Finite Group Databasebeta

← #14439176

Subgroups — #14439176

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×#91821C211yesmaximal, characteristic, complemented
2C2×C5×#940C211yesmaximal, characteristic, complemented
3C2×C3×#4078C211yesmaximal, characteristic, complemented
4#11754581C211yesmaximal, characteristic, complemented
5C2×#91304C211yesmaximal, characteristic, complemented
6C2×#91299C211yesmaximal, characteristic, complemented
7#11749108C212yesmaximal, complemented
8#11749097C212yesmaximal, complemented
9#11749076C212yesmaximal, complemented
10#11749071C212yesmaximal, complemented
11Dic3×#681C211yesmaximal, characteristic, complemented
12#10614894—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C22×C5×#67—22no—
16C22×C5×D12C2211yescharacteristic
17C2×C3×#709C2211yescharacteristic
18C2×#6716C2212yescomplemented
19#91821—24no—
20C2×#6715C2212yescomplemented
21C2×#6710C2211yescharacteristic
22C5×#940—22no—
23C5×#940C2212yes—
24C5×#940C2212yes—
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×#687C2212yescomplemented
27C3×#4078—24no—
28C2×C3×#686C2212yescomplemented
29C2×C3×#681C2211yescharacteristic
30#91569—22no—
31#91458C2211yescharacteristic, complemented
32C4×#1202—22no—
33#91389C2211yescharacteristic, complemented
34#91374C2211yescharacteristic, complemented
35#91364C2211yescharacteristic, complemented
36C2×#6659C2212yescomplemented
37C2×#6656C2212yescomplemented
38#91304—24no—
39C2×#6654C2212yescomplemented
40#91299—24no—
41C2×#6652C2212yescomplemented
42#90953C2212yescomplemented
43Dic3×#168C2212yescomplemented
44#83937—51nomaximal, Hall
45C2×C5×#127—31no—
46C2×#4078—31no—
47C2×#4078—31no—
48C2×#4078—31no—
49C2×#4078D311yescharacteristic, complemented
50#65811—31no—
51#65365—32no—
52#65363—32no—
53#65363—32no—
54#65362—32no—
55C4×#681—31no—
56C24×C3×C5—21no—
57C23×C5×D3—21no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—21no—
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817—22no—
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C2×C5×#67—24no—
70C2×C5×#67—24no—
71C2×C5×#67—48no—
72C22×C5×Dic3D412yes—
73C2×C5×D12—22no—
74C2×C5×D12—22no—
75C2×C5×D12—21no—
76C2×C5×D12C2312yes—
77C2×C3×C22⋊D5—21no—
78C3×#709—22no—
79C3×#709—22no—
80C2×C3×D20C2311yescharacteristic
81C2×C3×C4×D5—21no—
82C2×C3×Dic10C2311yescharacteristic
83C2×#1202—22no—
84#6716—24no—
85#6715—24no—
86#6710D414yescomplemented
87C2×C3⋊#168C2312yes—
88C4×C5×Dic3D412yes—
89C4×C5×Dic3C2311yescharacteristic
90C4×C5×Dic3C2311yescharacteristic
91C3×#687—24no—
92C3×#686—24no—
93C3×#681D414yescomplemented
94C2×C3×#168C2312yes—
95Dic3⋊Dic5—22no—
96#6667—22no—
97#6665—22no—
98#6659—24no—
99#6656—24no—
