Finite Group Databasebeta

← #14416825

Subgroups — #14416825

Order 1920.

968 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
2#11756281C211yesmaximal, characteristic
3C2×#91776C211yesmaximal, characteristic, complemented
4C3×C5×#428C211yesmaximal, characteristic, complemented
5M16×Dic15C211yesmaximal, characteristic, complemented
6#11751105C211yesmaximal, characteristic, complemented
7#11751067C211yesmaximal, characteristic
8#11750990C212yesmaximal, complemented
9#11750974C212yesmaximal, complemented
10#11750954C212yesmaximal, complemented
11#11750953C212yesmaximal, complemented
12#10610931—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×#6712—21no—
19C2×C4×Dic15—21no—
20C2×C4×Dic15C2211yescharacteristic
21C2×#6710C2211yescharacteristic
22#91798C418yescomplemented
23C2×Dic60C2212yes—
24C2×#6706C2212yes—
25#91782C2211yescharacteristic
26#91782C2211yescharacteristic
27#91776—21no—
28#91776—21no—
29#91776C2212yes—
30#91776C2211yescharacteristic
31#91776C2212yes—
32#91776C2211yescharacteristic
33#91770—21no—
34#91770—21no—
35#91761—21no—
36C42×D15—21no—
37C3×C5×#107C2212yes—
38C3×C5×#106C2212yes—
39#91099C2212yes—
40C8×Dic15C2212yes—
41#91094C2212yes—
42#91094C2212yes—
43#91094C2212yes—
44#91093C2212yes—
45#79200—51nomaximal, Hall
46C2×#4055—31no—
47#65856—31no—
48C2×#4033—31no—
49C5×#428D311yescharacteristic, complemented
50M16×Dic5—31no—
51#65293—31no—
52#65255—31no—
53#65178—32no—
54#65162—32no—
55#65142—32no—
56#65141—32no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C22×Dic15—21no—
61C22×Dic15D411yescharacteristic
62C22×Dic15D411yescharacteristic
63#6817—22no—
64#6817C2×C414yes—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×C4×D15—21no—
68C2×C4×D15—21no—
69C2×Dic30—21no—
70C2×Dic30—22no—
71C2×Dic30C2×C414yescomplemented
72C2×Dic30C2312yes—
73C2×Dic30C2311yescharacteristic
74C3×C5×M16C2×C414yescomplemented
75C2×C3×C5×C8C2312yes—
76C3×C5×C4⋊C4—21no—
77C3×C5×C4⋊C4C2312yes—
78C3×C5×C4⋊C4C2311yescharacteristic
79C3×C5×C4⋊C4C2311yescharacteristic
80C3×C5×C22⋊C4—21no—
81C3×C42×C5—21no—
82#6714—21no—
83#6714—21no—
84#6712—21no—
85#6712—21no—
86#6712—22no—
87#6712—22no—
88C4×Dic15—21no—
89C4×Dic15—21no—
90C4×Dic15—22no—
91C4×Dic15—22no—
92C4×Dic15D411yescharacteristic
93C4×Dic15D411yescharacteristic
94C4×Dic15C2311yescharacteristic
95C4×Dic15C2311yescharacteristic
96#6710—22no—
97C2×C3⋊#168C2312yes—
98Dic60C2×C418yescomplemented
99#6706C2×C418yescomplemented
100C2×#909—51no—
101#5522—51no—
102C2×#887—51no—
103C3×#428D511yescharacteristic, complemented
104Dic3×M16—51no—
105#5004—51no—
106#4966—51no—
107#4889—52no—
108#4873—52no—
109#4853—52no—
110#4852—52no—
111C2×#709—31no—
112C22×Dic10—31no—
113C2×C5×M16C2×D311yescharacteristic
114C5×#117C2×D311yescharacteristic
115C2×C5×C4⋊C4C2×D311yescharacteristic
116C2×#683—61no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—61no—
119C2×#681—31no—
120#4055—38no—
121C2×Dic20—32no—
122C2×#677—32no—
123#4039—31no—
124#4039—31no—
125#4033—32no—
126#4033—32no—
127#4033—31no—
128#4033—31no—
129#4033—61no—
130#4033—61no—
131#4027—61no—
132#4027—61no—
133#4018—61no—
134C42×D5—61no—
135C5×#107C2×D312yes—
136C5×#106C2×D312yes—
