Finite Group Databasebeta

← #14439710

Subgroups — #14439710

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91798C211yesmaximal, characteristic, complemented
2C2×C3×#4055C211yesmaximal, characteristic, complemented
3#11754278C211yesmaximal, characteristic, complemented
4#11754252C211yesmaximal, characteristic, complemented
5C22×#6662C211yesmaximal, characteristic, complemented
6C2×#91311C211yesmaximal, characteristic
7C5×#5122C211yesmaximal, characteristic, complemented
8#11748034C212yesmaximal, complemented
9#11748033C212yesmaximal, complemented
10#11747973C212yesmaximal, complemented
11#11747969C212yesmaximal, complemented
12#10610307—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C2×C3×C5×M16C2211yescharacteristic
18#91798—24no—
19C2×Dic60C2212yes—
20C2×#6706C2212yes—
21C5×#926C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C3×#4055—24no—
24C2×C3×Dic20C2212yes—
25C2×C3×#677C2212yes—
26#91546—22no—
27#91537—22no—
28#91390—22no—
29#91389C2212yes—
30#91389C2212yes—
31#91374C2212yes—
32#91364C2212yes—
33#91360—22no—
34C2×#6662—24no—
35C2×#6662C2212yes—
36C2×#6662C2212yes—
37C2×#6662C2211yescharacteristic
38C2×#6658C2211yescharacteristic
39#91311—24no—
40C2×#6657C2211yescharacteristic
41C2×#6653C2211yescharacteristic
42C5×#815C2212yes—
43C5×C8×Dic3C2212yes—
44#83975—51nomaximal, Hall
45C2×#4055—31no—
46C2×#4055D311yescharacteristic, complemented
47C22×Dic20—31no—
48C2×#4050—31no—
49#65860—31no—
50#65860—31no—
51C5×#405—31no—
52#65004—32no—
53#65004—32no—
54#64988—32no—
55#64985—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58C22×Dic15—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30—22no—
64C2×Dic30—22no—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
67C2×Dic30C2311yescharacteristic
68C2×C3×C22⋊D5—21no—
69C22×C3×Dic5—21no—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20C2311yescharacteristic
73C2×C3×C4×D5—21no—
74C2×C3×Dic10—22no—
75C2×C3×Dic10—22no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10C2312yes—
78C2×C3×Dic10C2311yescharacteristic
79C3×C5×M16D414yes—
80C2×C3×C5×C8C2312yes—
81Dic60—24no—
82#6706—24no—
83C5×#217D412yes—
84C5×C4⋊Dic3D412yes—
85C4×C5×Dic3C2312yes—
86C2×C5×C3⋊C8D414yes—
87C2×C5×C3⋊C8C2311yescharacteristic
88C2×C5×C3⋊C8C2311yescharacteristic
89C3×Dic20—24no—
90C3×#677—24no—
91Dic3⋊Dic5—24no—
92Dic3⋊Dic5—24no—
93#6667—24no—
94#6665—24no—
95#6662—22no—
96#6662—24no—
97#6662—24no—
98#6658—22no—
99#6657—22no—
100#6653—22no—
101C2×C3×#137—51no—
102#5825—51no—
103C2×#950—51no—
104#5816—51no—
105C22×#216—51no—
106C2×#909—51no—
107#5190—52no—
108#5183—52no—
109#5168—52no—
110#5167—52no—
111#5122D511yescharacteristic, complemented
112C2×#709—31no—
113C2×#709C2×D311yescharacteristic
114C22×Dic10—31no—
115C22×Dic10C2×D311yescharacteristic
116C2×C5×M16C2×D311yescharacteristic
117C22×C5×C8—31no—
118C5×#117—31no—
119#4055—24no—
120#4055—64no—
121C2×Dic20—31no—
122C2×Dic20—32no—
123C2×Dic20—32no—
124C2×Dic20—32no—
125C2×Dic20—64no—
126C2×Dic20C2×D312yes—
