Finite Group Databasebeta

← #14479184

Subgroups — #14479184

Order 1920.

3080 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2#11756586C211yesmaximal, characteristic, complemented
3C5×#5827C211yesmaximal, characteristic, complemented
4Dic3×#713C212yesmaximal, complemented
5#11755140C212yesmaximal, complemented
6#11754910C216yesmaximal, complemented
7Dic3×#711C216yesmaximal, complemented
8#11754509C213yesmaximal, complemented
9#11754499C213yesmaximal, complemented
10D5×#926C213yesmaximal, complemented
11C2×#91358C213yesmaximal, complemented
12#10617786—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C3×D5×#41C4116yescomplemented
15C2×C3×#713C2211yescharacteristic
16C2×C3×Q8×D5C2211yescharacteristic
17C2×C3×#711C2213yes—
18C2×C3×D4×D5C2213yes—
19C2×C3×#709C2213yes—
20C22×C3×C4×D5C2213yes—
21Q8×Dic15C2212yescomplemented
22D4×Dic15C2216yescomplemented
23#91815C2213yescomplemented
24C2×C4⋊Dic15C2213yescomplemented
25C5×Q8×Dic3C2212yescomplemented
26C5×D4×Dic3C2216yescomplemented
27C5×#926C2213yescomplemented
28C2×C5×C4⋊Dic3C2213yescomplemented
29#91559C22112yescomplemented
30Dic3×C22⋊D5C22112yescomplemented
31D5×#217C2216yes—
32C2×#6665C2216yes—
33#91528C2216yescomplemented
34C2×Dic3×Dic5C2216yescomplemented
35#91434C2216yescomplemented
36Dic3×D20C2216yescomplemented
37D5×C4⋊Dic3C2213yescomplemented
38D5×C4⋊Dic3C2213yescomplemented
39C4×D5×Dic3C2216yescomplemented
40#91358C2216yes—
41#91358C2211yescharacteristic
42#91358C2213yes—
43#91358C2216yescomplemented
44#91358C2216yescomplemented
45#91357C2216yes—
46#91331C2216yescomplemented
47Dic3×Dic10C2216yescomplemented
48#87260—51nomaximal, Hall
49C2×D5×#41D311yescharacteristic
50C5×#520—31no—
51#66161—31no—
52C4×#713—32no—
53#65906—32no—
54#65879—36no—
55C4×#711—36no—
56#65857—33no—
57D5×#117—33no—
58#65838—33no—
59C2×#4038—33no—
60C23×C3×D5C2313yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C22×Dic15C2316yes—
66C22×C5×Dic3C2316yes—
67C2×C3×C22⋊D5C2316yes—
68C22×C3×Dic5C2313yes—
69C3×#713C2×C418yescomplemented
70C3×Q8×D5C2×C418yescomplemented
71C3×#711C2×C4124yescomplemented
72C3×D4×D5C2×C4124yescomplemented
73C3×#709C2×C4124yescomplemented
74C2×C3×D20C2313yes—
75C2×C3×C4×D5C2×C4124yescomplemented
76C2×C3×C4×D5C2313yes—
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×C4×D5C2313yes—
79C2×C3×C4×D5C2313yes—
80C2×C3×Dic10C2313yes—
81C2×D5×Dic3C2316yes—
82C2×D5×Dic3C2316yes—
83#6719C2316yes—
84C4⋊Dic15C2311yescharacteristic
85C4⋊Dic15C2313yes—
86C4⋊Dic15C2316yes—
87C4×Dic15C2316yes—
88C5×#217C2316yes—
89C5×C4⋊Dic3C2311yescharacteristic
90C5×C4⋊Dic3C2313yes—
91C5×C4⋊Dic3C2316yes—
92C4×C5×Dic3C2316yes—
93#6668C2316yes—
94#6668C2316yes—
95#6665C23112yes—
96#6665C2316yes—
97#6665C2312yes—
98Dic3×Dic5C2316yes—
99Dic3×Dic5C23112yes—
100Dic3×Dic5C2312yes—
101C22×C3×#41—51no—
