Finite Group Databasebeta

← #14439335

Subgroups — #14439335

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91798C211yesmaximal, characteristic, complemented
2C2×C3×#4054C211yesmaximal, characteristic, complemented
3#11754581C211yesmaximal, characteristic, complemented
4C2×#91364C211yesmaximal, characteristic, complemented
5C2×#91313C211yesmaximal, characteristic, complemented
6C2×#91312C211yesmaximal, characteristic, complemented
7C5×Dic3×M16C211yesmaximal, characteristic, complemented
8#11748009C212yesmaximal, complemented
9#11747973C212yesmaximal, complemented
10#11747971C212yesmaximal, complemented
11#11747969C212yesmaximal, complemented
12#10610262—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91798—24no—
19C2×Dic60C2212yescomplemented
20C2×#6706C2212yescomplemented
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C5×#208C2211yescharacteristic
23C3×#4054—24no—
24C2×C3×D40C2212yes—
25C2×C3×#677C2212yes—
26#91569—22no—
27C2×#6665—22no—
28#91458C2211yescharacteristic, complemented
29C4×#1202—22no—
30#91389C2211yescharacteristic, complemented
31#91374C2211yescharacteristic, complemented
32#91364—22no—
33#91364C2212yes—
34#91364C2212yes—
35#91364C2211yescharacteristic, complemented
36C2×#6662C2212yescomplemented
37#91313—24no—
38#91312—24no—
39C2×#6657C2212yes—
40C2×#6657C2212yescomplemented
41C2×#6653C2212yes—
42C5×#815C2212yescomplemented
43C5×C8×Dic3C2212yescomplemented
44#83938—51nomaximal, Hall
45C2×#4055—31no—
46C2×#4055—31no—
47C2×#4054—31no—
48C2×#4054D311yescharacteristic, complemented
49#65811—31no—
50C2×#4021—31no—
51C4×C5×M16—31no—
52#65004—32no—
53#65001—32no—
54#64985—32no—
55#64985—32no—
56C23×C3×D5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59C22×Dic15—21no—
60#6817—22no—
61#6817—22no—
62C2×D60C2311yescharacteristic
63C2×C4×D15—21no—
64C2×Dic30—22no—
65C2×Dic30—22no—
66C2×Dic30—21no—
67C2×Dic30C2312yes—
68C2×Dic30C2311yescharacteristic
69C22×C5×Dic3D412yes—
70C2×C3×C22⋊D5—21no—
71C3×#709—22no—
72C3×#709—22no—
73C2×C3×D20—22no—
74C2×C3×D20—22no—
75C2×C3×D20—21no—
76C2×C3×D20C2311yescharacteristic
77C2×C3×D20C2312yes—
78C2×C3×C4×D5—21no—
79C2×C3×Dic10C2311yescharacteristic
80C2×#1202—22no—
81C3×C5×M16D414yescomplemented
82C2×C3×C5×C8C2312yes—
83Dic60—24no—
84#6706—24no—
85C4×C5×Dic3D412yes—
86C4×C5×Dic3C2311yescharacteristic
87C4×C5×Dic3C2311yescharacteristic
88C5×#208D414yescomplemented
89C2×C5×C3⋊C8C2312yes—
90C3×D40—24no—
91C3×#677—24no—
92Dic3⋊Dic5—22no—
93#6667—22no—
94#6665—22no—
95#6665—24no—
96#6665—24no—
97#6662—24no—
98#6657—24no—
99#6657—24no—
100#6653—24no—
101C2×C3×AGL(1,ℤ/8)—51no—
102#5832—51no—
