Finite Group Databasebeta

← #14427857

Subgroups — #14427857

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
1C3×#65858C211yesmaximal, characteristic, complemented
2#11754563C211yesmaximal, characteristic, complemented
3C2×#91297C211yesmaximal, characteristic, complemented
4C22×D5×C3⋊C8C211yesmaximal, characteristic, complemented
5#11751099C211yesmaximal, characteristic, complemented
6C5×#5002C211yesmaximal, characteristic, complemented
7#11748365C211yesmaximal, characteristic, complemented
8#11747341C212yesmaximal, complemented
9#11747339C212yesmaximal, complemented
10#11747309C212yesmaximal, complemented
11#11747307C212yesmaximal, complemented
12#10610569—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17#91815C2211yescharacteristic
18C22×C3⋊#168C2211yescharacteristic
19C22×C5×C3⋊C8C2211yescharacteristic
20C3×#4043C2212yes—
21C3×#4041C2212yes—
22C3×#4032—21no—
23C3×#4028—21no—
24C3×C4×D20—22no—
25#91563—21no—
26#91539—21no—
27#91449C2212yes—
28C4×#1201—22no—
29#91359C2212yes—
30C2×#6661C2211yescharacteristic, complemented
31C2×#6656C2211yescharacteristic, complemented
32C2×#6655C2211yescharacteristic, complemented
33#91297—24no—
34C2×#6652C2211yescharacteristic, complemented
35C2×D5×C3⋊C8—24no—
36C2×D5×C3⋊C8C2212yes—
37C2×D5×C3⋊C8C2212yes—
38#91092C2212yescomplemented
39#91091C2212yescomplemented
40C5×#810C2212yescomplemented
41C5×#809C2212yescomplemented
42#90971C2212yescomplemented
43#90965C2212yescomplemented
44#82922—51nomaximal, Hall
45#66162—31no—
46C2×#4096—31no—
47C22×C8×D5—31no—
48#65858D311yescharacteristic, complemented
49C5×#416—31no—
50#65402—31no—
51#65287—31no—
52#65102—32no—
53#65096—32no—
54#65067—32no—
55#65064—32no—
56C23×C3×D5D411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×C5×#67—21no—
59C5×#235—22no—
60C5×#235—22no—
61C2×C5×D12C2311yescharacteristic
62C2×C4×C5×D3—21no—
63C2×C5×Dic6C2311yescharacteristic
64C2×C3×C22⋊D5—21no—
65C22×C3×Dic5D411yescharacteristic
66C3×#709—22no—
67C3×#709—22no—
68C2×C3×D20—22no—
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—22no—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—21no—
73C2×C3×C4×D5D412yes—
74C2×C3×C4×D5C2312yes—
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
86C2×C5×C3⋊C8—22no—
87C2×C5×C3⋊C8C2312yes—
88C3×#685—22no—
89C3×#685—22no—
90C3×C4⋊Dic5—22no—
91#6669—22no—
92(C2×D3)⋊Dic5—22no—
93#6665—22no—
94#6661—22no—
95#6656—22no—
96#6655—22no—
97#6652—22no—
98D5×C3⋊C8—24no—
99D5×C3⋊C8—24no—
100C3×#525—51no—
101C2×#950—51no—
102#5791—51no—
103C23×C3⋊C8—51no—
104#5233—51no—
105#5051—52no—
106#5048—52no—
107#5041—52no—
108#5038—52no—
109#5002D511yescharacteristic, complemented
110#4998—51no—
111C2×C5×#41—31no—
112C2×#709C2×D311yescharacteristic
113C22×C4×D5C2×D311yescharacteristic
114C22×C5×C8—31no—
115C5×#117C2×D311yescharacteristic
116#4096—64no—
117#4092—32no—
118C2×#689—31no—
119C2×#688—31no—
120#4084—32no—
121#4083—61no—
122#4081—61no—
123C2×#687—31no—
124C2×#686—31no—
125C4×C22⋊D5—62no—
126#4072—31no—
127C22×#168—31no—
128C2×C8×D5—32no—
129C2×C8×D5—32no—
130C2×C8×D5—64no—
131#4043C2×D312yes—
132#4041C2×D312yes—
133#4032—21no—
