Finite Group Databasebeta

← #14427836

Subgroups — #14427836

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
1C22×C3×C8×D5C211yesmaximal, characteristic, complemented
2#11754527C212yesmaximal, complemented
3C2×#91271C211yesmaximal, characteristic, complemented
4#11751216C211yesmaximal, characteristic, complemented
5C5×#5116C211yesmaximal, characteristic, complemented
6#11748535C212yesmaximal, complemented
7#11747942C211yesmaximal, characteristic, complemented
8#11747938C212yesmaximal, complemented
9#11747899C211yesmaximal, characteristic, complemented
10#11747672C211yesmaximal, characteristic, complemented
11#11747642C212yesmaximal, complemented
12#10612489—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×#6773C2212yes—
15C22×C3×C5×C8C2211yescharacteristic
16#91819C2212yes—
17C2×D120C2211yescharacteristic, complemented
18C5×#924C2212yes—
19C2×C5×Dic12C2211yescharacteristic, complemented
20C22×C3×#168C2211yescharacteristic
21C2×C3×C8×D5—24no—
22C2×C3×C8×D5C2211yescharacteristic
23C2×C3×C8×D5C2211yescharacteristic
24C2×C3×C8×D5C2211yescharacteristic
25C2×C3×C8×D5C2211yescharacteristic
26#91564—22no—
27#91552—22no—
28#91450C2212yes—
29#91444—22no—
30#91359C2212yes—
31#91358C2212yes—
32#91348—22no—
33C2×#6660C2212yescomplemented
34#91271—24no—
35#91105C2212yescomplemented
36#91102C2211yescharacteristic, complemented
37C5×#818C2211yescharacteristic, complemented
38C5×#816C2212yescomplemented
39#90985C2212yescomplemented
40#90973C2212yescomplemented
41#90969C2212yescomplemented
42#83742—51nomaximal, Hall
43C2×#4065—31no—
44C22×C8×D5D311yescharacteristic, complemented
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—
54C23×C3×D5D411yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—22no—
57C2×D60C2312yes—
58C2×C5×Dic6C2312yes—
59C22×C3×Dic5D411yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5D411yescharacteristic
63C2×C3×C4×D5D411yescharacteristic
64C2×C3×C4×D5C2311yescharacteristic
65C2×C3×C4×D5C2311yescharacteristic
66C2×#1202—22no—
67C2×#1202—22no—
68C2×#1200—22no—
69#6773—24no—
70#6773—24no—
71C2×C3×C5×C8—22no—
72C2×C3×C5×C8C2311yescharacteristic
73C2×C3×C5×C8C2311yescharacteristic
74#6714—22no—
75C4⋊Dic15C2312yes—
76D120—22no—
77C5×#217—22no—
78C5×C4⋊Dic3C2312yes—
79C5×Dic3⋊C4—22no—
80C5×Dic12—22no—
81C2×C3×#168—22no—
82C2×C3×#168C2311yescharacteristic
83C2×C3×#168C2311yescharacteristic
84C3×C8×D5—22no—
85C3×C8×D5—22no—
86C3×C8×D5—22no—
87C3×C8×D5D414yescomplemented
88#6669—22no—
89#6667—22no—
90#6665—22no—
91#6665—22no—
92Dic3×Dic5—22no—
93#6660—24no—
94C23×C3×C8—51no—
95#5791—52no—
96C2×#904—51no—
97#5116—51no—
98#5116D511yescharacteristic, complemented
99#5115—51no—
100#5115—51no—
101#5114—52no—
102#5114—52no—
103#5113—52no—
104#5106—51no—
105C2×#713—32no—
106C22×C4×D5C2×D311yescharacteristic
107C2×C5×Q16—31no—
108C22×C5×C8C2×D311yescharacteristic
109C5×C22⋊Q8—32no—
110#4092—32no—
111C2×#688—32no—
112#4076—32no—
113C22×#168C2×D311yescharacteristic
114#4065—64no—
115C2×D40—31no—
116C2×C8×D5—24no—
117C2×C8×D5C2×D311yescharacteristic
118C2×C8×D5C2×D311yescharacteristic
119C2×C8×D5C2×D311yescharacteristic
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
