Finite Group Databasebeta

← #14439188

Subgroups — #14439188

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91838C211yesmaximal, characteristic, complemented
2C5×#5832C211yesmaximal, characteristic, complemented
3C2×C3×#4095C211yesmaximal, characteristic, complemented
4C2×#91458C211yesmaximal, characteristic, complemented
5C2×#91305C211yesmaximal, characteristic, complemented
6C2×#91298C211yesmaximal, characteristic, complemented
7#11749344C212yesmaximal, complemented
8#11749342C212yesmaximal, complemented
9#11749098C212yesmaximal, complemented
10#11749097C212yesmaximal, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12#10615018—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C5×#235C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C22×#1202—22no—
18#91838—24no—
19C2×#6717C2212yescomplemented
20C2×#6715C2212yescomplemented
21C2×#6710C2211yescharacteristic
22C5×#947C2211yescharacteristic, complemented
23C5×#944C2211yescharacteristic, complemented
24C5×#940C2211yescharacteristic, complemented
25C5×#939—22no—
26C5×#936C2211yescharacteristic, complemented
27C4×C5×#67—22no—
28C2×C4×C5×Dic3C2211yescharacteristic
29C3×#4095—24no—
30C2×C3×#688C2212yescomplemented
31C2×C3×#686C2212yescomplemented
32C2×C3×#681C2211yescharacteristic
33#91458—22no—
34#91458C2212yes—
35#91458C2212yes—
36C2×#6660C2212yescomplemented
37C2×#6655C2212yescomplemented
38#91305—24no—
39C2×#6654C2212yescomplemented
40#91298—24no—
41C2×#6652C2212yescomplemented
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83937—51nomaximal, Hall
45C5×#532—31no—
46C2×#4095—31no—
47C2×#4095—31no—
48C2×#4095—31no—
49C2×#4095D311yescharacteristic, complemented
50C2×#4020—31no—
51#65374—32no—
52#65362—32no—
53#65347—32no—
54#65347—32no—
55C4×#681—31no—
56C23×D15—21no—
57C23×C3×D5—21no—
58C3×C5×#41—22no—
59C3×C5×#41—22no—
60C2×C3×C5×Q8C2311yescharacteristic
61C2×C3×C5×D4—21no—
62C2×C3×C5×D4C2311yescharacteristic
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5C2311yescharacteristic
65C2×D60—22no—
66C2×D60—22no—
67C2×D60—21no—
68C2×D60C2312yes—
69C2×C5×#67—21no—
70C2×C5×#67—22no—
71C22×C5×Dic3D412yes—
72C5×#235—22no—
73C5×#235—22no—
74C2×C5×D12C2311yescharacteristic
75C2×C4×C5×D3—21no—
76C2×C5×Dic6C2311yescharacteristic
77C2×C3×D20—22no—
78C2×C3×D20—22no—
79C2×C3×D20—21no—
80C2×C3×D20C2312yes—
81C2×#1202—24no—
82C2×#1202—24no—
83C2×#1202—48no—
84#6717—24no—
85#6715—24no—
86#6710D414yescomplemented
87C2×C3⋊#168C2312yes—
88C5×#217—22no—
89C5×(C2×D3)⋊C4—22no—
90C5×Dic3⋊C4—22no—
91C4×C5×Dic3D412yes—
92C4×C5×Dic3C2311yescharacteristic
93C4×C5×Dic3C2311yescharacteristic
94C3×#688—24no—
95C3×#686—24no—
96C3×#681D414yescomplemented
97C2×C3×#168C2312yes—
98#6660—24no—
99#6655—24no—
100#6654—24no—
101#6652—24no—
102C2×C3×AGL(1,ℤ/8)—51no—
103#5832D511yescharacteristic, complemented
104C2×#949—51no—
105C2×#940—51no—
