#479—31no—
64#65352D311yescharacteristic, complemented
65#65311—31no—
66D5×#107—31no—
67#65166—31no—
68D5×#106—31no—
69#65146—31no—
70D5×C4⋊C8—31no—
71#65118—31no—
72D5×#103—31no—
73D5×#103—31no—
74#65088—31no—
75#65085—31no—
76C2×C4×D15—21no—
77C2×C4×D15—21no—
78C2×C4×D15D411yescharacteristic
79C2×C4×D15D411yescharacteristic
80C2×C4×D15C2311yescharacteristic
81C2×C5×Dic6C2311yescharacteristic
82C2×C3×Dic10C2311yescharacteristic
83C2×#1204—21no—
84C2×#1200—21no—
85C2×#1200—21no—
86D15⋊Q8—22no—
87D15⋊Q8Q814yes—
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C42×C5C2311yescharacteristic
93C4⋊Dic15—21no—
94C4⋊Dic15—21no—
95C4⋊Dic15C2311yescharacteristic
96C4⋊Dic15C2311yescharacteristic
97#6712—21no—
98#6712—21no—
99#6712—21no—
100#6712—21no—
101#6712—21no—
102#6712—21no—
103C4×Dic15D411yescharacteristic
104C4×Dic15D411yescharacteristic
105C4×Dic15C2311yescharacteristic
106C5×C4⋊Dic3C2311yescharacteristic
107C5×Dic3⋊C4—21no—
108C4×C5×Dic3—21no—
109C2×C5×C3⋊C8C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×C4×Dic5—21no—
114C2×C3×#168C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119Dic3×Dic5—21no—
120Dic3×Dic5—21no—
121#6648—22no—
122#6648—22no—
123D3×#125—51no—
124C4×D3×Q8—51no—
125C3×#479—51no—
126#5063D511yescharacteristic, complemented
127#5022—51no—
128D3×#107—51no—
129#4877—51no—
130D3×#106—51no—
131#4857—51no—
132D3×C4⋊C8—51no—
133#4829—51no—
134D3×#103—51no—
135D3×#103—51no—
136#4799—51no—
137#4796—51no—
138C2×Q8×D5—31no—
139C5×#125C2×D311yescharacteristic
140C4×C5×Q8—31no—
141Q8×Dic5—31no—
142C2×C8×D5—31no—
143C2×C8×D5—31no—
144D5×C4⋊C4—31no—
145D5×C4⋊C4—31no—
146D5×C4⋊C4—31no—
147D5×C4⋊C4—61no—
148D5×C4⋊C4—61no—
149D5×C4⋊C4—61no—
150#4036—31no—
151#4036—31no—
152#4035—61no—
153#4035—61no—
154#4033—31no—
155#4033—61no—
156C42×D5—31no—
157C42×D5—61no—
158#4016—31no—
159C4×Dic10—61no—
160C4×Dic10C2×D311yescharacteristic
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3967—31no—
168#3950—31no—
169#3949—31no—
170#3948—31no—
171#3948—31no—
172#3946—31no—
173#3946—31no—
174#3942C2×D311yescharacteristic
175#3942C2×D311yescharacteristic
176#3940—31no—
177#3940C2×D311yescharacteristic
178#3939—31no—
179#3939C2×D311yescharacteristic
180C4⋊#168C2×D311yescharacteristic
181C2×#479—151noSylow
182C22×D15C2×D411yescharacteristic
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15C2×D411yescharacteristic
191C2×Dic15C2×D411yescharacteristic
192C2×Dic15C2×D411yescharacteristic
193C4×D15—22no—
194C4×D15—22no—
195C4×D15—42no—
196C4×D15—42no—
197C4×D15C2×Q812yes—
198C4×D15#4112yes—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C5×Dic6—21no—
202C5×Dic6C2×Q812yes—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C3×Dic10—21no—
206C3×Dic10C2×Q812yes—
207#1204—24no—
208#1200—24no—
209#1200—42no—
210C3×#168—21no—
211C3×#168—21no—
212C5×C3⋊C8—21no—
213C5×C3⋊C8—21no—
214C2×D3×Q8—51no—
215C3×#125C2×D511yescharacteristic
216C3×C4×Q8—51no—
