Finite Group Databasebeta

← #14472078

Subgroups — #14472078

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
1#11756328C211yesmaximal, characteristic, complemented
2#11756327C211yesmaximal, characteristic
3C3×C4×C5×Q16C211yesmaximal, characteristic, complemented
4#11751286C211yesmaximal, characteristic
5#11751283C211yesmaximal, characteristic, complemented
6#11751129C211yesmaximal, characteristic
7#11751123C211yesmaximal, characteristic, complemented
8#11750991C211yesmaximal, characteristic
9#11750978C211yesmaximal, characteristic, complemented
10#11750901C211yesmaximal, characteristic
11#11750893C211yesmaximal, characteristic, complemented
12#11750891C211yesmaximal, characteristic, complemented
13#11750889C211yesmaximal, characteristic
14#11750798C211yesmaximal, characteristic
15C8×Dic30C211yesmaximal, characteristic, complemented
16#10611431—31nomaximal, Hall
17C2×C3×C5×Q16C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19C3×C4×C5×Q8C2211yescharacteristic
20#91836C2211yescharacteristic
21Q8×Dic15C2211yescharacteristic
22Q8×Dic15C2211yescharacteristic
23#91833C2211yescharacteristic
24C2×#6718C2211yescharacteristic
25C2×#6717C2211yescharacteristic
26#91787—21no—
27#91785—21no—
28#91782C2211yescharacteristic
29#91779—21no—
30#91779C2211yescharacteristic
31#91777—21no—
32#91777C2211yescharacteristic
33#91776C2211yescharacteristic
34#91765—21no—
35#91764C2211yescharacteristic
36#91761—21no—
37#91759—21no—
38#91759C2211yescharacteristic
39C4×Dic30—21no—
40C4×Dic30C2211yescharacteristic
41C3×C5×#107C2211yescharacteristic
42C3×C5×#103C2211yescharacteristic
43C3×C5×#103C2211yescharacteristic
44C3×C4×C5×C8C2211yescharacteristic
45#91119C2211yescharacteristic
46#91119C2211yescharacteristic
47#91105C2211yescharacteristic
48#91105C2211yescharacteristic
49#91100C2211yescharacteristic
50#91100C2211yescharacteristic
51#91098C2211yescharacteristic
52#91098C2211yescharacteristic
53C8×Dic15C2211yescharacteristic
54C8×Dic15C2211yescharacteristic
55#91094C2211yescharacteristic
56#91093C2211yescharacteristic
57#91092C2211yescharacteristic
58#91091C2211yescharacteristic
59C4⋊(C3⋊#168)C2211yescharacteristic
60#79700—51nomaximal, Hall
61#65903—31no—
62#65902—31no—
63C4×C5×Q16D311yescharacteristic, complemented
64#65474—31no—
65#65471—31no—
66#65317—31no—
67#65311—31no—
68#65179—31no—
69#65166—31no—
70#65089—31no—
71#65081—31no—
72#65079—31no—
73#65077—31no—
74#64986—31no—
75C8×Dic10—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×Dic30—21no—
81C2×Dic30D411yescharacteristic
82C2×Dic30C2311yescharacteristic
83C3×C5×Q16—22no—
84C2×C3×C5×C8C2311yescharacteristic
85C2×C3×C5×C8C2311yescharacteristic
86C3×C5×C4⋊C4—21no—
87C3×C5×C4⋊C4—21no—
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C42×C5—21no—
91C3×C42×C5—21no—