106C2×#932—51no—
107C2×#908—51no—
108#5176—52no—
109#5175—52no—
110#5154—52no—
111#5151—52no—
112Dic3×M16—51no—
113C2×C5×#41—31no—
114C2×C5×#41C2×D311yescharacteristic
115C22×D20—31no—
116C22×D20—62no—
117C22×D20C2×D311yescharacteristic
118C5×C4⋊Q8—31no—
119C5×#127—31no—
120C5×#124—31no—
121C5×#124—31no—
122C5×#121—62no—
123C4×C5×D4—62no—
124C2×C42×C5—31no—
125#4095—24no—
126#4095—64no—
127#4095—64no—
128#4095—64no—
129C2×#688—32no—
130C2×#688—32no—
131C2×#688—32no—
132C2×#688C2×D312yescomplemented
133C2×#686—32no—
134C2×#686—32no—
135C2×#686—32no—
136C2×#686C2×D312yescomplemented
137C2×#681—31no—
138C2×#681C2×D311yescharacteristic
139#4020—32no—
140#4020—32no—
141#4020—62no—
142#3935—32no—
143C4×#168—32no—
144#3151—151noSylow
145C23×C3×C5—21no—
146C23×C3×C5C2×D411yescharacteristic
147C22×D15—22no—
148C22×D15—44no—
149C22×D15—42no—
150C22×C5×D3—21no—
151C22×C3×D5—22no—
152C22×C3×D5—44no—
153C22×C3×D5—42no—
154C3×C5×Q8—21no—
155C3×C5×Q8—21no—
156C3×C5×D4—21no—
157C3×C5×D4—21no—
158C3×C5×D4—42no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—42no—
161C2×C3×C4×C5C2×D411yescharacteristic
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5C2411yescharacteristic
165D60—22no—
166D60—22no—
167D60—42no—
168C5×#67—42no—
169C5×#67—44no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3—21no—
172C2×C5×Dic3C2×D412yes—
173C2×C5×Dic3C2×D412yes—
174C5×D12—21no—
175C5×D12—21no—
176C4×C5×D3—42no—
177C5×Dic6—21no—
178C5×Dic6—21no—
179C3×D20—22no—
180C3×D20—22no—
181C3×D20—42no—
182#1202—48no—
183#1202—48no—
184C3⋊#168C2×D414yescomplemented
185C3×#168C2×D414yescomplemented
186C2×C3×#41C2×D511yescharacteristic
187C22×C3×D4—51no—
188C22×#67—102no—
189C2×#235C2×D511yescharacteristic
190C22×D12—51no—
191C3×AGL(1,ℤ/8)—104no—
192C2×C3×SD16—52no—
193C2×C3×D8—52no—
194C2×C3×M16—51no—
195#949—104no—
196#947C2×D511yescharacteristic, complemented
197#944C2×D511yescharacteristic, complemented
198C2×#215—52no—
199#940—52no—
200#940—52no—
201#940—102no—
202#940C2×D511yescharacteristic, complemented
203#939—22no—
204#936C2×D511yescharacteristic, complemented
205C2×#214—52no—
206#932—104no—
207C2×#213—52no—
208C2×#213—52no—
209C4×#67—22no—
210C2×C4×Dic3C2×D511yescharacteristic
211C2×#208—51no—
212#908—104no—
213C2×D24—52no—
214C2×#204—52no—
215#815—52no—
216C8×Dic3—52no—
217C23×D5—21no—
218C23×D5—61no—
219C5×#41—22no—
220C5×#41—22no—
221C5×#41—62no—
222C5×#41—62no—
223C2×C5×Q8—31no—
224C2×C5×Q8C22×D311yescharacteristic
225C2×C5×D4—21no—
226C2×C5×D4—31no—
227C2×C5×D4—62no—
228C2×C5×D4—61no—
229C2×C5×D4C22×D311yescharacteristic
230C22×C4×C5—21no—
231C22×C4×C5—32no—
232C22×C4×C5—61no—
233C22×C4×C5C22×D311yescharacteristic
234C2×D20—22no—
235C2×D20—22no—
236C2×D20—21no—
237C2×D20—32no—
238C2×D20—62no—
239C2×D20—62no—
240C2×D20—64no—
241C2×D20—64no—
242C2×D20—61no—
243C2×D20—128no—
244C2×D20C22×D312yes—
