Finite Group Databasebeta

← #14472084

Subgroups — #14472084

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#11756444C211yesmaximal, characteristic, complemented
2#11756327C211yesmaximal, characteristic
3C3×C5×#479C211yesmaximal, characteristic, complemented
4#11751169C211yesmaximal, characteristic
5C4×#6718C211yesmaximal, characteristic, complemented
6#11750991C211yesmaximal, characteristic
7#11750974C211yesmaximal, characteristic, complemented
8#11750958C211yesmaximal, characteristic, complemented
9#11750953C211yesmaximal, characteristic
10#11750946C211yesmaximal, characteristic
11#11750931C211yesmaximal, characteristic, complemented
12#11750901C211yesmaximal, characteristic
13#11750899C211yesmaximal, characteristic
14#11750896C211yesmaximal, characteristic, complemented
15#11750893C211yesmaximal, characteristic, complemented
16#10612947—31nomaximal, Hall
17C3×C5×#125C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19#91836C2211yescharacteristic
20#91833C2211yescharacteristic
21C2×#6718C2211yescharacteristic
22C2×Dic60C2211yescharacteristic
23C2×#6706C2211yescharacteristic
24#91787—21no—
25#91785—21no—
26#91782C2211yescharacteristic
27#91779C2211yescharacteristic
28#91778—21no—
29#91778—21no—
30#91777—21no—
31#91777C2211yescharacteristic
32#91776—21no—
33#91776C2211yescharacteristic
34#91776C2211yescharacteristic
35#91776C2211yescharacteristic
36#91765—21no—
37#91764C2211yescharacteristic
38#91761—21no—
39C4×Dic30C2211yescharacteristic
40C4×Dic30C2211yescharacteristic
41C3×C5×#107C2211yescharacteristic
42C3×C5×#106C2211yescharacteristic
43C3×C5×C4⋊C8C2211yescharacteristic
44C3×C5×#103C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46#91119C2211yescharacteristic
47#91105C2211yescharacteristic
48#91100C2211yescharacteristic
49#91098C2211yescharacteristic
50#91098C2211yescharacteristic
51C8×Dic15C2211yescharacteristic
52C8×Dic15C2211yescharacteristic
53#91094C2211yescharacteristic
54#91094C2211yescharacteristic
55#91094C2211yescharacteristic
56#91093C2211yescharacteristic
57#91093C2211yescharacteristic
58#91091C2211yescharacteristic
59C4×C3⋊#168C2211yescharacteristic
60#81216—51nomaximal, Hall
61#66019—31no—
62#65902—31no—
63C5×#479D311yescharacteristic, complemented
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×D60C2311yescharacteristic
78C2×C4×D15—21no—
79C2×Dic30—21no—
80C2×Dic30D411yescharacteristic
81C2×Dic30C2311yescharacteristic
82C2×Dic30C2311yescharacteristic
83C2×C3×C5×C8C2311yescharacteristic
84C2×C3×C5×C8C2311yescharacteristic
85C3×C5×C4⋊C4—21no—
86C3×C5×C4⋊C4—21no—
87C3×C5×C4⋊C4—21no—
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C42×C5—21no—
92C3×C42×C5C2311yescharacteristic
93#6718—22no—
94#6714—21no—
95#6714—21no—
96#6714—21no—
97#6714—21no—
98#6714—21no—
99C4⋊Dic15—21no—
100C4⋊Dic15D411yescharacteristic
101C4⋊Dic15C2311yescharacteristic
102#6712—21no—
103#6712—21no—
104#6712—21no—
105#6712—21no—
106#6712—21no—
107#6712—21no—
108#6712—21no—
109#6712—21no—
110#6712D411yescharacteristic
111#6712D411yescharacteristic
112C4×Dic15—21no—
113C4×Dic15—21no—