127#4050—64no—
128C2×D40—31no—
129C2×#677—31no—
130C2×#677—31no—
131C2×#677—32no—
132C2×#677C2×D312yes—
133#4043—62no—
134#4043—62no—
135#4032—62no—
136#4032—62no—
137#4021—32no—
138#4021—32no—
139#4015—32no—
140#4015—32no—
141C5×#97—32no—
142C4×C5×C8—32no—
143#3156—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C22×C3×D5—21no—
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2411yescharacteristic
151#1220—42no—
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—42no—
155D60—21no—
156D60—21no—
157C4×D15—42no—
158Dic30—21no—
159Dic30—22no—
160Dic30—22no—
161Dic30—21no—
162Dic30—42no—
163C2×C5×Dic3C2×D414yes—
164C3×C22⋊D5—42no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—42no—
168C3×D20—21no—
169C3×D20—21no—
170C3×C4×D5—42no—
171C3×Dic10—21no—
172C3×Dic10—22no—
173C3×Dic10—22no—
174C3×Dic10—21no—
175C3×Dic10—42no—
176C3×C5×C8C2×D414yes—
177C5×C3⋊C8C2×D412yes—
178C5×C3⋊C8C2×D412yes—
179C2×C3×#41—51no—
180C22×C3×Q8—51no—
181C2×#235—51no—
182C22×Dic6—51no—
183C3×#137—104no—
184C2×C3×Q16—52no—
185C2×C3×SD16—52no—
186C2×C3×M16C2×D511yescharacteristic
187#950—104no—
188#947—52no—
189#946—102no—
190#944—52no—
191#944—52no—
192C2×#216—52no—
193C2×#216—52no—
194C2×#216—51no—
195C2×#216—104no—
196C2×#215—51no—
197#936—52no—
198#935—102no—
199C2×#214—51no—
200C2×#213—51no—
201#929—102no—
202#926C2×D511yescharacteristic
203#924—102no—
204C22×C3⋊C8C2×D511yescharacteristic
205#909—104no—
206C2×Dic12—52no—
207C2×#204—52no—
208#815C2×D512yes—
209C8×Dic3C2×D512yes—
210C22×C4×C5C22×D311yescharacteristic
211C2×C22⋊D5—21no—
212C2×C22⋊D5—61no—
213C22×Dic5—21no—
214C22×Dic5—61no—
215#709—22no—
216#709—22no—
217#709—62no—
218#709—62no—
219C2×D20—31no—
220C2×D20C22×D311yescharacteristic
221C2×C4×D5—21no—
222C2×C4×D5—61no—
223C2×Dic10—22no—
224C2×Dic10—22no—
225C2×Dic10—21no—
226C2×Dic10—32no—
227C2×Dic10—31no—
228C2×Dic10—62no—
229C2×Dic10—62no—
230C2×Dic10—61no—
231C2×Dic10C22×D312yes—
232C2×Dic10C22×D311yescharacteristic
233C5×M16#6714yes—
234C2×C5×C8—34no—
235C2×C5×C8—31no—
236C2×C5×C8—31no—
237C2×C5×C8C22×D312yes—
238C5×C4⋊C4—32no—
239C5×C22⋊C4—32no—
240C42×C5—32no—
241#685—64no—
242#685—64no—
243C4⋊Dic5—64no—
244C4⋊Dic5—64no—
245Dic20—24no—
246Dic20—62no—
247Dic20—64no—
248Dic20—64no—
249Dic20—64no—
250D40—62no—
251#677—24no—
252#677—62no—
253#677—62no—
254#677—64no—
255C2×#137—51no—
256C2×#137—151no—
257C2×#135—151no—
258C22×Q16—151no—
259#536—151no—
260#536—151no—
261#497—152no—
262#497—152no—
263#495—152no—
264#494—152no—
265#405—31no—
266C22×C3×C5—22no—
267C22×C3×C5#12712yes—
268C22×C3×C5C22×D411yescharacteristic
269C2×D15—41no—
270C2×D15—42no—
271C2×C3×D5—41no—
272C2×C3×D5—42no—
273C3×C4×C5#12712yes—
274C3×C4×C5C22×D411yescharacteristic
275C3×C4×C5C22×D411yescharacteristic
276Dic15—42no—
277Dic15—41no—
278C3×Dic5—42no—
279C3×Dic5—41no—
280C5×Dic3—24no—
281C3×#41—102no—
282C3×#41—102no—
283C2×C3×Q8—51no—
284C2×C3×Q8—52no—
285C2×C3×Q8—101no—
286C2×C3×Q8—102no—
287C2×C3×Q8—102no—
288C2×C3×D4—51no—
