Finite Group Databasebeta

← #14412754

Subgroups — #14412754

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92000C211yesmaximal, characteristic
2C3×#65857C211yesmaximal, characteristic, complemented
3C2×#91284C211yesmaximal, characteristic, complemented
4#11751103C211yesmaximal, characteristic, complemented
5C5×#5004C211yesmaximal, characteristic, complemented
6#11748413C211yesmaximal, characteristic, complemented
7C2×#90972C211yesmaximal, characteristic, complemented
8#11747501C212yesmaximal, complemented
9#11747500C212yesmaximal, complemented
10#11747487C212yesmaximal, complemented
11D5×#810C212yesmaximal, complemented
12#10610688—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C2×#6779—22no—
17C2×#6773C2212yes—
18C2×D15⋊Q8—21no—
19#92000—24no—
20#92000C418yescomplemented
21C2×#6766—21no—
22C2×D5×Dic6C2212yes—
23C3×C5×#117C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25C2×C5×#208C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C3×#4038C2212yes—
28C3×D5×C4⋊C4C2212yes—
29C3×#4027—22no—
30C3×C4×D20—21no—
31C3×C4×Dic10—21no—
32C2×#6649C2212yes—
33#91284—24no—
34C2×D5×C3⋊C8C2212yes—
35#91094C2211yescharacteristic
36#91094C2211yescharacteristic
37#91093C2211yescharacteristic
38#91093C2211yescharacteristic
39C5×#810C2212yes—
40C5×#810C2212yes—
41#90974C2212yes—
42#90972C2212yes—
43#90972C2212yes—
44#90968C2212yes—
45#82570—51nomaximal, Hall
46C2×#4147—31no—
47C2×#4053—31no—
48#65857D311yescharacteristic, complemented
49C5×#419—31no—
50C2×#3967—31no—
51#65422—31no—
52#65291—31no—
53#65093—32no—
54#65092—32no—
55#65091—32no—
56D5×#103—32no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817C2×C414yescomplemented
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C22×C5×Dic3—21no—
65C2×C5×Dic6—21no—
66C2×C5×Dic6—22no—
67C2×C5×Dic6C2×C414yescomplemented
68C2×C5×Dic6C2312yes—
69C2×C3×C22⋊D5D412yes—
70C22×C3×Dic5—21no—
71C3×#709C2×C414yes—
72C3×#709D414yes—
73C2×C3×D20D411yescharacteristic
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5C2312yes—
76C2×C3×Dic10D411yescharacteristic
77C2×#1204—22no—
78C2×#1202—22no—
79C2×#1200—22no—
80#6779—216no—
81C2×D5×Dic3—22no—
82#6773—24no—
83#6773C2×C418yescomplemented
84D15⋊Q8—28no—
85#6766—28no—
86D5×Dic6—24no—
87D5×Dic6C2×C418yescomplemented
88C3×C5×C4⋊C4C2311yescharacteristic
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C3×C42×C5—21no—
92C2×C3⋊#168—22no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×#208—22no—
96C2×C5×C3⋊C8C2312yes—
97C3×#685—22no—
98C3×C4⋊Dic5—21no—
99C3×C4⋊Dic5C2312yes—
100C3×#683—22no—
101C3×C4×Dic5—22no—
102#6649—24no—
103D5×C3⋊C8—24no—
104C2×#1010—51no—
105C3×#520—51no—