100#6654—24no—
101#6652—24no—
102C2×C3×AGL(1,ℤ/8)—51no—
103#5832—51no—
104C2×#949—51no—
105C2×#940D511yescharacteristic, complemented
106C2×#932—51no—
107C2×#908—51no—
108#5176—52no—
109#5175—52no—
110#5154—52no—
111#5151—52no—
112Dic3×M16—51no—
113C22×C5×D4—31no—
114C22×C5×D4—62no—
115C22×C5×D4C2×D311yescharacteristic
116C2×#709—31no—
117C2×#709C2×D311yescharacteristic
118C5×#127—32no—
119C5×#127—32no—
120C5×#127—62no—
121C2×C42×C5—31no—
122C2×#687—32no—
123C2×#687—32no—
124C2×#687—32no—
125C2×#687C2×D312yescomplemented
126#4078—24no—
127#4078—64no—
128#4078—64no—
129#4078—64no—
130C2×#686—32no—
131C2×#686—32no—
132C2×#686—32no—
133C2×#686C2×D312yescomplemented
134#4076—62no—
135C2×#681—31no—
136C2×#681C2×D311yescharacteristic
137#4021—31no—
138#4021—31no—
139#4020—31no—
140C4×D20—62no—
141#4015—31no—
142#3935—32no—
143C4×#168—32no—
144#3151—151noSylow
145C23×C3×C5—22no—
146C23×C3×C5—44no—
147C23×C3×C5—42no—
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—21no—
150C22×C5×D3—22no—
151C22×C5×D3—44no—
152C22×C5×D3—42no—
153C22×C3×D5—21no—
154C3×C5×D4—22no—
155C3×C5×D4—22no—
156C3×C5×D4—42no—
157C2×C3×C4×C5C2×D411yescharacteristic
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2411yescharacteristic
161#1220—42no—
162C2×Dic15—21no—
163D60—21no—
164D60—21no—
165C4×D15—42no—
166Dic30—21no—
167Dic30—21no—
168C5×#67—48no—
169C5×#67—48no—
170C2×C5×Dic3—24no—
171C2×C5×Dic3C2×D412yes—
172C2×C5×Dic3C2×D412yes—
173C5×D12—22no—
174C5×D12—22no—
175C5×D12—42no—
176C3×C22⋊D5—42no—
177C2×C3×Dic5—21no—
178C3×D20—21no—
179C3×D20—21no—
180C3×C4×D5—42no—
181C3×Dic10—21no—
182C3×Dic10—21no—
183#1202—44no—
184C3⋊#168C2×D414yescomplemented
185C3×#168C2×D414yescomplemented
186C2×C3×#41—51no—
187C22×C3×D4C2×D511yescharacteristic
188C22×#67—22no—
189C2×#235—51no—
190C22×D12C2×D511yescharacteristic
191C3×AGL(1,ℤ/8)—104no—
192C2×C3×SD16—52no—
193C2×C3×D8—52no—
194C2×C3×M16—51no—
195#949—104no—
196#947—51no—
197#944—51no—
198C2×#215—52no—
199#940—22no—
200#940—51no—
201#940C2×D512yes—
202#940C2×D512yes—
203#939—102no—
204#936—51no—
205C2×#214—52no—
206#932—104no—
207C2×#213—52no—
208C2×#213—52no—
209C4×#67—102no—
210C2×C4×Dic3C2×D511yescharacteristic
211C2×#208—51no—
212#908—104no—
213C2×D24—52no—
214C2×#204—52no—
215#815—52no—
216C8×Dic3—52no—
217C24×C5—21no—
218C24×C5—61no—
219C2×C5×D4—22no—
220C2×C5×D4—21no—
221C2×C5×D4—22no—
222C2×C5×D4—32no—
223C2×C5×D4—64no—
224C2×C5×D4—64no—
225C2×C5×D4—62no—
226C2×C5×D4—61no—
227C2×C5×D4—62no—
228C2×C5×D4—128no—
229C2×C5×D4C22×D312yes—
230C22×C4×C5—32no—
231C22×C4×C5C22×D311yescharacteristic
232C2×C22⋊D5—21no—
233C2×C22⋊D5—61no—
234#709—22no—
235#709—22no—
236#709—62no—