134#4028—21no—
135C4×D20—22no—
136C5×#103—32no—
137C5×#102—32no—
138#3953—32no—
139#3948—32no—
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5C2×D411yescharacteristic
144C22×C5×D3—21no—
145C22×C3×D5—22no—
146C22×C3×D5—24no—
147C22×C3×D5—21no—
148C22×C3×D5C2×D412yes—
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—21no—
157C5×D12—21no—
158C5×D12—21no—
159C4×C5×D3—42no—
160C5×Dic6—21no—
161C5×Dic6—21no—
162C3×C22⋊D5—42no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5C2×D412yes—
166C3×D20—21no—
167C3×D20—21no—
168C3×D20—44no—
169C3×C4×D5—24no—
170C3×C4×D5—22no—
171C3×C4×D5—22no—
172C3×C4×D5—42no—
173C3×Dic10—21no—
174C3×Dic10—21no—
175#1201—44no—
176C3⋊#168C2×D412yes—
177C3⋊#168C2×D412yes—
178C5×C3⋊C8—22no—
179C2×C3×#41—51no—
180C23×C3×C4—51no—
181C2×#235C2×D511yescharacteristic
182C3×#123—101no—
183C3×C22⋊Q8—52no—
184C3×#121—52no—
185C3×#120—101no—
186C3×C4×D4—102no—
187C3×#117C2×D511yescharacteristic
188#953—101no—
189#950—104no—
190C2×#216—51no—
191C2×#215—51no—
192C2×#214—51no—
193C2×#213—51no—
194#930—52no—
195#929—101no—
196C4×#67—102no—
197#926—51no—
198#924—52no—
199C22×C3⋊C8—51no—
200C22×C3⋊C8—52no—
201C22×C3⋊C8—52no—
202C22×C3⋊C8—104no—
203C22×C3⋊C8C2×D511yescharacteristic
204#835—52no—
205#832—52no—
206#810C2×D512yescomplemented
207#809C2×D512yescomplemented
208#808—52no—
209#807—52no—
210C23×D5#6711yescharacteristic
211C5×#41—62no—
212C5×#41—62no—
213C2×C5×Q8—31no—
214C2×C5×D4—31no—
215C2×C5×D4—61no—
216C22×C4×C5—61no—
217C22×C4×C5C22×D311yescharacteristic
218C2×C22⋊D5—21no—
219C2×C22⋊D5—62no—
220C22×Dic5#6711yescharacteristic
221#709—22no—
222#709—22no—
223C2×D20—22no—
224C2×D20C22×D311yescharacteristic
225C2×C4×D5—22no—
226C2×C4×D5—22no—
227C2×C4×D5—21no—
228C2×C4×D5#6712yes—
229C2×C4×D5C22×D312yes—
230C2×Dic10C22×D311yescharacteristic
231C2×C5×C8—32no—
232C2×C5×C8—62no—
233C5×C4⋊C4C22×D312yes—
234C5×C22⋊C4—21no—
235C42×C5—21no—
236C22⋊Dic5—61no—
237C22⋊Dic5—62no—
238#689—62no—
239#688—62no—
240#687—62no—
241#686—62no—
242#685—22no—
243#685—22no—
244#685—62no—
245C4⋊Dic5—22no—
246C4⋊Dic5—32no—
247#683—62no—
248C4×Dic5—61no—
249C2×#168—34no—
250C2×#168—31no—
251C2×#168—31no—
252C8×D5—64no—
253C8×D5—64no—
254C2×#135—151no—
255C23×C8—151no—
256#525—51no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—31no—
264#416—151no—
265C22×C3×C5—22no—
266C22×C3×C5#12112yes—
267C22×C3×C5C22×D411yescharacteristic
268C2×C5×D3—41no—
269C2×C5×D3—42no—
270C2×C3×D5—28no—
271C2×C3×D5—22no—
272C2×C3×D5—22no—
273C2×C3×D5—41no—
274C2×C3×D5—42no—
275C2×C3×D5#13514yescomplemented
276C3×C4×C5—42no—
277C3×C4×C5#12112yes—
278C3×C4×C5C22×D411yescharacteristic
279C3×C4×C5C2×#4111yescharacteristic
280Dic15—42no—
281C3×Dic5—22no—
282C3×Dic5—41no—
283C5×Dic3—41no—
284C24×C3—51no—
285C3×#41—102no—
286C3×#41—102no—
287C2×C3×Q8—51no—
288C2×C3×D4—51no—
289C2×C3×D4—102no—
290C2×C3×D4—101no—
291C22×C3×C4—51no—
292C22×C3×C4—52no—
293C22×C3×C4—52no—
294C22×C3×C4—102no—
295C22×C3×C4—102no—
296C22×C3×C4—101no—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—21no—
299C2×#67—102no—
300#235—22no—
301#235—22no—
302C2×D12C22×D511yescharacteristic
