Finite Group Databasebeta

← #14427855

Subgroups — #14427855

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
1C5×#5524C211yesmaximal, characteristic, complemented
2#11754577C211yesmaximal, characteristic, complemented
3C2×#91297C211yesmaximal, characteristic, complemented
4C22×D3×#168C211yesmaximal, characteristic, complemented
5#11751099C211yesmaximal, characteristic, complemented
6C3×#65291C211yesmaximal, characteristic, complemented
7#11748388C211yesmaximal, characteristic, complemented
8#11747353C212yesmaximal, complemented
9#11747352C212yesmaximal, complemented
10#11747321C212yesmaximal, complemented
11#11747319C212yesmaximal, complemented
12#10614653—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17#91815C2211yescharacteristic
18C22×C3⋊#168C2211yescharacteristic
19C5×#897C2212yes—
20C5×#895C2212yes—
21C5×#886—21no—
22C5×#882—21no—
23C4×C5×D12—22no—
24C22×C3×#168C2211yescharacteristic
25#91568—21no—
26#91536—21no—
27#91456C2212yes—
28C4×#1201—22no—
29#91369C2212yes—
30C2×#6661C2211yescharacteristic, complemented
31C2×#6656C2211yescharacteristic, complemented
32C2×#6655C2211yescharacteristic, complemented
33#91297—24no—
34C2×#6652C2211yescharacteristic, complemented
35C2×D3×#168—24no—
36C2×D3×#168C2212yes—
37C2×D3×#168C2212yes—
38#91092C2212yescomplemented
39#91091C2212yescomplemented
40C3×#3942C2212yescomplemented
41C3×#3941C2212yescomplemented
42#90973C2212yescomplemented
43#90967C2212yescomplemented
44#78838—51nomaximal, Hall
45C5×#525—31no—
46C2×#4096—31no—
47#66125—31no—
48C23×#168—31no—
49#65522—31no—
50#65340—32no—
51#65337—32no—
52#65330—32no—
53#65327—32no—
54#65291D311yescharacteristic, complemented
55#65287—31no—
56C23×C5×D3D411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×C5×#67—21no—
59C22×C5×Dic3D411yescharacteristic
60C5×#235—22no—
61C5×#235—22no—
62C2×C5×D12—22no—
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—22no—
65C2×C4×C5×D3—22no—
66C2×C4×C5×D3—21no—
67C2×C4×C5×D3D412yes—
68C2×C4×C5×D3C2312yes—
69C2×C5×Dic6C2311yescharacteristic
70C2×C3×C22⋊D5—21no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20C2311yescharacteristic
74C2×C3×C4×D5—21no—
75C2×C3×Dic10C2311yescharacteristic
76C2×#1201—22no—
77C3×C5×C4⋊C4C2312yes—
78C3×C5×C22⋊C4—21no—
79C3×C42×C5—21no—
80#6719—21no—
81C4⋊Dic15C2312yes—
82C4×Dic15—21no—
83C2×C3⋊#168D414yescomplemented
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86C5×(C2×D3)⋊C4—22no—
87C5×(C2×D3)⋊C4—22no—
88C5×C4⋊Dic3—22no—
89C2×C3×#168—22no—
90C2×C3×#168C2312yes—
91#6669—22no—
92(C2×D3)⋊Dic5—22no—
93#6665—22no—
94#6661—22no—
95#6656—22no—
96#6655—22no—
97#6652—22no—
98D3×#168—24no—
99D3×#168—24no—
100#5828—51no—
101C2×#950—51no—
102C22×D3×C8—51no—
103#5524D511yescharacteristic, complemented
104C3×#416—51no—
105#5113—51no—
106#4998—51no—
107#4813—52no—
108#4807—52no—
109#4778—52no—
110#4775—52no—
111C2×C5×#41—31no—
112C23×C4×C5—31no—
113C2×#709C2×D311yescharacteristic
114C5×#123—61no—
115C5×C22⋊Q8—32no—
116C5×#121—32no—
117C5×#120—61no—
118C4×C5×D4—62no—
119C5×#117C2×D311yescharacteristic
