Finite Group Databasebeta

← #14472108

Subgroups — #14472108

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65902C211yesmaximal, characteristic
2#11752463C211yesmaximal, characteristic, complemented
3C4×#6718C211yesmaximal, characteristic, complemented
4C5×#5022C211yesmaximal, characteristic, complemented
5#11749349C211yesmaximal, characteristic, complemented
6#11749331C211yesmaximal, characteristic
7#11749248C211yesmaximal, characteristic
8#11749246C211yesmaximal, characteristic, complemented
9#11747410C211yesmaximal, characteristic
10#11747390C211yesmaximal, characteristic, complemented
11#11747270C211yesmaximal, characteristic, complemented
12#11747268C211yesmaximal, characteristic
13#11747084C211yesmaximal, characteristic
14#11746896C211yesmaximal, characteristic
15#11746846C211yesmaximal, characteristic, complemented
16#10612947—31nomaximal, Hall
17C3×C4×C5×Q8C2211yescharacteristic
18C2×#6718C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C5×#870C2211yescharacteristic
21C3×#4093C2211yescharacteristic
22C3×#4090C2211yescharacteristic
23C3×#4044—21no—
24C3×#4042—21no—
25C3×#4039C2211yescharacteristic
26C3×#4033C2211yescharacteristic
27C3×#4022—21no—
28C3×#4021C2211yescharacteristic
29C3×#4018—21no—
30C3×C4×Dic10C2211yescharacteristic
31#91468C2211yescharacteristic
32#91388C2211yescharacteristic
33#91382—21no—
34#91339—21no—
35#91333C2211yescharacteristic
36#91333C2211yescharacteristic
37#91327—21no—
38#91325—21no—
39C2×#6662C2211yescharacteristic
40C2×#6657C2211yescharacteristic
41#91119C2211yescharacteristic
42#91094C2211yescharacteristic
43#91091C2211yescharacteristic
44C4×C3⋊#168C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90982C2211yescharacteristic
51#90982C2211yescharacteristic
52#90971C2211yescharacteristic
53#90970C2211yescharacteristic
54#90970C2211yescharacteristic
55#90965C2211yescharacteristic
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58Dic5×C3⋊C8C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83676—51nomaximal, Hall
61#66019—31no—
62#65902D311yescharacteristic
63C5×#479—31no—
64#65357—31no—
65C4×#689—31no—
66#65179—31no—
67#65162—31no—
68#65146—31no—
69#65141—31no—
70#65134—31no—
71#65119—31no—
72#65089—31no—
73#65087—31no—
74#65082—31no—
75#65081—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×Dic30C2311yescharacteristic
78C2×C3×D20C2311yescharacteristic
79C2×C3×C4×D5—21no—
80C2×C3×Dic10D411yescharacteristic
81C2×C3×Dic10C2311yescharacteristic
82C2×#1204—21no—
83C3×C5×C4⋊C4—21no—
84C3×C5×C4⋊C4C2311yescharacteristic
85C3×C42×C5—21no—
86C3×C42×C5C2311yescharacteristic
87#6718—22no—
88C4⋊Dic15C2311yescharacteristic
89#6712—21no—
90C4×Dic15—21no—
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2311yescharacteristic
93C5×C4⋊Dic3C2311yescharacteristic
94C5×C4⋊Dic3C2311yescharacteristic
