Finite Group Databasebeta

← #14479185

Subgroups — #14479185

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×#41×D15C211yesmaximal, characteristic
2C5×#5827C211yesmaximal, characteristic, complemented
3C3×#66161C211yesmaximal, characteristic, complemented
4#11755200C212yesmaximal, complemented
5#11755124C212yesmaximal, complemented
6#11754922C216yesmaximal, complemented
7#11754853C216yesmaximal, complemented
8#11754506C213yesmaximal, complemented
9#11754496C213yesmaximal, complemented
10#11754461C213yesmaximal, complemented
11C2×#91347C213yesmaximal, complemented
12#10617786—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14#41×D15C4116yescomplemented
15C2×#6821C2211yescharacteristic
16C2×Q8×D15C2211yescharacteristic
17C2×#6819C2213yes—
18C2×D4×D15C2213yes—
19C2×#6817C2213yes—
20C22×C4×D15C2213yes—
21C5×Q8×Dic3C2212yescomplemented
22C5×D4×Dic3C2216yescomplemented
23C5×#926C2213yescomplemented
24C2×C5×C4⋊Dic3C2213yescomplemented
25C3×Q8×Dic5C2212yescomplemented
26C3×D4×Dic5C2216yescomplemented
27C3×#4072C2213yescomplemented
28C2×C3×C4⋊Dic5C2213yescomplemented
29#91561C2216yes—
30#91556C22112yescomplemented
31#91552C22112yescomplemented
32C2×#6667C2216yes—
33#91532C2216yescomplemented
34C2×Dic3×Dic5C2216yescomplemented
35#91437C2213yescomplemented
36#91437C2213yescomplemented
37#91428C2216yescomplemented
38#91418C2216yescomplemented
39C4×#1200C2216yescomplemented
40#91386C2216yes—
41#91347C2216yes—
42#91347C2211yescharacteristic
43#91347C2213yes—
44#91347C2216yescomplemented
45#91347C2216yescomplemented
46#91340C2216yescomplemented
47#91333C2216yescomplemented
48#85885—51nomaximal, Hall
49C2×D5×#41—31no—
50C5×#520—31no—
51#66161D311yescharacteristic, complemented
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×D15C2313yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C2×#1220C2316yes—
66C22×Dic15C2313yes—
67#6821C2×C418yescomplemented
68Q8×D15C2×C418yescomplemented
69#6819C2×C4124yescomplemented
70D4×D15C2×C4124yescomplemented
71#6817C2×C4124yescomplemented
72C2×D60C2313yes—
73C2×C4×D15C2×C4124yescomplemented
74C2×C4×D15C2313yes—
75C2×C4×D15C2313yes—
76C2×C4×D15C2311yescharacteristic
77C2×C4×D15C2313yes—
78C2×Dic30C2313yes—
79C22×C5×Dic3C2316yes—
80C22×C3×Dic5C2316yes—
81C2×#1200C2316yes—
82C2×#1200C2316yes—
83C5×#217C2316yes—
84C5×C4⋊Dic3C2316yes—
85C5×C4⋊Dic3C2311yescharacteristic
86C5×C4⋊Dic3C2313yes—
87C4×C5×Dic3C2316yes—
88C3×C22⋊Dic5C2316yes—
89C3×C4⋊Dic5C2316yes—
90C3×C4⋊Dic5C2311yescharacteristic
91C3×C4⋊Dic5C2313yes—
92C3×C4×Dic5C2316yes—
93#6669C2316yes—
94#6669C2316yes—