102#5827—51no—
103#5827—53no—
104#5827—53no—
105#5827D511yescharacteristic, complemented
106Dic3×#41—52no—
107Dic3×#41—56no—
108#5812—52no—
109#5798—56no—
110C2×#926—53no—
111C2×#926—53no—
112C2×C5×#41C2×D311yescharacteristic
113D5×#41Dic3116yescomplemented
114C2×#713C2×D311yescharacteristic
115C2×Q8×D5C2×D311yescharacteristic
116C2×#711C2×D313yes—
117C2×D4×D5C2×D313yes—
118C2×#709C2×D313yes—
119C22×C4×D5C2×D313yes—
120C4×C5×Q8—32no—
121C4×C5×D4—36no—
122C5×#117—33no—
123C2×C5×C4⋊C4—33no—
124Q8×Dic5—32no—
125D4×Dic5—36no—
126C4×C22⋊D5—312no—
127C2×#685—36no—
128#4072—33no—
129C2×C4⋊Dic5—33no—
130C2×C4×Dic5—36no—
131#4039—36no—
132#4038—33no—
133#4038—36no—
134#4038—36no—
135#4038—36no—
136#4038—31no—
137D5×C4⋊C4—33no—
138D5×C4⋊C4—33no—
139#4033—36no—
140#4027—312no—
141D5×C22⋊C4—36no—
142#4023—36no—
143C4×D20—36no—
144#4018—36no—
145C42×D5—36no—
146C4×Dic10—36no—
147#3428—151noSylow
148C23×C3×C5C2413yes—
149C22×C3×D5—43no—
150C22×C3×D5—43no—
151C22×C3×D5C22×C4112yes—
152C22×C3×D5C2411yescharacteristic
153C22×C3×D5C2413yes—
154C3×C5×Q8C22×C414yes—
155C3×C5×D4C22×C4112yes—
156C2×C3×C4×C5C22×C4112yes—
157C2×C3×C4×C5C2413yes—
158C2×C3×C4×C5C2411yescharacteristic
159C2×Dic15—46no—
160C2×Dic15C2416yes—
161C2×Dic15C2412yes—
162C2×C5×Dic3—46no—
163C2×C5×Dic3C2416yes—
164C2×C5×Dic3C2412yes—
165C3×C22⋊D5C22×C4124yes—
166C2×C3×Dic5C22×C4112yes—
167C2×C3×Dic5C2411yescharacteristic
168C2×C3×Dic5C2413yes—
169C3×D20C22×C4112yes—
170C3×C4×D5C22×C414yes—
171C3×C4×D5C22×C4112yes—
172C3×C4×D5C22×C4112yes—
173C3×C4×D5C22×C4112yes—
174C3×Dic10C22×C4112yes—
175D5×Dic3—46no—
176D5×Dic3—46no—
177C2×C3×#41—516no—
178C2×C3×#41—51no—
179C2×C3×#41—53no—
180C2×C3×#41—53no—
181C2×C3×#41C2×D511yescharacteristic
182C22×C3×Q8—51no—
183C22×C3×D4—53no—
184C23×C3×C4—53no—
185C2×#217—56no—
186C2×#217—56no—
187Q8×Dic3—52no—
188Q8×Dic3—56no—
189Q8×Dic3—56no—
190Q8×Dic3C2×D512yescomplemented
191D4×Dic3—56no—
192D4×Dic3—512no—
193D4×Dic3—512no—
194D4×Dic3—56no—
195D4×Dic3—56no—
196D4×Dic3C2×D516yescomplemented
197#926—53no—
198#926—56no—
199#926—51no—
200#926—53no—
201#926—56no—
202#926—56no—
203#926—56no—
204#926—56no—
205#926C2×D513yescomplemented
206C2×C4⋊Dic3—53no—
207C2×C4⋊Dic3—53no—
208C2×C4⋊Dic3—53no—
209C2×C4⋊Dic3C2×D513yescomplemented
210C2×C4×Dic3—56no—
211C2×C4×Dic3—56no—
212C23×D5C22×D313yes—
213C5×#41C2×Dic318yescomplemented
214C2×C5×Q8C22×D311yescharacteristic
215C2×C5×D4C22×D313yes—
216C22×C4×C5—36no—
217C22×C4×C5C22×D313yes—
218C2×C22⋊D5C22×D316yes—
219C22×Dic5—36no—
220C22×Dic5C22×D313yes—
221#713C2×Dic318yescomplemented
222Q8×D5C2×Dic318yescomplemented
223#711C2×Dic3124yescomplemented
224D4×D5C2×Dic3124yescomplemented
225#709C2×Dic3124yescomplemented
226C2×D20C22×D313yes—
227C2×C4×D5—36no—
228C2×C4×D5—36no—
229C2×C4×D5C2×Dic3124yescomplemented
230C2×C4×D5C22×D311yescharacteristic
