Finite Group Databasebeta

← #14436104

Subgroups — #14436104

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756384C211yesmaximal, characteristic, complemented
2#11756263C211yesmaximal, characteristic
3C3×C5×#483C211yesmaximal, characteristic, complemented
4#11751148C211yesmaximal, characteristic
5#11751071C211yesmaximal, characteristic, complemented
6#11750972C211yesmaximal, characteristic, complemented
7#11750958C211yesmaximal, characteristic, complemented
8#11750954C211yesmaximal, characteristic, complemented
9#11750953C211yesmaximal, characteristic, complemented
10#11750919C211yesmaximal, characteristic, complemented
11#11750918C211yesmaximal, characteristic, complemented
12#11750896C211yesmaximal, characteristic, complemented
13#11750891C211yesmaximal, characteristic, complemented
14#11750834C211yesmaximal, characteristic
15#11750821C211yesmaximal, characteristic, complemented
16#10613147—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C3×C5×C22⋊Q8C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic
21#91833C2211yescharacteristic
22C2×#6718C2211yescharacteristic
23C2×#6717C2211yescharacteristic
24C4×#1220—21no—
25C4×#1220—21no—
26#91815C2211yescharacteristic
27#91813C2211yescharacteristic
28C2×Dic60C2211yescharacteristic
29C2×#6706C2211yescharacteristic
30#91782C2211yescharacteristic
31#91782C2211yescharacteristic
32#91781—21no—
33C4⋊C4×D15—21no—
34#91779—21no—
35#91779C2211yescharacteristic
36#91778—21no—
37#91776C2211yescharacteristic
38#91776C2211yescharacteristic
39#91776C2211yescharacteristic
40#91768—21no—
41#91768—21no—
42C3×C5×#106C2211yescharacteristic
43C3×C5×#106C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46C3×C5×C22⋊C8C2211yescharacteristic
47#91114C2211yescharacteristic
48#91105C2211yescharacteristic
49#91100C2211yescharacteristic
50#91099C2211yescharacteristic
51#91098C2211yescharacteristic
52#91098C2211yescharacteristic
53C8×Dic15C2211yescharacteristic
54#91094C2211yescharacteristic
55#91094C2211yescharacteristic
56#91094C2211yescharacteristic
57#91093C2211yescharacteristic
58#91091C2211yescharacteristic
59#91091C2211yescharacteristic
60#81416—51nomaximal, Hall
61#65959—31no—
62#65838—31no—
63C5×#483D311yescharacteristic, complemented
64#65336—31no—
65#65259—31no—
66#65160—31no—
67#65146—31no—
68#65142—31no—
69#65141—31no—
70#65107—31no—
71#65106—31no—
72#65082—31no—
73#65079—31no—
74#65022—31no—
75#65009—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C22×C3×C4×C5C2311yescharacteristic
79C2×#1220—21no—
80#6817—22no—
81#6817—22no—
82C2×D60C2311yescharacteristic
83C2×C4×D15—21no—
84C2×C4×D15—21no—
85C2×C4×D15—21no—
86C2×Dic30C2311yescharacteristic
87C2×Dic30C2311yescharacteristic
88C2×C3×C5×C8C2311yescharacteristic
89C2×C3×C5×C8C2311yescharacteristic
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4C2311yescharacteristic
93C3×C5×C4⋊C4C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95C3×C5×C22⋊C4—21no—
96#6719—21no—
97#6719D411yescharacteristic
98#6719D411yescharacteristic
99#6718—22no—
100#6717—22no—
101#6714—21no—
102#6714—21no—
103C4⋊Dic15—21no—
104C4⋊Dic15—21no—
105C4⋊Dic15D411yescharacteristic
106C4⋊Dic15D411yescharacteristic
107C4⋊Dic15C2311yescharacteristic
108#6712—21no—
109#6712—21no—
110#6712—21no—
111#6712—21no—
112#6712—21no—
113#6712—21no—
114#6712—21no—
115C4×Dic15—21no—
116C4×Dic15—21no—
117C4×Dic15—21no—
118C4×Dic15—21no—
119C4×Dic15C2311yescharacteristic
120C4×Dic15C2311yescharacteristic
121C2×C3⋊#168C2311yescharacteristic