245C5×C4⋊C4—62no—
246C5×C22⋊C4—62no—
247C5×C22⋊C4—62no—
248C42×C5—32no—
249C42×C5—31no—
250C42×C5—31no—
251#688—24no—
252#688—64no—
253#688—64no—
254#688—64no—
255#686—24no—
256#686—64no—
257#686—64no—
258#686—64no—
259#681—34no—
260#681#6714yescomplemented
261C2×#168—32no—
262C2×#168C22×D312yes—
263C2×AGL(1,ℤ/8)—51no—
264C2×AGL(1,ℤ/8)—151no—
265C2×AGL(1,ℤ/8)—151no—
266C2×AGL(1,ℤ/8)—151no—
267#532—31no—
268C2×#127—151no—
269#496—152no—
270#496—152no—
271#493—152no—
272#492—152no—
273C4×M16—151no—
274C22×C3×C5—22no—
275C22×C3×C5—41no—
276C22×C3×C5—42no—
277C22×C3×C5#12712yes—
278C22×C3×C5C22×D411yescharacteristic
279C2×D15—42no—
280C2×D15—44no—
281C2×D15—84no—
282C2×C5×D3—41no—
283C2×C5×D3—42no—
284C2×C3×D5—42no—
285C2×C3×D5—44no—
286C2×C3×D5—84no—
287C3×C4×C5—41no—
288C3×C4×C5#12712yes—
289C3×C4×C5C22×D411yescharacteristic
290C3×C4×C5C22×D411yescharacteristic
291C5×Dic3—22no—
292C5×Dic3—41no—
293C5×Dic3AGL(1,ℤ/8)14yescomplemented
294C24×C3—101no—
295C23×D3—101no—
296C3×#41—22no—
297C3×#41—22no—
298C2×C3×Q8C22×D511yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—52no—
301C2×C3×D4—102no—
302C2×C3×D4—102no—
303C2×C3×D4—101no—
304C2×C3×D4C22×D511yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4C22×D511yescharacteristic
307C2×#67—21no—
308C2×#67—22no—
309C2×#67—104no—
310C2×#67—104no—
311C2×#67—208no—
312C22×Dic3C22⋊D512yes—
313#235—22no—
314#235—22no—
315C2×D12—52no—
316C2×D12—102no—
317C2×D12—102no—
318C2×D12—101no—
319C2×D12C22×D511yescharacteristic
320C2×C4×D3—21no—
321C2×Dic6C22×D511yescharacteristic
322C3×SD16—104no—
323C3×D8—104no—
324C3×M16—54no—
325C2×C3×C8—52no—
326#217—22no—
327#215—104no—
328#214—104no—
329#213—104no—
330#213—104no—
331(C2×D3)⋊C4—22no—
332Dic3⋊C4—22no—
333C4×Dic3C22⋊D512yes—
334C4×Dic3C22×D511yescharacteristic
335C4×Dic3C22×D511yescharacteristic
336#208—54no—
337C2×C3⋊C8—52no—
338D24—104no—
339#204—104no—
340C23×C5—21no—
341C23×C5—61no—
342C23×C5D3×D411yescharacteristic
343C22×D5—22no—
344C22×D5—44no—
345C22×D5—42no—
346C22×D5—62no—
347C22×D5—124no—
348C22×D5—122no—
349C5×Q8—21no—
350C5×Q8—21no—
351C5×Q8—61no—
352C5×Q8—61no—
353C5×D4—21no—
354C5×D4—21no—
355C5×D4—42no—
356C5×D4—61no—
357C5×D4—61no—
358C5×D4—124no—
359C5×D4—122no—
360C2×C4×C5—21no—
361C2×C4×C5—32no—
362C2×C4×C5—32no—
363C2×C4×C5—42no—
364C2×C4×C5—64no—
365C2×C4×C5—61no—
366C2×C4×C5—122no—
367C2×C4×C5D3×D411yescharacteristic
368C2×C4×C5D3×D412yes—
369C2×C4×C5C2×#6712yes—
370C2×C4×C5C23×D311yescharacteristic
371D20—22no—
372D20—22no—
373D20—42no—
374D20—62no—
375D20—62no—
376D20—128no—
377D20—128no—
378D20—122no—
379#168—34no—
380#168C2×#6714yescomplemented
381C2×#41—31no—
382C2×#41D3×D511yescharacteristic
383C22×D4—51no—
384C22×D4—151no—
385C22×D4—302no—
386AGL(1,ℤ/8)—104no—
387AGL(1,ℤ/8)—304no—
388AGL(1,ℤ/8)—304no—
389AGL(1,ℤ/8)—304no—
390C2×SD16—52no—
391C2×SD16—152no—