237#709—62no—
238C2×D20—31no—
239C2×D20—62no—
240C2×D20C22×D311yescharacteristic
241C2×C4×D5—21no—
242C2×C4×D5—61no—
243C2×Dic10—31no—
244C2×Dic10C22×D311yescharacteristic
245C42×C5—32no—
246C42×C5—31no—
247C42×C5—31no—
248#687—24no—
249#687—64no—
250#687—64no—
251#687—64no—
252#686—24no—
253#686—64no—
254#686—64no—
255#686—64no—
256#685—62no—
257#685—62no—
258C4⋊Dic5—62no—
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—151no—
268C2×#127—31no—
269#496—152no—
270#496—152no—
271#493—152no—
272#492—152no—
273C4×M16—151no—
274C22×C3×C5—22no—
275C22×C3×C5—42no—
276C22×C3×C5—44no—
277C22×C3×C5—84no—
278C22×C3×C5#12712yes—
279C22×C3×C5C22×D411yescharacteristic
280C2×D15—41no—
281C2×D15—42no—
282C2×C5×D3—42no—
283C2×C5×D3—44no—
284C2×C5×D3—84no—
285C2×C3×D5—41no—
286C2×C3×D5—42no—
287C3×C4×C5#12712yes—
288C3×C4×C5C22×D411yescharacteristic
289C3×C4×C5C22×D411yescharacteristic
290Dic15—41no—
291C3×Dic5—41no—
292C5×Dic3—22no—
293C5×Dic3AGL(1,ℤ/8)14yescomplemented
294C24×C3—21no—
295C23×D3—21no—
296C3×#41—102no—
297C3×#41—102no—
298C2×C3×Q8—51no—
299C2×C3×D4—22no—
300C2×C3×D4—22no—
301C2×C3×D4—21no—
302C2×C3×D4—51no—
303C2×C3×D4—101no—
304C2×C3×D4C22×D512yes—
305C22×C3×C4—101no—
306C22×C3×C4C22×D511yescharacteristic
307C2×#67—24no—
308C2×#67—24no—
309C2×#67—48no—
310C2×#67—101no—
311C2×#67—102no—
312C22×Dic3C22⋊D512yes—
313#235—102no—
314#235—102no—
315C2×D12—22no—
316C2×D12—22no—
317C2×D12—21no—
318C2×D12—51no—
319C2×D12C22×D512yes—
320C2×C4×D3—101no—
321C2×Dic6—51no—
322C3×SD16—104no—
323C3×D8—104no—
324C3×M16—54no—
325C2×C3×C8—52no—
326#217—102no—
327#215—104no—
328#214—104no—
329#213—104no—
330#213—104no—
331(C2×D3)⋊C4—102no—
332Dic3⋊C4—102no—
333C4×Dic3C22⋊D512yes—
334C4×Dic3C22×D511yescharacteristic
335C4×Dic3C22×D511yescharacteristic
336#208—54no—
337C2×C3⋊C8—52no—
338D24—104no—
339#204—104no—
340C23×C5—22no—
341C23×C5—44no—
342C23×C5—42no—
343C23×C5—62no—
344C23×C5—124no—
345C23×C5—122no—
346C23×C5D3×D411yescharacteristic
347C22×D5—21no—
348C22×D5—61no—
349C5×D4—22no—
350C5×D4—22no—
351C5×D4—42no—
352C5×D4—62no—
353C5×D4—62no—
354C5×D4—128no—
355C5×D4—128no—
356C5×D4—122no—
357C2×C4×C5—32no—
358C2×C4×C5—32no—
359C2×C4×C5—64no—
360C2×C4×C5D3×D411yescharacteristic
361C2×C4×C5D3×D412yes—
362C2×C4×C5C2×#6712yes—
363C2×C4×C5C23×D311yescharacteristic
364C22⋊D5—42no—
365C22⋊D5—122no—
366C2×Dic5—21no—
367C2×Dic5—61no—
368D20—21no—
369D20—21no—
370D20—61no—
371D20—61no—
372D20—124no—
373C4×D5—42no—
374C4×D5—122no—
375Dic10—21no—
376Dic10—21no—
377Dic10—61no—
378Dic10—61no—
379#168—34no—
380#168C2×#6714yescomplemented
381C2×#41—51no—
382C2×#41—151no—
383C22×D4—31no—
384C22×D4—62no—
385C22×D4D3×D511yescharacteristic