122C2×C3⋊#168C2311yescharacteristic
123Dic60—22no—
124#6706—22no—
125#5625—51no—
126#5504—51no—
127C3×#483D511yescharacteristic, complemented
128#5047—51no—
129#4970—51no—
130#4871—51no—
131#4857—51no—
132#4853—51no—
133#4852—51no—
134#4818—51no—
135#4817—51no—
136#4795—51no—
137#4790—51no—
138#4733—51no—
139#4720—51no—
140C2×#709—31no—
141C5×C22⋊Q8C2×D311yescharacteristic
142C2×C5×C4⋊C4C2×D311yescharacteristic
143Q8×Dic5—31no—
144#4090—31no—
145C2×#689—31no—
146C2×#688—31no—
147C4×C22⋊D5—61no—
148C4×C22⋊D5—61no—
149#4072—31no—
150#4070—31no—
151C2×Dic20—31no—
152C2×#677—31no—
153#4039—31no—
154#4039—31no—
155#4038—61no—
156D5×C4⋊C4—61no—
157#4036—31no—
158#4036—61no—
159#4035—61no—
160#4033—31no—
161#4033—31no—
162#4033—31no—
163#4025—61no—
164#4025—61no—
165C5×#106C2×D311yescharacteristic
166C5×#106C2×D311yescharacteristic
167C5×#103C2×D311yescharacteristic
168C5×#103C2×D311yescharacteristic
169C5×C22⋊C8C2×D311yescharacteristic
170C22⋊#168—31no—
171#3953—31no—
172#3948—31no—
173#3947—31no—
174#3946—31no—
175#3946—31no—
176C8×Dic5—31no—
177#3942—31no—
178#3942—31no—
179#3942—31no—
180#3941—31no—
181#3939—31no—
182#3939—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×D15—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—81no—
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2411yescharacteristic
197#1220—24no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15C2×D411yescharacteristic
202C2×Dic15C2×D411yescharacteristic
203C2×Dic15C2×D411yescharacteristic
204C2×Dic15C2×D411yescharacteristic
205D60—21no—
206D60#4112yes—
207C4×D15—24no—
208C4×D15—81no—
209C4×D15—81no—
210Dic30—21no—
211Dic30—21no—
212Dic30—21no—
213Dic30#4112yes—
214C3×C5×C8—21no—
215C3×C5×C8—21no—
216C3⋊#168—21no—
217C3⋊#168—21no—
218C2×#235—51no—
219C3×C22⋊Q8C2×D511yescharacteristic
220C2×C3×C4⋊C4C2×D511yescharacteristic
221Q8×Dic3—51no—
222#944—51no—
223C2×#216—51no—
224C2×#215—51no—
225C4×#67—101no—
226C4×#67—101no—
227#926—51no—
228#924—51no—
229C2×Dic12—51no—
230C2×#204—51no—
231#893—51no—
232#893—51no—
233#892—101no—
234D3×C4⋊C4—101no—
235#890—51no—
236#890—101no—
237#889—101no—
238#887—51no—
239#887—51no—
240#887—51no—
241#879—101no—
242#879—101no—
243C3×#106C2×D511yescharacteristic
244C3×#106C2×D511yescharacteristic
245C3×#103C2×D511yescharacteristic
246C3×#103C2×D511yescharacteristic
247C3×C22⋊C8C2×D511yescharacteristic
248#830—51no—
249#821—51no—
250#816—51no—
251#815—51no—
252Dic3⋊C8—51no—
253Dic3⋊C8—51no—
254C8×Dic3—51no—
255#810—51no—
256#810—51no—
257#810—51no—
258#809—51no—
259#807—51no—
260#807—51no—
261C2×C5×Q8C22×D311yescharacteristic
262C22×C4×C5—21no—
263C22×C4×C5C22×D311yescharacteristic
264C2×C22⋊D5—61no—
265#709—62no—
266#709—62no—
267C2×D20—31no—
268C2×C4×D5—61no—
269C2×C4×D5—61no—
270C2×C4×D5—61no—
271C2×Dic10—31no—
272C2×Dic10—31no—
273C2×C5×C8C22×D311yescharacteristic
274C2×C5×C8C22×D311yescharacteristic
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4C22×D311yescharacteristic
278C5×C4⋊C4C22×D311yescharacteristic
279C5×C4⋊C4C22×D311yescharacteristic
280C5×C22⋊C4—21no—
281C22⋊Dic5—31no—
282C22⋊Dic5—31no—
283C22⋊Dic5—61no—
284#689—62no—
285#688—62no—
286#685—61no—
287#685—61no—
288C4⋊Dic5—31no—
289C4⋊Dic5—31no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5—61no—
293#683—61no—
294#683—61no—
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300C4×Dic5—31no—
301C4×Dic5—31no—
302C4×Dic5—61no—
303C4×Dic5—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C2×#168—31no—
307C2×#168—31no—
308Dic20—62no—
309#677—62no—