217Q8×Dic3—51no—
218C2×D3×C8—51no—
219C2×D3×C8—51no—
220D3×C4⋊C4—51no—
221D3×C4⋊C4—51no—
222D3×C4⋊C4—51no—
223D3×C4⋊C4—101no—
224D3×C4⋊C4—101no—
225D3×C4⋊C4—101no—
226#890—51no—
227#890—51no—
228#889—101no—
229#889—101no—
230#887—51no—
231#887—101no—
232C42×D3—51no—
233C42×D3—101no—
234#870—51no—
235C4×Dic6—101no—
236C4×Dic6C2×D511yescharacteristic
237C3×#107—51no—
238C3×#106—51no—
239C3×C4⋊C8—51no—
240C3×#103—51no—
241C3×#103—51no—
242#835—51no—
243#835—51no—
244#818—51no—
245#817—51no—
246#816—51no—
247#816—51no—
248Dic3⋊C8—51no—
249Dic3⋊C8—51no—
250#810C2×D511yescharacteristic
251#810C2×D511yescharacteristic
252#808—51no—
253#808C2×D511yescharacteristic
254#807—51no—
255#807C2×D511yescharacteristic
256C4⋊(C3⋊C8)C2×D511yescharacteristic
257C2×C5×Q8—31no—
258Q8×D5—34no—
259Q8×D5—62no—
260C2×C4×D5—31no—
261C2×C4×D5—31no—
262C2×C4×D5—31no—
263C2×C4×D5—61no—
264C2×C4×D5—61no—
265C2×C4×D5—61no—
266C2×C4×D5—61no—
267C2×Dic10—61no—
268C2×Dic10C22×D311yescharacteristic
269C2×C5×C8—31no—
270C2×C5×C8—31no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—61no—
275C5×C4⋊C4C22×D311yescharacteristic
276C5×C4⋊C4C22×D311yescharacteristic
277C42×C5—61no—
278C42×C5C22×D311yescharacteristic
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283C4⋊Dic5—61no—
284C4⋊Dic5C22×D311yescharacteristic
285#683—21no—
286#683—61no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293#683—61no—
294C4×Dic5—21no—
295C4×Dic5—31no—
296C4×Dic5—31no—
297C4×Dic5—31no—
298C4×Dic5—61no—
299C4×Dic5—61no—
300C2×#168C22×D311yescharacteristic
301C2×#168C22×D311yescharacteristic
302C8×D5—62no—
303C8×D5—62no—
304C2×#125—151no—
305C2×C4×Q8—151no—
306#479—31no—
307#479—51no—
308#479—151no—
309#479—151no—
310#479—151no—
311#479—151no—
312#479—151no—
313#479—151no—
314C2×#107—151no—
315C2×#106—151no—
316C2×C4⋊C8—151no—
317C2×#103—151no—
318C2×#103—151no—
319C22×C3×C5C22×D411yescharacteristic
320C2×D15C22⋊Q812yes—
321C2×D15#13512yes—
322C2×D15#13712yes—
323C3×C4×C5—21no—
324C3×C4×C5—21no—
325C3×C4×C5—41no—
326C3×C4×C5—41no—
327C3×C4×C5C22×Q811yescharacteristic
328C3×C4×C5C2×#4111yescharacteristic
329Dic15—21no—
330Dic15—21no—
331Dic15—41no—
332Dic15—41no—
333Dic15C22⋊Q812yes—
334C3×Dic5—22no—
335C3×Dic5—41no—
336C5×Dic3—22no—
337C5×Dic3—41no—
338C2×C3×Q8—51no—
339D3×Q8—54no—
340D3×Q8—102no—
341C2×C4×D3—51no—
342C2×C4×D3—51no—
343C2×C4×D3—51no—
344C2×C4×D3—101no—
345C2×C4×D3—101no—
346C2×C4×D3—101no—
347C2×C4×D3—101no—
348C2×Dic6—101no—
349C2×Dic6C22×D511yescharacteristic
350C2×C3×C8—51no—
351C2×C3×C8—51no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—51no—
355C3×C4⋊C4—101no—
356C3×C4⋊C4C22×D511yescharacteristic
357C3×C4⋊C4C22×D511yescharacteristic
358C3×C42—101no—
359C3×C42C22×D511yescharacteristic
360C4⋊Dic3—51no—
361C4⋊Dic3—51no—
362C4⋊Dic3—101no—
363C4⋊Dic3—101no—
364C4⋊Dic3—101no—
365C4⋊Dic3C22×D511yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375C4×Dic3—21no—
376C4×Dic3—51no—