289C2×C3×D4—101no—
290C22×C3×C4—101no—
291C22×C3×C4—101no—
292C22×C3×C4C22×D511yescharacteristic
293C2×#67—101no—
294C22×Dic3—101no—
295#235—102no—
296#235—102no—
297C2×D12—51no—
298C2×C4×D3—101no—
299C2×Dic6—52no—
300C2×Dic6—51no—
301C2×Dic6—102no—
302C2×Dic6—102no—
303C2×Dic6—101no—
304C3×Q16—104no—
305C3×SD16—104no—
306C3×M16D2014yes—
307C2×C3×C8C22×D512yes—
308#217—104no—
309#217D2012yes—
310#216—104no—
311#216—104no—
312#216—102no—
313#215—102no—
314#214—102no—
315#213—102no—
316(C2×D3)⋊C4—104no—
317C4⋊Dic3D2012yes—
318Dic3⋊C4—104no—
319Dic3⋊C4—104no—
320C4×Dic3C22×D512yes—
321C2×C3⋊C8D2014yes—
322C2×C3⋊C8C22×D511yescharacteristic
323C2×C3⋊C8C22×D511yescharacteristic
324Dic12—104no—
325#204—104no—
326C23×C5D3×D411yescharacteristic
327C22×D5—21no—
328C22×D5—61no—
329C2×C4×C5—34no—
330C2×C4×C5D3×D411yescharacteristic
331C2×C4×C5D3×D412yes—
332C2×C4×C5C2×#6712yes—
333C2×C4×C5C23×D311yescharacteristic
334C22⋊D5—42no—
335C22⋊D5—122no—
336C2×Dic5—21no—
337C2×Dic5—22no—
338C2×Dic5—42no—
339C2×Dic5—61no—
340C2×Dic5—62no—
341C2×Dic5—122no—
342D20—21no—
343D20—21no—
344D20—61no—
345D20—61no—
346C4×D5—42no—
347C4×D5—122no—
348Dic10—21no—
349Dic10—22no—
350Dic10—22no—
351Dic10—21no—
352Dic10—42no—
353Dic10—61no—
354Dic10—62no—
355Dic10—62no—
356Dic10—61no—
357Dic10—122no—
358C5×C8—32no—
359C5×C8—32no—
360C5×C8C2×#6714yes—
361C2×#41—51no—
362C2×#41—151no—
363C22×Q8—51no—
364C22×Q8—151no—
365#137—104no—
366#137—304no—
367#135—304no—
368C2×Q16—52no—
369C2×Q16—152no—
370C2×Q16—152no—
371C2×Q16—151no—
372C2×Q16—152no—
373C2×Q16—304no—
374C2×SD16—52no—
375C2×SD16—151no—
376C2×SD16—151no—
377C2×SD16—152no—
378C2×D8—151no—
379C2×M16D3×D511yescharacteristic
380C22×C8—31no—
381C4⋊Q8—152no—
382C4⋊Q8—152no—
383#124—152no—
384#124—152no—
385#123—302no—
386#123—302no—
387C22⋊Q8—302no—
388C22⋊Q8—302no—
389#117—31no—
390#97—32no—
391C4×C8—32no—
392C2×C3×C5—22no—
393C2×C3×C5C2×#12711yescharacteristic
394C2×C3×C5#57812yes—
395D15—81no—
396C3×D5—81no—
397C23×C3—101no—
398C23×C3C2×D2011yescharacteristic
399C22×D3—101no—
400C3×Q8—101no—
401C3×Q8—102no—
402C3×Q8—102no—
403C3×Q8—101no—
404C3×Q8—202no—
405C3×D4—101no—
406C3×D4—101no—
407C3×D4—202no—
408C2×C3×C4—101no—
409C2×C3×C4—102no—
410C2×C3×C4—202no—
411C2×C3×C4—202no—
412C2×C3×C4C2×D2012yes—
413C2×C3×C4C2×D2011yescharacteristic
414C2×C3×C4C2×D2012yes—
415C2×C3×C4C23×D511yescharacteristic
416#67—202no—
417C2×Dic3—101no—
418C2×Dic3—102no—
419C2×Dic3—202no—
420C2×Dic3C2×D2014yes—
421D12—101no—
422D12—101no—
423C4×D3—202no—
424Dic6—102no—
425Dic6—101no—
426Dic6—101no—
427Dic6—102no—
428Dic6—202no—
429C3×C8C2×D2014yes—
430C3⋊C8C2×D2012yes—
431C3⋊C8C2×D2012yes—
432C22×C5—22no—
433C22×C5#94012yes—
434C22×C5C2×D3×D411yescharacteristic
435C2×D5—42no—
436C2×D5—41no—
437C2×D5—122no—
438C2×D5—121no—
439C4×C5—64no—
440C4×C5#94012yes—
441C4×C5C2×D3×D411yescharacteristic
442C4×C5C22×#6711yescharacteristic
443Dic5—42no—
444Dic5—41no—
445Dic5—122no—
446Dic5—121no—
447#41—102no—
448#41—102no—
