Finite Group Databasebeta

← #14427880

Subgroups — #14427880

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×#91277C211yesmaximal, characteristic, complemented
2C2×D3×C8×D5C211yesmaximal, characteristic, complemented
3#11753885C212yesmaximal, complemented
4#11750981C211yesmaximal, characteristic, complemented
5C5×#4887C211yesmaximal, characteristic, complemented
6C3×#65172C211yesmaximal, characteristic, complemented
7#11747942C211yesmaximal, characteristic, complemented
8#11747915C211yesmaximal, characteristic, complemented
9#11747506C212yesmaximal, complemented
10#11747339C212yesmaximal, complemented
11#11747321C212yesmaximal, complemented
12#10612489—31nomaximal, Hall
13C2×C4×D3×D5C2211yescharacteristic
14C2×#6766C2212yes—
15C2×C8×D15C2211yescharacteristic
16#91781C2212yes—
17C2×C5×Dic12C2211yescharacteristic, complemented
18C2×C5×D3×C8C2211yescharacteristic
19C5×#897C2212yes—
20C2×C3×D40C2211yescharacteristic, complemented
21C2×C3×C8×D5C2211yescharacteristic
22C3×#4041C2212yes—
23#91474—22no—
24#91456C2212yes—
25#91442—22no—
26#91434—22no—
27#91359C2212yes—
28#91356—22no—
29C2×#6655C2212yescomplemented
30C2×#6648C2211yescharacteristic
31C2×D3×#168C2211yescharacteristic
32C2×D5×C3⋊C8C2211yescharacteristic
33#91277—24no—
34D3×C8×D5—24no—
35C3×C5×#107C2211yescharacteristic, complemented
36#91102C2211yescharacteristic, complemented
37#91092C2212yescomplemented
38C5×#810C2212yescomplemented
39C3×#3941C2212yescomplemented
40#90973C2212yescomplemented
41#90965C2212yescomplemented
42#80714—51nomaximal, Hall
43C2×#4065—31no—
44C22×C8×D5—31no—
45#65961—32no—
46C5×#467—31no—
47#65477—31no—
48#65404—31no—
49#65337—32no—
50#65172D311yescharacteristic, complemented
51#65169—31no—
52#65096—32no—
53#65093—32no—
54C22×D3×D5D411yescharacteristic
55C2×C4×D15C2311yescharacteristic
56C2×C4×C5×D3C2311yescharacteristic
57C2×C5×Dic6C2312yes—
58C2×C3×D20—22no—
59C2×C3×D20C2312yes—
60C2×C3×C4×D5C2311yescharacteristic
61C2×#1202—22no—
62C2×#1201—22no—
63C2×#1200D411yescharacteristic
64C2×D3×Dic5D411yescharacteristic
65C2×D5×Dic3—22no—
66C2×D5×Dic3D411yescharacteristic
67C4×D3×D5—22no—
68C4×D3×D5—22no—
69#6766—24no—
70#6766—24no—
71C2×C3×C5×C8C2311yescharacteristic
72C3×C5×C4⋊C4C2312yes—
73#6714—22no—
74C4⋊Dic15C2312yes—
75C4×Dic15—22no—
76C2×C3⋊#168C2311yescharacteristic
77C8×D15D414yescomplemented
78C5×(C2×D3)⋊C4—22no—
79C5×C4⋊Dic3—22no—
80C2×C5×C3⋊C8C2311yescharacteristic
81C5×Dic12—22no—
82C5×D3×C8—22no—
83C3×#685—22no—
84C2×C3×#168C2311yescharacteristic
85C3×D40—22no—
86C3×C8×D5—22no—
87#6669—22no—
88#6665—22no—
89#6665—22no—
90#6655—24no—
91#6648—22no—
92D3×#168—22no—
93D5×C3⋊C8—22no—
94C2×#912—51no—
95C22×D3×C8—51no—
96#5606—52no—
97C3×#466—51no—
98#5157—51no—
99#5116—51no—
100#5041—52no—
101#4887D511yescharacteristic, complemented
102#4880—51no—
103#4778—52no—
104#4772—52no—
105C2×#713—32no—
106C22×C4×D5—31no—
107C2×C5×Q16—31no—
108C22×C5×C8—31no—
109C5×C22⋊Q8—32no—
110#4092—32no—
111C2×#688—32no—
112#4076—32no—
113C22×#168—31no—
114#4065—64no—
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#4041C2×D312yes—
122#4040—62no—
123#4039—62no—
124#4038—32no—
125#4028—62no—
126#4027—62no—
127C5×#107C2×D311yescharacteristic, complemented
128C5×#103—32no—
129#3967—32no—
130#3953—32no—
131#3950—31no—
132#3941C2×D312yescomplemented
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—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5C2411yescharacteristic
144C2×Dic15—22no—
145C2×Dic15C2×D411yescharacteristic
146C4×D15C2×D412yes—
147C4×D15#4112yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3C2×D411yescharacteristic
150C4×C5×D3—21no—
151C4×C5×D3—21no—
152C5×Dic6—22no—
153C5×Dic6—22no—
154C2×C3×Dic5C2×D411yescharacteristic