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—31no—
132C22×#168—32no—
133C22×#168—32no—
134C22×#168—64no—
135C22×#168C2×D311yescharacteristic
136#3967—32no—
137#3964—32no—
138#3942C2×D312yescomplemented
139#3941C2×D312yescomplemented
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5C2×D411yescharacteristic
144C22×C5×D3—22no—
145C22×C5×D3—24no—
146C22×C5×D3—21no—
147C22×C5×D3C2×D412yes—
148C22×C3×D5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5#4112yes—
153C2×C3×C4×C5C2411yescharacteristic
154C2×Dic15—22no—
155C5×#67—42no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3C2×D412yes—
159C5×D12—21no—
160C5×D12—21no—
161C5×D12—44no—
162C4×C5×D3—24no—
163C4×C5×D3—22no—
164C4×C5×D3—22no—
165C4×C5×D3—42no—
166C5×Dic6—21no—
167C5×Dic6—21no—
168C3×C22⋊D5—42no—
169C2×C3×Dic5—21no—
170C3×D20—21no—
171C3×D20—21no—
172C3×C4×D5—42no—
173C3×Dic10—21no—
174C3×Dic10—21no—
175#1201—44no—
176C3⋊#168C2×D412yes—
177C3⋊#168C2×D412yes—
178C3×#168—22no—
179C2×C3×#41—51no—
180C2×#235C2×D511yescharacteristic
181C22×C4×D3C2×D511yescharacteristic
182C22×C3×C8—51no—
183C3×#117C2×D511yescharacteristic
184#950—104no—
185#946—52no—
186C2×#216—51no—
187C2×#215—51no—
188#938—52no—
189#937—101no—
190#935—101no—
191C2×#214—51no—
192C2×#213—51no—
193C4×#67—102no—
194#926—51no—
195C22×C3⋊C8—51no—
196C2×D3×C8—52no—
197C2×D3×C8—52no—
198C2×D3×C8—104no—
199#897C2×D512yes—
200#895C2×D512yes—
201#886—21no—
202#882—21no—
203C4×D12—22no—
204C3×#103—52no—
205C3×#102—52no—
206#821—52no—
207#816—52no—
208#808—52no—
209#807—52no—
210C24×C5—31no—
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—31no—
218C22×C4×C5—32no—
219C22×C4×C5—32no—
220C22×C4×C5—62no—
221C22×C4×C5—62no—
222C22×C4×C5—61no—
223C22×C4×C5C22×D311yescharacteristic
224C2×C22⋊D5—21no—
225C2×C22⋊D5—62no—
226#709—22no—
227#709—22no—
228C2×D20C22×D311yescharacteristic
229C2×C4×D5—21no—
230C2×Dic10C22×D311yescharacteristic
231C5×C4⋊C4—62no—
232C5×C4⋊C4C22×D312yes—
233C5×C22⋊C4—21no—
234C5×C22⋊C4—62no—
235C5×C22⋊C4—62no—
236C42×C5—21no—
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—34no—
249C2×#168—31no—
250C2×#168—31no—
251C2×#168—64no—
252C2×#168—64no—
253C2×#168C22×D312yes—
254C2×#135—151no—
255C23×C8—151no—
256#525—31no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—51no—
264#416—151no—
265C22×C3×C5—22no—
266C22×C3×C5#12112yes—
267C22×C3×C5C22×D411yescharacteristic
268C2×C5×D3—28no—
269C2×C5×D3—22no—
270C2×C5×D3—22no—
271C2×C5×D3—41no—
272C2×C5×D3—42no—
273C2×C5×D3#13514yescomplemented
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C3×C4×C5—42no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—42no—
281C3×Dic5—41no—
282C5×Dic3—22no—
283C5×Dic3—41no—
284C23×D3C22⋊D511yescharacteristic
285C3×#41—102no—
286C3×#41—102no—
287C2×C3×Q8—51no—
288C2×C3×D4—51no—
289C2×C3×D4—101no—
290C22×C3×C4—101no—
291C22×C3×C4C22×D511yescharacteristic
292C2×#67—21no—
293C2×#67—102no—
294C22×Dic3C22⋊D511yescharacteristic
295#235—22no—
296#235—22no—
297C2×D12—22no—
298C2×D12C22×D511yescharacteristic
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—21no—
302C2×C4×D3C22⋊D512yes—