106C2×#948—51no—
107#5004—52no—
108#5004D511yescharacteristic, complemented
109#5002—51no—
110#5002—52no—
111C2×#810—51no—
112C2×#810—52no—
113#4966—51no—
114#4966—52no—
115C22×C5×Q8—31no—
116#4147—38no—
117#4147—64no—
118C2×#713—32no—
119C2×#713—61no—
120C2×Q8×D5—32no—
121C2×Q8×D5—61no—
122C2×#709—31no—
123C2×#709—62no—
124C2×#709C2×D311yescharacteristic
125C2×C5×M16—31no—
126C5×#117C2×D311yescharacteristic
127C2×C4⋊Dic5C2×D311yescharacteristic
128C22×#168—31no—
129#4053—64no—
130C2×#676—32no—
131C2×C8×D5—32no—
132#4038C2×D312yes—
133D5×C4⋊C4C2×D312yes—
134#4027—22no—
135C4×D20—21no—
136C4×Dic10—21no—
137C5×#103—32no—
138C5×#103—32no—
139#3967—32no—
140#3967—32no—
141#3953—32no—
142#3948—32no—
143#3942—31no—
144#3942—31no—
145#3941—31no—
146#3941—31no—
147#2898—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C22×C3×D5C2×D412yes—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5C2411yescharacteristic
157#1220—24no—
158C2×Dic15—21no—
159D60—21no—
160D60C22×C412yes—
161C4×D15—24no—
162Dic30—21no—
163Dic30C22×C412yes—
164C2×C5×Dic3—24no—
165C2×C5×Dic3—22no—
166C5×Dic6—24no—
167C5×Dic6—22no—
168C5×Dic6C22×C414yes—
169C3×C22⋊D5C22⋊C418yes—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—81no—
172C2×C3×Dic5C2×D412yes—
173C3×D20C22⋊C414yes—
174C3×C4×D5—82no—
175C3×C4×D5C22×C414yes—
176C3×C4×D5C2×D414yes—
177C3×Dic10C22⋊C414yes—
178#1204—28no—
179#1202—28no—
180#1200—28no—
181D5×Dic3—28no—
182C3⋊#168—21no—
183C3⋊#168—21no—
184C5×C3⋊C8—22no—
185C2×C3×#41—51no—
186#1010—58no—
187#1010—104no—
188C2×D3×Q8—101no—
189C2×#237—101no—
190C2×#237—102no—
191C2×#235—51no—
192C2×#235—52no—
193C22×Dic6—52no—
194C22×Dic6C2×D511yescharacteristic
195C3×C4×Q8—101no—
196C3×C4×D4—101no—
197C3×C4×D4—102no—
198C3×#117—52no—
199C3×#117C2×D511yescharacteristic
200C2×C3×C4⋊C4—51no—
201C2×C3×C4⋊C4—52no—
202#948—104no—
203C2×#208—52no—
204C2×#208C2×D511yescharacteristic
205C22×C3⋊C8—51no—
206C22×C3⋊C8—52no—
207#810—52no—
208#810—52no—
209#810—51no—
210#810—51no—
211#810—52no—
212#810C2×D512yes—
213#810C2×D512yes—
214#809—51no—
215#809—51no—
216#809—52no—
217C2×C5×Q8—34no—
218C2×C5×Q8—32no—
219C2×C5×Q8—62no—
220C2×C5×Q8—61no—
221C22×C4×C5—61no—
222C22×C4×C5C22×D311yescharacteristic
223C2×C22⋊D5—61no—
224C2×C22⋊D5#6712yes—
225C22×Dic5—21no—
226#713—38no—
227#713—68no—
228#713—64no—
229Q8×D5—38no—
230Q8×D5—64no—
231Q8×D5—68no—
232#709—34no—
233#709—62no—
234#709—616no—
235#709C4×D314yes—
236#709D1214yes—
237C2×D20—31no—
238C2×D20—62no—
239C2×D20#6711yescharacteristic
240C2×C4×D5—22no—
241C2×C4×D5—62no—
242C2×C4×D5—61no—
243C2×C4×D5—62no—
244C2×C4×D5C22×D312yes—
245C2×Dic10—31no—
246C2×Dic10—62no—
247C2×Dic10#6711yescharacteristic