95C5×Dic3⋊C4—21no—
96C5×Dic3⋊C4—21no—
97C2×C5×C3⋊C8C2311yescharacteristic
98C2×C5×C3⋊C8C2311yescharacteristic
99C3×#685—21no—
100C3×#685—21no—
101C3×#685—21no—
102C3×#685—21no—
103C3×#685—21no—
104C3×C4⋊Dic5D411yescharacteristic
105C3×#683—21no—
106C3×#683—21no—
107C3×#683—21no—
108C3×#683D411yescharacteristic
109C3×#683D411yescharacteristic
110C3×C4×Dic5—21no—
111C3×C4×Dic5C2311yescharacteristic
112C3×C4×Dic5C2311yescharacteristic
113Dic3⋊Dic5—21no—
114#6669—21no—
115#6669—21no—
116#6669—21no—
117#6668—21no—
118Dic3×Dic5—21no—
119Dic3×Dic5—21no—
120#6662—22no—
121#6657—22no—
122C3×#556—51no—
123#5567—51no—
124#5090—51no—
125#5079—51no—
126#5056—51no—
127#5056—51no—
128#5054—51no—
129#5054—51no—
130C4×#216—51no—
131C4×#216—51no—
132Q8×C3⋊C8—51no—
133#5022—51no—
134#5022D511yescharacteristic, complemented
135C4×#214—51no—
136#5007—51no—
137C5×#125—31no—
138C4×C5×Q8C2×D311yescharacteristic
139#4093C2×D311yescharacteristic
140#4090C2×D311yescharacteristic
141C2×#689—31no—
142C2×Dic20—31no—
143C2×#677—31no—
144#4044—21no—
145#4042—21no—
146#4039C2×D311yescharacteristic
147#4036—31no—
148#4035—61no—
149#4035—61no—
150#4034—31no—
151#4034—61no—
152#4033—31no—
153#4033—31no—
154#4033—61no—
155#4033C2×D311yescharacteristic
156#4022—21no—
157#4021C2×D311yescharacteristic
158#4018—21no—
159C4×Dic10—31no—
160C4×Dic10C2×D311yescharacteristic
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8—31no—
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3953—31no—
168#3948—31no—
169#3946—31no—
170#3946—31no—
171C8×Dic5—31no—
172C8×Dic5—31no—
173#3942—31no—
174#3942—31no—
175#3942—31no—
176#3941—31no—
177#3941—31no—
178#3939—31no—
179C4×#168—31no—
180#3364—151noSylow
181C22×C3×D5—21no—
182C3×C5×Q8—21no—
183C3×C5×Q8—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5C2×D411yescharacteristic
187C2×C3×C4×C5C2×D411yescharacteristic
188C2×C3×C4×C5C2411yescharacteristic
189C2×Dic15—21no—
190C2×Dic15—21no—
191Dic30—21no—
192Dic30#4112yes—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C3×Dic5—21no—
196C2×C3×Dic5C2×D411yescharacteristic
197C2×C3×Dic5C2×D411yescharacteristic
198C2×C3×Dic5C2×D411yescharacteristic
199C2×C3×Dic5C2×D411yescharacteristic
200C3×D20—21no—
201C3×D20—21no—
202C3×C4×D5—42no—
203C3×Dic10—22no—
204C3×Dic10—21no—
205C3×Dic10—21no—
206#1204—42no—
207C3⋊#168—21no—
208C3⋊#168—21no—
209C5×C3⋊C8—21no—
210C5×C3⋊C8—21no—
211C3×C4⋊Q8—51no—
212C3×#126—101no—
213C3×#126—101no—
214C3×#124—51no—
215C3×#124—51no—
216C3×C22⋊Q8—101no—
217C3×C4×Q8—51no—
218C3×C4×Q8—51no—
219C3×C4×Q8C2×D511yescharacteristic
220C3×C4×D4—51no—
221C3×#117—101no—
222#944—101no—
223C2×#216—51no—
224C2×#216—51no—
225C2×#214—51no—
226#889—101no—
227#889—101no—
228#887—101no—
229#870—51no—
230#870C2×D511yescharacteristic
231#869—51no—
232C4×Dic6—51no—