137#3947—32no—
138C8×Dic5—32no—
139#3942—32no—
140#3942—32no—
141#3942—32no—
142#3941—32no—
143C4×#137—151noSylow
144C23×C3×C5C2×D411yescharacteristic
145C22×D15—21no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—42no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5#4112yes—
153C2×C3×C4×C5C2411yescharacteristic
154#1220—24no—
155C2×Dic15—24no—
156C2×Dic15—22no—
157C2×Dic15—21no—
158C2×Dic15—22no—
159C2×Dic15—41no—
160C2×Dic15C2×D411yescharacteristic
161C2×Dic15C2×D411yescharacteristic
162C2×Dic15C2×D411yescharacteristic
163C2×Dic15C2×D411yescharacteristic
164D60—21no—
165D60C22×C412yes—
166C4×D15—24no—
167C4×D15—42no—
168C4×D15—42no—
169Dic30—24no—
170Dic30—22no—
171Dic30—21no—
172Dic30C22×C414yes—
173Dic30C22×C412yes—
174C3×C5×C8C22×C414yes—
175C3⋊#168—22no—
176C2×#235—51no—
177C22×Dic6—51no—
178C2×C3×M16C2×D511yescharacteristic
179C3×#117C2×D511yescharacteristic
180C2×C3×C4⋊C4C2×D511yescharacteristic
181C2×Dic3⋊C4—101no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—101no—
184C2×#208—51no—
185#909—58no—
186C2×Dic12—52no—
187C2×#204—52no—
188#893—51no—
189#893—51no—
190#887—51no—
191#887—52no—
192#887—52no—
193#887—51no—
194#887—101no—
195#887—101no—
196#67⋊C4—101no—
197#67⋊C4—101no—
198#872—101no—
199C42×D3—101no—
200C3×#107C2×D512yes—
201C3×#106C2×D512yes—
202#815—52no—
203C8×Dic3—52no—
204#810—52no—
205#810—52no—
206#810—52no—
207#809—52no—
208C22×C4×C5—21no—
209C22×C4×C5C22×D311yescharacteristic
210C2×C22⋊D5—61no—
211C22×Dic5—31no—
212C22×Dic5—31no—
213C22×Dic5—61no—
214#709—34no—
215#709—62no—
216C2×D20—31no—
217C2×C4×D5—61no—
218C2×C4×D5—61no—
219C2×C4×D5—61no—
220C2×Dic10—34no—
221C2×Dic10—32no—
222C2×Dic10—31no—
223C2×Dic10—61no—
224C2×Dic10—62no—
225C5×M16C4×D314yescomplemented
226C2×C5×C8C22×D312yes—
227C5×C4⋊C4—21no—
228C5×C4⋊C4C22×D312yes—
229C5×C4⋊C4C22×D311yescharacteristic
230C5×C4⋊C4C22×D311yescharacteristic
231C5×C22⋊C4—21no—
232C42×C5—21no—
233#685—61no—
234#685—61no—
235#683—61no—
236#683—61no—
237#683—62no—
238#683—62no—
239C4×Dic5—31no—
240C4×Dic5—31no—
241C4×Dic5—31no—
242C4×Dic5—31no—
243C4×Dic5—61no—
244C4×Dic5—61no—
245C4×Dic5—62no—
246C4×Dic5—62no—
247#681—62no—
248C2×#168—32no—
249Dic20—38no—
250#677—38no—
251C2×#137—151no—
252C4×#41—151no—
253C2×C4×Q8—151no—
254#441—152no—
255#440—152no—
256C4×Q16—152no—
257C4×SD16—152no—
258#428D1511yescharacteristic, complemented
259#419—151no—
260#417—151no—
261C4×M16—151no—
262C22×C3×C5—21no—
263C22×C3×C5—21no—
264C22×C3×C5C4×D412yes—
265C22×C3×C5C22×D411yescharacteristic
266C2×D15—22no—
267C2×D15—41no—
268C2×D15—41no—
269C3×C4×C5—41no—
270C3×C4×C5—41no—
271C3×C4×C5—42no—
272C3×C4×C5C4×D412yes—
273C3×C4×C5C23×C411yescharacteristic
274C3×C4×C5C2×#4111yescharacteristic
275Dic15—24no—
276Dic15—22no—
277Dic15—21no—
278Dic15—21no—
279Dic15—21no—
280Dic15#13712yescomplemented
281C22×C3×C4—21no—
282C22×C3×C4C22×D511yescharacteristic
283C2×#67—101no—
284C22×Dic3—51no—
285C22×Dic3—51no—
286C22×Dic3—101no—
287#235—54no—
288#235—102no—
289C2×D12—51no—
290C2×C4×D3—101no—
291C2×C4×D3—101no—
292C2×C4×D3—101no—
293C2×Dic6—54no—
294C2×Dic6—52no—
295C2×Dic6—51no—
296C2×Dic6—101no—
297C2×Dic6—102no—
