Finite Group Databasebeta

← #14427882

Subgroups — #14427882

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4065C211yesmaximal, characteristic, complemented
2#11755270C212yesmaximal, complemented
3C2×D3×C8×D5C211yesmaximal, characteristic, complemented
4#11751289C211yesmaximal, characteristic, complemented
5C5×#5188C211yesmaximal, characteristic, complemented
6#11749277C212yesmaximal, complemented
7#11749274C212yesmaximal, complemented
8#11749207C212yesmaximal, complemented
9#11747932C211yesmaximal, characteristic, complemented
10#11747915C211yesmaximal, characteristic, complemented
11#11747672C211yesmaximal, characteristic, complemented
12#10612489—31nomaximal, Hall
13C2×C3×#713C2212yes—
14C2×C4×D3×D5C2211yescharacteristic
15C2×C3×C5×Q16C2211yescharacteristic, complemented
16#91835C2212yes—
17C2×C8×D15C2211yescharacteristic
18C5×#946C2212yes—
19C2×C5×D3×C8C2211yescharacteristic
20C2×C3×#688C2212yescomplemented
21C3×#4065—24no—
22C2×C3×D40C2211yescharacteristic, complemented
23C2×C3×C8×D5C2211yescharacteristic
24#91474—22no—
25#91465C2212yes—
26#91456C2212yes—
27#91444—22no—
28#91440—22no—
29#91407—22no—
30#91358C2212yes—
31C2×#6648C2211yescharacteristic
32C2×D3×#168C2211yescharacteristic
33C2×D5×C3⋊C8C2211yescharacteristic
34D3×C8×D5—24no—
35#91119C2212yescomplemented
36#91102C2211yescharacteristic, complemented
37C5×#835C2212yescomplemented
38C5×#818C2211yescharacteristic, complemented
39#90985C2212yescomplemented
40#90965C2212yescomplemented
41#90964C2212yescomplemented
42#83914—51nomaximal, Hall
43C2×#4065D311yescharacteristic, complemented
44C22×C8×D5—31no—
45#65961—32no—
46C5×#467—31no—
47#65477—31no—
48#65404—31no—
49#65337—32no—
50#65172—31no—
51#65169—31no—
52#65096—32no—
53#65093—32no—
54C22×D3×D5D411yescharacteristic
55C2×C3×C5×Q8C2312yes—
56C2×C4×D15C2311yescharacteristic
57C2×C4×C5×D3C2311yescharacteristic
58C3×#713—24no—
59C3×#713—24no—
60C2×C3×D20—22no—
61C2×C3×D20C2312yes—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5C2311yescharacteristic
64C2×#1202—22no—
65C2×#1201—22no—
66C2×#1200D411yescharacteristic
67C2×D3×Dic5D411yescharacteristic
68C2×D5×Dic3D411yescharacteristic
69C4×D3×D5—22no—
70C4×D3×D5—22no—
71C3×C5×Q16—22no—
72C2×C3×C5×C8C2311yescharacteristic
73#6714—22no—
74C4⋊Dic15C2312yes—
75#6712—22no—
76C2×C3⋊#168C2311yescharacteristic
77C8×D15—22no—
78C5×(C2×D3)⋊C4—22no—
79C5×C4⋊Dic3C2312yes—
80C5×Dic3⋊C4—22no—
81C2×C5×C3⋊C8C2311yescharacteristic
82C5×D3×C8—22no—
83C3×#688—24no—
84C2×C3×#168C2311yescharacteristic
85C3×D40—22no—
86C3×C8×D5D414yescomplemented
87#6665—22no—
88#6665—22no—
89#6665—22no—
90Dic3×Dic5—22no—
91#6648—22no—
92D3×#168—22no—