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—22no—
137C22×C3×D5—22no—
138C22×C3×D5—22no—
139C22×C3×D5—22no—
140C22×C3×D5C2×D411yescharacteristic
141C22×C3×D5C2×D411yescharacteristic
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2411yescharacteristic
146#1220—44no—
147C2×Dic15—22no—
148D60—22no—
149D60—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C5×Dic6—22no—
153C5×Dic6—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5C2×D411yescharacteristic
156C2×C3×Dic5C2×D411yescharacteristic
157C3×C4×D5—22no—
158C3×C4×D5—21no—
159C3×C4×D5—21no—
160C3×C4×D5—22no—
161C3×C4×D5C2×D412yes—
162C3×C4×D5#4112yes—
163#1202—44no—
164#1202—44no—
165#1200—44no—
166C3×C5×C8—21no—
167C3×C5×C8C2×D412yes—
168C3×#168—21no—
169C3×#168C2×D412yes—
170C23×C3×C4—51no—
171C2×#235—52no—
172C22×C3×C8—51no—
173C22×C3×C8—51no—
174C22×C3×C8—51no—
175C22×C3×C8—51no—
176C22×C3×C8—51no—
177C22×C3×C8—104no—
178C22×C3×C8C2×D511yescharacteristic
179#953—102no—
180#930—52no—
181#930—52no—
182#929—102no—
183C4×#67—102no—
184C4×#67—102no—
185#926—52no—
186#924—52no—
187#924C2×D512yes—
188C2×Dic12C2×D511yescharacteristic, complemented
189#904—104no—
190C2×D24—51no—
191C2×#204—52no—
192#821—52no—
193#821—52no—
194#818—51no—
195#818C2×D511yescharacteristic, complemented
196#817—52no—
197#816—52no—
198#816C2×D512yescomplemented
199C23×D5D1211yescharacteristic
200C2×C5×Q8—32no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—62no—
203C22×Dic5D1211yescharacteristic
204#713—64no—
205#713—64no—
206C2×D20—32no—
207C2×D20—62no—
208C2×D20—62no—
209C2×C4×D5—22no—
210C2×C4×D5—22no—
211C2×C4×D5—62no—
212C2×C4×D5D1211yescharacteristic
213C2×C4×D5D1211yescharacteristic
214C2×C4×D5C22×D311yescharacteristic
215C2×C4×D5C22×D311yescharacteristic
216C5×Q16—62no—
217C2×C5×C8—22no—
218C2×C5×C8C22×D311yescharacteristic
219C2×C5×C8C22×D311yescharacteristic
220C5×C4⋊C4—32no—
221C5×C4⋊C4—62no—
222C5×C22⋊C4—62no—
223#688—64no—
224#685—62no—
225#685—62no—
226#685—62no—
227#685—62no—
228C4⋊Dic5—32no—
229#683—62no—
230C4×Dic5—62no—
231C2×#168—22no—
232C2×#168C22×D311yescharacteristic
233C2×#168C22×D311yescharacteristic
234D40—62no—
235C8×D5—22no—
236C8×D5—22no—
237C8×D5—22no—
238C8×D5#6714yescomplemented
239C2×#135—151no—
240C23×C8—51no—
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×C5—21no—
251C22×C3×C5—21no—
252C22×C3×C5#13512yescomplemented
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—42no—
255C2×D15—42no—
256C2×D15—42no—
257C2×C3×D5—28no—
258C2×C3×D5—21no—
259C2×C3×D5—21no—
260C2×C3×D5—21no—
261C2×C3×D5—21no—
262C2×C3×D5#12112yes—
263C2×C3×D5#13512yescomplemented
264C3×C4×C5—21no—
265C3×C4×C5C22×D411yescharacteristic
266C3×C4×C5C2×#4111yescharacteristic
267Dic15—42no—
268C3×Dic5—21no—
269C3×Dic5#12112yes—
270C5×Dic3—42no—
271C5×Dic3—42no—
272C24×C3—51no—
273C22×C3×C4—51no—
274C22×C3×C4—51no—
275C22×C3×C4—51no—
276C22×C3×C4—51no—
277C22×C3×C4—51no—
278C22×C3×C4—102no—
279C22×C3×C4—102no—
280C22×C3×C4C22×D511yescharacteristic
281C2×#67—102no—
282C2×#67—102no—
283C2×#67—102no—
284#235—104no—
285#235—104no—
286C2×D12—52no—
287C2×C4×D3—102no—
288C2×Dic6C22×D512yes—
289C2×C3×C8—22no—
290C2×C3×C8—51no—
291C2×C3×C8—54no—