298C3×M16C4×D514yescomplemented
299C2×C3×C8C22×D512yes—
300C3×C4⋊C4—21no—
301C3×C4⋊C4C22×D512yes—
302C3×C4⋊C4C22×D511yescharacteristic
303C3×C4⋊C4C22×D511yescharacteristic
304C3×C22⋊C4—21no—
305C3×C42—21no—
306(C2×D3)⋊C4—101no—
307(C2×D3)⋊C4—101no—
308Dic3⋊C4—101no—
309Dic3⋊C4—101no—
310Dic3⋊C4—102no—
311Dic3⋊C4—102no—
312C4×Dic3—51no—
313C4×Dic3—51no—
314C4×Dic3—51no—
315C4×Dic3—51no—
316C4×Dic3—101no—
317C4×Dic3—101no—
318C4×Dic3—102no—
319C4×Dic3—102no—
320#208—102no—
321C2×C3⋊C8—52no—
322Dic12—58no—
323#204—58no—
324C23×C5D3×D411yescharacteristic
325C22×D5—61no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—21no—
329C2×C4×C5—42no—
330C2×C4×C5C2×C4×D312yes—
331C2×C4×C5D3×D411yescharacteristic
332C2×C4×C5#23912yes—
333C2×C4×C5C23×D311yescharacteristic
334C22⋊D5—64no—
335C2×Dic5—31no—
336C2×Dic5—31no—
337C2×Dic5—31no—
338C2×Dic5—31no—
339C2×Dic5—62no—
340C2×Dic5—64no—
341C2×Dic5—62no—
342C2×Dic5—61no—
343C2×Dic5—121no—
344D20—32no—
345D20—61no—
346C4×D5—64no—
347C4×D5—122no—
348C4×D5—122no—
349Dic10—34no—
350Dic10—32no—
351Dic10—64no—
352Dic10—62no—
353Dic10—61no—
354C5×C8C2×C4×D314yes—
355#168—62no—
356C2×#41—151no—
357C22×Q8—151no—
358#137—158no—
359C2×Q16—152no—
360C2×SD16—152no—
361C2×M16—151no—
362C2×M16C2×D1511yescharacteristic
363C4×Q8—152no—
364C4×Q8—152no—
365C4×Q8—151no—
366C4×Q8—151no—
367C4×Q8—301no—
368C4×Q8—301no—
369C4×D4—151no—
370C4×D4—151no—
371C4×D4—301no—
372C4×D4—301no—
373#117—301no—
374#117C2×D1511yescharacteristic
375C2×C4⋊C4—301no—
376C2×C4⋊C4C2×D1511yescharacteristic
377C2×C42—151no—
378C2×C42—301no—
379C2×C42—301no—
380#107C2×D1512yes—
381#106C2×D1512yes—
382#103—152no—
383#103—152no—
384#103—152no—
385#102—152no—
386#97—152no—
387C4×C8—152no—
388C2×C3×C5—22no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C2×#13711yescharacteristic
391C2×C3×C5#57511yescharacteristic
392D15—42no—
393C23×C3D4×D511yescharacteristic
394C22×D3—101no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—42no—
399C2×C3×C4C2×C4×D512yes—
400C2×C3×C4D4×D511yescharacteristic
401C2×C3×C4#71312yes—
402C2×C3×C4C23×D511yescharacteristic
403#67—104no—
404C2×Dic3—51no—
405C2×Dic3—51no—
406C2×Dic3—51no—
407C2×Dic3—51no—
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3—101no—
411C2×Dic3—104no—
412C2×Dic3—201no—
413D12—52no—
414D12—101no—
415C4×D3—104no—
416C4×D3—202no—
417C4×D3—202no—
418Dic6—54no—
419Dic6—52no—
420Dic6—102no—
421Dic6—101no—
422Dic6—104no—
423C3×C8C2×C4×D514yes—
424C3⋊C8—102no—
425C22×C5—21no—
426C22×C5—21no—
427C22×C5#89312yes—
428C22×C5C2×D3×D411yescharacteristic
429C2×D5—62no—
430C2×D5—121no—
431C2×D5—121no—
432C4×C5—41no—
433C4×C5—42no—
434C4×C5—41no—
435C4×C5#89312yes—
436C4×C5C22×C4×D311yescharacteristic
437C4×C5C2×#23911yescharacteristic
438Dic5—32no—
439Dic5—64no—
440Dic5—62no—
441Dic5—61no—
442Dic5—61no—
443Dic5—61no—
444#41—154no—
445#41—302no—
446C2×Q8—154no—
447C2×Q8—152no—
448C2×Q8—151no—
449C2×Q8—301no—
450C2×Q8—302no—
451C2×D4—151no—
452C2×D4—301no—
453C22×C4—21no—
454C22×C4—151no—
455C22×C4—151no—
456C22×C4—301no—
457C22×C4—301no—
458C22×C4—301no—
459C22×C4—301no—
460C22×C4C22×D1511yescharacteristic
461Q16—158no—
462SD16—158no—
463M16—302no—