92C3×C42×C5C2311yescharacteristic
93#6718—22no—
94#6717—22no—
95#6714—21no—
96#6714—21no—
97#6714—21no—
98#6714—21no—
99#6714—21no—
100C4⋊Dic15—21no—
101C4⋊Dic15—21no—
102C4⋊Dic15—21no—
103C4⋊Dic15D411yescharacteristic
104C4⋊Dic15C2311yescharacteristic
105C4⋊Dic15C2311yescharacteristic
106#6712—21no—
107#6712—21no—
108#6712—21no—
109#6712—21no—
110#6712—21no—
111#6712—21no—
112#6712—21no—
113#6712D411yescharacteristic
114#6712D411yescharacteristic
115C4×Dic15—21no—
116C4×Dic15—21no—
117C4×Dic15—21no—
118C4×Dic15C2311yescharacteristic
119C4×Dic15C2311yescharacteristic
120C2×C3⋊#168C2311yescharacteristic
121C2×C3⋊#168C2311yescharacteristic
122#5569—51no—
123#5568—51no—
124C3×C4×Q16D511yescharacteristic, complemented
125#5185—51no—
126#5182—51no—
127#5028—51no—
128#5022—51no—
129#4890—51no—
130#4877—51no—
131#4800—51no—
132#4792—51no—
133#4790—51no—
134#4788—51no—
135#4697—51no—
136C8×Dic6—51no—
137C2×C5×Q16C2×D311yescharacteristic
138C4×C5×Q8C2×D311yescharacteristic
139C4×C5×Q8C2×D311yescharacteristic
140#4093—31no—
141Q8×Dic5—31no—
142Q8×Dic5—31no—
143#4090—31no—
144C2×#689—31no—
145C2×#688—31no—
146#4044—61no—
147#4042—61no—
148#4039—31no—
149#4036—31no—
150#4036—61no—
151#4034—31no—
152#4034—61no—
153#4033—31no—
154#4022—61no—
155#4021—31no—
156#4018—61no—
157#4016—31no—
158#4016—61no—
159C4×Dic10—31no—
160C4×Dic10—61no—
161C5×#107C2×D311yescharacteristic
162C5×#103C2×D311yescharacteristic
163C5×#103C2×D311yescharacteristic
164C4×C5×C8C2×D311yescharacteristic
165#3967—31no—
166#3967—31no—
167#3953—31no—
168#3953—31no—
169#3948—31no—
170#3948—31no—
171#3946—31no—
172#3946—31no—
173C8×Dic5—31no—
174C8×Dic5—31no—
175#3942—31no—
176#3941—31no—
177#3940—31no—
178#3939—31no—
179C4⋊#168—31no—
180#3364—151noSylow
181C22×D15—21no—
182C3×C5×Q8—21no—
183C3×C5×Q8—21no—
184C3×C5×Q8—21no—
185C3×C5×Q8#4112yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
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—
195C2×Dic15—21no—
196C2×Dic15C2×D411yescharacteristic
197C2×Dic15C2×D411yescharacteristic
198C2×Dic15C2×D411yescharacteristic
199C2×Dic15C2×D411yescharacteristic
200D60—21no—
201D60—21no—
202C4×D15—42no—
203Dic30—22no—
204Dic30—21no—
205Dic30—21no—
206Dic30—42no—
207C3×C5×C8—21no—
208C3×C5×C8—21no—
209C3⋊#168—21no—
210C3⋊#168—21no—
211C2×C3×Q16C2×D511yescharacteristic
212C3×C4×Q8C2×D511yescharacteristic
213C3×C4×Q8C2×D511yescharacteristic
214#947—51no—
215Q8×Dic3—51no—
216Q8×Dic3—51no—
217#944—51no—
218C2×#216—51no—
219C2×#215—51no—
220#898—101no—
221#896—101no—
222#893—51no—
223#890—51no—
224#890—101no—
225#888—51no—
226#888—101no—
227#887—51no—
228#876—101no—
229#875—51no—
230#872—101no—
231#870—51no—
232#870—101no—
233C4×Dic6—51no—
234C4×Dic6—101no—
235C3×#107C2×D511yescharacteristic
236C3×#103C2×D511yescharacteristic