303C2×C4×D3C22×D512yes—
304C2×Dic6C22×D511yescharacteristic
305C2×C3×C8—52no—
306C2×C3×C8—102no—
307C3×C4⋊C4C22×D512yes—
308C3×C22⋊C4—21no—
309C3×C42—21no—
310#217—101no—
311#217—102no—
312#216—102no—
313#215—102no—
314#214—102no—
315#213—102no—
316(C2×D3)⋊C4—22no—
317(C2×D3)⋊C4—22no—
318(C2×D3)⋊C4—102no—
319C4⋊Dic3—22no—
320C4⋊Dic3—52no—
321Dic3⋊C4—102no—
322C4×Dic3—101no—
323C2×C3⋊C8—54no—
324C2×C3⋊C8—51no—
325C2×C3⋊C8—51no—
326D3×C8—104no—
327D3×C8—104no—
328C23×C5—32no—
329C23×C5—64no—
330C23×C5—62no—
331C23×C5—61no—
332C23×C5D3×D411yescharacteristic
333C22×D5—21no—
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—32no—
342C2×C4×C5—62no—
343C2×C4×C5—64no—
344C2×C4×C5—62no—
345C2×C4×C5—62no—
346C2×C4×C5—61no—
347C2×C4×C5—122no—
348C2×C4×C5#23512yes—
349C2×C4×C5D3×D412yes—
350C2×C4×C5D3×D411yescharacteristic
351C2×C4×C5C23×D311yescharacteristic
352C22⋊D5—42no—
353C22⋊D5—124no—
354C2×Dic5—21no—
355C2×Dic5—62no—
356D20—21no—
357D20—21no—
358C4×D5—42no—
359Dic10—21no—
360Dic10—21no—
361#168—22no—
362#168—32no—
363#168—32no—
364C2×#41—31no—
365C2×#41—51no—
366C23×C4—31no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—51no—
373C22×C8—152no—
374C22×C8—152no—
375C22×C8—151no—
376C22×C8—304no—
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—151no—
388#117D3×D511yescharacteristic
389#107—152no—
390#106—152no—
391#103—52no—
392#103—152no—
393#102—52no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5C2×#12111yescharacteristic
397C2×C3×C5C2×#13512yes—
398C3×D5—81no—
399C5×D3—24no—
400C5×D3—81no—
401C23×C3—101no—
402C23×C3C2×C22⋊D511yescharacteristic
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—21no—
406C22×D3C2×C22⋊D512yes—
407C3×Q8—101no—
408C3×Q8—101no—
409C3×D4—101no—
410C3×D4—101no—
411C3×D4—202no—
412C2×C3×C4—22no—
413C2×C3×C4—101no—
414C2×C3×C4—202no—
415C2×C3×C4D4×D512yes—
416C2×C3×C4#71112yes—
417C2×C3×C4C2×C22⋊D511yescharacteristic
418C2×C3×C4C23×D511yescharacteristic
419#67—42no—
420#67—204no—
421C2×Dic3—22no—
422C2×Dic3—21no—
423C2×Dic3—102no—
424C2×Dic3C2×C22⋊D512yes—
425D12—21no—
426D12—21no—
427D12—44no—
428C4×D3—22no—
429C4×D3—22no—
430C4×D3—24no—
431C4×D3—42no—
432Dic6—21no—
433Dic6—21no—
434C3×C8—102no—
435C3⋊C8—52no—
436C3⋊C8—52no—
437C22×C5—22no—
438C22×C5—34no—
439C22×C5—68no—
440C22×C5—62no—
441C22×C5—62no—
442C22×C5—121no—
443C22×C5—122no—
444C22×C5#88412yes—
445C22×C5C2×D3×D411yescharacteristic
446C2×D5—41no—
447C2×D5—42no—
448C4×C5—42no—
449C4×C5—62no—
450C4×C5—121no—
451C4×C5#88412yes—
452C4×C5C2×#23511yescharacteristic
453C4×C5C2×D3×D411yescharacteristic
454Dic5—41no—
455Dic5—122no—
456C24—31no—
457#41—62no—
458#41—62no—
459#41—102no—
460#41—102no—
461C2×Q8—31no—
462C2×Q8—51no—
463C2×D4—31no—
464C2×D4—51no—
465C2×D4—62no—
466C2×D4—61no—
467C2×D4—101no—
468C2×D4—302no—
469C22×C4—31no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—61no—
475C22×C4—101no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—52no—
482C2×C8—102no—
483C2×C8—154no—
484C2×C8—151no—
485C2×C8—151no—
486C2×C8—304no—
487C2×C8—304no—
488C4⋊C4—62no—
489C4⋊C4—152no—
490C4⋊C4—302no—