248C5×M16—62no—
249C2×C5×C8—32no—
250C5×C4⋊C4C22×D311yescharacteristic
251C5×C4⋊C4C22×D311yescharacteristic
252C5×C22⋊C4—21no—
253C42×C5—21no—
254#685—22no—
255C4⋊Dic5—21no—
256C4⋊Dic5C22×D312yes—
257#683—22no—
258C4×Dic5—22no—
259C2×#168—31no—
260C2×#168—31no—
261C2×#168—62no—
262#676—64no—
263C8×D5—64no—
264C2×2−1+4—151no—
265C2×#131—151no—
266#520—51no—
267#419—31no—
268#419—152no—
269#417—152no—
270#417—151no—
271#416—152no—
272#416—151no—
273C2×#103—152no—
274C2×#103—151no—
275C22×C3×C5—21no—
276C22×C3×C5—21no—
277C22×C3×C5C2×C22⋊C412yes—
278C22×C3×C5C22×D411yescharacteristic
279C2×D15—22no—
280C2×D15—41no—
281C2×D15—41no—
282C2×C3×D5—22no—
283C2×C3×D5—22no—
284C2×C3×D5C2×C22⋊C414yes—
285C3×C4×C5—41no—
286C3×C4×C5—41no—
287C3×C4×C5C2×C22⋊C412yes—
288C3×C4×C5C23×C411yescharacteristic
289C3×C4×C5C22×D411yescharacteristic
290Dic15—22no—
291C3×Dic5—42no—
292C3×Dic5C2×C22⋊C414yes—
293C5×Dic3—24no—
294C3×#41—54no—
295C3×#41—54no—
296C2×C3×Q8—51no—
297C2×C3×D4—52no—
298C2×C3×D4—51no—
299C22×C3×C4—52no—
300C22×C3×C4—102no—
301C22×C3×C4—101no—
302C22×C3×C4C22×D511yescharacteristic
303C2×#67—102no—
304C2×#67—101no—
305C22×Dic3—21no—
306C22×Dic3—102no—
307D3×Q8—108no—
308#237—108no—
309#237—1016no—
310#235—54no—
311#235—58no—
312#235—104no—
313#235—102no—
314C2×D12—51no—
315C2×C4×D3—102no—
316C2×C4×D3—101no—
317C2×Dic6—21no—
318C2×Dic6—22no—
319C2×Dic6—51no—
320C2×Dic6—58no—
321C2×Dic6—104no—
322C2×Dic6—102no—
323C2×Dic6C4×D514yescomplemented
324C2×Dic6C22×D512yes—
325C3×C4⋊C4—52no—
326C3×C4⋊C4—102no—
327C3×C4⋊C4—101no—
328C3×C4⋊C4C22×D511yescharacteristic
329C3×C4⋊C4C22×D511yescharacteristic
330C3×C22⋊C4—21no—
331C3×C22⋊C4—102no—
332C3×C42—21no—
333C3×C42—102no—
334#208—22no—
335#208—104no—
336C2×C3⋊C8—51no—
337C2×C3⋊C8—51no—
338C2×C3⋊C8—104no—
339C2×C3⋊C8—102no—
340C2×C3⋊C8C22×D512yes—
341C23×C5C2×#6711yescharacteristic
342C22×D5—61no—
343C22×D5C2×#6712yes—
344C5×Q8—34no—
345C5×Q8—64no—
346C5×Q8—62no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—64no—
350C2×C4×C5—62no—
351C2×C4×C5C2×C4×D312yes—
352C2×C4×C5C2×D1212yes—
353C2×C4×C5C2×#6711yescharacteristic
354C2×C4×C5C23×D311yescharacteristic
355C22⋊D5—64no—
356C22⋊D5(C2×D3)⋊C418yes—
357C2×Dic5—22no—
358C2×Dic5—61no—
359C2×Dic5—81no—
360C2×Dic5C2×#6712yes—
361D20—32no—
362D20—68no—
363D20—61no—
364D20(C2×D3)⋊C414yes—
365C4×D5—68no—
366C4×D5—64no—
367C4×D5—68no—
368C4×D5—82no—
369C4×D5C2×C4×D314yes—
370C4×D5C2×D1214yes—
371Dic10—32no—
372Dic10—61no—
373Dic10—68no—
374Dic10(C2×D3)⋊C414yes—
375C5×C8—62no—
376#168—61no—
377#168—61no—
3782−1+4—158no—
3792−1+4—304no—
380C2×#41—51no—
381C2×#41—152no—
382C2×#41—151no—
