Finite Group Databasebeta

← #14427849

Subgroups — #14427849

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756550C211yesmaximal, characteristic, complemented
2C5×#5791C211yesmaximal, characteristic, complemented
3C23×C3×#168C211yesmaximal, characteristic, complemented
4C2×#91303C211yesmaximal, characteristic, complemented
5#11748557C212yesmaximal, complemented
6#11748535C212yesmaximal, complemented
7#11748533C212yesmaximal, complemented
8#11748514C212yesmaximal, complemented
9#11748458C211yesmaximal, characteristic, complemented
10#11748393C211yesmaximal, characteristic, complemented
11#11748388C211yesmaximal, characteristic, complemented
12#10614653—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16#91842—21no—
17#91819C2212yes—
18#91818—21no—
19C4×#1220—22no—
20#91815C2211yescharacteristic
21#91813C2212yes—
22C5×#953—21no—
23C5×#930C2212yes—
24C5×#929—21no—
25C4×C5×#67—22no—
26C5×#926C2211yescharacteristic
27C5×#924C2212yes—
28C22×C3×#168—24no—
29C22×C3×#168C2211yescharacteristic
30C22×C3×#168C2212yes—
31C22×C3×#168C2212yes—
32C22×C3×#168C2211yescharacteristic
33C2×#6663C2211yescharacteristic, complemented
34C2×#6660C2211yescharacteristic, complemented
35C2×#6659C2211yescharacteristic, complemented
36#91303—24no—
37C2×#6654C2211yescharacteristic, complemented
38#90988C2212yescomplemented
39#90985C2212yescomplemented
40#90975C2212yescomplemented
41#90973C2212yescomplemented
42#90969C2212yescomplemented
43#90967C2212yescomplemented
44#83742—51nomaximal, Hall
45C5×#525—31no—
46C2×#4096—31no—
47#66125—31no—
48C23×#168D311yescharacteristic, complemented
49#65522—31no—
50#65340—32no—
51#65337—32no—
52#65330—32no—
53#65327—32no—
54#65291—31no—
55#65287—31no—
56C24×C3×C5D411yescharacteristic
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5D412yes—
60C22×C3×C4×C5D411yescharacteristic
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—22no—
64C2×#1220—21no—
65#6817—22no—
66#6817—22no—
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×Dic30C2311yescharacteristic
70C2×C5×#67—22no—
71C2×C5×#67—21no—
72C5×#235—22no—
73C5×#235—22no—
74C2×C5×D12C2311yescharacteristic
75C2×C4×C5×D3—21no—
76C2×C5×Dic6C2311yescharacteristic
77#6719—22no—
78#6719—21no—
79#6714—22no—
80C4⋊Dic15C2312yes—
81#6712—22no—
82C4×Dic15—21no—
83C5×#217—22no—
84C5×#217—21no—
85C5×(C2×D3)⋊C4—22no—
86C5×C4⋊Dic3C2312yes—
87C5×Dic3⋊C4—22no—
88C4×C5×Dic3—21no—
89C2×C3×#168—22no—
90C2×C3×#168—24no—
91C2×C3×#168—24no—
92C2×C3×#168D414yescomplemented
93C2×C3×#168C2312yes—
94C2×C3×#168C2311yescharacteristic
95C2×C3×#168C2311yescharacteristic
96#6663—22no—
97#6660—22no—
98#6659—22no—
99#6654—22no—
100C23×C3×C8—51no—
101#5791—51no—
102#5791D511yescharacteristic, complemented
103C2×#904—51no—
104#5116—52no—
105#5115—52no—
106#5114—52no—
107#5114—52no—
108#5113—51no—
109#5113—51no—
110#5106—51no—
111C2×C5×#41—31no—
112C23×C4×C5C2×D311yescharacteristic
113C2×#709—31no—
114C5×#123—61no—
115C5×C22⋊Q8—32no—
116C5×#121—32no—
117C5×#120—61no—
118C4×C5×D4—62no—
119C5×#117—31no—
120#4099—61no—
121#4096—64no—
122C2×#689—31no—
123C2×#688—31no—
124C2×#687—31no—
125C2×#686—31no—
126#4076—32no—
127#4075—61no—
128C4×C22⋊D5—62no—
129#4072—31no—
130#4070—32no—
131C22×#168—24no—