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—151no—
401#127—32no—
402#127—32no—
403#127—62no—
404#127—151no—
405#124—151no—
406#124—151no—
407#121—302no—
408C4×D4—302no—
409C2×C42—31no—
410#97—152no—
411C4×C8—152no—
412C2×C3×C5—22no—
413C2×C3×C5—82no—
414C2×C3×C5C2×#12711yescharacteristic
415C2×C3×C5C2×AGL(1,ℤ/8)12yes—
416D15—81no—
417C3×D5—81no—
418C5×D3—82no—
419C23×C3—22no—
420C23×C3—44no—
421C23×C3—42no—
422C23×C3—101no—
423C23×C3C2×C22⋊D511yescharacteristic
424C22×D3—22no—
425C22×D3—44no—
426C22×D3—42no—
427C22×D3—101no—
428C3×Q8—101no—
429C3×Q8—101no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—42no—
433C3×D4—101no—
434C3×D4—101no—
435C3×D4—202no—
436C2×C3×C4—101no—
437C2×C3×C4—202no—
438C2×C3×C4D4×D512yes—
439C2×C3×C4D4×D512yes—
440C2×C3×C4C2×C22⋊D511yescharacteristic
441C2×C3×C4C23×D511yescharacteristic
442#67—48no—
443#67—48no—
444#67—202no—
445#67—204no—
446C2×Dic3—24no—
447C2×Dic3—101no—
448C2×Dic3C2×C22⋊D512yes—
449C2×Dic3C2×C22⋊D512yes—
450D12—22no—
451D12—22no—
452D12—42no—
453D12—101no—
454D12—101no—
455C4×D3—202no—
456Dic6—101no—
457Dic6—101no—
458C3×C8—54no—
459C3⋊C8—54no—
460C22×C5—22no—
461C22×C5—44no—
462C22×C5—42no—
463C22×C5—84no—
464C22×C5—124no—
465C22×C5—122no—
466C22×C5—244no—
467C22×C5#94012yes—
468C22×C5C2×D3×D411yescharacteristic
469C2×D5—42no—
470C2×D5—41no—
471C2×D5—122no—
472C2×D5—121no—
473C4×C5—34no—
474C4×C5—62no—
475C4×C5#94012yes—
476C4×C5C2×D3×D411yescharacteristic
477C4×C5C22×#6711yescharacteristic
478Dic5—41no—
479Dic5—121no—
480C24—21no—
481C24—61no—
482#41—102no—
483#41—102no—
484#41—302no—
485#41—302no—
486C2×Q8—51no—
487C2×Q8—151no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—32no—
492C2×D4—51no—
493C2×D4—64no—
494C2×D4—64no—
495C2×D4—62no—
496C2×D4—61no—
497C2×D4—62no—
498C2×D4—101no—
499C2×D4—128no—
500C2×D4—151no—
501C2×D4—302no—
502C2×D4—301no—
503C2×D4C2×D3×D512yes—
504C22×C4—32no—
505C22×C4—101no—
506C22×C4—301no—
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—302no—
521C22⋊C4—302no—
522C22⋊C4—302no—
523C42—32no—
524C42—31no—
525C42—31no—
526C3×C5#315111yescharacteristic, complemented, Hall
527C22×C3—22no—
528C22×C3—44no—
529C22×C3—42no—
530C22×C3—84no—
531C22×C3—202no—
532C22×C3—201no—
533C22×C3#408612yes—
534C22×C3C22×C22⋊D511yescharacteristic
535C2×D3—44no—
536C2×D3—42no—
537C2×D3—84no—
538C2×D3—202no—
539C2×D3—201no—
540C3×C4—201no—
541C3×C4#408612yes—
542C3×C4C2×D4×D511yescharacteristic
543C3×C4C2×D4×D511yescharacteristic
544Dic3—22no—
545Dic3—201no—
546Dic3#407814yescomplemented
547C2×C5—22no—
548C2×C5—82no—
549C2×C5—242no—
550C2×C5D3×AGL(1,ℤ/8)12yes—
551C2×C5C2×#94011yescharacteristic
552D5—81no—