93D5×C3⋊C8—22no—
94C2×C3×#135—51no—
95#5828—52no—
96C22×D3×C8—51no—
97#5233—52no—
98#5188—51no—
99#5188D511yescharacteristic, complemented
100#5171—52no—
101#5171—52no—
102#5157—51no—
103#5157—51no—
104#5106—51no—
105C2×#713C2×D312yes—
106C22×C4×D5—31no—
107C2×C5×Q16C2×D311yescharacteristic, complemented
108C22×C5×C8—31no—
109C5×C22⋊Q8—32no—
110#4092—32no—
111C2×#688C2×D312yescomplemented
112#4076—32no—
113C22×#168—31no—
114#4065—24no—
115C2×D40C2×D311yescharacteristic, complemented
116C2×C8×D5—31no—
117C2×C8×D5—31no—
118C2×C8×D5—31no—
119C2×C8×D5—64no—
120C2×C8×D5C2×D311yescharacteristic
121#4041—32no—
122#4040—62no—
123#4039—62no—
124#4038—32no—
125#4028—62no—
126#4027—62no—
127C5×#107—31no—
128C5×#103—32no—
129#3967—32no—
130#3953—32no—
131#3950—31no—
132#3941—32no—
133#3940—32no—
134#3050—151noSylow
135C22×D15C2×D411yescharacteristic
136C22×C5×D3C2×D411yescharacteristic
137C22×C3×D5—22no—
138C22×C3×D5C2×D411yescharacteristic
139C2×D3×D5—22no—
140C2×D3×D5—22no—
141C2×D3×D5—22no—
142C3×C5×Q8—22no—
143C3×C5×Q8—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2411yescharacteristic
146C2×Dic15—22no—
147C2×Dic15C2×D411yescharacteristic
148C4×D15—21no—
149C4×D15—21no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3C2×D411yescharacteristic
152C4×C5×D3—21no—
153C4×C5×D3—21no—
154C2×C3×Dic5C2×D411yescharacteristic
155C3×D20—22no—
156C3×D20—22no—
157C3×D20—44no—
158C3×C4×D5—44no—
159C3×C4×D5C2×D412yes—
160C3×C4×D5#4112yes—
161#1202—44no—
162#1201—44no—
163#1200—22no—
164D3×Dic5—22no—
165D5×Dic3—22no—
166C3×C5×C8C2×D412yes—
167C3⋊#168—21no—
168C3×#168C2×D412yes—
169C5×C3⋊C8—21no—
170C2×C3×#41—52no—
171C22×C4×D3—51no—
172C3×#135—104no—
173C2×C3×Q16C2×D511yescharacteristic, complemented
174C2×C3×SD16—52no—
175C2×C3×D8—51no—
176C22×C3×C8—51no—
177#946—52no—
178#946C2×D512yes—
179#938—52no—
180#938—52no—
181#937—102no—
182#935—102no—
183C4×#67—102no—
184C4×#67—102no—
185#926—52no—
186C22×C3⋊C8—51no—
187C2×D3×C8—51no—
188C2×D3×C8—51no—
189C2×D3×C8—51no—
190C2×D3×C8—104no—
191C2×D3×C8C2×D511yescharacteristic
192#835—52no—
193#835C2×D512yescomplemented
194#832—52no—
195#832—52no—
196#818—51no—
197#818C2×D511yescharacteristic, complemented
198#817—52no—
199C23×D5—31no—
200C2×C5×Q8C22×D312yes—
201C22×C4×C5—31no—
202C2×C22⋊D5—62no—
203C22×Dic5—31no—
204#713—24no—
205#713—24no—
206C2×D20—22no—
207C2×D20—62no—
208C2×D20C22×D312yes—
209C2×C4×D5—22no—
210C2×C4×D5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—31no—
213C2×C4×D5—62no—
214C2×C4×D5—62no—
215C2×C4×D5C22×D311yescharacteristic
216C5×Q16—22no—
217C2×C5×C8—31no—
218C2×C5×C8—62no—
219C2×C5×C8C22×D311yescharacteristic
220C5×C4⋊C4—32no—