231C2×C4×D5C22×D313yes—
232C2×C4×D5C22×D313yes—
233C2×C4×D5C22×D313yes—
234C2×Dic10C22×D313yes—
235C5×C4⋊C4—33no—
236C5×C4⋊C4—36no—
237C5×C4⋊C4—31no—
238C5×C22⋊C4—36no—
239C42×C5—36no—
240C22⋊Dic5—36no—
241#685—32no—
242#685—36no—
243#685—312no—
244C4⋊Dic5—36no—
245C4⋊Dic5—31no—
246C4⋊Dic5—33no—
247#683—36no—
248#683—36no—
249C4×Dic5—36no—
250C4×Dic5—312no—
251C4×Dic5—32no—
252C4×Dic5—36no—
253C22×#41—51no—
254#520—31no—
255#520—153no—
256#520—153no—
257#520—151no—
258#519—152no—
259#518—156no—
260C4×#41—156no—
261C4×#41—152no—
262C2×#117—153no—
263C2×#117—153no—
264C22×C3×C5—23no—
265C22×C3×C5—23no—
266C22×C3×C5C23×C416yes—
267C22×C3×C5C2511yescharacteristic
268C2×C3×D5—23no—
269C2×C3×D5—23no—
270C2×C3×D5—21no—
271C2×C3×D5—21no—
272C2×C3×D5—412no—
273C2×C3×D5C23×C412yes—
274C2×C3×D5C23×C416yes—
275C3×C4×C5C23×C416yes—
276C3×C4×C5C23×C412yes—
277Dic15—22no—
278Dic15—26no—
279C3×Dic5C23×C416yes—
280C3×Dic5C23×C412yes—
281C5×Dic3—22no—
282C5×Dic3—26no—
283C24×C3—53no—
284C3×#41—58no—
285C3×#41—524no—
286C3×#41—524no—
287C3×#41C4×D518yescomplemented
288C2×C3×Q8—58no—
289C2×C3×Q8—53no—
290C2×C3×Q8C22×D511yescharacteristic
291C2×C3×D4—56no—
292C2×C3×D4—524no—
293C2×C3×D4—53no—
294C2×C3×D4C22×D513yes—
295C22×C3×C4—53no—
296C22×C3×C4—524no—
297C22×C3×C4—53no—
298C22×C3×C4—53no—
299C22×C3×C4—51no—
300C22×C3×C4—53no—
301C22×C3×C4C22×D513yes—
302C22×Dic3—56no—
303C22×Dic3—56no—
304C22×Dic3—56no—
305C22×Dic3C22×D516yes—
306#217—56no—
307#217—56no—
308#217—52no—
309#217—512no—
310#217C22×D516yes—
311C4⋊Dic3—51no—
312C4⋊Dic3—53no—
313C4⋊Dic3—56no—
314C4⋊Dic3—56no—
315C4⋊Dic3—56no—
316C4⋊Dic3C22×D511yescharacteristic
317C4⋊Dic3C22×D513yes—
318C4⋊Dic3C22×D516yes—
319C4×Dic3—56no—
320C4×Dic3—56no—
321C4×Dic3—52no—
322C4×Dic3—512no—
323C4×Dic3C22×D516yes—
324C23×C5C23×D313yes—
325C22×D5—43no—
326C22×D5—43no—
327C22×D5C22×Dic3112yes—
328C22×D5C23×D311yescharacteristic
329C22×D5C23×D313yes—
330C5×Q8C22×Dic314yes—
331C5×D4C22×Dic3112yes—
332C2×C4×C5—36no—
333C2×C4×C5—32no—
334C2×C4×C5—126no—
335C2×C4×C5C22×Dic3112yes—
336C2×C4×C5C23×D313yes—
337C2×C4×C5C23×D311yescharacteristic
338C22⋊D5C22×Dic3124yes—
339C2×Dic5—32no—
340C2×Dic5—36no—
341C2×Dic5—126no—
342C2×Dic5C22×Dic3112yes—
343C2×Dic5C23×D311yescharacteristic
344C2×Dic5C23×D313yes—
345D20C22×Dic3112yes—
346C4×D5—126no—
347C4×D5—126no—
348C4×D5C22×Dic314yes—
349C4×D5C22×Dic3112yes—
350C4×D5C22×Dic3112yes—
351C4×D5C22×Dic3112yes—
352Dic10C22×Dic3112yes—
353C2×#41—516no—
354C2×#41—51no—
355C2×#41—53no—
356C2×#41—53no—
357C2×#41D3×D511yescharacteristic
358C22×Q8—51no—
359C22×D4—53no—
360C23×C4—53no—
361C4×Q8—32no—
362C4×Q8—156no—
363C4×Q8—156no—
364C4×Q8—152no—
365C4×D4—36no—
366C4×D4—156no—
367C4×D4—1512no—
368C4×D4—156no—
369C4×D4—1512no—
370C4×D4—156no—
371#117—33no—
372#117—156no—
373#117—156no—