310#541—151no—
311#520—151no—
312#484—151no—
313#483D1511yescharacteristic, complemented
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—151no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5—41no—
335C3×C4×C5—41no—
336C3×C4×C5—41no—
337C3×C4×C5C2×#4111yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339Dic15—22no—
340Dic15—21no—
341Dic15—21no—
342Dic15—21no—
343Dic15—21no—
344Dic15—41no—
345Dic15—41no—
346C2×C3×Q8C22×D511yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4C22×D511yescharacteristic
349C2×#67—101no—
350#235—102no—
351#235—102no—
352C2×D12—51no—
353C2×C4×D3—101no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
356C2×Dic6—51no—
357C2×Dic6—51no—
358C2×C3×C8C22×D511yescharacteristic
359C2×C3×C8C22×D511yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4C22×D511yescharacteristic
363C3×C4⋊C4C22×D511yescharacteristic
364C3×C4⋊C4C22×D511yescharacteristic
365C3×C22⋊C4—21no—
366#217—51no—
367#217—51no—
368#217—101no—
369#216—102no—
370#215—102no—
371(C2×D3)⋊C4—101no—
372(C2×D3)⋊C4—101no—
373C4⋊Dic3—51no—
374C4⋊Dic3—51no—
375C4⋊Dic3—51no—
376C4⋊Dic3—101no—
377C4⋊Dic3—101no—
378Dic3⋊C4—101no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385C4×Dic3—51no—
386C4×Dic3—51no—
387C4×Dic3—101no—
388C4×Dic3—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393Dic12—102no—
394#204—102no—
395C23×C5D3×D411yescharacteristic
396C22×D5—61no—
397C5×Q8—21no—
398C5×Q8—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—81no—
406C2×C4×C5D3×D411yescharacteristic
407C2×C4×C5C23×D311yescharacteristic
408C22⋊D5—64no—
409C2×Dic5—31no—
410C2×Dic5—31no—
411C2×Dic5—31no—
412C2×Dic5—31no—
413C2×Dic5—61no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416D20—32no—
417D20—61no—
418C4×D5—64no—
419C4×D5—241no—
420C4×D5—241no—
421Dic10—32no—
422Dic10—61no—
423Dic10—61no—
424Dic10—61no—
425C5×C8—21no—
426C5×C8—21no—
427#168—61no—
428#168—61no—
429C2×#41—151no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—151no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—151no—
441C22⋊Q8C2×D1511yescharacteristic
442C4×Q8—151no—
443C4×Q8—151no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—151no—
451#117—301no—
452C2×C4⋊C4—301no—
453C2×C4⋊C4C2×D1511yescharacteristic
454#107—151no—
455#107—151no—
456#106C2×D1511yescharacteristic
457#106C2×D1511yescharacteristic
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—151no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103C2×D1511yescharacteristic
465#103C2×D1511yescharacteristic
466#102—151no—
467#102—151no—
468C22⋊C8—151no—
469C22⋊C8C2×D1511yescharacteristic
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476D15—42no—
477C23×C3D4×D511yescharacteristic
478C22×D3—101no—
479C3×Q8—21no—
480C3×Q8—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—81no—
488C2×C3×C4D4×D511yescharacteristic
489C2×C3×C4C23×D511yescharacteristic
490#67—104no—
491C2×Dic3—51no—
492C2×Dic3—51no—
493C2×Dic3—51no—
494C2×Dic3—51no—
495C2×Dic3—101no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498D12—52no—
499D12—101no—
500C4×D3—104no—
501C4×D3—401no—
502C4×D3—401no—
503Dic6—52no—
504Dic6—101no—
505Dic6—101no—
506Dic6—101no—
507C3×C8—21no—
508C3×C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C2×D3×D411yescharacteristic
515C2×D5—62no—
516C2×D5—121no—
517C2×D5—121no—
518C4×C5—21no—
519C4×C5—41no—
520C4×C5—41no—
521C4×C5—41no—
522C4×C5—41no—
523C4×C5D3×#4111yescharacteristic
524C4×C5D3×#4111yescharacteristic
525Dic5—62no—
526Dic5—61no—
527Dic5—61no—