95#6667C23112yes—
96#6667C2316yes—
97#6667C2312yes—
98Dic3×Dic5C2312yes—
99Dic3×Dic5C2316yes—
100Dic3×Dic5C23112yes—
101C2×D3×#41—51no—
102C3×#520—51no—
103#5827D511yescharacteristic, complemented
104C4×#239—52no—
105#5572—52no—
106#5545—56no—
107C4×#237—56no—
108#5523—53no—
109D3×#117—53no—
110#5504—53no—
111C2×#892—53no—
112C2×C5×#41C2×D311yescharacteristic
113D5×#41—316no—
114C2×#713—31no—
115C2×Q8×D5—31no—
116C2×#711—33no—
117C2×D4×D5—33no—
118C2×#709—33no—
119C22×C4×D5—33no—
120C4×C5×Q8—32no—
121C4×C5×D4—36no—
122C5×#117—33no—
123C2×C5×C4⋊C4—33no—
124Q8×Dic5C2×D312yescomplemented
125D4×Dic5C2×D316yescomplemented
126C4×C22⋊D5—312no—
127C2×#685—36no—
128#4072C2×D313yescomplemented
129C2×C4⋊Dic5C2×D313yescomplemented
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×D15—43no—
150C22×D15—43no—
151C22×D15C22×C4112yes—
152C22×D15C2411yescharacteristic
153C22×D15C2413yes—
154C3×C5×Q8C22×C414yes—
155C3×C5×D4C22×C4112yes—
156C2×C3×C4×C5C22×C4112yes—
157C2×C3×C4×C5C2413yes—
158C2×C3×C4×C5C2411yescharacteristic
159#1220C22×C4124yes—
160C2×Dic15C22×C4112yes—
161C2×Dic15C2411yescharacteristic
162C2×Dic15C2413yes—
163D60C22×C4112yes—
164C4×D15C22×C414yes—
165C4×D15C22×C4112yes—
166C4×D15C22×C4112yes—
167C4×D15C22×C4112yes—
168Dic30C22×C4112yes—
169C2×C5×Dic3—46no—
170C2×C5×Dic3C2416yes—
171C2×C5×Dic3C2412yes—
172C2×C3×Dic5—46no—
173C2×C3×Dic5C2416yes—
174C2×C3×Dic5C2412yes—
175#1200—46no—
176#1200—46no—
177C2×C3×#41C2×D511yescharacteristic
178D3×#41—516no—
179C2×#239—51no—
180C2×D3×Q8—51no—
181C2×#237—53no—
182C2×D3×D4—53no—
183C2×#235—53no—
184C22×C4×D3—53no—
185C3×C4×Q8—52no—
186C3×C4×D4—56no—
187C3×#117—53no—
188C2×C3×C4⋊C4—53no—
189Q8×Dic3C2×D512yescomplemented
190D4×Dic3C2×D516yescomplemented
191C4×#67—512no—
192C2×(C2×D3)⋊C4—56no—
193#926C2×D513yescomplemented
194C2×C4⋊Dic3C2×D513yescomplemented
195C2×C4×Dic3—56no—
196#893—56no—
197#892—53no—
198#892—56no—
199#892—56no—
200#892—56no—
201#892—51no—
202D3×C4⋊C4—53no—
203D3×C4⋊C4—53no—
204#887—56no—
205#67⋊C4—512no—
206D3×C22⋊C4—56no—
207#877—56no—
208C4×D12—56no—
209#872—56no—
210C42×D3—56no—
211C4×Dic6—56no—
212C23×D5—33no—
213C5×#41C4×D318yescomplemented
214C2×C5×Q8C22×D311yescharacteristic
215C2×C5×D4C22×D313yes—
216C22×C4×C5—36no—
217C22×C4×C5C22×D313yes—
218C2×C22⋊D5—36no—
219C22×Dic5—33no—
220C22×Dic5C22×D316yes—
221#713—38no—
222Q8×D5—38no—
223#711—324no—
224D4×D5—324no—
225#709—324no—
226C2×D20—33no—
227C2×C4×D5—324no—
228C2×C4×D5—31no—
229C2×C4×D5—33no—
230C2×C4×D5—33no—
231C2×C4×D5—33no—
232C2×C4×D5—36no—
233C2×C4×D5—36no—
234C2×Dic10—33no—
235C5×C4⋊C4—33no—