114C4×Dic15—21no—
115C4×Dic15—21no—
116C4×Dic15C2311yescharacteristic
117C4×Dic15C2311yescharacteristic
118C2×C3⋊#168C2311yescharacteristic
119C2×C3⋊#168C2311yescharacteristic
120Dic60—22no—
121#6706—22no—
122#5685—51no—
123#5568—51no—
124C3×#479D511yescharacteristic, complemented
125#5068—51no—
126C4×#216—51no—
127#4890—51no—
128#4873—51no—
129#4857—51no—
130#4852—51no—
131#4845—51no—
132#4830—51no—
133#4800—51no—
134#4798—51no—
135#4795—51no—
136#4792—51no—
137C5×#125C2×D311yescharacteristic
138C4×C5×Q8C2×D311yescharacteristic
139#4093—31no—
140#4090—31no—
141C2×#689—31no—
142C2×Dic20—31no—
143C2×#677—31no—
144#4044—61no—
145#4042—61no—
146#4039—31no—
147#4036—31no—
148#4035—61no—
149#4035—61no—
150#4034—31no—
151#4034—61no—
152#4033—31no—
153#4033—31no—
154#4033—31no—
155#4033—61no—
156#4022—61no—
157#4021—31no—
158#4018—61no—
159C4×Dic10—31no—
160C4×Dic10—31no—
161C5×#107C2×D311yescharacteristic
162C5×#106C2×D311yescharacteristic
163C5×C4⋊C8C2×D311yescharacteristic
164C5×#103C2×D311yescharacteristic
165C5×#103C2×D311yescharacteristic
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×D15—21no—
182C3×C5×Q8—21no—
183C3×C5×Q8—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15C2×D411yescharacteristic
195C2×Dic15C2×D411yescharacteristic
196C2×Dic15C2×D411yescharacteristic
197C2×Dic15C2×D411yescharacteristic
198D60—21no—
199D60—21no—
200C4×D15—42no—
201Dic30—21no—
202Dic30—22no—
203Dic30—21no—
204Dic30—21no—
205Dic30—42no—
206Dic30#4112yes—
207C3×C5×C8—21no—
208C3×C5×C8—21no—
209C3⋊#168—21no—
210C3⋊#168—21no—
211C3×#125C2×D511yescharacteristic
212C3×C4×Q8C2×D511yescharacteristic
213#947—51no—
214#944—51no—
215C2×#216—51no—
216C2×Dic12—51no—
217C2×#204—51no—
218#898—101no—
219#896—101no—
220#893—51no—
221#890—51no—
222#889—101no—
223#889—101no—
224#888—51no—
225#888—101no—
226#887—51no—
227#887—51no—
228#887—51no—
229#887—101no—
230#876—101no—
231#875—51no—
232#872—101no—
233C4×Dic6—51no—
234C4×Dic6—51no—
235C3×#107C2×D511yescharacteristic
236C3×#106C2×D511yescharacteristic
237C3×C4⋊C8C2×D511yescharacteristic
238C3×#103C2×D511yescharacteristic
239C3×#103C2×D511yescharacteristic
240#835—51no—
241#821—51no—
242#816—51no—
243Dic3⋊C8—51no—
244Dic3⋊C8—51no—
245C8×Dic3—51no—
246C8×Dic3—51no—
247#810—51no—
248#810—51no—
249#810—51no—
250#809—51no—
251#809—51no—
252#807—51no—
253C4×C3⋊C8—51no—
254C2×C5×Q8C22×D311yescharacteristic
255C2×D20—31no—
256C2×C4×D5—61no—
257C2×Dic10—31no—
258C2×Dic10—31no—
259C2×Dic10—31no—
260C2×Dic10—61no—
261C2×C5×C8C22×D311yescharacteristic
262C2×C5×C8C22×D311yescharacteristic
263C5×C4⋊C4—21no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4—21no—
266C5×C4⋊C4C22×D311yescharacteristic
267C5×C4⋊C4C22×D311yescharacteristic
268C5×C4⋊C4C22×D311yescharacteristic
269C42×C5—21no—
270C42×C5C22×D311yescharacteristic
271#689—62no—
272#685—61no—
273#685—61no—
274#685—61no—
275#685—61no—
276#685—61no—
277C4⋊Dic5—31no—
278C4⋊Dic5—31no—
279C4⋊Dic5—61no—
280#683—31no—
281#683—31no—
282#683—61no—
283#683—61no—
284#683—61no—
285#683—61no—
286#683—61no—
287#683—61no—
288#683—61no—
289#683—61no—