132C22×#168C2×D311yescharacteristic
133C22×#168C2×D312yes—
134C22×#168C2×D312yes—
135C22×#168C2×D311yescharacteristic
136#3967—32no—
137#3964—32no—
138#3942—32no—
139#3941—32no—
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5—22no—
144C23×C3×C5—24no—
145C23×C3×C5C2×D411yescharacteristic
146C23×C3×C5C2×D412yes—
147C22×D15—21no—
148C22×C5×D3—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—24no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5C2411yescharacteristic
158#1220—42no—
159#1220—44no—
160C2×Dic15—22no—
161C2×Dic15—21no—
162D60—21no—
163D60—21no—
164C4×D15—42no—
165Dic30—21no—
166Dic30—21no—
167C5×#67—42no—
168C5×#67—44no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—21no—
171C5×D12—21no—
172C5×D12—21no—
173C4×C5×D3—42no—
174C5×Dic6—21no—
175C5×Dic6—21no—
176C3×#168—22no—
177C3×#168C2×D412yes—
178C3×#168C2×D412yes—
179C23×C3×C4C2×D511yescharacteristic
180C2×#235—51no—
181C2×#235C2×D511yescharacteristic
182C22×C3×C8—51no—
183C22×C3×C8—51no—
184C22×C3×C8—52no—
185C22×C3×C8—52no—
186C22×C3×C8—104no—
187#953—21no—
188#953—101no—
189#930—52no—
190#930C2×D512yes—
191#929—21no—
192#929—101no—
193C4×#67—22no—
194C4×#67—102no—
195#926—51no—
196#926C2×D511yescharacteristic
197#924—52no—
198#924C2×D512yes—
199C2×Dic12—51no—
200#904—104no—
201C2×D24—51no—
202C2×#204—51no—
203C2×#204—51no—
204#821—52no—
205#821—52no—
206#818—52no—
207#817—52no—
208#816—52no—
209#816—52no—
210C24×C5D1211yescharacteristic
211C5×#41—62no—
212C5×#41—62no—
213C2×C5×Q8—31no—
214C2×C5×D4—31no—
215C2×C5×D4—62no—
216C2×C5×D4—61no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—61no—
220C22×C4×C5D1212yes—
221C22×C4×C5D1211yescharacteristic
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—61no—
225C2×C22⋊D5—62no—
226#709—62no—
227#709—62no—
228C2×D20—31no—
229C2×C4×D5—61no—
230C2×Dic10—31no—
231C5×C4⋊C4—32no—
232C5×C4⋊C4—62no—
233C5×C22⋊C4—61no—
234C5×C22⋊C4—62no—
235C5×C22⋊C4—62no—
236C42×C5—61no—
237C22⋊Dic5—62no—
238C22⋊Dic5—61no—
239#689—62no—
240#688—62no—
241#687—62no—
242#686—62no—
243#685—62no—
244C4⋊Dic5—32no—
245#683—62no—
246C4×Dic5—61no—
247C2×#168—22no—
248C2×#168—24no—
249C2×#168—24no—
250C2×#168#6714yescomplemented
251C2×#168C22×D312yes—
252C2×#168C22×D311yescharacteristic
253C2×#168C22×D311yescharacteristic
254C2×#135—151no—
255C23×C8—51no—
256#525—31no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—151no—
264#416—151no—
265C22×C3×C5—28no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5—22no—
269C22×C3×C5#12112yes—
270C22×C3×C5#13514yescomplemented
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—41no—
273C2×D15—42no—
274C2×C5×D3—41no—
275C2×C5×D3—42no—
276C3×C4×C5—22no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—41no—
281Dic15—42no—
282C5×Dic3—41no—
283C5×Dic3—42no—
284C24×C3C22⋊D511yescharacteristic
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4C22⋊D512yes—
288C22×C3×C4C22⋊D511yescharacteristic
289C22×C3×C4C22×D512yes—
290C22×C3×C4C22×D511yescharacteristic
291C2×#67—22no—
292C2×#67—21no—
293C2×#67—102no—
294C2×#67—101no—
295#235—22no—
296#235—22no—
297#235—102no—
298#235—102no—
299C2×D12—51no—
300C2×D12C22×D511yescharacteristic
301C2×C4×D3—21no—
302C2×C4×D3—101no—
303C2×Dic6—51no—
304C2×Dic6C22×D511yescharacteristic