237C3×#103C2×D511yescharacteristic
238C3×C4×C8C2×D511yescharacteristic
239#835—51no—
240#835—51no—
241#821—51no—
242#821—51no—
243#816—51no—
244#816—51no—
245Dic3⋊C8—51no—
246Dic3⋊C8—51no—
247C8×Dic3—51no—
248C8×Dic3—51no—
249#810—51no—
250#809—51no—
251#808—51no—
252#807—51no—
253C4⋊(C3⋊C8)—51no—
254C2×C5×Q8C22×D311yescharacteristic
255C2×C5×Q8C22×D311yescharacteristic
256C2×D20—31no—
257C2×C4×D5—61no—
258C2×Dic10—31no—
259C2×Dic10—31no—
260C2×Dic10—61no—
261C5×Q16—22no—
262C2×C5×C8C22×D311yescharacteristic
263C2×C5×C8C22×D311yescharacteristic
264C5×C4⋊C4—21no—
265C5×C4⋊C4—21no—
266C5×C4⋊C4C22×D311yescharacteristic
267C5×C4⋊C4C22×D311yescharacteristic
268C42×C5—21no—
269C42×C5—21no—
270C42×C5C22×D311yescharacteristic
271#689—62no—
272#688—62no—
273#685—61no—
274#685—61no—
275#685—61no—
276#685—61no—
277#685—61no—
278C4⋊Dic5—31no—
279C4⋊Dic5—31no—
280C4⋊Dic5—31no—
281C4⋊Dic5—61no—
282C4⋊Dic5—61no—
283C4⋊Dic5—61no—
284#683—31no—
285#683—31no—
286#683—61no—
287#683—61no—
288#683—61no—
289#683—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293C4×Dic5—31no—
294C4×Dic5—31no—
295C4×Dic5—61no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C2×#168—31no—
299C2×#168—31no—
300#557—151no—
301#556—151no—
302#488—151no—
303#488—151no—
304#487—151no—
305#479—151no—
306#479—151no—
307#474—151no—
308#464—151no—
309#464—151no—
310#462—151no—
311C8×Q8—151no—
312C4×Q16—151no—
313C4×Q16D1511yescharacteristic, complemented
314C4×SD16—151no—
315C22×C3×C5C22×D411yescharacteristic
316C2×D15—41no—
317C2×D15—41no—
318C2×D15—41no—
319C3×C4×C5—22no—
320C3×C4×C5—21no—
321C3×C4×C5—21no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×C4×C5C2×#4111yescharacteristic
326C3×C4×C52−1+411yescharacteristic
327Dic15—21no—
328Dic15—21no—
329Dic15—21no—
330Dic15—41no—
331Dic15—41no—
332Dic15—41no—
333Dic15#13512yes—
334C2×C3×Q8C22×D511yescharacteristic
335C2×C3×Q8C22×D511yescharacteristic
336C2×D12—51no—
337C2×C4×D3—101no—
338C2×Dic6—51no—
339C2×Dic6—51no—
340C2×Dic6—101no—
341C3×Q16—22no—
342C2×C3×C8C22×D511yescharacteristic
343C2×C3×C8C22×D511yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4C22×D511yescharacteristic
347C3×C4⋊C4C22×D511yescharacteristic
348C3×C42—21no—
349C3×C42—21no—
350C3×C42C22×D511yescharacteristic
351#216—102no—
352#215—102no—
353(C2×D3)⋊C4—101no—
354(C2×D3)⋊C4—101no—
355(C2×D3)⋊C4—101no—
356(C2×D3)⋊C4—101no—
357(C2×D3)⋊C4—101no—
358C4⋊Dic3—51no—
359C4⋊Dic3—51no—
360C4⋊Dic3—51no—
361C4⋊Dic3—101no—
362C4⋊Dic3—101no—
363C4⋊Dic3—101no—
364Dic3⋊C4—51no—
365Dic3⋊C4—51no—
366Dic3⋊C4—101no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373C4×Dic3—51no—
374C4×Dic3—51no—
375C4×Dic3—101no—
376C4×Dic3—101no—
377C4×Dic3—101no—
378C2×C3⋊C8—51no—
379C2×C3⋊C8—51no—
380C22×D5—61no—
381C5×Q8—21no—
382C5×Q8—21no—
