Finite Group Databasebeta

← #14484693

Subgroups — #14484693

Order 1920.

2136 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756328C211yesmaximal, characteristic, complemented
2C5×#5569C211yesmaximal, characteristic, complemented
3C3×C4×#713C211yesmaximal, characteristic
4#11755267C211yesmaximal, characteristic, complemented
5Q8×#1204C211yesmaximal, characteristic, complemented
6Dic3×#713C211yesmaximal, characteristic
7Dic3×#713C211yesmaximal, characteristic
8#11753611C213yesmaximal, complemented
9#11753568C213yesmaximal, complemented
10#11753527C213yesmaximal, complemented
11#11753429C213yesmaximal, complemented
12#11752618C213yesmaximal, complemented
13#11752597C213yesmaximal, complemented
14C4×D5×Dic6C213yesmaximal, complemented
15#11752498C213yesmaximal, complemented
16#10618916—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×D5×Dic6C2213yes—
19C3×C4×C5×Q8C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic
21Q8×Dic15C2211yescharacteristic
22#91779C2213yes—
23#91777C2213yes—
24#91759C2213yes—
25C4×Dic30C2213yes—
26C5×Q8×Dic3C2211yescharacteristic
27C5×Q8×Dic3C2211yescharacteristic
28C5×#890C2213yes—
29C5×#888C2213yes—
30C5×#870C2213yes—
31C4×C5×Dic6C2213yes—
32C3×Q8×Dic5C2211yescharacteristic
33C3×#4039C2213yes—
34C3×#4038C2213yes—
35C3×C4×D20C2213yes—
36C3×C42×D5C2213yes—
37#91470C2213yes—
38#91469C2213yes—
39#91468C2213yes—
40#91468C2213yes—
41C4×#1204C2213yes—
42C4×#1204C2213yes—
43#91434C2213yes—
44#91434C2213yes—
45#91431C2216yes—
46#91430C2216yes—
47Dic3×D20C2213yes—
48Dic3×D20C2213yes—
49#91422C2216yes—
50#91421C2216yes—
51D5×C4⋊Dic3C2213yes—
52D5×Dic3⋊C4C2213yes—
53D5×Dic3⋊C4C2213yes—
54C4×D5×Dic3C2213yes—
55C4×D5×Dic3C2213yes—
56#91384C2213yes—
57#91381C2213yes—
58#91358C2213yes—
59#91358C2213yes—
60#91349C2216yes—
61#91349C2216yes—
62#91333C2213yes—
63Dic5×Dic6C2213yes—
64#91323C2213yes—
65#91323C2216yes—
66#91323C2211yescharacteristic
67#41×Dic6—51nomaximal, Hall
68C5×#557—31no—
69#66062—33no—
70#66061—33no—
71#66024—33no—
72#66024—33no—
73#66022—33no—
74#66022—33no—
75#65913—33no—
76C4×#713—31no—
77C4×#713—31no—
78C4×#713D311yescharacteristic
79C4×Q8×D5—33no—
80#65903—31no—
81#65903—31no—
82Q8×Dic10—31no—
83C2×C3×C5×Q8C2311yescharacteristic
84C2×Dic30C2313yes—
85C2×C5×Dic6C2313yes—
86C3×#713Q818yescomplemented
87C2×C3×D20C2313yes—
88C2×C3×C4×D5C2313yes—
89C2×C3×C4×D5C2313yes—
90C2×C3×C4×D5C2313yes—
91C2×#1204C2313yes—
92C2×#1204C2316yes—
93C2×#1204C2311yescharacteristic