305C2×C3×C8—54no—
306C2×C3×C8—51no—
307C2×C3×C8—51no—
308C2×C3×C8—52no—
309C2×C3×C8—104no—
310C2×C3×C8—104no—
311C2×C3×C8—102no—
312#217—22no—
313#217—21no—
314#217—102no—
315#217—101no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3—52no—
319C4⋊Dic3C22×D512yes—
320Dic3⋊C4—22no—
321Dic3⋊C4—102no—
322C4×Dic3—21no—
323C4×Dic3—101no—
324Dic12—102no—
325D24—102no—
326#204—102no—
327#204—102no—
328C23×C5—24no—
329C23×C5—22no—
330C23×C5—61no—
331C23×C5C2×D1212yes—
332C23×C5C2×D1211yescharacteristic
333C22×D5—61no—
334C5×Q8—61no—
335C5×Q8—61no—
336C5×D4—61no—
337C5×D4—61no—
338C5×D4—124no—
339C5×D4—122no—
340C2×C4×C5—22no—
341C2×C4×C5—24no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—62no—
345C2×C4×C5—61no—
346C2×C4×C5—122no—
347C2×C4×C5C2×D1212yes—
348C2×C4×C5C2×D1211yescharacteristic
349C2×C4×C5#23512yes—
350C2×C4×C5C2×#6712yes—
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—124no—
353C22⋊D5—122no—
354C2×Dic5—62no—
355C2×Dic5—61no—
356D20—61no—
357D20—61no—
358C4×D5—122no—
359Dic10—61no—
360Dic10—61no—
361#168—22no—
362#168C2×#6712yes—
363#168C2×#6712yes—
364C2×#41—31no—
365C2×#41—151no—
366C23×C4D3×D511yescharacteristic
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—51no—
373C22×C8—51no—
374C22×C8—52no—
375C22×C8—52no—
376C22×C8—104no—
377#123—61no—
378#123—301no—
379C22⋊Q8—32no—
380C22⋊Q8—152no—
381#121—32no—
382#121—152no—
383#120—61no—
384#120—301no—
385C4×D4—62no—
386C4×D4—302no—
387#117—31no—
388#117—151no—
389#107—152no—
390#106—152no—
391#103—152no—
392#103—152no—
393#102—152no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5—24no—
397C2×C3×C5C2×#12111yescharacteristic
398C2×C3×C5C2×#13512yes—
399D15—81no—
400C5×D3—81no—
401C23×C3—24no—
402C23×C3—22no—
403C23×C3C2×C22⋊D512yes—
404C23×C3C2×C22⋊D511yescharacteristic
405C22×D3—21no—
406C22×D3—101no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—24no—
411C2×C3×C4D4×D512yes—
412C2×C3×C4#71112yes—
413C2×C3×C4C2×C22⋊D512yes—
414C2×C3×C4C2×C22⋊D511yescharacteristic
415C2×C3×C4C23×D511yescharacteristic
416#67—44no—
417#67—42no—
418#67—204no—
419#67—202no—
420C2×Dic3—22no—
421C2×Dic3—21no—
422C2×Dic3—102no—
423C2×Dic3—101no—
424D12—21no—
425D12—21no—
426D12—101no—
427D12—101no—
428C4×D3—42no—
429C4×D3—202no—
430Dic6—21no—
431Dic6—21no—
432Dic6—101no—
433Dic6—101no—
434C3×C8—52no—
435C3×C8—52no—
436C3×C8—102no—
437C22×C5—28no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—122no—
442C22×C5—121no—
443C22×C5#90414yescomplemented
444C22×C5#93012yes—
445C22×C5C22×D1211yescharacteristic
446C2×D5—122no—
447C2×D5—121no—
448C4×C5—22no—
449C4×C5—122no—
450C4×C5—121no—
451C4×C5#93012yes—
452C4×C5C2×#23511yescharacteristic
453C4×C5C22×#6711yescharacteristic
454Dic5—122no—
455Dic5—121no—
456C24#120311yescharacteristic
457#41—62no—
458#41—62no—
459#41—302no—
460#41—302no—
461C2×Q8—31no—
462C2×Q8—151no—
463C2×D4—31no—
464C2×D4—62no—
465C2×D4—61no—
466C2×D4—151no—
467C2×D4—302no—
468C2×D4—301no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—61no—
472C22×C4—301no—
473C22×C4#120311yescharacteristic
474C22×C4#120312yes—
475C22×C4C2×D3×D512yes—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—54no—
482C2×C8—51no—
483C2×C8—51no—
484C2×C8—52no—
485C2×C8—104no—