383C5×Q8—21no—
384C5×Q8#23512yes—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5D3×D411yescharacteristic
390C2×C4×C5D3×D411yescharacteristic
391C2×C4×C5C23×D311yescharacteristic
392C2×Dic5—31no—
393C2×Dic5—31no—
394C2×Dic5—31no—
395C2×Dic5—31no—
396C2×Dic5—61no—
397C2×Dic5—61no—
398C2×Dic5—61no—
399D20—61no—
400D20—61no—
401C4×D5—122no—
402Dic10—62no—
403Dic10—61no—
404Dic10—61no—
405Dic10—122no—
406C5×C8—21no—
407C5×C8—21no—
408#168—61no—
409#168—61no—
410C2×Q16—151no—
411C2×Q16C2×D1511yescharacteristic
412C2×SD16—151no—
413C4⋊Q8—151no—
414C4⋊Q8—151no—
415C4⋊Q8—301no—
416#126—301no—
417#126—301no—
418#125—151no—
419#125—151no—
420#125—301no—
421#125—301no—
422#124—151no—
423#124—151no—
424C22⋊Q8—301no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—151no—
429C4×Q8—301no—
430C4×Q8C2×D1511yescharacteristic
431C4×Q8C2×D1511yescharacteristic
432C4×D4—151no—
433#117—301no—
434#107—151no—
435#107C2×D1511yescharacteristic
436#106—151no—
437C4⋊C8—151no—
438C4⋊C8—151no—
439C4⋊C8—151no—
440#103—151no—
441#103—151no—
442#103—151no—
443#103—151no—
444#103—151no—
445#103C2×D1511yescharacteristic
446#103C2×D1511yescharacteristic
447#102—151no—
448#102—151no—
449#102—151no—
450C4×C8—151no—
451C4×C8—151no—
452C4×C8C2×D1511yescharacteristic
453C2×C3×C5#54811yescharacteristic
454C2×C3×C5C2×#13511yescharacteristic
455C2×C3×C5#57811yescharacteristic
456D15—81no—
457C22×D3—101no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8#70912yes—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4D4×D511yescharacteristic
467C2×C3×C4D4×D511yescharacteristic
468C2×C3×C4C23×D511yescharacteristic
469C2×Dic3—51no—
470C2×Dic3—51no—
471C2×Dic3—51no—
472C2×Dic3—51no—
473C2×Dic3—101no—
474C2×Dic3—101no—
475C2×Dic3—101no—
476D12—101no—
477D12—101no—
478C4×D3—202no—
479Dic6—102no—
480Dic6—101no—
481Dic6—101no—
482Dic6—202no—
483C3×C8—21no—
484C3×C8—21no—
485C3⋊C8—101no—
486C3⋊C8—101no—
487C22×C5C2×D3×D411yescharacteristic
488C2×D5—121no—
489C2×D5—121no—
490C2×D5—121no—
491C4×C5—21no—
492C4×C5—21no—
493C4×C5—22no—
494C4×C5—41no—
495C4×C5—41no—
496C4×C5—41no—
497C4×C5C2×#23511yescharacteristic
498C4×C5#101011yescharacteristic
499Dic5—32no—
500Dic5—61no—
501Dic5—61no—
502Dic5—61no—
503Dic5—121no—
504Dic5—121no—
505Dic5—121no—
506C2×Q8—151no—
507C2×Q8—151no—
508C2×Q8—301no—
509C2×Q8C22×D1511yescharacteristic
510C2×Q8C22×D1511yescharacteristic
511C2×D4—151no—
512C22×C4—301no—
513Q16—22no—
514Q16—302no—
515SD16—302no—
516C2×C8—151no—
517C2×C8—151no—
518C2×C8C22×D1511yescharacteristic
519C2×C8C22×D1511yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—151no—
523C4⋊C4—151no—
524C4⋊C4—151no—
525C4⋊C4—151no—
526C4⋊C4—151no—
527C4⋊C4—301no—
528C4⋊C4—301no—
529C4⋊C4—301no—
530C4⋊C4—301no—
531C4⋊C4—301no—
532C4⋊C4—301no—
533C4⋊C4—301no—