155C3×D20—22no—
156C3×D20—22no—
157C3×D20—44no—
158C3×C4×D5—21no—
159C3×C4×D5—21no—
160#1202—44no—
161#1201—44no—
162#1200—22no—
163D3×Dic5—22no—
164D5×Dic3—22no—
165D5×Dic3—44no—
166C3×C5×C8C2×D412yes—
167C3⋊#168C2×D412yes—
168C3×#168—21no—
169C5×C3⋊C8—21no—
170C2×#237—52no—
171C22×C4×D3—51no—
172C2×C3×D8—51no—
173C22×C3×C8—51no—
174C3×#121—52no—
175#938—52no—
176#937—102no—
177D4×Dic3—102no—
178C2×#214—52no—
179#924—52no—
180C22×C3⋊C8—51no—
181#912—104no—
182C2×Dic12C2×D511yescharacteristic, complemented
183C2×D3×C8—51no—
184C2×D3×C8—51no—
185C2×D3×C8—51no—
186C2×D3×C8—104no—
187C2×D3×C8C2×D511yescharacteristic
188#897C2×D512yes—
189#892—52no—
190#883—102no—
191#67⋊C4—102no—
192C3×#107C2×D511yescharacteristic, complemented
193C3×#102—52no—
194#832—52no—
195#818—51no—
196#816—52no—
197#810C2×D512yescomplemented
198#808—52no—
199C23×D5—31no—
200C2×C5×Q8—32no—
201C22×C4×C5—31no—
202C2×C22⋊D5—62no—
203C22×Dic5—31no—
204#713—64no—
205#713—64no—
206C2×D20—22no—
207C2×D20—62no—
208C2×D20C22×D312yes—
209C2×C4×D5—31no—
210C2×C4×D5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—62no—
213C2×C4×D5—62no—
214C2×C4×D5—62no—
215C2×C4×D5C22×D311yescharacteristic
216C5×Q16—62no—
217C2×C5×C8—31no—
218C2×C5×C8—62no—
219C2×C5×C8C22×D311yescharacteristic
220C5×C4⋊C4—62no—
221C5×C4⋊C4C22×D312yes—
222C5×C22⋊C4—62no—
223#688—64no—
224#685—22no—
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—22no—
236C8×D5—34no—
237C8×D5—62no—
238C8×D5—62no—
239C2×#135—151no—
240C23×C8—151no—
241#525—152no—
242#467—31no—
243#467—151no—
244#466—51no—
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#12112yes—
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#13512yescomplemented
263D3×D5—28no—
264C3×C4×C5—42no—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C2×#4111yescharacteristic
267Dic15—42no—
268Dic15#12112yes—
269C3×Dic5—21no—
270C5×Dic3—21no—
271C5×Dic3—42no—
272C23×D3—51no—
273C2×C3×D4—52no—
274C2×C3×D4—102no—
275C22×C3×C4—51no—
276C2×#67—102no—
277C2×#67—102no—
278C22×Dic3—51no—
279C22×Dic3—102no—
280#237—104no—
281#237—104no—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—51no—
285C2×C4×D3—102no—
286C2×C4×D3—102no—
287C2×C4×D3C22×D511yescharacteristic
288C2×Dic6C22×D512yes—
289C3×D8—102no—
290C2×C3×C8—51no—
291C2×C3×C8—102no—
292C2×C3×C8C22×D511yescharacteristic
293C3×C4⋊C4C22×D512yes—
294C3×C22⋊C4—102no—
295#217—102no—
296#217—102no—
297#214—104no—
298(C2×D3)⋊C4—22no—
299(C2×D3)⋊C4—102no—
300C4⋊Dic3—22no—
301C4⋊Dic3—52no—
302Dic3⋊C4—102no—
303C4×Dic3—102no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—102no—
306C2×C3⋊C8C22×D511yescharacteristic
307Dic12—22no—
308D3×C8—22no—
309D3×C8—54no—
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—62no—
320C5×Q8—62no—
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—21no—
337C4×D5—21no—
338C4×D5—32no—
339C4×D5—32no—
340C4×D5—62no—
341C4×D5—62no—
342C4×D5—124no—
343C5×C8—61no—
344C5×C8D3×D412yes—
345#168—21no—
346#168—32no—
347C2×#41—152no—
348C23×C4—151no—
349#135—304no—
350C2×Q16—31no—
351C2×SD16—152no—
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—52no—
364#121—152no—
365#120—302no—
366C4×D4—302no—
367C4×D4—302no—
368#117—152no—
369#107—151no—
370#107D3×D511yescharacteristic, complemented
371#106—152no—
372#103—32no—
373#103—152no—
374#102—52no—
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×D4—102no—
391C3×D4—102no—
392C3×D4—204no—
393C2×C3×C4—22no—
394C2×C3×C4—51no—
395C2×C3×C4—101no—
396C2×C3×C4—101no—
397C2×C3×C4C23×D511yescharacteristic
398#67—204no—
399#67—204no—
400C2×Dic3—22no—
401C2×Dic3—51no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—204no—
405C2×Dic3D4×D511yescharacteristic