233C4×Dic6—51no—
234C4×Dic6—51no—
235#835—51no—
236#835—51no—
237#835—51no—
238#835—51no—
239#835C2×D511yescharacteristic
240#835C2×D511yescharacteristic
241#832—51no—
242#832—51no—
243#832—51no—
244#810—51no—
245#808C2×D511yescharacteristic
246#807—51no—
247#807C2×D511yescharacteristic
248C4⋊(C3⋊C8)—51no—
249C4⋊(C3⋊C8)—51no—
250C4⋊(C3⋊C8)C2×D511yescharacteristic
251C4×C3⋊C8—51no—
252C4×C3⋊C8—51no—
253C4×C3⋊C8—51no—
254C2×C5×Q8C22×D311yescharacteristic
255C2×D20C22×D311yescharacteristic
256C2×C4×D5—21no—
257C2×Dic10—31no—
258C2×Dic10—61no—
259C2×Dic10#6711yescharacteristic
260C2×Dic10C22×D311yescharacteristic
261C2×C5×C8—31no—
262C2×C5×C8—31no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—31no—
265C5×C4⋊C4—31no—
266C5×C4⋊C4—61no—
267C5×C4⋊C4—61no—
268C5×C4⋊C4C22×D311yescharacteristic
269C42×C5—21no—
270C42×C5C22×D311yescharacteristic
271#689—62no—
272#685—21no—
273#685—21no—
274#685—21no—
275#685—21no—
276#685—21no—
277C4⋊Dic5—31no—
278C4⋊Dic5—61no—
279C4⋊Dic5#6711yescharacteristic
280#683—21no—
281#683—21no—
282#683—21no—
283#683—61no—
284#683—61no—
285#683—61no—
286#683—61no—
287#683—61no—
288#683#6711yescharacteristic
289#683#6711yescharacteristic
290C4×Dic5—21no—
291C4×Dic5—61no—
292C4×Dic5—61no—
293C4×Dic5—61no—
294C4×Dic5C22×D311yescharacteristic
295C4×Dic5C22×D311yescharacteristic
296C2×#168—31no—
297C2×#168—31no—
298Dic20—62no—
299#677—62no—
300#557—151no—
301#556—51no—
302#488—151no—
303#488—151no—
304#487—151no—
305#479—31no—
306#479—151no—
307#474—151no—
308#464—151no—
309#464—151no—
310#462—151no—
311C8×Q8—151no—
312C4×Q16—151no—
313C4×Q16—151no—
314C4×SD16—151no—
315C22×C3×C5C22×D411yescharacteristic
316C2×C3×D5—41no—
317C2×C3×D5—41no—
318C2×C3×D5—41no—
319C3×C4×C5—21no—
320C3×C4×C5—21no—
321C3×C4×C5—41no—
322C3×C4×C5—41no—
323C3×C4×C5C2×#4111yescharacteristic
324C3×C4×C52−1+411yescharacteristic
325Dic15—22no—
326Dic15—41no—
327C3×Dic5—21no—
328C3×Dic5—21no—
329C3×Dic5—21no—
330C3×Dic5—41no—
331C3×Dic5#13512yes—
332C5×Dic3—41no—
333C5×Dic3—41no—
334C2×C3×Q8—51no—
335C2×C3×Q8—51no—
336C2×C3×Q8C22×D511yescharacteristic
337C2×C3×D4—51no—
338C22×C3×C4—101no—
339C2×Dic6—51no—
340C2×Dic6—101no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—51no—
343C3×C4⋊C4—51no—
344C3×C4⋊C4—51no—
345C3×C4⋊C4—101no—
346C3×C4⋊C4—101no—
347C3×C4⋊C4—101no—
348C3×C4⋊C4C22×D511yescharacteristic
349C3×C22⋊C4—101no—
350C3×C22⋊C4—101no—
351C3×C22⋊C4—101no—
352C3×C22⋊C4—101no—
353C3×C22⋊C4—101no—
354C3×C42—21no—
355C3×C42—51no—
356C3×C42—51no—
357C3×C42—101no—
358C3×C42C22×D511yescharacteristic
359#216—102no—
360#216—102no—
361#214—102no—
362C4⋊Dic3—51no—
363C4⋊Dic3—101no—
364C4⋊Dic3C22×D511yescharacteristic
365C4⋊Dic3C22×D511yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373C4×Dic3—101no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C2×C3⋊C8—51no—