221C5×C4⋊C4—62no—
222C5×C22⋊C4—62no—
223#688—24no—
224#685—62no—
225#685—62no—
226#685—62no—
227#685—62no—
228C4⋊Dic5—32no—
229#683—62no—
230C4×Dic5—62no—
231C2×#168—31no—
232C2×#168—62no—
233C2×#168C22×D311yescharacteristic
234D40—22no—
235C8×D5—62no—
236C8×D5—62no—
237C8×D5—62no—
238C8×D5#6714yescomplemented
239C2×#135—51no—
240C23×C8—151no—
241#525—152no—
242#467—31no—
243#467—151no—
244#466—151no—
245#466—151no—
246#465—152no—
247#465—152no—
248#427—151no—
249#416—152no—
250C22×C3×C5C22×D411yescharacteristic
251C2×D15—21no—
252C2×D15—21no—
253C2×D15#13512yescomplemented
254C2×C5×D3—21no—
255C2×C5×D3—21no—
256C2×C5×D3#13512yescomplemented
257C2×C3×D5—21no—
258C2×C3×D5—21no—
259C2×C3×D5—42no—
260C2×C3×D5—42no—
261C2×C3×D5—42no—
262C2×C3×D5#12112yes—
263D3×D5—28no—
264C3×C4×C5—42no—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C2×#4111yescharacteristic
267Dic15—21no—
268Dic15—42no—
269C3×Dic5#12112yes—
270C5×Dic3—21no—
271C5×Dic3—42no—
272C23×D3—51no—
273C3×#41—104no—
274C3×#41—104no—
275C2×C3×Q8C22×D512yes—
276C2×C3×D4—52no—
277C2×C3×D4—102no—
278C22×C3×C4—51no—
279C22×C3×C4—102no—
280C2×#67—102no—
281C2×#67—102no—
282C22×Dic3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—51no—
285C2×C4×D3—51no—
286C2×C4×D3—102no—
287C2×C4×D3—102no—
288C2×C4×D3C22×D511yescharacteristic
289C3×Q16—22no—
290C3×SD16—104no—
291C3×D8—102no—
292C2×C3×C8—51no—
293C2×C3×C8—54no—
294C2×C3×C8C22×D511yescharacteristic
295#217—102no—
296#217—102no—
297#217—102no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—102no—
300C4⋊Dic3—52no—
301C4⋊Dic3C22×D512yes—
302Dic3⋊C4—22no—
303Dic3⋊C4—102no—
304C4×Dic3—102no—
305C2×C3⋊C8—51no—
306C2×C3⋊C8—102no—
307C2×C3⋊C8C22×D511yescharacteristic
308D3×C8—22no—
309D3×C8—102no—
310D3×C8—102no—
311D3×C8—102no—
312C23×C5—31no—
313C22×D5—22no—
314C22×D5—31no—
315C22×D5—62no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5D3×D411yescharacteristic
319C5×Q8—22no—
320C5×Q8—22no—
321C2×C4×C5—22no—
322C2×C4×C5—31no—
323C2×C4×C5—61no—
324C2×C4×C5—61no—
325C2×C4×C5—62no—
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—124no—
328C2×Dic5—31no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5D3×D411yescharacteristic
332D20—22no—
333D20—22no—
334D20—44no—
335D20—124no—
336C4×D5—44no—
337C4×D5—62no—
338C4×D5—61no—
339C4×D5—61no—
340C4×D5—62no—
341C4×D5#23712yes—
342C4×D5C2×#6712yes—
343C5×C8—61no—
344C5×C8C2×#6712yes—
345#168—61no—
346#168C2×#6712yes—
347C2×#41—52no—
348C23×C4—151no—
349#135—104no—
350C2×Q16D3×D511yescharacteristic, complemented
351C2×SD16—52no—
352C2×D8—51no—
353C22×C8—31no—
354C22×C8—51no—
355C22×C8—151no—
356C22×C8—151no—
357C22×C8—151no—
358C22×C8—151no—