290C4×Dic5—31no—
291C4×Dic5—31no—
292C4×Dic5—61no—
293C4×Dic5—61no—
294C4×Dic5—61no—
295C4×Dic5—61no—
296C2×#168—31no—
297C2×#168—31no—
298Dic20—62no—
299#677—62no—
300#557—151no—
301#556—151no—
302#488—151no—
303#488—151no—
304#487—151no—
305#479—151no—
306#479D1511yescharacteristic, complemented
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×D15—41no—
317C2×D15—41no—
318C2×D15—41no—
319C3×C4×C5—21no—
320C3×C4×C5—21no—
321C3×C4×C5—41no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×C4×C5C2×#4111yescharacteristic
326C3×C4×C52−1+411yescharacteristic
327Dic15—22no—
328Dic15—21no—
329Dic15—21no—
330Dic15—21no—
331Dic15—41no—
332Dic15—41no—
333Dic15#13512yes—
334C2×C3×Q8C22×D511yescharacteristic
335C2×D12—51no—
336C2×C4×D3—101no—
337C2×Dic6—51no—
338C2×Dic6—51no—
339C2×Dic6—51no—
340C2×Dic6—101no—
341C2×C3×C8C22×D511yescharacteristic
342C2×C3×C8C22×D511yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4C22×D511yescharacteristic
347C3×C4⋊C4C22×D511yescharacteristic
348C3×C4⋊C4C22×D511yescharacteristic
349C3×C42—21no—
350C3×C42C22×D511yescharacteristic
351#216—102no—
352(C2×D3)⋊C4—101no—
353(C2×D3)⋊C4—101no—
354(C2×D3)⋊C4—101no—
355(C2×D3)⋊C4—101no—
356(C2×D3)⋊C4—101no—
357C4⋊Dic3—51no—
358C4⋊Dic3—51no—
359C4⋊Dic3—101no—
360Dic3⋊C4—51no—
361Dic3⋊C4—51no—
362Dic3⋊C4—101no—
363Dic3⋊C4—101no—
364Dic3⋊C4—101no—
365Dic3⋊C4—101no—
366Dic3⋊C4—101no—
367Dic3⋊C4—101no—
368Dic3⋊C4—101no—
369Dic3⋊C4—101no—
370C4×Dic3—51no—
371C4×Dic3—51no—
372C4×Dic3—101no—
373C4×Dic3—101no—
374C4×Dic3—101no—
375C4×Dic3—101no—
376C2×C3⋊C8—51no—
377C2×C3⋊C8—51no—
378Dic12—102no—
379#204—102no—
380C22×D5—61no—
381C5×Q8—21no—
382C5×Q8—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5D3×D411yescharacteristic
388C2×C4×C5D3×D411yescharacteristic
389C2×C4×C5C23×D311yescharacteristic
390C2×Dic5—31no—
391C2×Dic5—31no—
392C2×Dic5—31no—
393C2×Dic5—31no—
394C2×Dic5—61no—
395C2×Dic5—61no—
396C2×Dic5—61no—
397D20—61no—
398D20—61no—
399C4×D5—122no—
400Dic10—32no—
401Dic10—62no—
402Dic10—61no—
403Dic10—61no—
404Dic10—61no—
405Dic10—122no—
406C5×C8—21no—
407C5×C8—21no—
408#168—61no—
409#168—61no—
410C2×Q16—151no—
411C2×Q16—151no—
412C2×SD16—151no—
413C4⋊Q8—151no—
414C4⋊Q8—151no—
415C4⋊Q8—301no—
416#126—301no—
417#126—301no—
418#125—151no—
419#125—301no—
420#125—301no—
421#125C2×D1511yescharacteristic
422#124—151no—
423#124—151no—
424C22⋊Q8—301no—
425C4×Q8—151no—
426C4×Q8—151no—
427C4×Q8—151no—
428C4×Q8—151no—
429C4×Q8—151no—
430C4×Q8—301no—
431C4×Q8C2×D1511yescharacteristic
432C4×D4—151no—
433#117—301no—
434#107—151no—
435#107C2×D1511yescharacteristic
436#106C2×D1511yescharacteristic
437C4⋊C8—151no—
438C4⋊C8—151no—
439C4⋊C8C2×D1511yescharacteristic
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×C8—151no—
453C2×C3×C5#54811yescharacteristic
454C2×C3×C5C2×#13511yescharacteristic
455C2×C3×C5#57811yescharacteristic
456D15—81no—
457C22×D3—101no—
458C3×Q8—21no—
459C3×Q8—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4D4×D511yescharacteristic
465C2×C3×C4D4×D511yescharacteristic
466C2×C3×C4C23×D511yescharacteristic
467C2×Dic3—51no—