292C2×C3×C8—51no—
293C2×C3×C8—102no—
294C2×C3×C8—102no—
295C2×C3×C8—102no—
296C2×C3×C8—102no—
297C2×C3×C8C22×D511yescharacteristic
298C2×C3×C8C22×D511yescharacteristic
299#217—22no—
300#217—102no—
301#217—102no—
302(C2×D3)⋊C4—102no—
303(C2×D3)⋊C4—102no—
304C4⋊Dic3—52no—
305C4⋊Dic3C22×D512yes—
306Dic3⋊C4—22no—
307Dic3⋊C4—102no—
308C4×Dic3—102no—
309Dic12—22no—
310D24—102no—
311#204—104no—
312C23×C5C2×D1211yescharacteristic
313C22×D5—22no—
314C22×D5—22no—
315C22×D5—22no—
316C22×D5—62no—
317C22×D5C2×D1211yescharacteristic
318C22×D5C2×D1211yescharacteristic
319C5×Q8—62no—
320C5×Q8—62no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—62no—
324C2×C4×C5—62no—
325C2×C4×C5C2×D1211yescharacteristic
326C2×C4×C5C23×D311yescharacteristic
327C22⋊D5—124no—
328C2×Dic5—22no—
329C2×Dic5—62no—
330C2×Dic5C2×D1211yescharacteristic
331C2×Dic5C2×D1211yescharacteristic
332D20—62no—
333D20—62no—
334D20—124no—
335D20—124no—
336C4×D5—22no—
337C4×D5—21no—
338C4×D5—21no—
339C4×D5—22no—
340C4×D5—124no—
341C4×D5#23512yes—
342C4×D5C2×#6712yes—
343C5×C8—21no—
344C5×C8C2×#6712yes—
345#168—21no—
346#168C2×#6712yes—
347C2×#41—152no—
348C23×C4—51no—
349#135—304no—
350C2×Q16—31no—
351C2×SD16—152no—
352C2×D8—151no—
353C22×C8—51no—
354C22×C8—51no—
355C22×C8—51no—
356C22×C8—51no—
357C22×C8—51no—
358C22×C8—104no—
359C22×C8D3×D511yescharacteristic
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×C5—22no—
377C2×C3×C5C2×#12111yescharacteristic
378C2×C3×C5C2×#13511yescharacteristic
379C2×C3×C5C2×#13511yescharacteristic
380D15—82no—
381C3×D5—22no—
382C3×D5—22no—
383C23×C3—51no—
384C23×C3—51no—
385C23×C3—102no—
386C23×C3—102no—
387C23×C3—102no—
388C23×C3D4×D511yescharacteristic
389C22×D3—102no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—51no—
393C2×C3×C4—52no—
394C2×C3×C4—52no—
395C2×C3×C4—51no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4—102no—
399C2×C3×C4—101no—
400C2×C3×C4—101no—
401C2×C3×C4D4×D511yescharacteristic
402C2×C3×C4C23×D511yescharacteristic
403#67—204no—
404#67—204no—
405#67—204no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—102no—
409D12—102no—
410D12—102no—
411C4×D3—204no—
412Dic6—22no—
413Dic6—22no—
414C3×C8—21no—
415C3×C8—52no—
416C3×C8—101no—
417C3×C8D4×D512yes—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5#90412yescomplemented
421C22×C5C22×D1211yescharacteristic
422C2×D5—28no—
423C2×D5—21no—
424C2×D5—21no—
425C2×D5—21no—
426C2×D5—21no—
427C2×D5—122no—
428C2×D5—122no—
429C2×D5—122no—
430C2×D5#90412yescomplemented
431C2×D5#93012yes—
432C4×C5—21no—
433C4×C5—122no—
434C4×C5—122no—
435C4×C5C2×#23511yescharacteristic
436C4×C5C22×#6711yescharacteristic
437Dic5—21no—
438Dic5—122no—
439Dic5#93012yes—
440C24—51no—
441#41—304no—
442#41—304no—
443C2×Q8—32no—
444C2×D4—152no—
445C2×D4—302no—
446C2×D4—302no—
447C2×D4—302no—
448C22×C4—51no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—51no—
452C22×C4—51no—
453C22×C4—102no—
454C22×C4—102no—
455C22×C4—302no—
456C22×C4C2×D3×D511yescharacteristic
457Q16—62no—
458SD16—304no—
459D8—302no—
460C2×C8—22no—
461C2×C8—51no—
462C2×C8—54no—
463C2×C8—51no—
464C2×C8—102no—
465C2×C8—102no—
466C2×C8—102no—
467C2×C8—102no—
468C2×C8C2×D3×D511yescharacteristic