236C5×C4⋊C4—36no—
237C5×C4⋊C4—31no—
238C5×C22⋊C4—36no—
239C42×C5—36no—
240C22⋊Dic5C22×D316yes—
241#685—32no—
242#685—36no—
243#685—312no—
244C4⋊Dic5C22×D316yes—
245C4⋊Dic5C22×D311yescharacteristic
246C4⋊Dic5C22×D313yes—
247#683—36no—
248#683—36no—
249C4×Dic5—312no—
250C4×Dic5—32no—
251C4×Dic5—36no—
252C4×Dic5C22×D316yes—
253C22×#41—151no—
254#520—31no—
255#520—51no—
256#520—153no—
257#520—153no—
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×D15—23no—
269C2×D15—23no—
270C2×D15—21no—
271C2×D15—21no—
272C2×D15—412no—
273C2×D15C23×C412yes—
274C2×D15C23×C416yes—
275C3×C4×C5C23×C416yes—
276C3×C4×C5C23×C412yes—
277Dic15C23×C416yes—
278Dic15C23×C412yes—
279C3×Dic5—22no—
280C3×Dic5—26no—
281C5×Dic3—22no—
282C5×Dic3—26no—
283C23×D3—53no—
284C3×#41C4×D518yescomplemented
285C2×C3×Q8C22×D511yescharacteristic
286C2×C3×D4C22×D513yes—
287C22×C3×C4—56no—
288C22×C3×C4C22×D513yes—
289C2×#67—56no—
290C22×Dic3—53no—
291C22×Dic3C22×D516yes—
292#239—58no—
293D3×Q8—58no—
294#237—524no—
295D3×D4—524no—
296#235—524no—
297C2×D12—53no—
298C2×C4×D3—524no—
299C2×C4×D3—53no—
300C2×C4×D3—53no—
301C2×C4×D3—53no—
302C2×C4×D3—51no—
303C2×C4×D3—56no—
304C2×C4×D3—56no—
305C2×Dic6—53no—
306C3×C4⋊C4—56no—
307C3×C4⋊C4—51no—
308C3×C4⋊C4—53no—
309C3×C22⋊C4—56no—
310C3×C42—56no—
311#217C22×D516yes—
312(C2×D3)⋊C4—52no—
313(C2×D3)⋊C4—56no—
314(C2×D3)⋊C4—512no—
315C4⋊Dic3C22×D516yes—
316C4⋊Dic3C22×D511yescharacteristic
317C4⋊Dic3C22×D513yes—
318Dic3⋊C4—56no—
319Dic3⋊C4—56no—
320C4×Dic3—512no—
321C4×Dic3—52no—
322C4×Dic3—56no—
323C4×Dic3C22×D516yes—
324C23×C5C23×D313yes—
325C22×D5—31no—
326C22×D5—33no—
327C22×D5—312no—
328C22×D5—123no—
329C22×D5—123no—
330C5×Q8C2×C4×D314yes—
331C5×D4C2×C4×D3112yes—
332C2×C4×C5—36no—
333C2×C4×C5—32no—
334C2×C4×C5—126no—
335C2×C4×C5C2×C4×D3112yes—
336C2×C4×C5C23×D313yes—
337C2×C4×C5C23×D311yescharacteristic
338C22⋊D5—324no—
339C2×Dic5—312no—
340C2×Dic5—31no—
341C2×Dic5—33no—
342C2×Dic5—46no—
343C2×Dic5C23×D316yes—
344C2×Dic5C23×D312yes—
345D20—312no—
346C4×D5—34no—
347C4×D5—312no—
348C4×D5—312no—
349C4×D5—312no—
350C4×D5—126no—
351C4×D5—126no—
352Dic10—312no—
353C2×#41—1516no—
354C2×#41—151no—
355C2×#41—153no—
356C2×#41—153no—
357C2×#41D3×D511yescharacteristic
358C22×Q8—151no—
359C22×D4—153no—
360C23×C4—153no—
361C4×Q8—32no—
362C4×Q8—52no—
363C4×Q8—156no—
364C4×Q8—156no—
365C4×D4—36no—
366C4×D4—56no—
367C4×D4—156no—
368C4×D4—156no—
369C4×D4—1512no—
370C4×D4—1512no—
371#117—33no—
372#117—53no—
373#117—156no—
374#117—156no—
375#117—153no—
376#117—151no—
377#117—156no—
378#117—156no—
379#117—156no—
380C2×C4⋊C4—33no—
