Finite Group Databasebeta

← #14427878

Subgroups — #14427878

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×#91273C211yesmaximal, characteristic, complemented
2C2×D3×C8×D5C211yesmaximal, characteristic, complemented
3#11753879C212yesmaximal, complemented
4#11750988C211yesmaximal, characteristic, complemented
5C5×#4880C211yesmaximal, characteristic, complemented
6C3×#65172C211yesmaximal, characteristic, complemented
7#11747943C211yesmaximal, characteristic, complemented
8#11747932C211yesmaximal, characteristic, complemented
9#11747502C212yesmaximal, complemented
10#11747444C212yesmaximal, complemented
11#11747327C212yesmaximal, complemented
12#10610911—31nomaximal, Hall
13C2×C4×D3×D5C2211yescharacteristic
14C2×#6765C2212yes—
15C2×Dic60C2211yescharacteristic, complemented
16C2×C8×D15C2211yescharacteristic
17#91786C2212yes—
18C2×C5×D3×C8C2211yescharacteristic
19C5×#892C2212yes—
20C2×C3×D40C2211yescharacteristic, complemented
21C2×C3×C8×D5C2211yescharacteristic
22C3×#4041C2212yes—
23#91474—22no—
24#91465C2212yes—
25#91457—22no—
26Dic3×D20—22no—
27#91395—22no—
28#91360C2212yes—
29C2×#6657C2212yescomplemented
30C2×#6648C2211yescharacteristic
31C2×D3×#168C2211yescharacteristic
32C2×D5×C3⋊C8C2211yescharacteristic
33#91273—24no—
34D3×C8×D5—24no—
35C3×C5×#107C2211yescharacteristic, complemented
36#91094C2212yescomplemented
37C5×#818C2211yescharacteristic, complemented
38C5×#808C2212yescomplemented
39C3×#3941C2212yescomplemented
40#90975C2212yescomplemented
41#90964C2212yescomplemented
42#80714—51nomaximal, Hall
43C2×#4050—31no—
44C22×C8×D5—31no—
45#65858—32no—
46C5×#427—31no—
47#65291—32no—
48#65176—31no—
49#65176—31no—
50#65172—31no—
51#65172D311yescharacteristic, complemented
52#65153—32no—
53#65153—32no—
54C22×D3×D5D411yescharacteristic
55C2×C4×D15C2311yescharacteristic
56C2×Dic30C2312yes—
57C2×C4×C5×D3C2311yescharacteristic
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#6765—24no—
70#6765—24no—
71C2×C3×C5×C8C2311yescharacteristic
72C3×C5×C4⋊C4C2312yes—
73#6714—22no—
74C4⋊Dic15—22no—
75C2×C3⋊#168C2311yescharacteristic
76Dic60—22no—
77C8×D15—22no—
78C5×(C2×D3)⋊C4—22no—
79C5×C4⋊Dic3C2312yes—
80C4×C5×Dic3—22no—
81C2×C5×C3⋊C8C2311yescharacteristic
82C5×D3×C8D414yescomplemented
83C3×#685—22no—
84C2×C3×#168C2311yescharacteristic
85C3×D40—22no—
86C3×C8×D5—22no—
87Dic3⋊Dic5—22no—
88#6665—22no—
89#6665—22no—
90#6657—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#4887—51no—
102#4880D511yescharacteristic, complemented
103#4778—52no—
104#4772—52no—
105C2×#709—32no—
106C22×C4×D5—31no—
107C22×C5×C8—31no—
108C5×#117—32no—
109C22×#168—31no—
110C2×Dic20—31no—
111#4050—64no—
112C2×D40C2×D311yescharacteristic, complemented
113C2×#677—32no—
114C2×C8×D5—31no—
115C2×C8×D5—31no—
116C2×C8×D5—31no—
117C2×C8×D5—64no—
118C2×C8×D5C2×D311yescharacteristic
119#4043—32no—
120#4043—32no—
121#4041—32no—
122#4041C2×D312yes—
123#4032—62no—
124#4028—62no—
125C4×D20—62no—
126C4×D20—62no—
127C5×#107—31no—
128C5×#107C2×D311yescharacteristic, complemented
129C5×#106—32no—
130#3942—32no—
131#3942—32no—
132#3941—32no—
133#3941C2×D312yescomplemented
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×D15—21no—
147C4×D15—21no—
148Dic30—22no—