491C4⋊C4C2×D3×D512yes—
492C22⋊C4—21no—
493C22⋊C4—62no—
494C22⋊C4—62no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—21no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—201no—
503C22×C3—202no—
504C22×C3#408512yes—
505C22×C3C22×C22⋊D511yescharacteristic
506C2×D3—28no—
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—41no—
510C2×D3—42no—
511C2×D3#409614yescomplemented
512C3×C4—42no—
513C3×C4—201no—
514C3×C4#408512yes—
515C3×C4C2×D4×D511yescharacteristic
516C3×C4C2×#71111yescharacteristic
517Dic3—22no—
518Dic3—41no—
519Dic3—202no—
520C2×C5—22no—
521C2×C5—64no—
522C2×C5—241no—
523C2×C5C2×#88411yescharacteristic
524C2×C5D3×#13512yes—
525D5—81no—
526C23—32no—
527C23—64no—
528C23—62no—
529C23—61no—
530C23—101no—
531C23D3×C22⋊D511yescharacteristic
532Q8—61no—
533Q8—61no—
534Q8—101no—
535Q8—101no—
536D4—61no—
537D4—61no—
538D4—101no—
539D4—101no—
540D4—124no—
541D4—122no—
542D4—202no—
543D4—604no—
544C2×C4—22no—
545C2×C4—32no—
546C2×C4—62no—
547C2×C4—64no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—101no—
552C2×C4—122no—
553C2×C4—202no—
554C2×C4—302no—
555C2×C4#677212yes—
556C2×C4#677712yes—
557C2×C4D3×C22⋊D511yescharacteristic
558C2×C4C22×D3×D511yescharacteristic
559C8—102no—
560C8—152no—
561C8—152no—
562C2×C3—22no—
563C2×C3—401no—
564C2×C3C2×#408511yescharacteristic
565C2×C3C2×#409612yes—
566D3—24no—
567D3—81no—
568C5#7883811yescharacteristic, complemented, Sylow
569C22—22no—
570C22—34no—
571C22—68no—
572C22—62no—
573C22—62no—
574C22—121no—
575C22—122no—
576C22—201no—
577C22—202no—
578C22#9145312yes—
579C22C2×D3×C22⋊D511yescharacteristic
580C4—42no—
581C4—62no—
582C4—121no—
583C4—201no—
584C4—602no—
585C4#9145312yes—
586C4C2×#677211yescharacteristic
587C4C2×#677711yescharacteristic
588C3#1061465311yescharacteristic, complemented, Sylow
589C2—22no—
590C2—64no—
591C2—241no—
592C2—401no—
593C2C2×#9145311yescharacteristic
594C2D3×#409612yes—
subgroupG/H
centerC2×C4D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
hypercenter#117D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C5×#5524C2semidirect
2. #11754577C2semidirect
3. C2×#91297C2semidirect
4. C22×D3×#168C2semidirect
5. #11751099C2semidirect
6. C3×#65291C2semidirect
7. #11748388C2semidirect
8. #11747353C2semidirect
9. #11747352C2semidirect
10. #11747321C2semidirect
11. #11747319C2semidirect
30. C2×#6661C22semidirect
31. C2×#6656C22semidirect
32. C2×#6655C22semidirect
34. C2×#6652C22semidirect
38. #91092C22semidirect
39. #91091C22semidirect
40. C3×#3942C22semidirect
41. C3×#3941C22semidirect
42. #90973C22semidirect
43. #90967C22semidirect
54. #65291D3semidirect
83. C2×C3⋊#168D4semidirect
103. #5524D5semidirect
138. #3942C2×D3semidirect
139. #3941C2×D3semidirect
273. C2×C5×D3#135semidirect
500. C3×C5#3050semidirect
511. C2×D3#4096semidirect
568. C5#78838semidirect
588. C3#10614653semidirect

Maximal subgroups

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

subgroupindex
C5×#55242
#117545772
C2×#912972
C22×D3×#1682
#117510992
C3×#652912
#117483882
#117473532
#117473522
#117473212
#117473192
#106146533
#788385