528Dic5—61no—
529Dic5—61no—
530Dic5—121no—
531Dic5—121no—
532#41—302no—
533#41—302no—
534C2×Q8—151no—
535C2×Q8—151no—
536C2×Q8C22×D1511yescharacteristic
537C2×D4—151no—
538C2×D4—301no—
539C22×C4—21no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4C22×D1511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—151no—
549C2×C8—151no—
550C2×C8C22×D1511yescharacteristic
551C2×C8C22×D1511yescharacteristic
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—151no—
555C4⋊C4—151no—
556C4⋊C4—151no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4—301no—
560C4⋊C4—301no—
561C4⋊C4—301no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4C22×D1511yescharacteristic
567C4⋊C4C22×D1511yescharacteristic
568C4⋊C4C22×D1511yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—151no—
571C22⋊C4—151no—
572C22⋊C4—301no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C42—151no—
576C42—151no—
577C42—301no—
578C42—301no—
579C42—301no—
580C42—301no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3C2×D4×D511yescharacteristic
586C2×D3—102no—
587C2×D3—201no—
588C2×D3—201no—
589C3×C4—21no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4D5×#4111yescharacteristic
595C3×C4D5×#4111yescharacteristic
596Dic3—101no—
597Dic3—101no—
598Dic3—101no—
599Dic3—101no—
600Dic3—102no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5#565611yescharacteristic
605C2×C5#576211yescharacteristic
606C2×C5#577911yescharacteristic
607D5—122no—
608C23—301no—
609C23D4×D1511yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—152no—
613Q8—301no—
614Q8—301no—
615Q8—301no—
616D4—152no—
617D4—304no—
618D4—301no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—81no—
626C2×C4—151no—
627C2×C4—151no—
628C2×C4—151no—
629C2×C4—151no—
630C2×C4—304no—
631C2×C4—301no—
632C2×C4—301no—
633C2×C4—301no—
634C2×C4—1201no—
635C2×C4—1201no—
636C2×C4D4×D1511yescharacteristic
637C2×C4C23×D1511yescharacteristic
638C8—21no—
639C8—21no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3#6599011yescharacteristic
644C2×C3#6609611yescharacteristic
645C2×C3#6611311yescharacteristic
646D3—202no—
647C5#8141611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—302no—
652C22—601no—
653C22—601no—
654C22C2×D4×D1511yescharacteristic
655C4—21no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—302no—
661C4—301no—
662C4—301no—
663C4—301no—
664C4—301no—
665C4—601no—
666C4—601no—
667C4#41×D1511yescharacteristic
668C4#41×D1511yescharacteristic
669C3#1061314711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—602no—
672C2#1175641511yescharacteristic
673C2#1175652111yescharacteristic
674C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#483C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenter#483D15
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #11756384C2semidirect
3. C3×C5×#483C2semidirect
5. #11751071C2semidirect
6. #11750972C2semidirect
7. #11750958C2semidirect
8. #11750954C2semidirect
9. #11750953C2semidirect
10. #11750919C2semidirect
11. #11750918C2semidirect
12. #11750896C2semidirect
13. #11750891C2semidirect
15. #11750821C2semidirect
63. C5×#483D3semidirect
127. C3×#483D5semidirect
313. #483D15semidirect
581. C3×C5#3120semidirect
647. C5#81416semidirect
669. C3#10613147semidirect

Maximal subgroups

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

subgroupindex
#117563842
#117562632
C3×C5×#4832
#117511482
#117510712
#117509722
#117509582
#117509542
#117509532
#117509192
#117509182
#117508962
#117508912
#117508342
#117508212
#106131473
#814165