374#117—153no—
375#117—151no—
376#117—156no—
377#117—156no—
378#117—156no—
379#117—153no—
380C2×C4⋊C4—33no—
381C2×C4⋊C4—153no—
382C2×C4⋊C4—153no—
383C2×C4⋊C4—153no—
384C2×C22⋊C4—156no—
385C2×C22⋊C4—156no—
386C2×C42—156no—
387C2×C42—156no—
388C2×C3×C5—26no—
389C2×C3×C5C24×C411yescharacteristic
390C2×C3×C5#58511yescharacteristic
391C2×C3×C5#58511yescharacteristic
392C3×D5—22no—
393C3×D5—26no—
394C23×C3—51no—
395C23×C3—53no—
396C23×C3—512no—
397C23×C3—203no—
398C23×C3—203no—
399C23×C3C23×D513yes—
400C3×Q8—512no—
401C3×Q8C2×C4×D514yes—
402C3×D4—524no—
403C3×D4—512no—
404C3×D4C2×C4×D5112yes—
405C2×C3×C4—512no—
406C2×C3×C4—51no—
407C2×C3×C4—53no—
408C2×C3×C4—54no—
409C2×C3×C4—512no—
410C2×C3×C4—512no—
411C2×C3×C4—512no—
412C2×C3×C4C2×C4×D5112yes—
413C2×C3×C4C23×D513yes—
414C2×C3×C4C23×D511yescharacteristic
415C2×Dic3—46no—
416C2×Dic3—52no—
417C2×Dic3—56no—
418C2×Dic3—206no—
419C2×Dic3—206no—
420C2×Dic3—206no—
421C2×Dic3C23×D516yes—
422C2×Dic3C23×D512yes—
423C22×C5—23no—
424C22×C5—23no—
425C22×C5C23×Dic316yes—
426C22×C5C24×D311yescharacteristic
427C2×D5—23no—
428C2×D5—23no—
429C2×D5—21no—
430C2×D5—21no—
431C2×D5—412no—
432C2×D5C23×Dic312yes—
433C2×D5C23×Dic316yes—
434C4×C5—62no—
435C4×C5—66no—
436C4×C5C23×Dic316yes—
437C4×C5C23×Dic312yes—
438Dic5—62no—
439Dic5—66no—
440Dic5C23×Dic316yes—
441Dic5C23×Dic312yes—
442C24—53no—
443#41—58no—
444#41—524no—
445#41—524no—
446#41D5×Dic318yescomplemented
447C2×Q8—58no—
448C2×Q8—53no—
449C2×Q8C2×D3×D511yescharacteristic
450C2×D4—56no—
451C2×D4—524no—
452C2×D4—53no—
453C2×D4C2×D3×D513yes—
454C22×C4—36no—
455C22×C4—53no—
456C22×C4—524no—
457C22×C4—53no—
458C22×C4—53no—
459C22×C4—51no—
460C22×C4—53no—
461C22×C4—156no—
462C22×C4—156no—
463C22×C4—156no—
464C22×C4C2×D3×D513yes—
465C4⋊C4—33no—
466C4⋊C4—36no—
467C4⋊C4—31no—
468C4⋊C4—156no—
469C4⋊C4—156no—
470C4⋊C4—151no—
471C4⋊C4—153no—
472C4⋊C4—156no—
473C22⋊C4—36no—
474C22⋊C4—152no—
475C22⋊C4—156no—
476C22⋊C4—1512no—
477C22⋊C4—156no—
478C42—36no—
479C42—152no—
480C42—156no—
481C42—1512no—
482C42—156no—
483C3×C5#342811yescharacteristic, complemented, Hall
484C22×C3—23no—
485C22×C3—23no—
486C22×C3—52no—
487C22×C3—56no—
488C22×C3—103no—
489C22×C3—101no—
490C22×C3—103no—
491C22×C3—101no—
492C22×C3—2012no—
493C22×C3C22×C4×D516yes—
494C22×C3C24×D511yescharacteristic
495C3×C4—52no—
496C3×C4—56no—
497C3×C4C22×C4×D512yes—
498C3×C4C22×C4×D516yes—
499Dic3—26no—
500Dic3—22no—
501Dic3—102no—
502Dic3—106no—
503C2×C5—26no—
504C2×C5#596411yescharacteristic
505C2×C5#596411yescharacteristic
506C2×C5C24×Dic311yescharacteristic
507D5—22no—
508D5—26no—
509C23—51no—
510C23—53no—
511C23—512no—
512C23—203no—
513C23—203no—
514C23C22×D3×D513yes—
515Q8—512no—
516Q8C2×D5×Dic314yes—
517D4—524no—
518D4—512no—
519D4C2×D5×Dic3112yes—
520C2×C4—32no—
521C2×C4—36no—
522C2×C4—512no—
523C2×C4—51no—