392C2×SD16—152no—
393C2×SD16—152no—
394C2×D8—52no—
395C2×D8—152no—
396C2×D8—152no—
397C2×D8—152no—
398C2×M16—51no—
399C2×M16—151no—
400C4⋊Q8—31no—
401#127—31no—
402#127—152no—
403#127—152no—
404#127—302no—
405#124—31no—
406#124—31no—
407#121—62no—
408C4×D4—62no—
409C2×C42—31no—
410#97—152no—
411C4×C8—152no—
412C2×C3×C5—22no—
413C2×C3×C5—81no—
414C2×C3×C5C2×#12711yescharacteristic
415C2×C3×C5C2×AGL(1,ℤ/8)12yes—
416D15—82no—
417C3×D5—82no—
418C5×D3—81no—
419C23×C3—21no—
420C23×C3—102no—
421C23×C3—204no—
422C23×C3—202no—
423C23×C3C2×C22⋊D511yescharacteristic
424C22×D3—21no—
425C22×D3—102no—
426C22×D3—204no—
427C22×D3—202no—
428C3×Q8—21no—
429C3×Q8—21no—
430C3×D4—21no—
431C3×D4—21no—
432C3×D4—42no—
433C3×D4—102no—
434C3×D4—102no—
435C3×D4—202no—
436C2×C3×C4—21no—
437C2×C3×C4—42no—
438C2×C3×C4D4×D512yes—
439C2×C3×C4D4×D512yes—
440C2×C3×C4C2×C22⋊D511yescharacteristic
441C2×C3×C4C23×D511yescharacteristic
442#67—42no—
443#67—44no—
444#67—208no—
445#67—208no—
446C2×Dic3—24no—
447C2×Dic3—21no—
448C2×Dic3C2×C22⋊D512yes—
449C2×Dic3C2×C22⋊D512yes—
450D12—21no—
451D12—21no—
452D12—102no—
453D12—102no—
454D12—202no—
455C4×D3—42no—
456Dic6—21no—
457Dic6—21no—
458C3×C8—54no—
459C3⋊C8—54no—
460C22×C5—22no—
461C22×C5—42no—
462C22×C5—41no—
463C22×C5—122no—
464C22×C5—121no—
465C22×C5#94012yes—
466C22×C5C2×D3×D411yescharacteristic
467C2×D5—44no—
468C2×D5—42no—
469C2×D5—84no—
470C2×D5—124no—
471C2×D5—122no—
472C2×D5—244no—
473C4×C5—34no—
474C4×C5—41no—
475C4×C5—62no—
476C4×C5—121no—
477C4×C5#94012yes—
478C4×C5C2×D3×D411yescharacteristic
479C4×C5C22×#6711yescharacteristic
480C24—101no—
481C24—301no—
482#41—22no—
483#41—22no—
484#41—62no—
485#41—62no—
486C2×Q8—31no—
487C2×Q8C2×D3×D511yescharacteristic
488C2×D4—21no—
489C2×D4—31no—
490C2×D4—52no—
491C2×D4—62no—
492C2×D4—61no—
493C2×D4—102no—
494C2×D4—101no—
495C2×D4—102no—
496C2×D4—152no—
497C2×D4—304no—
498C2×D4—304no—
499C2×D4—302no—
500C2×D4—301no—
501C2×D4—302no—
502C2×D4—608no—
503C2×D4C2×D3×D511yescharacteristic
504C22×C4—21no—
505C22×C4—32no—
506C22×C4—61no—
507C22×C4C2×D3×D511yescharacteristic
508SD16—104no—
509SD16—304no—
510SD16—304no—
511SD16—304no—
512D8—104no—
513D8—304no—
514D8—304no—
515D8—304no—
516M16—54no—
517M16—154no—
518C2×C8—52no—
519C2×C8—152no—
520C4⋊C4—62no—
521C22⋊C4—62no—
522C22⋊C4—62no—
523C42—32no—
524C42—31no—
525C42—31no—
526C3×C5#315111yescharacteristic, complemented, Hall
527C22×C3—22no—
528C22×C3—41no—
529C22×C3—42no—
530C22×C3—202no—
531C22×C3—204no—
532C22×C3—404no—
533C22×C3#408612yes—
534C22×C3C22×C22⋊D511yescharacteristic
535C2×D3—41no—
536C2×D3—42no—
537C2×D3—202no—
538C2×D3—204no—
539C2×D3—404no—
540C3×C4—41no—
541C3×C4#408612yes—
542C3×C4C2×D4×D511yescharacteristic
543C3×C4C2×D4×D511yescharacteristic
544Dic3—22no—
545Dic3—41no—
546Dic3#409514yescomplemented
547C2×C5—22no—
548C2×C5—81no—
549C2×C5—241no—