94C2×D5×Dic3C2313yes—
95C2×D5×Dic3C2313yes—
96C2×D5×Dic3C2313yes—
97C2×D5×Dic3C2313yes—
98D5×Dic6—212no—
99C3×C5×C4⋊C4C2313yes—
100C3×C42×C5C2313yes—
101C4⋊Dic15C2313yes—
102C4⋊Dic15C2313yes—
103C4⋊Dic15C2313yes—
104#6712C2311yescharacteristic
105#6712C2313yes—
106#6712C2316yes—
107C4×Dic15C2313yes—
108C4×Dic15C2313yes—
109C5×C4⋊Dic3C2313yes—
110C5×C4⋊Dic3C2313yes—
111C5×C4⋊Dic3C2313yes—
112C5×Dic3⋊C4C2311yescharacteristic
113C5×Dic3⋊C4C2313yes—
114C5×Dic3⋊C4C2316yes—
115C4×C5×Dic3C2313yes—
116C4×C5×Dic3C2313yes—
117C3×#685C2316yes—
118C3×C4⋊Dic5C2313yes—
119C3×C4×Dic5C2313yes—
120C3×C4×Dic5C2311yescharacteristic
121C3×C4×Dic5C2313yes—
122Dic3⋊Dic5C2313yes—
123Dic3⋊Dic5C2313yes—
124#6669C2313yes—
125#6669C2313yes—
126#6668C2311yescharacteristic
127#6668C2313yes—
128#6668C2316yes—
129#6665C2316yes—
130#6665C2316yes—
131Dic3×Dic5C2313yes—
132Dic3×Dic5C2313yes—
133Dic3×Dic5C2311yescharacteristic
134Dic3×Dic5C2311yescharacteristic
135C3×C4×#41—51no—
136Dic3×#41—51no—
137Dic3×#41—51no—
138#5570—51no—
139#5569—51no—
140#5569D511yescharacteristic, complemented
141Q8×Dic6—51no—
142#5543—53no—
143#5539—53no—
144#5539—53no—
145D4×Dic6—53no—
146#5517—53no—
147#5517—53no—
148#5470—53no—
149C2×C4×Dic6—53no—
150C2×#713C2×D311yescharacteristic
151C2×Q8×D5—33no—
152C5×C4⋊Q8—33no—
153C5×#125—33no—
154C5×#125—33no—
155C4×C5×Q8—31no—
156C4×C5×Q8—31no—
157C4×C5×Q8—33no—
158C4×C5×Q8C2×D311yescharacteristic
159#4092—36no—
160Q8×Dic5—31no—
161Q8×Dic5—31no—
162Q8×Dic5—33no—
163Q8×Dic5C2×D311yescharacteristic
164#4043—36no—
165#4042—36no—
166#4042—36no—
167#4042—36no—
168#4042—36no—
169#4039—33no—
170#4039—33no—
171#4039C2×D313yes—
172#4038—33no—
173#4038—33no—
174#4038C2×D313yes—
175D5×C4⋊C4—33no—
176D5×C4⋊C4—33no—
177D5×C4⋊C4—33no—
178#4036—33no—
179#4036—33no—
180#4034—33no—
181#4034—33no—
182#4034—33no—
183#4034—33no—
184#4033—36no—
185#4033—31no—
186#4033—33no—
187#4033—33no—
188C4×D20—33no—
189C4×D20—33no—
190C4×D20C2×D313yes—
191C42×D5—33no—
192C42×D5—33no—
193C42×D5C2×D313yes—
194#4016—33no—
195#4016—33no—
196#4015—33no—
197C4×Dic10—33no—
198C4×Dic10—33no—
199C4×Dic10—33no—
200Q8×#41—151noSylow
201C22×C3×D5C2413yes—
202C3×C5×Q8C2×Q814yescomplemented
203C2×C3×C4×C5C2413yes—
204C2×C3×C4×C5C2411yescharacteristic
205C2×C3×C4×C5C2413yes—
206C2×Dic15C2413yes—
207C2×Dic15C2413yes—
208C2×Dic15C2411yescharacteristic
209C2×Dic15C2411yescharacteristic
210Dic30—26no—
211C2×C5×Dic3C2413yes—
212C2×C5×Dic3C2413yes—
213C2×C5×Dic3C2411yescharacteristic