383C2×#41—302no—
384C2×#41—301no—
385C22×Q8—31no—
386C22×Q8—152no—
387C22×Q8—301no—
388#131—304no—
389C2×M16—31no—
390C2×M16—152no—
391C22×C8—152no—
392C22×C8—151no—
393C4×Q8—101no—
394C4×D4—101no—
395C4×D4—102no—
396#117—52no—
397#117D3×D511yescharacteristic
398C2×C4⋊C4—51no—
399C2×C4⋊C4—52no—
400#103—32no—
401#103—32no—
402#103—152no—
403#103—152no—
404#103—152no—
405#103—151no—
406#103—151no—
407#102—152no—
408#102—151no—
409#102—151no—
410C2×C3×C5—22no—
411C2×C3×C5C22×C22⋊C411yescharacteristic
412C2×C3×C5#57711yescharacteristic
413C2×C3×C5#57811yescharacteristic
414D15—42no—
415C3×D5—24no—
416C23×C3—52no—
417C23×C3D4×D511yescharacteristic
418C22×D3—101no—
419C3×Q8—54no—
420C3×D4—58no—
421C3×D4—54no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—52no—
425C2×C3×C4—54no—
426C2×C3×C4—54no—
427C2×C3×C4—102no—
428C2×C3×C4—402no—
429C2×C3×C4—401no—
430C2×C3×C4C2×C4×D512yes—
431C2×C3×C4D4×D512yes—
432C2×C3×C4D4×D511yescharacteristic
433C2×C3×C4C23×D511yescharacteristic
434#67—108no—
435#67—104no—
436C2×Dic3—22no—
437C2×Dic3—24no—
438C2×Dic3—108no—
439C2×Dic3—101no—
440D12—52no—
441D12—101no—
442C4×D3—108no—
443C4×D3—104no—
444Dic6—22no—
445Dic6—24no—
446Dic6—52no—
447Dic6—108no—
448Dic6—101no—
449Dic6C2×C4×D514yes—
450C3⋊C8—22no—
451C3⋊C8—101no—
452C3⋊C8—101no—
453C22×C5—21no—
454C22×C5—21no—
455C22×C5C2×(C2×D3)⋊C412yes—
456C22×C5C22×#6711yescharacteristic
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—62no—
460C2×D5—121no—
461C2×D5—121no—
462C2×D5C2×(C2×D3)⋊C414yes—
463C4×C5—41no—
464C4×C5—41no—
465C4×C5—64no—
466C4×C5C2×(C2×D3)⋊C412yes—
467C4×C5C22×C4×D311yescharacteristic
468C4×C5C22×D1211yescharacteristic
469Dic5—42no—
470Dic5—62no—
471Dic5C2×(C2×D3)⋊C414yes—
472#41—54no—
473#41—54no—
474#41—158no—
475#41—154no—
476#41—304no—
477#41—3016no—
478#41—308no—
479#41—302no—
480C2×Q8—34no—
481C2×Q8—32no—
482C2×Q8—51no—
483C2×Q8—62no—
484C2×Q8—61no—
485C2×Q8—158no—
486C2×Q8—151no—
487C2×Q8—302no—
488C2×Q8—304no—
489C2×Q8—308no—
490C2×D4—52no—
491C2×D4—51no—
492C2×D4—151no—
493C2×D4—302no—
494C2×D4—301no—
495C22×C4—52no—
496C22×C4—61no—
497C22×C4—102no—
498C22×C4—101no—
499C22×C4—302no—
500C22×C4—302no—
501C22×C4—301no—
502C22×C4C2×D3×D511yescharacteristic
503M16—62no—
504M16—304no—
505C2×C8—32no—
506C2×C8—151no—
507C2×C8—151no—
508C2×C8—304no—
509C2×C8—302no—
510C4⋊C4—52no—
511C4⋊C4—102no—
512C4⋊C4—101no—
513C4⋊C4C2×D3×D511yescharacteristic
514C4⋊C4C2×D3×D511yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—102no—
517C42—21no—
518C42—102no—
519C3×C5#289811yescharacteristic, complemented, Hall
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—54no—
523C22×C3—102no—
524C22×C3—102no—