550C2×C5D3×AGL(1,ℤ/8)12yes—
551C2×C5C2×#94011yescharacteristic
552D5—82no—
553D5—242no—
554C23—21no—
555C23—61no—
556C23—102no—
557C23—204no—
558C23—202no—
559C23—302no—
560C23—604no—
561C23—602no—
562C23D3×C22⋊D511yescharacteristic
563Q8—21no—
564Q8—21no—
565Q8—61no—
566Q8—61no—
567D4—21no—
568D4—21no—
569D4—42no—
570D4—61no—
571D4—61no—
572D4—102no—
573D4—102no—
574D4—124no—
575D4—122no—
576D4—202no—
577D4—302no—
578D4—302no—
579D4—608no—
580D4—608no—
581D4—602no—
582C2×C4—21no—
583C2×C4—32no—
584C2×C4—32no—
585C2×C4—42no—
586C2×C4—64no—
587C2×C4—61no—
588C2×C4—122no—
589C2×C4D5×#6712yes—
590C2×C4D3×C22⋊D511yescharacteristic
591C2×C4#679012yes—
592C2×C4C22×D3×D511yescharacteristic
593C8—54no—
594C8—154no—
595C2×C3—22no—
596C2×C3—81no—
597C2×C3—402no—
598C2×C3C2×#408611yescharacteristic
599C2×C3C2×#409512yes—
600D3—81no—
601D3—402no—
602C5#8393711yescharacteristic, complemented, Sylow
603C22—22no—
604C22—42no—
605C22—41no—
606C22—122no—
607C22—121no—
608C22—204no—
609C22—202no—
610C22—404no—
611C22—604no—
612C22—602no—
613C22—1204no—
614C22#9156712yes—
615C22C2×D3×C22⋊D511yescharacteristic
616C4—34no—
617C4—41no—
618C4—62no—
619C4—121no—
620C4#9156712yes—
621C4C2×D5×#6711yescharacteristic
622C4C2×#679011yescharacteristic
623C3#1061501811yescharacteristic, complemented, Sylow
624C2—22no—
625C2—81no—
626C2—241no—
627C2—402no—
628C2—1202no—
629C2D3×#409512yes—
630C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3151
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#91838C2semidirect
2. C5×#5832C2semidirect
3. C2×C3×#4095C2semidirect
4. C2×#91458C2semidirect
5. C2×#91305C2semidirect
6. C2×#91298C2semidirect
7. #11749344C2semidirect
8. #11749342C2semidirect
9. #11749098C2semidirect
10. #11749097C2semidirect
11. Dic3×#681C2semidirect
19. C2×#6717C22semidirect
20. C2×#6715C22semidirect
22. C5×#947C22semidirect
23. C5×#944C22semidirect
24. C5×#940C22semidirect
26. C5×#936C22semidirect
30. C2×C3×#688C22semidirect
31. C2×C3×#686C22semidirect
36. C2×#6660C22semidirect
37. C2×#6655C22semidirect
39. C2×#6654C22semidirect
41. C2×#6652C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
49. C2×#4095D3semidirect
86. #6710D4semidirect
96. C3×#681D4semidirect
103. #5832D5semidirect
132. C2×#688C2×D3semidirect
136. C2×#686C2×D3semidirect
184. C3⋊#168C2×D4semidirect
185. C3×#168C2×D4semidirect
196. #947C2×D5semidirect
197. #944C2×D5semidirect
202. #940C2×D5semidirect
204. #936C2×D5semidirect
260. #681#67semidirect
293. C5×Dic3AGL(1,ℤ/8)semidirect
380. #168C2×#67semidirect
526. C3×C5#3151semidirect
546. Dic3#4095semidirect
602. C5#83937semidirect
623. C3#10615018semidirect

Maximal subgroups

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

subgroupindex
C2×#918382
C5×#58322
C2×C3×#40952
C2×#914582
C2×#913052
C2×#912982
#117493442
#117493422
#117490982
#117490972
Dic3×#6812
#106150183
#839375