149Dic30—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3C2×D411yescharacteristic
152C4×C5×D3C2×D412yes—
153C4×C5×D3#4112yes—
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⋊#168—21no—
168C3×#168—21no—
169C5×C3⋊C8C2×D412yes—
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×Dic12—51no—
183C2×D3×C8—51no—
184C2×D3×C8—51no—
185C2×D3×C8—51no—
186C2×D3×C8—104no—
187C2×D3×C8C2×D511yescharacteristic
188#897—52no—
189#892C2×D512yes—
190#883—102no—
191#67⋊C4—102no—
192C3×#107C2×D511yescharacteristic, complemented
193C3×#102—52no—
194#832—52no—
195#818C2×D511yescharacteristic, complemented
196#816—52no—
197#810—52no—
198#808C2×D512yescomplemented
199C23×D5—31no—
200C22×C4×C5—31no—
201C2×C22⋊D5—62no—
202C22×Dic5—31no—
203#709—64no—
204#709—64no—
205C2×D20—22no—
206C2×D20—62no—
207C2×D20C22×D312yes—
208C2×C4×D5—31no—
209C2×C4×D5—31no—
210C2×C4×D5—31no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C2×C4×D5—62no—
214C2×C4×D5C22×D311yescharacteristic
215C2×Dic10—32no—
216C2×C5×C8—31no—
217C2×C5×C8—34no—
218C2×C5×C8C22×D311yescharacteristic
219C5×C4⋊C4—32no—
220C5×C4⋊C4C22×D312yes—
221C5×C22⋊C4—62no—
222C42×C5—62no—
223#685—22no—
224#685—62no—
225#685—62no—
226#685—62no—
227C4⋊Dic5—62no—
228C4⋊Dic5—62no—
229C2×#168—31no—
230C2×#168—62no—
231C2×#168C22×D311yescharacteristic
232Dic20—62no—
233D40—22no—
234#677—64no—
235C8×D5—22no—
236C8×D5—62no—
237C8×D5—62no—
238C8×D5—62no—
239C2×#135—151no—
240C23×C8—151no—
241#525—152no—
242#467—151no—
243#467—151no—
244#466—51no—
245#466—151no—
246#465—152no—
247#465—152no—
248#427—31no—
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#12112yes—
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—21no—
268Dic15—42no—
269C3×Dic5—21no—
270C5×Dic3—42no—
271C5×Dic3#12112yes—
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×Dic6—52no—
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—102no—
301C4⋊Dic3C22×D512yes—
302Dic3⋊C4—102no—
303C4×Dic3—22no—
304C2×C3⋊C8—51no—
305C2×C3⋊C8—102no—
306C2×C3⋊C8C22×D511yescharacteristic
307Dic12—102no—
308D3×C8—102no—
309D3×C8—102no—
310D3×C8—102no—
311D3×C8D2014yescomplemented
312C23×C5—31no—
313C22×D5—22no—
314C22×D5—31no—
315C22×D5—62no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5D3×D411yescharacteristic
319C2×C4×C5—22no—
320C2×C4×C5—31no—
321C2×C4×C5—32no—
322C2×C4×C5—32no—
323C2×C4×C5—62no—
324C2×C4×C5C23×D311yescharacteristic
325C22⋊D5—124no—
326C2×Dic5—31no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5D3×D411yescharacteristic
330D20—22no—
331D20—22no—
332D20—44no—
333D20—124no—
334C4×D5—21no—
335C4×D5—21no—
336C4×D5—62no—
337C4×D5—62no—
338C4×D5—61no—
339C4×D5—61no—
340C4×D5—124no—
341Dic10—62no—
342Dic10—62no—
343C5×C8—32no—
344C5×C8D3×D412yes—
345#168—21no—
346#168—61no—
347C2×#41—152no—
348C23×C4—151no—
349#135—304no—
350C2×Q16—151no—
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—152no—
362C22⋊Q8—152no—
363#121—52no—
364#121—152no—
365#120—302no—
366C4×D4—302no—
367C4×D4—302no—
368#117—32no—
369#107—31no—
370#107D3×D511yescharacteristic, complemented
371#106—32no—
372#103—152no—
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—102no—
407C4×D3—101no—
408C4×D3—101no—
409C4×D3—102no—
410C4×D3C2×D2012yes—
411C4×D3#71312yes—
412Dic6—102no—
413Dic6—102no—
414C3×C8—101no—