103C2×#951—51no—
104C2×#936—51no—
105C2×#932—51no—
106C2×#909—51no—
107#5168—52no—
108#5167—52no—
109#5155—52no—
110#5154—52no—
111Dic3×M16D511yescharacteristic, complemented
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×D20C2×D311yescharacteristic
115C22×Dic10—31no—
116C2×C5×M16—31no—
117C2×C5×M16C2×D311yescharacteristic
118C2×C42×C5—31no—
119#4076—62no—
120C2×#685—62no—
121#4055—64no—
122#4055—64no—
123#4054—24no—
124#4054—64no—
125C2×Dic20—32no—
126C2×Dic20—32no—
127C2×D40—32no—
128C2×D40C2×D312yes—
129C2×#677—32no—
130C2×#677—32no—
131C2×#677—32no—
132C2×#677C2×D312yes—
133#4021—32no—
134#4021—32no—
135#4021—31no—
136#4021—31no—
137#4021—62no—
138#4020—31no—
139C4×D20—62no—
140#4015—31no—
141C5×#97—32no—
142C4×C5×C8—32no—
143#3153—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C3×D5—22no—
147C22×C3×D5—21no—
148C22×C3×D5—44no—
149C22×C3×D5—42no—
150C2×C3×C4×C5C2×D411yescharacteristic
151C2×C3×C4×C5C2×D412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5C2411yescharacteristic
154#1220—42no—
155C2×Dic15—22no—
156C2×Dic15—21no—
157C2×Dic15—42no—
158D60—21no—
159D60—21no—
160C4×D15—42no—
161Dic30—21no—
162Dic30—22no—
163Dic30—22no—
164Dic30—21no—
165Dic30—42no—
166C2×C5×Dic3—42no—
167C2×C5×Dic3C2×D412yes—
168C2×C5×Dic3C2×D412yes—
169C3×C22⋊D5—42no—
170C2×C3×Dic5—21no—
171C3×D20—21no—
172C3×D20—22no—
173C3×D20—22no—
174C3×D20—21no—
175C3×D20—42no—
176C3×C4×D5—42no—
177C3×Dic10—21no—
178C3×Dic10—21no—
179#1202—44no—
180C3×C5×C8C2×D414yes—
181C5×C3⋊C8C2×D414yes—
182C2×C3×#41—51no—
183C22×C3×D4—51no—
184C2×#235—51no—
185C22×Dic6—51no—
186C3×AGL(1,ℤ/8)—104no—
187C2×C3×SD16—52no—
188C2×C3×D8—52no—
189C2×C3×M16C2×D511yescharacteristic
190C2×#217—102no—
191#951—104no—
192#947—51no—
193#944—51no—
194C2×#216—52no—
195#940—51no—
196#939—102no—
197#936—52no—
198#936—51no—
199#936—52no—
200#936—102no—
201C2×#214—52no—
202C2×#214—52no—
203#932—104no—
204C2×#213—52no—
205C4×#67—102no—
206C2×C4×Dic3C2×D511yescharacteristic
207C2×#208C2×D511yescharacteristic
208#909—104no—
209C2×Dic12—52no—
210C2×#204—52no—
211#815C2×D512yescomplemented
212C8×Dic3C2×D512yescomplemented
213C23×D5—21no—
214C22×C4×C5—32no—
215C22×C4×C5C22×D311yescharacteristic
216C2×C22⋊D5—21no—
217C2×C22⋊D5—61no—
218C22×Dic5—61no—
219#709—22no—
220#709—22no—
221#709—62no—
222#709—62no—
223C2×D20—22no—
224C2×D20—22no—
225C2×D20—21no—
226C2×D20—31no—
227C2×D20—62no—
228C2×D20C22×D312yes—
229C2×D20C22×D311yescharacteristic
230C2×C4×D5—21no—
231C2×C4×D5—61no—
232C2×Dic10—32no—
233C2×Dic10—31no—
234C2×Dic10—62no—
235C2×Dic10—62no—
236C2×Dic10—61no—
237C2×Dic10C22×D311yescharacteristic
238C5×M16—34no—