464M16C4×D1514yescomplemented
465C2×C8—152no—
466C2×C8C22×D1512yes—
467C4⋊C4—21no—
468C4⋊C4—302no—
469C4⋊C4—302no—
470C4⋊C4—301no—
471C4⋊C4—301no—
472C4⋊C4C22×D1512yes—
473C4⋊C4C22×D1511yescharacteristic
474C4⋊C4C22×D1511yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—301no—
477C22⋊C4—301no—
478C42—21no—
479C42—151no—
480C42—151no—
481C42—151no—
482C42—151no—
483C42—301no—
484C42—301no—
485C42—302no—
486C42—302no—
487C3×C5C4×#13711yescharacteristic, complemented, Hall
488C22×C3—21no—
489C22×C3—21no—
490C22×C3#403912yes—
491C22×C3C2×D4×D511yescharacteristic
492C2×D3—102no—
493C2×D3—201no—
494C2×D3—201no—
495C3×C4—41no—
496C3×C4—42no—
497C3×C4—41no—
498C3×C4#403912yes—
499C3×C4C22×C4×D511yescharacteristic
500C3×C4C2×#71311yescharacteristic
501Dic3—52no—
502Dic3—104no—
503Dic3—102no—
504Dic3—101no—
505Dic3—101no—
506Dic3—101no—
507C2×C5—22no—
508C2×C5C2×#89311yescharacteristic
509C2×C5#577311yescharacteristic
510C2×C5D3×#13711yescharacteristic
511D5—122no—
512C23—301no—
513C23D4×D1511yescharacteristic
514Q8—154no—
515Q8—152no—
516Q8—304no—
517Q8—302no—
518Q8—301no—
519D4—152no—
520D4—304no—
521D4—301no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—42no—
526C2×C4—151no—
527C2×C4—151no—
528C2×C4—151no—
529C2×C4—151no—
530C2×C4—302no—
531C2×C4—304no—
532C2×C4—301no—
533C2×C4—302no—
534C2×C4—304no—
535C2×C4—602no—
536C2×C4—602no—
537C2×C4—601no—
538C2×C4C2×C4×D1512yes—
539C2×C4D4×D1511yescharacteristic
540C2×C4#682112yes—
541C2×C4C23×D1511yescharacteristic
542C8—302no—
543C8C2×C4×D1514yes—
544C2×C3—22no—
545C2×C3C2×#403911yescharacteristic
546C2×C3#6610711yescharacteristic
547C2×C3D5×#13711yescharacteristic
548D3—202no—
549C5#7920011yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—302no—
553C22—601no—
554C22—601no—
555C22#9178212yes—
556C22C2×D4×D1511yescharacteristic
557C4—42no—
558C4—41no—
559C4—41no—
560C4—152no—
561C4—302no—
562C4—304no—
563C4—301no—
564C4—301no—
565C4—301no—
566C4#9178212yes—
567C4C22×C4×D1511yescharacteristic
568C4C2×#682111yescharacteristic
569C3#1061093111yescharacteristic, complemented, Sylow
570C2—22no—
571C2—602no—
572C2C2×#9178211yescharacteristic
573C2#1175653211yescharacteristic
574C2D15×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
cosocleC2×C3×C4×C5C24
hypercenter#428D15
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C2×#91776C2semidirect
4. C3×C5×#428C2semidirect
5. M16×Dic15C2semidirect
6. #11751105C2semidirect
8. #11750990C2semidirect
9. #11750974C2semidirect
10. #11750954C2semidirect
11. #11750953C2semidirect
22. #91798C4semidirect
49. C5×#428D3semidirect
71. C2×Dic30C2×C4semidirect
74. C3×C5×M16C2×C4semidirect
98. Dic60C2×C4semidirect
99. #6706C2×C4semidirect
103. C3×#428D5semidirect
225. C5×M16C4×D3semidirect
258. #428D15semidirect
280. Dic15#137semidirect
298. C3×M16C4×D5semidirect
464. M16C4×D15semidirect
487. C3×C5C4×#137semidirect
549. C5#79200semidirect
569. C3#10610931semidirect

Maximal subgroups

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

subgroupindex
C2×#917982
#117562812
C2×#917762
C3×C5×#4282
M16×Dic152
#117511052
#117510672
#117509902
#117509742
#117509542
#117509532
#106109313
#792005