486C2×C8—104no—
487C2×C8—102no—
488C4⋊C4—32no—
489C4⋊C4—62no—
490C4⋊C4—152no—
491C4⋊C4—302no—
492C22⋊C4—61no—
493C22⋊C4—62no—
494C22⋊C4—62no—
495C22⋊C4—301no—
496C22⋊C4—302no—
497C22⋊C4—302no—
498C42—61no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—28no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3#408512yes—
506C22×C3#409614yescomplemented
507C22×C3C22×C22⋊D511yescharacteristic
508C2×D3—41no—
509C2×D3—42no—
510C2×D3—201no—
511C2×D3—202no—
512C3×C4—22no—
513C3×C4#408512yes—
514C3×C4C2×D4×D511yescharacteristic
515C3×C4C2×#71111yescharacteristic
516Dic3—41no—
517Dic3—42no—
518Dic3—201no—
519Dic3—202no—
520C2×C5—24no—
521C2×C5—22no—
522C2×C5—241no—
523C2×C5C2×#90412yes—
524C2×C5C2×#93011yescharacteristic
525D5—241no—
526C23—24no—
527C23—22no—
528C23—61no—
529C23—301no—
530C23C2×#120312yes—
531C23C2×#120311yescharacteristic
532Q8—61no—
533Q8—61no—
534Q8—301no—
535Q8—301no—
536D4—61no—
537D4—61no—
538D4—124no—
539D4—122no—
540D4—301no—
541D4—301no—
542D4—604no—
543D4—602no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—62no—
549C2×C4—61no—
550C2×C4—122no—
551C2×C4—302no—
552C2×C4—301no—
553C2×C4—602no—
554C2×C4#678212yes—
555C2×C4C2×#120312yes—
556C2×C4C2×#120311yescharacteristic
557C2×C4D5×#6712yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—52no—
560C8—52no—
561C8—102no—
562C2×C3—24no—
563C2×C3—22no—
564C2×C3C2×#408511yescharacteristic
565C2×C3C2×#409612yes—
566D3—81no—
567D3—401no—
568C5#8374211yescharacteristic, complemented, Sylow
569C22—28no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—121no—
574C22—122no—
575C22—601no—
576C22—602no—
577C22#9130314yescomplemented
578C22#9156612yes—
579C22C22×#120311yescharacteristic
580C4—22no—
581C4—121no—
582C4—122no—
583C4—601no—
584C4—602no—
585C4#9156612yes—
586C4C2×#678211yescharacteristic
587C4C2×D5×#6711yescharacteristic
588C3#1061465311yescharacteristic, complemented, Sylow
589C2—24no—
590C2—22no—
591C2—241no—
592C2—1201no—
593C2C2×#9130312yes—
594C2C2×#9156611yescharacteristic
subgroupG/H
centerC2×C4C2×#1203
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C22×D4
hypercenterC23×C4D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #11756550C2semidirect
2. C5×#5791C2semidirect
3. C23×C3×#168C2semidirect
4. C2×#91303C2semidirect
5. #11748557C2semidirect
6. #11748535C2semidirect
7. #11748533C2semidirect
8. #11748514C2semidirect
9. #11748458C2semidirect
10. #11748393C2semidirect
11. #11748388C2semidirect
33. C2×#6663C22semidirect
34. C2×#6660C22semidirect
35. C2×#6659C22semidirect
37. C2×#6654C22semidirect
38. #90988C22semidirect
39. #90985C22semidirect
40. #90975C22semidirect
41. #90973C22semidirect
42. #90969C22semidirect
43. #90967C22semidirect
48. C23×#168D3semidirect
92. C2×C3×#168D4semidirect
102. #5791D5semidirect
250. C2×#168#67semidirect
270. C22×C3×C5#135semidirect
443. C22×C5#904semidirect
500. C3×C5#3050semidirect
506. C22×C3#4096semidirect
568. C5#83742semidirect
577. C22#91303semidirect
588. C3#10614653semidirect

Maximal subgroups

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

subgroupindex
#117565502
C5×#57912
C23×C3×#1682
C2×#913032
#117485572
#117485352
#117485332
#117485142
#117484582
#117483932
#117483882
#106146533
#837425