303C2×C4×D3—21no—
304C2×Dic6C22×D511yescharacteristic
305C3×C4⋊C4—102no—
306C3×C4⋊C4C22×D512yes—
307C3×C22⋊C4—21no—
308C3×C22⋊C4—102no—
309C3×C22⋊C4—102no—
310C3×C42—21no—
311#217—102no—
312#217—101no—
313#216—102no—
314#215—102no—
315#214—102no—
316#213—102no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3—52no—
319Dic3⋊C4—102no—
320C4×Dic3—101no—
321C2×C3⋊C8—22no—
322C2×C3⋊C8—54no—
323C2×C3⋊C8—51no—
324C2×C3⋊C8—51no—
325C2×C3⋊C8—104no—
326C2×C3⋊C8—104no—
327C2×C3⋊C8C22×D512yes—
328C23×C5—61no—
329C23×C5C2×#6711yescharacteristic
330C22×D5—22no—
331C22×D5—24no—
332C22×D5—21no—
333C22×D5C2×#6712yes—
334C5×Q8—61no—
335C5×Q8—61no—
336C5×D4—61no—
337C5×D4—61no—
338C5×D4—122no—
339C2×C4×C5—22no—
340C2×C4×C5—61no—
341C2×C4×C5—122no—
342C2×C4×C5D3×D412yes—
343C2×C4×C5#23712yes—
344C2×C4×C5C2×#6711yescharacteristic
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—42no—
347C22⋊D5—124no—
348C2×Dic5—22no—
349C2×Dic5—21no—
350C2×Dic5—62no—
351C2×Dic5C2×#6712yes—
352D20—21no—
353D20—21no—
354D20—44no—
355C4×D5—24no—
356C4×D5—22no—
357C4×D5—22no—
358C4×D5—42no—
359Dic10—21no—
360Dic10—21no—
361C5×C8—62no—
362#168—32no—
363#168—32no—
364C2×#41—31no—
365C2×#41—51no—
366C23×C4—51no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—31no—
373C22×C8—152no—
374C22×C8—152no—
375C22×C8—151no—
376C22×C8—304no—
377#123—101no—
378#123—301no—
379C22⋊Q8—52no—
380C22⋊Q8—152no—
381#121—52no—
382#121—152no—
383#120—101no—
384#120—301no—
385C4×D4—102no—
386C4×D4—302no—
387#117—151no—
388#117D3×D511yescharacteristic
389#107—152no—
390#106—152no—
391#103—32no—
392#103—152no—
393#102—32no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5C2×#12111yescharacteristic
397C2×C3×C5C2×#13512yes—
398C3×D5—24no—
399C3×D5—81no—
400C5×D3—81no—
401C23×C3—52no—
402C23×C3—104no—
403C23×C3—102no—
404C23×C3—101no—
405C23×C3D4×D511yescharacteristic
406C22×D3—21no—
407C3×Q8—101no—
408C3×Q8—101no—
409C3×D4—101no—
410C3×D4—101no—
411C3×D4—204no—
412C3×D4—202no—
413C2×C3×C4—22no—
414C2×C3×C4—52no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4—102no—
418C2×C3×C4—104no—
419C2×C3×C4—101no—
420C2×C3×C4—202no—
421C2×C3×C4#70912yes—
422C2×C3×C4D4×D512yes—
423C2×C3×C4D4×D511yescharacteristic
424C2×C3×C4C23×D511yescharacteristic
425#67—42no—
426#67—204no—
427C2×Dic3—21no—
428C2×Dic3—102no—
429D12—21no—
430D12—21no—
431C4×D3—42no—
432Dic6—21no—
433Dic6—21no—
434C3⋊C8—22no—
435C3⋊C8—52no—
436C3⋊C8—52no—
437C22×C5—22no—
438C22×C5—121no—
439C22×C5—122no—
440C22×C5#93912yes—
441C22×C5C22×#6711yescharacteristic
442C2×D5—28no—
443C2×D5—22no—
444C2×D5—22no—
445C2×D5—41no—
446C2×D5—42no—
447C2×D5#95014yescomplemented
448C4×C5—42no—
449C4×C5—121no—
450C4×C5#93912yes—
451C4×C5C2×D3×D411yescharacteristic
452C4×C5C2×#23711yescharacteristic
453Dic5—22no—
454Dic5—41no—
455Dic5—122no—
456C24—51no—
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—61no—
466C2×D4—102no—
467C2×D4—101no—
468C2×D4—302no—
469C22×C4—51no—
470C22×C4—52no—
471C22×C4—52no—
472C22×C4—61no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—101no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—32no—
482C2×C8—62no—