239C5×M16#6714yescomplemented
240C2×C5×C8—32no—
241C2×C5×C8C22×D312yes—
242C42×C5—32no—
243C42×C5—31no—
244C42×C5—31no—
245#685—62no—
246#685—62no—
247#685—64no—
248#685—64no—
249C4⋊Dic5—62no—
250Dic20—64no—
251Dic20—64no—
252D40—24no—
253D40—64no—
254#677—24no—
255#677—64no—
256#677—64no—
257#677—64no—
258C2×#137—151no—
259C2×#137—151no—
260C2×AGL(1,ℤ/8)—51no—
261C2×AGL(1,ℤ/8)—151no—
262#532—151no—
263C2×#124—151no—
264#497—152no—
265#496—152no—
266#495—152no—
267#495—152no—
268C4×M16—31no—
269C22×C3×C5—22no—
270C22×C3×C5#12712yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—41no—
273C2×D15—42no—
274C2×C3×D5—41no—
275C2×C3×D5—42no—
276C2×C3×D5—42no—
277C2×C3×D5—44no—
278C2×C3×D5—84no—
279C3×C4×C5#12712yes—
280C3×C4×C5C22×D411yescharacteristic
281C3×C4×C5C22×D411yescharacteristic
282Dic15—42no—
283Dic15—41no—
284C3×Dic5—41no—
285C5×Dic3—22no—
286C5×Dic3—22no—
287C24×C3—101no—
288C3×#41—102no—
289C3×#41—102no—
290C2×C3×Q8—51no—
291C2×C3×D4—52no—
292C2×C3×D4—51no—
293C2×C3×D4—101no—
294C2×C3×D4—102no—
295C2×C3×D4—102no—
296C2×C3×D4—101no—
297C22×C3×C4—101no—
298C22×C3×C4C22×D511yescharacteristic
299C2×#67—101no—
300C2×#67—102no—
301C22×Dic3—101no—
302C22×Dic3D2012yes—
303#235—102no—
304#235—102no—
305C2×D12—51no—
306C2×C4×D3—101no—
307C2×Dic6—52no—
308C2×Dic6—51no—
309C2×Dic6—102no—
310C2×Dic6—102no—
311C2×Dic6—101no—
312C3×SD16—104no—
313C3×D8—104no—
314C3×M16D2014yescomplemented
315C2×C3×C8C22×D512yes—
316#217—102no—
317#217—104no—
318#217—104no—
319#216—104no—
320#214—104no—
321#214—104no—
322#213—104no—
323(C2×D3)⋊C4—102no—
324Dic3⋊C4—102no—
325C4×Dic3D2012yes—
326C4×Dic3C22×D511yescharacteristic
327C4×Dic3C22×D511yescharacteristic
328#208D2014yescomplemented
329C2×C3⋊C8C22×D512yes—
330Dic12—104no—
331#204—104no—
332C23×C5D3×D411yescharacteristic
333C22×D5—22no—
334C22×D5—21no—
335C22×D5—44no—
336C22×D5—42no—
337C22×D5—61no—
338C2×C4×C5—32no—
339C2×C4×C5—32no—
340C2×C4×C5—122no—
341C2×C4×C5D3×D411yescharacteristic
342C2×C4×C5D3×D412yes—
343C2×C4×C5C2×#6712yes—
344C2×C4×C5C23×D311yescharacteristic
345C22⋊D5—42no—
346C22⋊D5—122no—
347C2×Dic5—21no—
348C2×Dic5—61no—
349C2×Dic5—62no—
350C2×Dic5—122no—
351D20—21no—
352D20—22no—
353D20—22no—
354D20—21no—
355D20—42no—
356D20—61no—
357D20—61no—
358D20—124no—
359C4×D5—42no—
360C4×D5—122no—
361Dic10—21no—
362Dic10—21no—
363Dic10—61no—
364Dic10—62no—
365Dic10—62no—
366Dic10—61no—
367Dic10—122no—
368C5×C8—34no—
369C5×C8C2×#6714yes—
370C2×#41—51no—
371C2×#41—151no—
372C22×Q8—151no—
373C22×D4—51no—
374#137—304no—
375#137—304no—
376AGL(1,ℤ/8)—104no—
377AGL(1,ℤ/8)—304no—
378C2×Q16—152no—
379C2×Q16—152no—