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—21no—
482C22×C3—21no—
483C22×C3—52no—
484C22×C3—52no—
485C22×C3—108no—
486C22×C3—101no—
487C22×C3—101no—
488C22×C3—101no—
489C22×C3—101no—
490C22×C3#406512yescomplemented
491C22×C3C2×D4×D511yescharacteristic
492C2×D3—202no—
493C2×D3—202no—
494C2×D3—202no—
495C3×C4—21no—
496C3×C4—52no—
497C3×C4—101no—
498C3×C4C2×D4×D511yescharacteristic
499C3×C4D5×#4111yescharacteristic
500Dic3—42no—
501Dic3—42no—
502Dic3—202no—
503C2×C5—22no—
504C2×C5C2×#90411yescharacteristic
505C2×C5C2×#90411yescharacteristic
506C2×C5C2×#93011yescharacteristic
507D5—22no—
508D5—22no—
509D5—242no—
510C23—51no—
511C23—51no—
512C23—102no—
513C23—102no—
514C23—102no—
515C23—302no—
516C23D5×D1211yescharacteristic
517Q8—62no—
518Q8—62no—
519D4—302no—
520D4—302no—
521D4—604no—
522D4—604no—
523D4—604no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—51no—
527C2×C4—52no—
528C2×C4—52no—
529C2×C4—51no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—102no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—302no—
538C2×C4—604no—
539C2×C4D5×D1211yescharacteristic
540C2×C4C22×D3×D511yescharacteristic
541C8—21no—
542C8—52no—
543C8—101no—
544C8D5×#6712yes—
545C2×C3—22no—
546C2×C3—102no—
547C2×C3—102no—
548C2×C3D5×#12111yescharacteristic
549C2×C3C2×#406511yescharacteristic
550C2×C3D5×#13511yescharacteristic
551D3—402no—
552C5#8374211yescharacteristic, complemented, Sylow
553C22—21no—
554C22—21no—
555C22—52no—
556C22—52no—
557C22—108no—
558C22—101no—
559C22—101no—
560C22—101no—
561C22—101no—
562C22—602no—
563C22—602no—
564C22—602no—
565C22#9127112yescomplemented
566C22C2×D5×D1211yescharacteristic
567C4—21no—
568C4—52no—
569C4—101no—
570C4—122no—
571C4—122no—
572C4—602no—
573C4D5×#23511yescharacteristic
574C4C2×D5×#6711yescharacteristic
575C3#1061248911yescharacteristic, complemented, Sylow
576C2—22no—
577C2—102no—
578C2—102no—
579C2—1202no—
580C2D5×#90411yescharacteristic
581C2C2×#9127111yescharacteristic
582C2D5×#93011yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C8×D5C2semidirect
2. #11754527C2semidirect
3. C2×#91271C2semidirect
4. #11751216C2semidirect
5. C5×#5116C2semidirect
6. #11748535C2semidirect
7. #11747942C2semidirect
8. #11747938C2semidirect
9. #11747899C2semidirect
10. #11747672C2semidirect
11. #11747642C2semidirect
17. C2×D120C22semidirect
19. C2×C5×Dic12C22semidirect
33. C2×#6660C22semidirect
35. #91105C22semidirect
36. #91102C22semidirect
37. C5×#818C22semidirect
38. C5×#816C22semidirect
39. #90985C22semidirect
40. #90973C22semidirect
41. #90969C22semidirect
44. C22×C8×D5D3semidirect
87. C3×C8×D5D4semidirect
98. #5116D5semidirect
188. C2×Dic12C2×D5semidirect
195. #818C2×D5semidirect
198. #816C2×D5semidirect
238. C8×D5#67semidirect
252. C22×C3×C5#135semidirect
263. C2×C3×D5#135semidirect
420. C22×C5#904semidirect
430. C2×D5#904semidirect
480. C3×C5#3050semidirect
490. C22×C3#4065semidirect
552. C5#83742semidirect
565. C22#91271semidirect
575. C3#10612489semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C8×D52
#117545272
C2×#912712
#117512162
C5×#51162
#117485352
#117479422
#117479382
#117478992
#117476722
#117476422
#106124893
#837425