553D5—241no—
554C23—22no—
555C23—44no—
556C23—42no—
557C23—62no—
558C23—101no—
559C23—124no—
560C23—122no—
561C23—301no—
562C23D3×C22⋊D511yescharacteristic
563Q8—101no—
564Q8—101no—
565Q8—301no—
566Q8—301no—
567D4—22no—
568D4—22no—
569D4—42no—
570D4—62no—
571D4—62no—
572D4—101no—
573D4—101no—
574D4—128no—
575D4—128no—
576D4—122no—
577D4—202no—
578D4—301no—
579D4—301no—
580D4—604no—
581D4—602no—
582C2×C4—32no—
583C2×C4—32no—
584C2×C4—64no—
585C2×C4—101no—
586C2×C4—202no—
587C2×C4—301no—
588C2×C4—602no—
589C2×C4D5×#6712yes—
590C2×C4D3×C22⋊D511yescharacteristic
591C2×C4#679012yes—
592C2×C4C22×D3×D511yescharacteristic
593C8—54no—
594C8—154no—
595C2×C3—22no—
596C2×C3—82no—
597C2×C3—401no—
598C2×C3C2×#407812yes—
599C2×C3C2×#408611yescharacteristic
600D3—82no—
601D3—401no—
602C5#8393711yescharacteristic, complemented, Sylow
603C22—22no—
604C22—42no—
605C22—44no—
606C22—84no—
607C22—122no—
608C22—124no—
609C22—201no—
610C22—202no—
611C22—244no—
612C22—601no—
613C22—602no—
614C22#9156712yes—
615C22C2×D3×C22⋊D511yescharacteristic
616C4—34no—
617C4—62no—
618C4—201no—
619C4—601no—
620C4#9156712yes—
621C4C2×D5×#6711yescharacteristic
622C4C2×#679011yescharacteristic
623C3#1061489411yescharacteristic, complemented, Sylow
624C2—22no—
625C2—82no—
626C2—242no—
627C2—401no—
628C2—1201no—
629C2D3×#407812yes—
630C2C2×#9156711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3151
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91821C2semidirect
2. C2×C5×#940C2semidirect
3. C2×C3×#4078C2semidirect
4. #11754581C2semidirect
5. C2×#91304C2semidirect
6. C2×#91299C2semidirect
7. #11749108C2semidirect
8. #11749097C2semidirect
9. #11749076C2semidirect
10. #11749071C2semidirect
11. Dic3×#681C2semidirect
18. C2×#6716C22semidirect
20. C2×#6715C22semidirect
26. C2×C3×#687C22semidirect
28. C2×C3×#686C22semidirect
31. #91458C22semidirect
33. #91389C22semidirect
34. #91374C22semidirect
35. #91364C22semidirect
36. C2×#6659C22semidirect
37. C2×#6656C22semidirect
39. C2×#6654C22semidirect
41. C2×#6652C22semidirect
42. #90953C22semidirect
43. Dic3×#168C22semidirect
49. C2×#4078D3semidirect
86. #6710D4semidirect
93. C3×#681D4semidirect
105. C2×#940D5semidirect
125. C2×#687C2×D3semidirect
133. C2×#686C2×D3semidirect
184. C3⋊#168C2×D4semidirect
185. C3×#168C2×D4semidirect
260. #681#67semidirect
293. C5×Dic3AGL(1,ℤ/8)semidirect
380. #168C2×#67semidirect
526. C3×C5#3151semidirect
546. Dic3#4078semidirect
602. C5#83937semidirect
623. C3#10614894semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C2×C5×#9402
C2×C3×#40782
#117545812
C2×#913042
C2×#912992
#117491082
#117490972
#117490762
#117490712
Dic3×#6812
#106148943
#839375