377C2×C3⋊C8—51no—
378C2×C3⋊C8C22×D511yescharacteristic
379C2×C3⋊C8C22×D511yescharacteristic
380C22×D5—21no—
381C5×Q8—21no—
382C5×Q8—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—61no—
386C2×C4×C5—61no—
387C2×C4×C5C2×#6711yescharacteristic
388C2×C4×C5C2×#6711yescharacteristic
389C2×C4×C5C23×D311yescharacteristic
390C2×Dic5—21no—
391C2×Dic5—61no—
392C2×Dic5—61no—
393C2×Dic5C2×#6711yescharacteristic
394C2×Dic5C2×#6711yescharacteristic
395C2×Dic5C2×#6711yescharacteristic
396C2×Dic5C2×#6711yescharacteristic
397D20—21no—
398D20—21no—
399C4×D5—42no—
400Dic10—22no—
401Dic10—21no—
402Dic10—21no—
403Dic10—32no—
404Dic10—61no—
405Dic10—122no—
406C5×C8—61no—
407C5×C8—61no—
408#168—61no—
409#168—61no—
410C2×Q16—151no—
411C2×Q16—151no—
412C2×SD16—151no—
413C4⋊Q8—51no—
414C4⋊Q8—151no—
415C4⋊Q8—301no—
416#126—101no—
417#126—101no—
418#125—31no—
419#125—151no—
420#125—301no—
421#125—301no—
422#124—51no—
423#124—51no—
424C22⋊Q8—101no—
425C4×Q8—51no—
426C4×Q8—51no—
427C4×Q8—151no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—301no—
431C4×Q8D3×D511yescharacteristic
432C4×D4—51no—
433#117—101no—
434#107—31no—
435#107—151no—
436#106—31no—
437C4⋊C8—31no—
438C4⋊C8—151no—
439C4⋊C8—151no—
440#103—31no—
441#103—31no—
442#103—151no—
443#103—151no—
444#103—151no—
445#103—151no—
446#103—151no—
447#102—151no—
448#102—151no—
449#102—151no—
450C4×C8—151no—
451C4×C8—151no—
452C4×C8—151no—
453C2×C3×C5#54811yescharacteristic
454C2×C3×C5C2×#13511yescharacteristic
455C2×C3×C5#57811yescharacteristic
456C3×D5—81no—
457C23×C3—101no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—102no—
461C3×Q8—101no—
462C3×Q8—101no—
463C3×D4—101no—
464C3×D4—101no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—51no—
468C2×C3×C4—51no—
469C2×C3×C4—51no—
470C2×C3×C4—51no—
471C2×C3×C4—101no—
472C2×C3×C4—202no—
473C2×C3×C4D4×D511yescharacteristic
474C2×C3×C4D4×D511yescharacteristic
475C2×C3×C4C23×D511yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—101no—
479C2×Dic3—101no—
480Dic6—52no—
481Dic6—101no—
482Dic6—202no—
483C3⋊C8—21no—
484C3⋊C8—21no—
485C3⋊C8—101no—
486C3⋊C8—101no—
487C22×C5C22×#6711yescharacteristic
488C2×D5—41no—
489C2×D5—41no—
490C2×D5—41no—
491C4×C5—21no—
492C4×C5—21no—
493C4×C5—41no—
494C4×C5—41no—
495C4×C5—121no—
496C4×C5—121no—
497C4×C5D3×#4111yescharacteristic
498C4×C5#101011yescharacteristic
499Dic5—21no—
500Dic5—21no—
501Dic5—21no—
502Dic5—41no—
503Dic5—62no—
504Dic5—121no—
505Dic5#95012yes—
506C2×Q8—51no—
507C2×Q8—51no—
508C2×Q8—151no—
509C2×Q8—301no—
510C2×Q8C2×D3×D511yescharacteristic
511C2×D4—51no—
512C22×C4—101no—
513Q16—302no—
514Q16—302no—
515SD16—302no—
516C2×C8—31no—
517C2×C8—31no—
518C2×C8—151no—
519C2×C8—151no—
520C4⋊C4—21no—
521C4⋊C4—31no—
522C4⋊C4—31no—
523C4⋊C4—51no—
524C4⋊C4—51no—
525C4⋊C4—51no—