483C2×C8—154no—
484C2×C8—151no—
485C2×C8—151no—
486C2×C8—304no—
487C2×C8—304no—
488C4⋊C4—102no—
489C4⋊C4—152no—
490C4⋊C4—302no—
491C4⋊C4C2×D3×D512yes—
492C22⋊C4—21no—
493C22⋊C4—102no—
494C22⋊C4—102no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—21no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—54no—
503C22×C3—108no—
504C22×C3—102no—
505C22×C3—102no—
506C22×C3—201no—
507C22×C3—202no—
508C22×C3#403012yes—
509C22×C3C2×D4×D511yescharacteristic
510C2×D3—41no—
511C2×D3—42no—
512C3×C4—42no—
513C3×C4—102no—
514C3×C4—201no—
515C3×C4#403012yes—
516C3×C4C2×#70911yescharacteristic
517C3×C4C2×D4×D511yescharacteristic
518Dic3—41no—
519Dic3—202no—
520C2×C5—22no—
521C2×C5—241no—
522C2×C5C2×#93911yescharacteristic
523C2×C5C2×#95012yes—
524D5—24no—
525D5—81no—
526C23—52no—
527C23—61no—
528C23—104no—
529C23—102no—
530C23—101no—
531C23D5×#6711yescharacteristic
532Q8—61no—
533Q8—61no—
534Q8—101no—
535Q8—101no—
536D4—61no—
537D4—61no—
538D4—101no—
539D4—101no—
540D4—122no—
541D4—204no—
542D4—202no—
543D4—604no—
544C2×C4—22no—
545C2×C4—52no—
546C2×C4—61no—
547C2×C4—102no—
548C2×C4—104no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—101no—
552C2×C4—122no—
553C2×C4—202no—
554C2×C4—302no—
555C2×C4#676512yes—
556C2×C4#677712yes—
557C2×C4D5×#6711yescharacteristic
558C2×C4C22×D3×D511yescharacteristic
559C8—62no—
560C8—152no—
561C8—152no—
562C2×C3—22no—
563C2×C3—104no—
564C2×C3—401no—
565C2×C3C2×#403011yescharacteristic
566C2×C3D5×#13512yes—
567D3—81no—
568C5#8292211yescharacteristic, complemented, Sylow
569C22—22no—
570C22—54no—
571C22—108no—
572C22—102no—
573C22—102no—
574C22—122no—
575C22—121no—
576C22—202no—
577C22—201no—
578C22#9140812yes—
579C22C2×D5×#6711yescharacteristic
580C4—42no—
581C4—102no—
582C4—121no—
583C4—201no—
584C4—602no—
585C4#9140812yes—
586C4C2×#676511yescharacteristic
587C4C2×#677711yescharacteristic
588C3#1061056911yescharacteristic, complemented, Sylow
589C2—22no—
590C2—104no—
591C2—241no—
592C2—401no—
593C2C2×#9140811yescharacteristic
594C2D5×#95012yes—
subgroupG/H
centerC2×C4D5×#67
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. C3×#65858C2semidirect
2. #11754563C2semidirect
3. C2×#91297C2semidirect
4. C22×D5×C3⋊C8C2semidirect
5. #11751099C2semidirect
6. C5×#5002C2semidirect
7. #11748365C2semidirect
8. #11747341C2semidirect
9. #11747339C2semidirect
10. #11747309C2semidirect
11. #11747307C2semidirect
30. C2×#6661C22semidirect
31. C2×#6656C22semidirect
32. C2×#6655C22semidirect
34. C2×#6652C22semidirect
38. #91092C22semidirect
39. #91091C22semidirect
40. C5×#810C22semidirect
41. C5×#809C22semidirect
42. #90971C22semidirect
43. #90965C22semidirect
48. #65858D3semidirect
83. C2×C3⋊#168D4semidirect
109. #5002D5semidirect
206. #810C2×D5semidirect
207. #809C2×D5semidirect
275. C2×C3×D5#135semidirect
447. C2×D5#950semidirect
500. C3×C5#3050semidirect
568. C5#82922semidirect
588. C3#10610569semidirect

Maximal subgroups

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

subgroupindex
C3×#658582
#117545632
C2×#912972
C22×D5×C3⋊C82
#117510992
C5×#50022
#117483652
#117473412
#117473392
#117473092
#117473072
#106105693
#829225