377C4×Dic3—51no—
378C4×Dic3—51no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C2×C3⋊C8C22×D511yescharacteristic
382C2×C3⋊C8C22×D511yescharacteristic
383D3×C8—102no—
384D3×C8—102no—
385C22×D5—31no—
386C5×Q8—32no—
387C5×Q8—61no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—61no—
391C2×C4×C5—61no—
392C2×C4×C5D3×D411yescharacteristic
393C2×C4×C5D3×D411yescharacteristic
394C2×C4×C5C23×D311yescharacteristic
395C2×Dic5—21no—
396C2×Dic5—21no—
397C2×Dic5—31no—
398C2×Dic5—31no—
399C2×Dic5—31no—
400C2×Dic5—61no—
401C2×Dic5—61no—
402C4×D5—32no—
403C4×D5—32no—
404C4×D5—64no—
405C4×D5—62no—
406C4×D5—62no—
407C4×D5—122no—
408C4×D5—122no—
409C4×D5—122no—
410Dic10—21no—
411Dic10—64no—
412Dic10D3×Q812yes—
413C5×C8—61no—
414C5×C8—61no—
415#168—21no—
416#168—21no—
417C22×Q8—151no—
418C22×C8—151no—
419C22×C8—151no—
420#125—151no—
421#125—151no—
422#125—151no—
423#125—301no—
424#125—301no—
425#125D3×D511yescharacteristic
426C4×Q8—31no—
427C4×Q8—51no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—301no—
431C4×Q8—301no—
432C2×C4⋊C4—151no—
433C2×C4⋊C4—151no—
434C2×C4⋊C4—151no—
435C2×C4⋊C4—301no—
436C2×C4⋊C4—301no—
437C2×C4⋊C4—301no—
438C2×C42—151no—
439C2×C42—301no—
440#107—31no—
441#107—51no—
442#107—151no—
443#107—151no—
444#106—31no—
445#106—51no—
446#106—151no—
447#106—151no—
448C4⋊C8—31no—
449C4⋊C8—51no—
450C4⋊C8—151no—
451C4⋊C8—151no—
452#103—31no—
453#103—31no—
454#103—51no—
455#103—51no—
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460C2×C3×C5C2×C22⋊Q811yescharacteristic
461C2×C3×C5C2×#13511yescharacteristic
462C2×C3×C5C2×#13711yescharacteristic
463D15#47914yescomplemented
464C22×D3—51no—
465C3×Q8—52no—
466C3×Q8—101no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—101no—
470C2×C3×C4—101no—
471C2×C3×C4D4×D511yescharacteristic
472C2×C3×C4D4×D511yescharacteristic
473C2×C3×C4C23×D511yescharacteristic
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—51no—
477C2×Dic3—51no—
478C2×Dic3—51no—
479C2×Dic3—101no—
480C2×Dic3—101no—
481C4×D3—52no—
482C4×D3—52no—
483C4×D3—104no—
484C4×D3—102no—
485C4×D3—102no—
486C4×D3—202no—
487C4×D3—202no—
488C4×D3—202no—
489Dic6—21no—
490Dic6—104no—
491Dic6Q8×D512yes—
492C3×C8—101no—
493C3×C8—101no—
494C3⋊C8—21no—
495C3⋊C8—21no—
496C22×C5C2×D3×D411yescharacteristic
497C2×D5—32no—
498C2×D5—32no—
499C2×D5—32no—
500C4×C5—21no—
501C4×C5—21no—
502C4×C5—41no—
503C4×C5—41no—
504C4×C5—62no—
505C4×C5—121no—
506C4×C5C2×D3×Q811yescharacteristic
507C4×C5D3×#4111yescharacteristic
508Dic5—22no—
509Dic5—32no—
510Dic5—41no—
511Dic5—61no—
512Dic5—61no—
513Dic5—121no—
514Dic5—121no—
515C2×Q8—31no—
516C2×Q8—51no—
517C2×Q8—154no—
518C2×Q8—301no—
519C2×Q8—302no—
520C22×C4—151no—
521C22×C4—151no—
522C22×C4—151no—
523C22×C4—301no—
524C22×C4—301no—
525C22×C4—301no—
526C22×C4—301no—
527C2×C8—31no—
528C2×C8—31no—
529C2×C8—51no—
530C2×C8—51no—
531C2×C8—302no—
532C2×C8—302no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—31no—