525C22×C3D5×C22⋊C412yes—
526C22×C3C2×D4×D511yescharacteristic
527C2×D3—102no—
528C2×D3—201no—
529C2×D3—201no—
530C3×C4—41no—
531C3×C4—41no—
532C3×C4—54no—
533C3×C4—202no—
534C3×C4D5×C22⋊C412yes—
535C3×C4C22×C4×D511yescharacteristic
536C3×C4C2×D4×D511yescharacteristic
537Dic3—24no—
538Dic3—102no—
539C2×C5—22no—
540C2×C5C22×(C2×D3)⋊C411yescharacteristic
541C2×C5#583611yescharacteristic
542C2×C5#583811yescharacteristic
543D5—24no—
544D5—122no—
545C23—52no—
546C23—301no—
547C23D5×#6711yescharacteristic
548Q8—34no—
549Q8—54no—
550Q8—64no—
551Q8—62no—
552Q8—152no—
553Q8—308no—
554Q8—301no—
555D4—58no—
556D4—54no—
557D4—152no—
558D4—308no—
559D4—304no—
560D4—301no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—52no—
564C2×C4—54no—
565C2×C4—54no—
566C2×C4—64no—
567C2×C4—62no—
568C2×C4—102no—
569C2×C4—308no—
570C2×C4—308no—
571C2×C4—301no—
572C2×C4—304no—
573C2×C4—402no—
574C2×C4—401no—
575C2×C4C4×D3×D512yes—
576C2×C4D5×D1212yes—
577C2×C4D5×#6711yescharacteristic
578C2×C4C22×D3×D511yescharacteristic
579C8—62no—
580C8—301no—
581C8—301no—
582C2×C3—22no—
583C2×C3—104no—
584C2×C3C2×D5×C22⋊C411yescharacteristic
585C2×C3#6611211yescharacteristic
586C2×C3#6611311yescharacteristic
587D3—202no—
588C5#8257011yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—54no—
592C22—102no—
593C22—102no—
594C22—302no—
595C22—601no—
596C22—601no—
597C22D5×(C2×D3)⋊C412yes—
598C22C2×D5×#6711yescharacteristic
599C4—41no—
600C4—41no—
601C4—54no—
602C4—64no—
603C4—202no—
604C4—302no—
605C4D5×(C2×D3)⋊C412yes—
606C4C2×C4×D3×D511yescharacteristic
607C4C2×D5×D1211yescharacteristic
608C3#1061068811yescharacteristic, complemented, Sylow
609C2—22no—
610C2—104no—
611C2—602no—
612C2C2×D5×(C2×D3)⋊C411yescharacteristic
613C2#1175533511yescharacteristic
614C2#1175533611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#92000C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#65857C2semidirect
3. C2×#91284C2semidirect
4. #11751103C2semidirect
5. C5×#5004C2semidirect
6. #11748413C2semidirect
7. C2×#90972C2semidirect
8. #11747501C2semidirect
9. #11747500C2semidirect
10. #11747487C2semidirect
11. D5×#810C2semidirect
20. #92000C4semidirect
48. #65857D3semidirect
60. #6817C2×C4semidirect
67. C2×C5×Dic6C2×C4semidirect
83. #6773C2×C4semidirect
87. D5×Dic6C2×C4semidirect
108. #5004D5semidirect
323. C2×Dic6C4×D5semidirect
519. C3×C5#2898semidirect
588. C5#82570semidirect
608. C3#10610688semidirect

Maximal subgroups

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

subgroupindex
C2×#920002
C3×#658572
C2×#912842
#117511032
C5×#50042
#117484132
C2×#909722
#117475012
#117475002
#117474872
D5×#8102
#106106883
#825705