526C4⋊C4—61no—
527C4⋊C4—61no—
528C4⋊C4—101no—
529C4⋊C4—101no—
530C4⋊C4—101no—
531C4⋊C4—151no—
532C4⋊C4—301no—
533C4⋊C4—301no—
534C4⋊C4—301no—
535C4⋊C4—301no—
536C4⋊C4—301no—
537C4⋊C4—301no—
538C4⋊C4C2×D3×D511yescharacteristic
539C22⋊C4—101no—
540C22⋊C4—101no—
541C22⋊C4—101no—
542C22⋊C4—101no—
543C22⋊C4—101no—
544C42—21no—
545C42—51no—
546C42—51no—
547C42—101no—
548C42—301no—
549C42—301no—
550C42—301no—
551C42C2×D3×D511yescharacteristic
552C3×C5#336411yescharacteristic, complemented, Hall
553C22×C3—201no—
554C22×C3—201no—
555C22×C3—201no—
556C22×C3C2×D4×D511yescharacteristic
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—41no—
560C3×C4—41no—
561C3×C4—52no—
562C3×C4—101no—
563C3×C4—101no—
564C3×C4—101no—
565C3×C4—201no—
566C3×C4#414711yescharacteristic
567C3×C4D5×#4111yescharacteristic
568Dic3—41no—
569Dic3—41no—
570Dic3—102no—
571Dic3—201no—
572C2×C5C2×#95011yescharacteristic
573C2×C5#583111yescharacteristic
574C2×C5#583811yescharacteristic
575D5—81no—
576C23—101no—
577Q8—21no—
578Q8—21no—
579Q8—102no—
580Q8—101no—
581Q8—101no—
582Q8—152no—
583Q8—301no—
584Q8—602no—
585D4—101no—
586D4—101no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—51no—
590C2×C4—51no—
591C2×C4—51no—
592C2×C4—51no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—101no—
596C2×C4—202no—
597C2×C4—301no—
598C2×C4—301no—
599C2×C4D5×#6711yescharacteristic
600C2×C4D5×#6711yescharacteristic
601C2×C4C22×D3×D511yescharacteristic
602C8—61no—
603C8—61no—
604C8—301no—
605C8—301no—
606C2×C3—401no—
607C2×C3#6596711yescharacteristic
608C2×C3D5×#13511yescharacteristic
609C2×C3#6611311yescharacteristic
610C5#8367611yescharacteristic, complemented, Sylow
611C22—201no—
612C22—201no—
613C22—201no—
614C22C2×D5×#6711yescharacteristic
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—52no—
620C4—101no—
621C4—101no—
622C4—101no—
623C4—121no—
624C4—121no—
625C4—201no—
626C4—302no—
627C4—601no—
628C4#9200011yescharacteristic
629C4#9201611yescharacteristic
630C3#1061294711yescharacteristic, complemented, Sylow
631C2—401no—
632C2#1175421511yescharacteristic
633C2#1175510211yescharacteristic
634C2D5×#95011yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3364
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
2. #11752463C2semidirect
3. C4×#6718C2semidirect
4. C5×#5022C2semidirect
5. #11749349C2semidirect
8. #11749246C2semidirect
10. #11747390C2semidirect
11. #11747270C2semidirect
15. #11746846C2semidirect
134. #5022D5semidirect
552. C3×C5#3364semidirect
610. C5#83676semidirect
630. C3#10612947semidirect

Maximal subgroups

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

subgroupindex
C3×#659022
#117524632
C4×#67182
C5×#50222
#117493492
#117493312
#117492482
#117492462
#117474102
#117473902
#117472702
#117472682
#117470842
#117468962
#117468462
#106129473
#836765