468C2×Dic3—51no—
469C2×Dic3—51no—
470C2×Dic3—51no—
471C2×Dic3—101no—
472C2×Dic3—101no—
473C2×Dic3—101no—
474D12—101no—
475D12—101no—
476C4×D3—202no—
477Dic6—52no—
478Dic6—102no—
479Dic6—101no—
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—41no—
494C4×C5—41no—
495C4×C5—41no—
496C4×C5—41no—
497C4×C5#100711yescharacteristic
498C4×C5D3×#4111yescharacteristic
499Dic5—32no—
500Dic5—62no—
501Dic5—61no—
502Dic5—61no—
503Dic5—61no—
504Dic5—121no—
505Dic5—121no—
506C2×Q8—151no—
507C2×Q8—151no—
508C2×Q8—151no—
509C2×Q8—301no—
510C2×Q8C22×D1511yescharacteristic
511C2×D4—151no—
512C22×C4—301no—
513Q16—302no—
514Q16—302no—
515SD16—302no—
516C2×C8—151no—
517C2×C8—151no—
518C2×C8C22×D1511yescharacteristic
519C2×C8C22×D1511yescharacteristic
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
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⋊C4C22×D1511yescharacteristic
537C4⋊C4C22×D1511yescharacteristic
538C4⋊C4C22×D1511yescharacteristic
539C22⋊C4—301no—
540C22⋊C4—301no—
541C22⋊C4—301no—
542C22⋊C4—301no—
543C22⋊C4—301no—
544C42—21no—
545C42—151no—
546C42—151no—
547C42—301no—
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—41no—
560C3×C4—41no—
561C3×C4—41no—
562C3×C4—41no—
563C3×C4#414711yescharacteristic
564C3×C4D5×#4111yescharacteristic
565Dic3—52no—
566Dic3—101no—
567Dic3—101no—
568Dic3—101no—
569Dic3—102no—
570Dic3—201no—
571Dic3—201no—
572C2×C5#563311yescharacteristic
573C2×C5D3×#13511yescharacteristic
574C2×C5#577911yescharacteristic
575D5—241no—
576C23—301no—
577Q8—21no—
578Q8—21no—
579Q8—152no—
580Q8—302no—
581Q8—301no—
582Q8—301no—
583Q8—301no—
584Q8—602no—
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#6596711yescharacteristic
607C2×C3D5×#13511yescharacteristic
608C2×C3#6611311yescharacteristic
609D3—401no—
610C5#8121611yescharacteristic, complemented, Sylow
611C22—601no—
612C22—601no—
613C22—601no—
614C22C2×D4×D1511yescharacteristic
615C4—21no—
616C4—21no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—152no—
622C4—302no—
623C4—301no—
624C4—301no—
625C4—301no—
626C4—601no—
627C4—601no—
628C4#9209811yescharacteristic
629C4#41×D1511yescharacteristic
630C3#1061294711yescharacteristic, complemented, Sylow
631C2—1201no—
632C2#1175639211yescharacteristic
633C2D15×#13511yescharacteristic
634C2#1175653811yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#479C2
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenter#479D15
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #11756444C2semidirect
3. C3×C5×#479C2semidirect
5. C4×#6718C2semidirect
7. #11750974C2semidirect
8. #11750958C2semidirect
11. #11750931C2semidirect
14. #11750896C2semidirect
15. #11750893C2semidirect
63. C5×#479D3semidirect
124. C3×#479D5semidirect
306. #479D15semidirect
552. C3×C5#3364semidirect
610. C5#81216semidirect
630. C3#10612947semidirect

Maximal subgroups

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

subgroupindex
#117564442
#117563272
C3×C5×#4792
#117511692
C4×#67182
#117509912
#117509742
#117509582
#117509532
#117509462
#117509312
#117509012
#117508992
#117508962
#117508932
#106129473
#812165