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—52no—
409C4×D3—52no—
410C4×D3—102no—
411C4×D3—102no—
412Dic6—22no—
413Dic6—22no—
414C3×C8—101no—
415C3×C8D4×D512yes—
416C3⋊C8—21no—
417C3⋊C8—52no—
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#91212yescomplemented
432C4×C5—42no—
433C4×C5—61no—
434C4×C5—122no—
435C4×C5C2×D3×D411yescharacteristic
436C4×C5D3×#4111yescharacteristic
437Dic5—21no—
438Dic5—32no—
439Dic5—122no—
440C24—151no—
441#41—304no—
442#41—304no—
443C2×Q8—32no—
444C2×D4—52no—
445C2×D4—102no—
446C2×D4—302no—
447C2×D4—302no—
448C22×C4—31no—
449C22×C4—51no—
450C22×C4—151no—
451C22×C4—151no—
452C22×C4—151no—
453C22×C4—151no—
454C22×C4—302no—
455C22×C4—302no—
456C22×C4—302no—
457Q16—62no—
458SD16—304no—
459D8—102no—
460C2×C8—31no—
461C2×C8—51no—
462C2×C8—62no—
463C2×C8—102no—
464C2×C8—151no—
465C2×C8—154no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—62no—
471C4⋊C4—152no—
472C4⋊C4—302no—
473C4⋊C4C2×D3×D512yes—
474C22⋊C4—62no—
475C22⋊C4—102no—
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—101no—
497C3×C4C2×D4×D511yescharacteristic
498C3×C4D5×#4111yescharacteristic
499Dic3—21no—
500Dic3—42no—
501Dic3—52no—
502Dic3—202no—
503C2×C5—62no—
504C2×C5D3×#12111yescharacteristic
505C2×C5C2×#91211yescharacteristic
506C2×C5D3×#13511yescharacteristic
507D5—22no—
508D5—62no—
509D5—82no—
510C23—31no—
511C23—51no—
512C23—102no—
513C23—151no—
514C23—302no—
515C23—302no—
516C23—302no—
517Q8—62no—
518Q8—62no—
519D4—102no—
520D4—102no—
521D4—204no—
522D4—604no—
523D4—604no—
524C2×C4—22no—
525C2×C4—31no—
526C2×C4—51no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—151no—
533C2×C4—152no—
534C2×C4—152no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4—604no—
540C2×C4C22×D3×D511yescharacteristic
541C8—61no—
542C8—101no—
543C8—152no—
544C8#677712yes—
545C2×C3—102no—
546C2×C3—402no—
547C2×C3D5×#12111yescharacteristic
548C2×C3C2×#406511yescharacteristic
549C2×C3D5×#13511yescharacteristic
550D3—22no—
551D3—102no—
552C5#8071411yescharacteristic, 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—61no—
569C4—101no—
570C4—122no—
571C4—152no—
572C4—602no—
573C4C2×#677711yescharacteristic
574C4#9203411yescharacteristic
575C3#1061248911yescharacteristic, complemented, Sylow
576C2—62no—
577C2—102no—
578C2—302no—
579C2—402no—
580C2#1175385011yescharacteristic
581C2D5×#91211yescharacteristic
582C2D3×#406511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C22×D4
hypercenter#107D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. C2×#91277C2semidirect
2. C2×D3×C8×D5C2semidirect
3. #11753885C2semidirect
4. #11750981C2semidirect
5. C5×#4887C2semidirect
6. C3×#65172C2semidirect
7. #11747942C2semidirect
8. #11747915C2semidirect
9. #11747506C2semidirect
10. #11747339C2semidirect
11. #11747321C2semidirect
17. C2×C5×Dic12C22semidirect
20. C2×C3×D40C22semidirect
29. C2×#6655C22semidirect
35. C3×C5×#107C22semidirect
36. #91102C22semidirect
37. #91092C22semidirect
38. C5×#810C22semidirect
39. C3×#3941C22semidirect
40. #90973C22semidirect
41. #90965C22semidirect
50. #65172D3semidirect
77. C8×D15D4semidirect
101. #4887D5semidirect
115. C2×D40C2×D3semidirect
127. C5×#107C2×D3semidirect
132. #3941C2×D3semidirect
182. C2×Dic12C2×D5semidirect
192. C3×#107C2×D5semidirect
197. #810C2×D5semidirect
256. C2×C5×D3#135semidirect
262. C2×C3×D5#135semidirect
370. #107D3×D5semidirect
431. C2×D5#912semidirect
480. C3×C5#3050semidirect
494. C2×D3#4065semidirect
552. C5#80714semidirect
575. C3#10612489semidirect

Maximal subgroups

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

subgroupindex
C2×#912772
C2×D3×C8×D52
#117538852
#117509812
C5×#48872
C3×#651722
#117479422
#117479152
#117475062
#117473392
#117473212
#106124893
#807145