536C4⋊C4—51no—
537C4⋊C4—61no—
538C4⋊C4—101no—
539C4⋊C4—151no—
540C4⋊C4—151no—
541C4⋊C4—301no—
542C4⋊C4—301no—
543C4⋊C4—301no—
544C4⋊C4—301no—
545C4⋊C4—301no—
546C4⋊C4—301no—
547C4⋊C4—301no—
548C4⋊C4—301no—
549C4⋊C4—301no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4C2×D3×D511yescharacteristic
553C4⋊C4C2×D3×D511yescharacteristic
554C42—61no—
555C42—101no—
556C42—151no—
557C42—151no—
558C42—151no—
559C42—301no—
560C42—301no—
561C42C2×D3×D511yescharacteristic
562C3×C5C2×#47911yescharacteristic, complemented, Hall
563C22×C3C2×D4×D511yescharacteristic
564C2×D3—52no—
565C2×D3—52no—
566C2×D3—52no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—102no—
572C3×C4—201no—
573C3×C4C2×Q8×D511yescharacteristic
574C3×C4D5×#4111yescharacteristic
575Dic3—22no—
576Dic3—41no—
577Dic3—52no—
578Dic3—101no—
579Dic3—101no—
580Dic3—201no—
581Dic3—201no—
582C2×C5D3×C22⋊Q811yescharacteristic
583C2×C5D3×#13511yescharacteristic
584C2×C5D3×#13711yescharacteristic
585D5—34no—
586C23—151no—
587Q8—32no—
588Q8—52no—
589Q8—61no—
590Q8—101no—
591Q8—304no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—61no—
595C2×C4—61no—
596C2×C4—101no—
597C2×C4—101no—
598C2×C4—151no—
599C2×C4—152no—
600C2×C4—152no—
601C2×C4—151no—
602C2×C4—151no—
603C2×C4—302no—
604C2×C4—302no—
605C2×C4—304no—
606C2×C4—301no—
607C2×C4—301no—
608C2×C4—602no—
609C2×C4—602no—
610C2×C4—602no—
611C2×C4#679011yescharacteristic
612C2×C4#679011yescharacteristic
613C2×C4C22×D3×D511yescharacteristic
614C8—61no—
615C8—61no—
616C8—101no—
617C8—101no—
618C2×C3D5×C22⋊Q811yescharacteristic
619C2×C3D5×#13511yescharacteristic
620C2×C3D5×#13711yescharacteristic
621D3—54no—
622C5D3×#47911yescharacteristic, complemented, Sylow
623C22—152no—
624C22—152no—
625C22—152no—
626C22C2×#679011yescharacteristic
627C4—21no—
628C4—21no—
629C4—41no—
630C4—41no—
631C4—62no—
632C4—102no—
633C4—121no—
634C4—152no—
635C4—201no—
636C4—301no—
637C4—301no—
638C4—601no—
639C4—601no—
640C4D3×Q8×D511yescharacteristic
641C4#9203411yescharacteristic
642C3D5×#47911yescharacteristic, complemented, Sylow
643C2—154no—
644C2#1175528111yescharacteristic
645C2#1175532811yescharacteristic
646C2#1175534211yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenter#125D3×D5
hypocenterC3×C5C2×#479
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. C5×#5063C2semidirect
4. C3×#65352C2semidirect
9. #11747302C2semidirect
10. #11747301C2semidirect
11. #11747299C2semidirect
12. #11747298C2semidirect
14. #11746965C2semidirect
15. #11746944C2semidirect
64. #65352D3semidirect
126. #5063D5semidirect
463. D15#479semidirect
562. C3×C5C2×#479semidirect
622. C5D3×#479semidirect
642. C3D5×#479semidirect

Maximal subgroups

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

subgroupindex
D15×#1252
C4×D15⋊Q82
C5×#50632
C3×#653522
#117474902
#117474412
#117474382
#117473022
#117473012
#117472992
#117472982
#117470002
#117469652
#117469442
D5×#4793
D3×#4795