534C4⋊C4—301no—
535C4⋊C4—301no—
536C4⋊C4—301no—
537C4⋊C4C22×D1511yescharacteristic
538C4⋊C4C22×D1511yescharacteristic
539C22⋊C4—301no—
540C22⋊C4—301no—
541C22⋊C4—301no—
542C22⋊C4—301no—
543C22⋊C4—301no—
544C42—21no—
545C42—21no—
546C42—151no—
547C42—151no—
548C42—301no—
549C42—301no—
550C42—301no—
551C42C22×D1511yescharacteristic
552C3×C5#336411yescharacteristic, complemented, Hall
553C22×C3C2×D4×D511yescharacteristic
554C2×D3—201no—
555C2×D3—201no—
556C2×D3—201no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—22no—
560C3×C4—41no—
561C3×C4—41no—
562C3×C4—41no—
563C3×C4C2×#70911yescharacteristic
564C3×C4#415011yescharacteristic
565Dic3—52no—
566Dic3—101no—
567Dic3—101no—
568Dic3—101no—
569Dic3—201no—
570Dic3—201no—
571Dic3—201no—
572C2×C5#555211yescharacteristic
573C2×C5#576611yescharacteristic
574C2×C5D3×#13511yescharacteristic
575D5—241no—
576C23—301no—
577Q8—21no—
578Q8—21no—
579Q8—21no—
580Q8—302no—
581Q8—301no—
582Q8—301no—
583Q8—602no—
584Q8#681712yes—
585D4—301no—
586D4—301no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—151no—
592C2×C4—151no—
593C2×C4—151no—
594C2×C4—151no—
595C2×C4—301no—
596C2×C4—301no—
597C2×C4—301no—
598C2×C4—602no—
599C2×C4D4×D1511yescharacteristic
600C2×C4D4×D1511yescharacteristic
601C2×C4C23×D1511yescharacteristic
602C8—21no—
603C8—21no—
604C8—301no—
605C8—301no—
606C2×C3#6588611yescharacteristic
607C2×C3#6610011yescharacteristic
608C2×C3D5×#13511yescharacteristic
609D3—401no—
610C5#7970011yescharacteristic, complemented, Sylow
611C22—601no—
612C22—601no—
613C22—601no—
614C22C2×D4×D1511yescharacteristic
615C4—22no—
616C4—21no—
617C4—21no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—152no—
622C4—301no—
623C4—301no—
624C4—301no—
625C4—601no—
626C4—601no—
627C4—601no—
628C4C2×#681711yescharacteristic
629C4#9210111yescharacteristic
630C3#1061143111yescharacteristic, complemented, Sylow
631C2—1201no—
632C2#1175631111yescharacteristic
633C2#1175652511yescharacteristic
634C2D15×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×Q16C2
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4×Q16D15
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
1. #11756328C2semidirect
3. C3×C4×C5×Q16C2semidirect
5. #11751283C2semidirect
7. #11751123C2semidirect
9. #11750978C2semidirect
11. #11750893C2semidirect
12. #11750891C2semidirect
15. C8×Dic30C2semidirect
63. C4×C5×Q16D3semidirect
124. C3×C4×Q16D5semidirect
313. C4×Q16D15semidirect
552. C3×C5#3364semidirect
610. C5#79700semidirect
630. C3#10611431semidirect

Maximal subgroups

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

subgroupindex
#117563282
#117563272
C3×C4×C5×Q162
#117512862
#117512832
#117511292
#117511232
#117509912
#117509782
#117509012
#117508932
#117508912
#117508892
#117507982
C8×Dic302
#106114313
#797005