214C2×C5×Dic3C2411yescharacteristic
215C5×Dic6—26no—
216C2×C3×Dic5C2413yes—
217C2×C3×Dic5C2411yescharacteristic
218C2×C3×Dic5C2411yescharacteristic
219C3×D20C2×Q8112yescomplemented
220C3×C4×D5—26no—
221C3×C4×D5—43no—
222C3×C4×D5C2×Q8112yescomplemented
223#1204—26no—
224#1204—46no—
225#1204#4114yescomplemented
226D5×Dic3—26no—
227D5×Dic3—26no—
228D5×Dic3—43no—
229D5×Dic3—43no—
230C2×C3×#41—51no—
231C22×Dic6—53no—
232C3×C4×Q8—51no—
233C3×C4×Q8C2×D511yescharacteristic
234C3×C4×D4—53no—
235C3×C4×D4—53no—
236C3×#117—53no—
237C2×C3×C42—53no—
238Q8×Dic3—51no—
239Q8×Dic3—51no—
240Q8×Dic3C2×D511yescharacteristic
241Q8×Dic3C2×D511yescharacteristic
242D4×Dic3—53no—
243D4×Dic3—53no—
244D4×Dic3—53no—
245D4×Dic3—53no—
246#926—53no—
247#926—53no—
248C2×C4⋊Dic3—53no—
249#924—56no—
250#924—56no—
251C2×Dic3⋊C4—53no—
252C2×Dic3⋊C4—53no—
253C2×C4×Dic3—53no—
254C2×C4×Dic3—53no—
255#890—53no—
256#890—53no—
257#890—53no—
258#890C2×D513yes—
259#888—53no—
260#888—53no—
261#888—53no—
262#888C2×D513yes—
263#878—56no—
264#878—56no—
265#878—56no—
266#878—56no—
267#870—53no—
268#870C2×D513yes—
269#869—53no—
270#869—53no—
271C4×Dic6—53no—
272C4×Dic6—53no—
273C4×Dic6—53no—
274C4×Dic6—51no—
275C4×Dic6—53no—
276C4×Dic6—56no—
277C4×Dic6—53no—
278C4×Dic6—53no—
279C4×Dic6C2×D513yes—
280C2×C5×Q8—33no—
281C2×C5×Q8C22×D311yescharacteristic
282#713Dic618yescomplemented
283Q8×D5—612no—
284C2×D20C22×D313yes—
285C2×C4×D5—33no—
286C2×C4×D5—33no—
287C2×C4×D5—33no—
288C2×C4×D5—33no—
289C2×C4×D5C22×D313yes—
290C2×C4×D5C22×D313yes—
291C2×C4×D5C22×D313yes—
292C2×Dic10—31no—
293C2×Dic10—33no—
294C2×Dic10—33no—
295C2×Dic10—36no—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—33no—
298C5×C4⋊C4—33no—
299C5×C4⋊C4—33no—
300C5×C4⋊C4—33no—
301C5×C4⋊C4—36no—
302C5×C4⋊C4C22×D313yes—
303C42×C5—33no—
304C42×C5—33no—
305C42×C5C22×D313yes—
306#685—36no—
307#685—36no—
308#685C22×D316yes—
309C4⋊Dic5—33no—
310C4⋊Dic5—33no—
311C4⋊Dic5—33no—
312C4⋊Dic5—33no—
313C4⋊Dic5—33no—
314C4⋊Dic5C22×D313yes—
315#683—31no—
316#683—33no—
317#683—36no—
318#683—31no—
319#683—33no—
320#683—36no—
321#683—33no—
322#683—33no—
323C4×Dic5—33no—
324C4×Dic5—33no—
325C4×Dic5—31no—
326C4×Dic5—31no—
327C4×Dic5—33no—
328C4×Dic5—33no—
329C4×Dic5C22×D313yes—
330C4×Dic5C22×D311yescharacteristic
331C4×Dic5C22×D313yes—
332Q82—151no—
333#557—31no—
334#557—151no—
335#557—151no—
336#554—153no—
337#554—153no—
338#554—153no—
339D4×Q8—153no—
340#533—153no—
341#533—153no—
342#533—153no—
343C4×#41—51no—