380C2×SD16—52no—
381C2×SD16—152no—
382C2×SD16—152no—
383C2×SD16—152no—
384C2×D8—52no—
385C2×D8—152no—
386C2×M16—31no—
387C2×M16D3×D511yescharacteristic
388C4⋊Q8—151no—
389#127—151no—
390#124—152no—
391#124—152no—
392#124—151no—
393#124—151no—
394#124—302no—
395#121—302no—
396C4×D4—302no—
397C2×C22⋊C4—302no—
398C2×C42—31no—
399#97—32no—
400C4×C8—32no—
401C2×C3×C5—22no—
402C2×C3×C5C2×#12711yescharacteristic
403C2×C3×C5#57512yes—
404D15—81no—
405C3×D5—81no—
406C3×D5—82no—
407C23×C3—102no—
408C23×C3—101no—
409C23×C3—204no—
410C23×C3—202no—
411C23×C3C2×D2011yescharacteristic
412C22×D3—101no—
413C3×Q8—101no—
414C3×Q8—101no—
415C3×D4—102no—
416C3×D4—101no—
417C3×D4—101no—
418C3×D4—102no—
419C3×D4—202no—
420C3×D4—202no—
421C2×C3×C4—101no—
422C2×C3×C4—202no—
423C2×C3×C4C2×D2012yes—
424C2×C3×C4C2×D2011yescharacteristic
425C2×C3×C4C2×D2012yes—
426C2×C3×C4C23×D511yescharacteristic
427#67—204no—
428#67—202no—
429C2×Dic3—42no—
430C2×Dic3—101no—
431C2×Dic3—102no—
432C2×Dic3—202no—
433C2×Dic3C2×D2012yes—
434C2×Dic3C2×D2012yes—
435D12—101no—
436D12—101no—
437C4×D3—202no—
438Dic6—102no—
439Dic6—101no—
440Dic6—101no—
441Dic6—102no—
442Dic6—202no—
443C3×C8C2×D2014yes—
444C3⋊C8C2×D2014yes—
445C22×C5—22no—
446C22×C5#94012yes—
447C22×C5C2×D3×D411yescharacteristic
448C2×D5—42no—
449C2×D5—44no—
450C2×D5—41no—
451C2×D5—42no—
452C2×D5—84no—
453C2×D5—122no—
454C2×D5—121no—
455C4×C5—62no—
456C4×C5—62no—
457C4×C5#94012yes—
458C4×C5C2×D3×D411yescharacteristic
459C4×C5C22×#6711yescharacteristic
460Dic5—41no—
461Dic5—122no—
462Dic5—121no—
463C24—101no—
464#41—102no—
465#41—102no—
466#41—302no—
467#41—302no—
468C2×Q8—51no—
469C2×Q8—152no—
470C2×Q8—151no—
471C2×Q8—301no—
472C2×Q8—302no—
473C2×Q8—302no—
474C2×D4—52no—
475C2×D4—51no—
476C2×D4—101no—
477C2×D4—102no—
478C2×D4—101no—
479C2×D4—102no—
480C2×D4—151no—
481C2×D4—302no—
482C2×D4—301no—
483C22×C4—32no—
484C22×C4—101no—
485C22×C4—301no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488Q16—304no—
489Q16—304no—
490SD16—104no—
491SD16—304no—
492SD16—304no—
493SD16—304no—
494D8—104no—
495D8—304no—
496M16—34no—
497M16#120214yescomplemented
498C2×C8—32no—
499C2×C8C2×D3×D512yes—
500C4⋊C4—302no—
501C22⋊C4—302no—
502C22⋊C4—304no—
503C22⋊C4—304no—
504C22⋊C4—302no—
505C42—32no—
506C42—31no—
507C42—31no—
508C3×C5#315311yescharacteristic, complemented, Hall
509C22×C3—22no—
510C22×C3—201no—
511C22×C3—202no—
512C22×C3—202no—
513C22×C3—204no—
514C22×C3—404no—
515C22×C3#402012yes—
516C22×C3C22×D2011yescharacteristic
517C2×D3—201no—
518C2×D3—202no—
519C3×C4—201no—
520C3×C4#402012yes—
521C3×C4C22×D2011yescharacteristic
522C3×C4C22×D2011yescharacteristic