415C3×C8C2×D2012yes—
416C3⋊C8—101no—
417C3⋊C8C2×D2012yes—
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—32no—
433C4×C5—42no—
434C4×C5—122no—
435C4×C5C2×D3×D411yescharacteristic
436C4×C5D3×#4111yescharacteristic
437Dic5—21no—
438Dic5—61no—
439Dic5—122no—
440C24—151no—
441#41—304no—
442#41—304no—
443C2×Q8—152no—
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—302no—
458SD16—304no—
459D8—102no—
460C2×C8—31no—
461C2×C8—34no—
462C2×C8—51no—
463C2×C8—102no—
464C2×C8—151no—
465C2×C8—302no—
466C2×C8—302no—
467C2×C8—302no—
468C2×C8—302no—
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—32no—
471C4⋊C4—302no—
472C4⋊C4—302no—
473C4⋊C4C2×D3×D512yes—
474C22⋊C4—62no—
475C22⋊C4—102no—
476C22⋊C4—302no—
477C22⋊C4—302no—
478C22⋊C4—302no—
479C42—62no—
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#404112yes—
495C3×C4—42no—
496C3×C4—101no—
497C3×C4C22×D2011yescharacteristic
498C3×C4C2×#71311yescharacteristic
499Dic3—42no—
500Dic3—101no—
501Dic3—202no—
502Dic3#404112yes—
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—302no—
518Q8—302no—
519D4—102no—
520D4—102no—
521D4—204no—
522D4—604no—
523D4—604no—
524C2×C4—22no—
525C2×C4—31no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—51no—
529C2×C4—62no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—151no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—302no—
539C2×C4—604no—
540C2×C4C22×D3×D511yescharacteristic
541C8—32no—
542C8—101no—
543C8—301no—
544C8D3×D2012yes—
545C2×C3—102no—
546C2×C3—402no—
547C2×C3C2×#404111yescharacteristic
548C2×C3D5×#13511yescharacteristic
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—32no—
568C4—42no—
569C4—101no—
570C4—122no—
571C4—301no—
572C4—602no—
573C4C2×D3×D2011yescharacteristic
574C4D3×#71311yescharacteristic
575C3#1061091111yescharacteristic, complemented, Sylow
576C2—62no—
577C2—102no—
578C2—302no—
579C2—402no—
580C2D3×#404111yescharacteristic
581C2D5×#91211yescharacteristic
582C2#1175410511yescharacteristic
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×#91273C2semidirect
2. C2×D3×C8×D5C2semidirect
3. #11753879C2semidirect
4. #11750988C2semidirect
5. C5×#4880C2semidirect
6. C3×#65172C2semidirect
7. #11747943C2semidirect
8. #11747932C2semidirect
9. #11747502C2semidirect
10. #11747444C2semidirect
11. #11747327C2semidirect
15. C2×Dic60C22semidirect
20. C2×C3×D40C22semidirect
29. C2×#6657C22semidirect
35. C3×C5×#107C22semidirect
36. #91094C22semidirect
37. C5×#818C22semidirect
38. C5×#808C22semidirect
39. C3×#3941C22semidirect
40. #90975C22semidirect
41. #90964C22semidirect
51. #65172D3semidirect
82. C5×D3×C8D4semidirect
102. #4880D5semidirect
112. C2×D40C2×D3semidirect
128. C5×#107C2×D3semidirect
133. #3941C2×D3semidirect
192. C3×#107C2×D5semidirect
195. #818C2×D5semidirect
198. #808C2×D5semidirect
253. C2×D15#135semidirect
262. C2×C3×D5#135semidirect
311. D3×C8D20semidirect
370. #107D3×D5semidirect
431. C2×D5#912semidirect
480. C3×C5#3050semidirect
552. C5#80714semidirect
575. C3#10610911semidirect

Maximal subgroups

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

subgroupindex
C2×#912732
C2×D3×C8×D52
#117538792
#117509882
C5×#48802
C3×#651722
#117479432
#117479322
#117475022
#117474442
#117473272
#106109113
#807145