344C4×#41—151no—
345C4×#41—151no—
346C2×C4×Q8—153no—
347C22×C3×C5C2511yescharacteristic
348C2×C3×D5—23no—
349C2×C3×D5—23no—
350C2×C3×D5C22×Q816yes—
351C3×C4×C5—23no—
352C3×C4×C5—21no—
353C3×C4×C5C22×Q816yes—
354Dic15—23no—
355Dic15—21no—
356Dic15—23no—
357Dic15C2×#4112yes—
358C3×Dic5—23no—
359C3×Dic5C22×Q812yes—
360C3×Dic5C2×#4112yes—
361C5×Dic3—23no—
362C5×Dic3—21no—
363C5×Dic3—23no—
364C5×Dic3C2×#4112yes—
365C3×#41—58no—
366C2×C3×Q8C22×D511yescharacteristic
367C2×C3×D4—53no—
368C22×C3×C4—53no—
369C22×C3×C4—53no—
370C22×C3×C4—53no—
371C22×Dic3—53no—
372C22×Dic3—53no—
373C22×Dic3—53no—
374C22×Dic3—53no—
375C2×Dic6—51no—
376C2×Dic6—53no—
377C2×Dic6—53no—
378C2×Dic6—56no—
379C2×Dic6—1012no—
380C2×Dic6C22×D513yes—
381C3×C4⋊C4—53no—
382C3×C4⋊C4C22×D513yes—
383C3×C22⋊C4—56no—
384C3×C42—51no—
385C3×C42—53no—
386C3×C42—53no—
387C3×C42C22×D513yes—
388#217—56no—
389#217—56no—
390C4⋊Dic3—53no—
391C4⋊Dic3—53no—
392C4⋊Dic3—53no—
393C4⋊Dic3—51no—
394C4⋊Dic3—53no—
395C4⋊Dic3—56no—
396C4⋊Dic3C22×D513yes—
397C4⋊Dic3C22×D513yes—
398C4⋊Dic3C22×D513yes—
399Dic3⋊C4—51no—
400Dic3⋊C4—53no—
401Dic3⋊C4—56no—
402Dic3⋊C4—53no—
403Dic3⋊C4—53no—
404Dic3⋊C4—53no—
405Dic3⋊C4—53no—
406Dic3⋊C4C22×D511yescharacteristic
407Dic3⋊C4C22×D513yes—
408Dic3⋊C4C22×D516yes—
409C4×Dic3—53no—
410C4×Dic3—53no—
411C4×Dic3—51no—
412C4×Dic3—51no—
413C4×Dic3—53no—
414C4×Dic3—53no—
415C4×Dic3C22×D513yes—
416C4×Dic3C22×D513yes—
417C22×D5C23×D313yes—
418C5×Q8—66no—
419C5×Q8C2×Dic614yescomplemented
420C2×C4×C5—31no—
421C2×C4×C5—31no—
422C2×C4×C5—33no—
423C2×C4×C5—33no—
424C2×C4×C5C23×D311yescharacteristic
425C2×C4×C5C23×D313yes—
426C2×C4×C5C23×D313yes—
427C2×Dic5—31no—
428C2×Dic5—31no—
429C2×Dic5—33no—
430C2×Dic5—33no—
431C2×Dic5C23×D313yes—
432C2×Dic5C23×D311yescharacteristic
433C2×Dic5C23×D311yescharacteristic
434D20C2×Dic6112yescomplemented
435C4×D5—26no—
436C4×D5—43no—
437C4×D5—66no—
438C4×D5—66no—
439C4×D5—123no—
440C4×D5—123no—
441C4×D5C2×Dic6112yescomplemented
442Dic10—34no—
443Dic10—66no—
444Dic10—66no—
445Dic10—126no—
446C2×#41—51no—
447C22×Q8—153no—
448C4⋊Q8—33no—
449C4⋊Q8—153no—
450C4⋊Q8—153no—
451C4⋊Q8—153no—
452C4⋊Q8—153no—
453C4⋊Q8—153no—
454#125—33no—
455#125—33no—
456#125—153no—
457#125—153no—
458#125—153no—
459#125—153no—
460C22⋊Q8—156no—
461C22⋊Q8—156no—
462C22⋊Q8—156no—
463C22⋊Q8—156no—
464C22⋊Q8—156no—
465C22⋊Q8—156no—
466C4×Q8—31no—
467C4×Q8—31no—
468C4×Q8—33no—
469C4×Q8—51no—
470C4×Q8—153no—
471C4×Q8—153no—
472C4×Q8—151no—
473C4×Q8—153no—
474C4×Q8—153no—