381C2×C4⋊C4—53no—
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
392D15—22no—
393D15—26no—
394C23×C3C23×D513yes—
395C22×D3—51no—
396C22×D3—53no—
397C22×D3—512no—
398C22×D3—203no—
399C22×D3—203no—
400C3×Q8C2×C4×D514yes—
401C3×D4C2×C4×D5112yes—
402C2×C3×C4—56no—
403C2×C3×C4—52no—
404C2×C3×C4—206no—
405C2×C3×C4C2×C4×D5112yes—
406C2×C3×C4C23×D513yes—
407C2×C3×C4C23×D511yescharacteristic
408#67—524no—
409C2×Dic3—46no—
410C2×Dic3—512no—
411C2×Dic3—51no—
412C2×Dic3—53no—
413C2×Dic3C23×D516yes—
414C2×Dic3C23×D512yes—
415D12—512no—
416C4×D3—54no—
417C4×D3—512no—
418C4×D3—512no—
419C4×D3—512no—
420C4×D3—206no—
421C4×D3—206no—
422Dic6—512no—
423C22×C5—23no—
424C22×C5—23no—
425C22×C5C22×C4×D316yes—
426C22×C5C24×D311yescharacteristic
427C2×D5—32no—
428C2×D5—36no—
429C2×D5—63no—
430C2×D5—61no—
431C2×D5—63no—
432C2×D5—61no—
433C2×D5—1212no—
434C4×C5—62no—
435C4×C5—66no—
436C4×C5C22×C4×D316yes—
437C4×C5C22×C4×D312yes—
438Dic5—26no—
439Dic5—22no—
440Dic5—36no—
441Dic5—32no—
442C24—153no—
443#41—158no—
444#41—1524no—
445#41—1524no—
446#41#120018yescomplemented
447C2×Q8—158no—
448C2×Q8—153no—
449C2×Q8C2×D3×D511yescharacteristic
450C2×D4—156no—
451C2×D4—1524no—
452C2×D4—153no—
453C2×D4C2×D3×D513yes—
454C22×C4—36no—
455C22×C4—56no—
456C22×C4—156no—
457C22×C4—156no—
458C22×C4—153no—
459C22×C4—1524no—
460C22×C4—153no—
461C22×C4—153no—
462C22×C4—151no—
463C22×C4—153no—
464C22×C4C2×D3×D513yes—
465C4⋊C4—33no—
466C4⋊C4—36no—
467C4⋊C4—31no—
468C4⋊C4—53no—
469C4⋊C4—56no—
470C4⋊C4—51no—
471C4⋊C4—156no—
472C4⋊C4—156no—
473C22⋊C4—36no—
474C22⋊C4—56no—
475C22⋊C4—152no—
476C22⋊C4—156no—
477C22⋊C4—1512no—
478C42—36no—
479C42—56no—
480C42—152no—
481C42—156no—
482C42—1512no—
483C3×C5#342811yescharacteristic, complemented, Hall
484C22×C3—23no—
485C22×C3—23no—
486C22×C3C22×C4×D516yes—
487C22×C3C24×D511yescharacteristic
488C2×D3—52no—
489C2×D3—56no—
490C2×D3—103no—
491C2×D3—101no—
492C2×D3—103no—
493C2×D3—101no—
494C2×D3—2012no—
495C3×C4—102no—
496C3×C4—106no—
497C3×C4C22×C4×D516yes—
498C3×C4C22×C4×D512yes—
499Dic3—26no—
500Dic3—22no—
501Dic3—56no—
502Dic3—52no—
503C2×C5—26no—
504C2×C5C23×C4×D311yescharacteristic
505C2×C5#596611yescharacteristic
506C2×C5#596811yescharacteristic
507D5—62no—
508D5—66no—
509C23—151no—
510C23—153no—
511C23—1512no—
512C23—603no—
513C23—603no—
514C23C22×D3×D513yes—
515Q8—1512no—
516Q8C2×#120014yes—
517D4—1524no—
518D4—1512no—
519D4C2×#1200112yes—
520C2×C4—32no—
521C2×C4—36no—
522C2×C4—52no—
523C2×C4—56no—
524C2×C4—126no—
525C2×C4—1512no—
526C2×C4—151no—
527C2×C4—153no—
528C2×C4—154no—
529C2×C4—1512no—
530C2×C4—1512no—