449#41—302no—
450#41—302no—
451C2×Q8—52no—
452C2×Q8—51no—
453C2×Q8—101no—
454C2×Q8—102no—
455C2×Q8—102no—
456C2×Q8—152no—
457C2×Q8—151no—
458C2×Q8—301no—
459C2×Q8—302no—
460C2×Q8—302no—
461C2×D4—51no—
462C2×D4—101no—
463C2×D4—151no—
464C2×D4—301no—
465C22×C4—101no—
466C22×C4—101no—
467C22×C4—301no—
468C22×C4—301no—
469C22×C4C2×D3×D511yescharacteristic
470Q16—104no—
471Q16—304no—
472Q16—304no—
473Q16—302no—
474Q16—304no—
475SD16—104no—
476SD16—302no—
477SD16—302no—
478SD16—304no—
479D8—302no—
480M16#120214yes—
481C2×C8—34no—
482C2×C8—31no—
483C2×C8—31no—
484C2×C8C2×D3×D512yes—
485C4⋊C4—32no—
486C4⋊C4—304no—
487C4⋊C4—304no—
488C22⋊C4—32no—
489C22⋊C4—304no—
490C22⋊C4—304no—
491C42—32no—
492C3×C5#315611yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3—201no—
495C22×C3—202no—
496C22×C3#402012yes—
497C22×C3C22×D2011yescharacteristic
498C2×D3—201no—
499C2×D3—202no—
500C3×C4—201no—
501C3×C4—202no—
502C3×C4#402012yes—
503C3×C4C22×D2011yescharacteristic
504C3×C4C22×D2011yescharacteristic
505Dic3—24no—
506Dic3—202no—
507Dic3—201no—
508C2×C5—22no—
509C2×C5#577912yes—
510C2×C5C2×#94011yescharacteristic
511D5—81no—
512D5—241no—
513C23—101no—
514C23—301no—
515C23D3×D2011yescharacteristic
516Q8—101no—
517Q8—102no—
518Q8—102no—
519Q8—101no—
520Q8—202no—
521Q8—301no—
522Q8—302no—
523Q8—302no—
524Q8—301no—
525Q8—602no—
526D4—101no—
527D4—101no—
528D4—202no—
529D4—301no—
530D4—301no—
531D4—602no—
532C2×C4—34no—
533C2×C4—102no—
534C2×C4—101no—
535C2×C4—202no—
536C2×C4—202no—
537C2×C4—302no—
538C2×C4—301no—
539C2×C4—602no—
540C2×C4—602no—
541C2×C4D3×D2011yescharacteristic
542C2×C4D3×D2012yes—
543C2×C4C2×#120212yes—
544C2×C4C22×D3×D511yescharacteristic
545C8—32no—
546C8—32no—
547C8C2×#120214yes—
548C2×C3—22no—
549C2×C3—401no—
550C2×C3C2×#402011yescharacteristic
551C2×C3#6608712yes—
552D3—401no—
553C5#8397511yescharacteristic, complemented, Sylow
554C22—22no—
555C22—201no—
556C22—202no—
557C22—601no—
558C22—602no—
559C22#9145812yes—
560C22C2×D3×D2011yescharacteristic
561C4—64no—
562C4—201no—
563C4—202no—
564C4—601no—
565C4—602no—
566C4#9145812yes—
567C4C2×D3×D2011yescharacteristic
568C4C22×#120211yescharacteristic
569C3#1061030711yescharacteristic, complemented, Sylow
570C2—22no—
571C2—401no—
572C2—1201no—
573C2#1175404212yes—
574C2C2×#9145811yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×#91311C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#3156
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×#4055C2semidirect
3. #11754278C2semidirect
4. #11754252C2semidirect
5. C22×#6662C2semidirect
7. C5×#5122C2semidirect
8. #11748034C2semidirect
9. #11748033C2semidirect
10. #11747973C2semidirect
11. #11747969C2semidirect
46. C2×#4055D3semidirect
111. #5122D5semidirect
492. C3×C5#3156semidirect
553. C5#83975semidirect
569. C3#10610307semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
C2×C3×#40552
#117542782
#117542522
C22×#66622
C2×#913112
C5×#51222
#117480342
#117480332
#117479732
#117479692
#106103073
#839755