475C4×Q8—156no—
476C4×Q8—153no—
477C4×Q8—151no—
478C4×Q8—151no—
479C4×Q8—153no—
480C4×Q8D3×D511yescharacteristic
481C4×D4—53no—
482C4×D4—53no—
483C4×D4—153no—
484C4×D4—153no—
485C4×D4—153no—
486C4×D4—153no—
487#117—53no—
488#117—153no—
489#117—153no—
490C2×C4⋊C4—153no—
491C2×C4⋊C4—153no—
492C2×C4⋊C4—153no—
493C2×C42—53no—
494C2×C42—153no—
495C2×C42—153no—
496C2×C3×C5C23×Q811yescharacteristic
497C2×C3×C5C22×#4111yescharacteristic
498C2×C3×C5#58511yescharacteristic
499C3×D5—26no—
500C23×C3—53no—
501C3×Q8Q8×D514yescomplemented
502C3×D4—512no—
503C2×C3×C4—51no—
504C2×C3×C4—51no—
505C2×C3×C4—512no—
506C2×C3×C4—53no—
507C2×C3×C4—106no—
508C2×C3×C4—203no—
509C2×C3×C4C23×D511yescharacteristic
510C2×C3×C4C23×D513yes—
511C2×C3×C4C23×D513yes—
512C2×Dic3—51no—
513C2×Dic3—51no—
514C2×Dic3—53no—
515C2×Dic3—53no—
516C2×Dic3—106no—
517C2×Dic3—106no—
518C2×Dic3—203no—
519C2×Dic3—203no—
520C2×Dic3C23×D511yescharacteristic
521C2×Dic3C23×D513yes—
522C2×Dic3C23×D513yes—
523C2×Dic3C23×D511yescharacteristic
524Dic6—26no—
525Dic6—54no—
526Dic6—106no—
527Dic6—106no—
528Dic6—206no—
529C22×C5C24×D311yescharacteristic
530C2×D5—23no—
531C2×D5—23no—
532C2×D5C22×Dic616yes—
533C4×C5—23no—
534C4×C5—21no—
535C4×C5—32no—
536C4×C5—63no—
537C4×C5—63no—
538C4×C5—61no—
539C4×C5C22×Dic616yes—
540Dic5—23no—
541Dic5—32no—
542Dic5—63no—
543Dic5—63no—
544Dic5—61no—
545Dic5C22×Dic612yes—
546Dic5D3×#4112yes—
547#41—58no—
548C2×Q8—33no—
549C2×Q8—151no—
550C2×Q8—153no—
551C2×Q8—156no—
552C2×Q8—153no—
553C2×Q8—3012no—
554C2×Q8C2×D3×D511yescharacteristic
555C2×D4—53no—
556C22×C4—53no—
557C22×C4—53no—
558C22×C4—53no—
559C22×C4—153no—
560C22×C4—153no—
561C22×C4—153no—
562C22×C4—153no—
563C4⋊C4—31no—
564C4⋊C4—33no—
565C4⋊C4—33no—
566C4⋊C4—33no—
567C4⋊C4—33no—
568C4⋊C4—36no—
569C4⋊C4—53no—
570C4⋊C4—151no—
571C4⋊C4—153no—
572C4⋊C4—153no—
573C4⋊C4—153no—
574C4⋊C4—153no—
575C4⋊C4—153no—
576C4⋊C4—156no—
577C4⋊C4—151no—
578C4⋊C4—153no—
579C4⋊C4—153no—
580C4⋊C4—153no—
581C4⋊C4—153no—
582C4⋊C4—156no—
583C4⋊C4C2×D3×D513yes—
584C22⋊C4—56no—
585C22⋊C4—156no—
586C22⋊C4—156no—
587C42—33no—
588C42—33no—
589C42—51no—
590C42—53no—
591C42—53no—
592C42—151no—
593C42—151no—
594C42—153no—
595C42—153no—
596C42—153no—
597C42—153no—
598C42C2×D3×D513yes—
599C3×C5Q8×#4111yescharacteristic, complemented, Hall
600C22×C3—56no—
601C22×C3—103no—
602C22×C3—103no—
603C22×C3C24×D511yescharacteristic
604C3×C4—23no—
605C3×C4—21no—
606C3×C4—52no—
607C3×C4—52no—
608C3×C4—103no—
609C3×C4C2×Q8×D516yes—