524C2×C4—53no—
525C2×C4—54no—
526C2×C4—512no—
527C2×C4—512no—
528C2×C4—512no—
529C2×C4—126no—
530C2×C4—152no—
531C2×C4—156no—
532C2×C4—606no—
533C2×C4—606no—
534C2×C4—606no—
535C2×C4C2×D5×Dic3112yes—
536C2×C4C22×D3×D513yes—
537C2×C4C22×D3×D511yescharacteristic
538C2×C3—26no—
539C2×C3—102no—
540C2×C3—106no—
541C2×C3C23×C4×D511yescharacteristic
542C2×C3#6628511yescharacteristic
543C2×C3#6628711yescharacteristic
544C5#8726011yescharacteristic, complemented, Sylow
545C22—23no—
546C22—23no—
547C22—52no—
548C22—56no—
549C22—103no—
550C22—101no—
551C22—103no—
552C22—101no—
553C22—2012no—
554C22C22×D5×Dic316yes—
555C22C23×D3×D511yescharacteristic
556C4—52no—
557C4—56no—
558C4—66no—
559C4—62no—
560C4—302no—
561C4—306no—
562C4C22×D5×Dic312yes—
563C4C22×D5×Dic316yes—
564C3#1061778611yescharacteristic, complemented, Sylow
565C2—26no—
566C2—102no—
567C2—106no—
568C2#1175705911yescharacteristic
569C2#1175706011yescharacteristic
570C2C23×D5×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×C3×D5×#41C2
hypercenterC2×#41D3×D5
hypocenterC3×C5#3428
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11756586C2semidirect
3. C5×#5827C2semidirect
4. Dic3×#713C2semidirect
5. #11755140C2semidirect
6. #11754910C2semidirect
7. Dic3×#711C2semidirect
8. #11754509C2semidirect
9. #11754499C2semidirect
10. D5×#926C2semidirect
11. C2×#91358C2semidirect
14. C3×D5×#41C4semidirect
21. Q8×Dic15C22semidirect
22. D4×Dic15C22semidirect
23. #91815C22semidirect
24. C2×C4⋊Dic15C22semidirect
25. C5×Q8×Dic3C22semidirect
26. C5×D4×Dic3C22semidirect
27. C5×#926C22semidirect
28. C2×C5×C4⋊Dic3C22semidirect
29. #91559C22semidirect
30. Dic3×C22⋊D5C22semidirect
33. #91528C22semidirect
34. C2×Dic3×Dic5C22semidirect
35. #91434C22semidirect
36. Dic3×D20C22semidirect
37. D5×C4⋊Dic3C22semidirect
38. D5×C4⋊Dic3C22semidirect
39. C4×D5×Dic3C22semidirect
43. #91358C22semidirect
44. #91358C22semidirect
46. #91331C22semidirect
47. Dic3×Dic10C22semidirect
61. C3×C5×#41C2×C4semidirect
69. C3×#713C2×C4semidirect
70. C3×Q8×D5C2×C4semidirect
71. C3×#711C2×C4semidirect
72. C3×D4×D5C2×C4semidirect
73. C3×#709C2×C4semidirect
75. C2×C3×C4×D5C2×C4semidirect
105. #5827D5semidirect
113. D5×#41Dic3semidirect
190. Q8×Dic3C2×D5semidirect
196. D4×Dic3C2×D5semidirect
205. #926C2×D5semidirect
209. C2×C4⋊Dic3C2×D5semidirect
213. C5×#41C2×Dic3semidirect
221. #713C2×Dic3semidirect
222. Q8×D5C2×Dic3semidirect
223. #711C2×Dic3semidirect
224. D4×D5C2×Dic3semidirect
225. #709C2×Dic3semidirect
229. C2×C4×D5C2×Dic3semidirect
287. C3×#41C4×D5semidirect
446. #41D5×Dic3semidirect
483. C3×C5#3428semidirect
544. C5#87260semidirect
564. C3#10617786semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
#117565862
C5×#58272
Dic3×#7132
#117551402
#117549102
Dic3×#7112
#117545092
#117544992
D5×#9262
C2×#913582
#106177863
#872605