359C22×C8—304no—
360#123—302no—
361C22⋊Q8—32no—
362C22⋊Q8—152no—
363#121—152no—
364#121—152no—
365#120—302no—
366C4×D4—302no—
367C4×D4—302no—
368#117—152no—
369#107—31no—
370#107—151no—
371#106—152no—
372#103—32no—
373#103—152no—
374#102—152no—
375#102—152no—
376C2×C3×C5C2×#12111yescharacteristic
377C2×C3×C5C2×#13511yescharacteristic
378C2×C3×C5C2×#13511yescharacteristic
379D15—22no—
380C3×D5—22no—
381C3×D5—82no—
382C5×D3—22no—
383C23×C3—51no—
384C23×C3—102no—
385C22×D3—51no—
386C22×D3—102no—
387C22×D3—102no—
388C22×D3—102no—
389C22×D3D4×D511yescharacteristic
390C3×Q8—22no—
391C3×Q8—22no—
392C3×D4—102no—
393C3×D4—102no—
394C3×D4—204no—
395C2×C3×C4—22no—
396C2×C3×C4—51no—
397C2×C3×C4—52no—
398C2×C3×C4—52no—
399C2×C3×C4—204no—
400C2×C3×C4C23×D511yescharacteristic
401#67—204no—
402#67—204no—
403C2×Dic3—22no—
404C2×Dic3—51no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3D4×D511yescharacteristic
408C4×D3—21no—
409C4×D3—21no—
410C4×D3—102no—
411C4×D3—102no—
412C4×D3—101no—
413C4×D3—101no—
414C3×C8—52no—
415C3×C8D4×D512yes—
416C3⋊C8—21no—
417C3⋊C8—101no—
418C22×C5—32no—
419C22×C5—61no—
420C22×C5—61no—
421C22×C5C2×D3×D411yescharacteristic
422C2×D5—21no—
423C2×D5—21no—
424C2×D5—32no—
425C2×D5—42no—
426C2×D5—42no—
427C2×D5—42no—
428C2×D5—68no—
429C2×D5—61no—
430C2×D5—61no—
431C2×D5#93812yes—
432C4×C5—42no—
433C4×C5—61no—
434C4×C5—122no—
435C4×C5C2×#23711yescharacteristic
436C4×C5C22×#6711yescharacteristic
437Dic5—61no—
438Dic5—122no—
439Dic5#93812yes—
440C24—151no—
441#41—104no—
442#41—104no—
443C2×Q8C2×D3×D512yes—
444C2×D4—52no—
445C2×D4—102no—
446C2×D4—302no—
447C2×D4—302no—
448C22×C4—31no—
449C22×C4—51no—
450C22×C4—102no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—151no—
455C22×C4—302no—
456C22×C4—302no—
457Q16—22no—
458SD16—104no—
459D8—102no—
460C2×C8—31no—
461C2×C8—51no—
462C2×C8—54no—
463C2×C8—62no—
464C2×C8—151no—
465C2×C8—302no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—32no—
471C4⋊C4—62no—
472C4⋊C4—152no—
473C4⋊C4—302no—
474C22⋊C4—62no—
475C22⋊C4—302no—
476C22⋊C4—302no—
477C22⋊C4—302no—
478C22⋊C4—302no—
479C42—302no—
480C3×C5#305011yescharacteristic, complemented, Hall
481C22×C3—52no—
482C22×C3—101no—
483C22×C3—101no—
484C22×C3—202no—
485C22×C3—202no—
486C22×C3—202no—
487C22×C3C2×D4×D511yescharacteristic
488C2×D3—21no—
489C2×D3—21no—
490C2×D3—52no—
491C2×D3—108no—
492C2×D3—101no—
493C2×D3—101no—
494C2×D3#406512yescomplemented
495C3×C4—42no—
496C3×C4—52no—
497C3×C4C2×D4×D511yescharacteristic
498C3×C4D5×#4111yescharacteristic
499Dic3—21no—
500Dic3—42no—
501Dic3—101no—
502Dic3—202no—
503C2×C5—62no—
504C2×C5D3×#13511yescharacteristic
505C2×C5D3×#13511yescharacteristic