610Dic3—23no—
611Dic3—23no—
612Dic3—21no—
613Dic3—52no—
614Dic3—103no—
615Dic3—103no—
616Dic3—101no—
617Dic3D5×#4112yes—
618C2×C5C23×Dic611yescharacteristic
619C2×C5C2×D3×#4111yescharacteristic
620C2×C5#596411yescharacteristic
621D5—26no—
622C23—53no—
623Q8—66no—
624Q8—154no—
625Q8—306no—
626Q8—306no—
627Q8—606no—
628Q8D5×Dic614yescomplemented
629D4—512no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—33no—
633C2×C4—33no—
634C2×C4—51no—
635C2×C4—51no—
636C2×C4—512no—
637C2×C4—53no—
638C2×C4—106no—
639C2×C4—151no—
640C2×C4—151no—
641C2×C4—153no—
642C2×C4—153no—
643C2×C4—203no—
644C2×C4—306no—
645C2×C4—306no—
646C2×C4—603no—
647C2×C4—603no—
648C2×C4C22×D3×D511yescharacteristic
649C2×C4C22×D3×D513yes—
650C2×C4C22×D3×D513yes—
651C2×C3—106no—
652C2×C3C22×Q8×D511yescharacteristic
653C2×C3C2×D5×#4111yescharacteristic
654C2×C3#6628711yescharacteristic
655C5#41×Dic611yescharacteristic, complemented, Sylow
656C22—56no—
657C22—103no—
658C22—103no—
659C22C23×D3×D511yescharacteristic
660C4—21no—
661C4—23no—
662C4—32no—
663C4—52no—
664C4—52no—
665C4—61no—
666C4—63no—
667C4—63no—
668C4—103no—
669C4—152no—
670C4—301no—
671C4—303no—
672C4—303no—
673C4C2×D5×Dic616yes—
674C3#1061891611yescharacteristic, complemented, Sylow
675C2—106no—
676C2C22×D5×Dic611yescharacteristic
677C2#1175704811yescharacteristic
678C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC2×C3×#713C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5Q8×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756328C2semidirect
2. C5×#5569C2semidirect
4. #11755267C2semidirect
5. Q8×#1204C2semidirect
8. #11753611C2semidirect
9. #11753568C2semidirect
10. #11753527C2semidirect
11. #11753429C2semidirect
12. #11752618C2semidirect
13. #11752597C2semidirect
14. C4×D5×Dic6C2semidirect
15. #11752498C2semidirect
86. C3×#713Q8semidirect
140. #5569D5semidirect
202. C3×C5×Q8C2×Q8semidirect
219. C3×D20C2×Q8semidirect
222. C3×C4×D5C2×Q8semidirect
225. #1204#41semidirect
282. #713Dic6semidirect
419. C5×Q8C2×Dic6semidirect
434. D20C2×Dic6semidirect
441. C4×D5C2×Dic6semidirect
501. C3×Q8Q8×D5semidirect
599. C3×C5Q8×#41semidirect
628. Q8D5×Dic6semidirect
655. C5#41×Dic6semidirect
674. C3#10618916semidirect

Maximal subgroups

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

subgroupindex
#117563282
C5×#55692
C3×C4×#7132
#117552672
Q8×#12042
Dic3×#7132
#117536112
#117535682
#117535272
#117534292
#117526182
#117525972
C4×D5×Dic62
#117524982
#106189163
#41×Dic65