523Dic3—22no—
524Dic3—22no—
525Dic3—202no—
526Dic3—201no—
527C2×C5—22no—
528C2×C5#577312yes—
529C2×C5C2×#94011yescharacteristic
530D5—82no—
531D5—81no—
532D5—241no—
533C23—102no—
534C23—101no—
535C23—204no—
536C23—202no—
537C23—301no—
538C23D3×D2011yescharacteristic
539Q8—101no—
540Q8—101no—
541Q8—301no—
542Q8—302no—
543Q8—302no—
544Q8—301no—
545Q8—602no—
546D4—102no—
547D4—101no—
548D4—101no—
549D4—102no—
550D4—202no—
551D4—202no—
552D4—301no—
553D4—301no—
554D4—604no—
555D4—602no—
556C2×C4—32no—
557C2×C4—32no—
558C2×C4—101no—
559C2×C4—122no—
560C2×C4—202no—
561C2×C4—302no—
562C2×C4—301no—
563C2×C4—602no—
564C2×C4—602no—
565C2×C4D3×D2011yescharacteristic
566C2×C4D3×D2012yes—
567C2×C4C2×#120212yes—
568C2×C4C22×D3×D511yescharacteristic
569C8—34no—
570C8C2×#120214yes—
571C2×C3—22no—
572C2×C3—402no—
573C2×C3—401no—
574C2×C3C2×#402011yescharacteristic
575C2×C3#6608212yes—
576D3—401no—
577C5#8393811yescharacteristic, complemented, Sylow
578C22—22no—
579C22—202no—
580C22—204no—
581C22—201no—
582C22—202no—
583C22—404no—
584C22—602no—
585C22—601no—
586C22#9145812yes—
587C22C2×D3×D2011yescharacteristic
588C4—62no—
589C4—62no—
590C4—201no—
591C4—601no—
592C4—602no—
593C4#9145812yes—
594C4C2×D3×D2011yescharacteristic
595C4C22×#120211yescharacteristic
596C3#1061026211yescharacteristic, complemented, Sylow
597C2—22no—
598C2—402no—
599C2—401no—
600C2—1201no—
601C2#1175402912yes—
602C2C2×#9145811yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
hypercenterC2×M16D3×D5
hypocenterC3×C5#3153
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#91798C2semidirect
2. C2×C3×#4054C2semidirect
3. #11754581C2semidirect
4. C2×#91364C2semidirect
5. C2×#91313C2semidirect
6. C2×#91312C2semidirect
7. C5×Dic3×M16C2semidirect
8. #11748009C2semidirect
9. #11747973C2semidirect
10. #11747971C2semidirect
11. #11747969C2semidirect
19. C2×Dic60C22semidirect
20. C2×#6706C22semidirect
28. #91458C22semidirect
30. #91389C22semidirect
31. #91374C22semidirect
35. #91364C22semidirect
36. C2×#6662C22semidirect
40. C2×#6657C22semidirect
42. C5×#815C22semidirect
43. C5×C8×Dic3C22semidirect
48. C2×#4054D3semidirect
81. C3×C5×M16D4semidirect
88. C5×#208D4semidirect
111. Dic3×M16D5semidirect
211. #815C2×D5semidirect
212. C8×Dic3C2×D5semidirect
239. C5×M16#67semidirect
314. C3×M16D20semidirect
328. #208D20semidirect
497. M16#1202semidirect
508. C3×C5#3153semidirect
577. C5#83938semidirect
596. C3#10610262semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
C2×C3×#40542
#117545812
C2×#913642
C2×#913132
C2×#913122
C5×Dic3×M162
#117480092
#117479732
#117479712
#117479692
#106102623
#839385