506C2×C5C2×#93811yescharacteristic
507D5—22no—
508D5—62no—
509D5—82no—
510C23—31no—
511C23—51no—
512C23—102no—
513C23—151no—
514C23—302no—
515C23—302no—
516C23—302no—
517Q8—22no—
518Q8—22no—
519D4—102no—
520D4—102no—
521D4—204no—
522D4—604no—
523D4—604no—
524C2×C4—22no—
525C2×C4—31no—
526C2×C4—51no—
527C2×C4—52no—
528C2×C4—52no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—151no—
533C2×C4—204no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—301no—
538C2×C4—301no—
539C2×C4—302no—
540C2×C4C22×D3×D511yescharacteristic
541C8—52no—
542C8—61no—
543C8—301no—
544C8D5×#6712yes—
545C2×C3—102no—
546C2×C3—402no—
547C2×C3D5×#12111yescharacteristic
548C2×C3C2×#406511yescharacteristic
549C2×C3D5×#13511yescharacteristic
550D3—22no—
551D3—102no—
552C5#8391411yescharacteristic, complemented, Sylow
553C22—32no—
554C22—52no—
555C22—61no—
556C22—61no—
557C22—101no—
558C22—101no—
559C22—152no—
560C22—202no—
561C22—202no—
562C22—202no—
563C22—308no—
564C22—301no—
565C22—301no—
566C22D3×D4×D511yescharacteristic
567C4—42no—
568C4—52no—
569C4—61no—
570C4—122no—
571C4—301no—
572C4—602no—
573C4D5×#23711yescharacteristic
574C4C2×D5×#6711yescharacteristic
575C3#1061248911yescharacteristic, complemented, Sylow
576C2—62no—
577C2—102no—
578C2—302no—
579C2—402no—
580C2D3×#406511yescharacteristic
581C2#1175410511yescharacteristic
582C2D5×#93811yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
hypercenterC2×Q16D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4065C2semidirect
2. #11755270C2semidirect
3. C2×D3×C8×D5C2semidirect
4. #11751289C2semidirect
5. C5×#5188C2semidirect
6. #11749277C2semidirect
7. #11749274C2semidirect
8. #11749207C2semidirect
9. #11747932C2semidirect
10. #11747915C2semidirect
11. #11747672C2semidirect
15. C2×C3×C5×Q16C22semidirect
20. C2×C3×#688C22semidirect
22. C2×C3×D40C22semidirect
35. #91119C22semidirect
36. #91102C22semidirect
37. C5×#835C22semidirect
38. C5×#818C22semidirect
39. #90985C22semidirect
40. #90965C22semidirect
41. #90964C22semidirect
43. C2×#4065D3semidirect
86. C3×C8×D5D4semidirect
99. #5188D5semidirect
107. C2×C5×Q16C2×D3semidirect
111. C2×#688C2×D3semidirect
115. C2×D40C2×D3semidirect
173. C2×C3×Q16C2×D5semidirect
193. #835C2×D5semidirect
197. #818C2×D5semidirect
238. C8×D5#67semidirect
253. C2×D15#135semidirect
256. C2×C5×D3#135semidirect
350. C2×Q16D3×D5semidirect
480. C3×C5#3050semidirect
494. C2×D3#4065semidirect
552. C5#83914semidirect
575. C3#10612489semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40652
#117552702
C2×D3×C8×D52
#117512892
C5×#51882
#117492772
#117492742
#117492072
#117479322
#117479152
#117476722
#106124893
#839145