531C2×C4—1512no—
532C2×C4—206no—
533C2×C4—606no—
534C2×C4—606no—
535C2×C4C2×#1200112yes—
536C2×C4C22×D3×D513yes—
537C2×C4C22×D3×D511yescharacteristic
538C2×C3—26no—
539C2×C3C23×C4×D511yescharacteristic
540C2×C3#6628511yescharacteristic
541C2×C3#6628711yescharacteristic
542D3—102no—
543D3—106no—
544C5#8588511yescharacteristic, complemented, Sylow
545C22—23no—
546C22—23no—
547C22—152no—
548C22—156no—
549C22—303no—
550C22—301no—
551C22—303no—
552C22—301no—
553C22—6012no—
554C22C22×#120016yes—
555C22C23×D3×D511yescharacteristic
556C4—62no—
557C4—66no—
558C4—106no—
559C4—102no—
560C4—152no—
561C4—156no—
562C4C22×#120012yes—
563C4C22×#120016yes—
564C3#1061778611yescharacteristic, complemented, Sylow
565C2—26no—
566C2—302no—
567C2—306no—
568C2#1175706211yescharacteristic
569C2#1175706411yescharacteristic
570C2C23×#120011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×#41×D15C2
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. C5×#5827C2semidirect
3. C3×#66161C2semidirect
4. #11755200C2semidirect
5. #11755124C2semidirect
6. #11754922C2semidirect
7. #11754853C2semidirect
8. #11754506C2semidirect
9. #11754496C2semidirect
10. #11754461C2semidirect
11. C2×#91347C2semidirect
14. #41×D15C4semidirect
21. C5×Q8×Dic3C22semidirect
22. C5×D4×Dic3C22semidirect
23. C5×#926C22semidirect
24. C2×C5×C4⋊Dic3C22semidirect
25. C3×Q8×Dic5C22semidirect
26. C3×D4×Dic5C22semidirect
27. C3×#4072C22semidirect
28. C2×C3×C4⋊Dic5C22semidirect
30. #91556C22semidirect
31. #91552C22semidirect
33. #91532C22semidirect
34. C2×Dic3×Dic5C22semidirect
35. #91437C22semidirect
36. #91437C22semidirect
37. #91428C22semidirect
38. #91418C22semidirect
39. C4×#1200C22semidirect
44. #91347C22semidirect
45. #91347C22semidirect
46. #91340C22semidirect
47. #91333C22semidirect
51. #66161D3semidirect
61. C3×C5×#41C2×C4semidirect
67. #6821C2×C4semidirect
68. Q8×D15C2×C4semidirect
69. #6819C2×C4semidirect
70. D4×D15C2×C4semidirect
71. #6817C2×C4semidirect
73. C2×C4×D15C2×C4semidirect
103. #5827D5semidirect
124. Q8×Dic5C2×D3semidirect
125. D4×Dic5C2×D3semidirect
128. #4072C2×D3semidirect
129. C2×C4⋊Dic5C2×D3semidirect
189. Q8×Dic3C2×D5semidirect
190. D4×Dic3C2×D5semidirect
193. #926C2×D5semidirect
194. C2×C4⋊Dic3C2×D5semidirect
213. C5×#41C4×D3semidirect
284. C3×#41C4×D5semidirect
446. #41#1200semidirect
483. C3×C5#3428semidirect
544. C5#85885semidirect
564. C3#10617786semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D152
C5×#58272
C3×#661612
#117552002
#117551242
#117549222
#117548532
#117545062
#117544962
#117544612
C2×#913472
#106177863
#858855