Finite Group Databasebeta

← #14479186

Subgroups — #14479186

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×C5×D3×#41C211yesmaximal, characteristic
2#11756586C211yesmaximal, characteristic, complemented
3C3×#66161C211yesmaximal, characteristic, complemented
4Dic5×#239C212yesmaximal, complemented
5#11755144C212yesmaximal, complemented
6#11754914C216yesmaximal, complemented
7Dic5×#237C216yesmaximal, complemented
8#11754513C213yesmaximal, complemented
9#11754492C213yesmaximal, complemented
10D3×#4072C213yesmaximal, complemented
11C2×#91338C213yesmaximal, complemented
12#10619161—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C5×D3×#41C4116yescomplemented
15C2×C5×#239C2211yescharacteristic
16C2×C5×D3×Q8C2211yescharacteristic
17C2×C5×#237C2213yes—
18C2×C5×D3×D4C2213yes—
19C2×C5×#235C2213yes—
20C22×C4×C5×D3C2213yes—
21Q8×Dic15C2212yescomplemented
22D4×Dic15C2216yescomplemented
23#91815C2213yescomplemented
24C2×C4⋊Dic15C2213yescomplemented
25C3×Q8×Dic5C2212yescomplemented
26C3×D4×Dic5C2216yescomplemented
27C3×#4072C2213yescomplemented
28C2×C3×C4⋊Dic5C2213yescomplemented
29#67⋊Dic5C22112yescomplemented
30D3×C22⋊Dic5C2216yes—
31Dic5×#67C22112yescomplemented
32C2×(C2×D3)⋊Dic5C2216yes—
33#91529C2216yescomplemented
34C2×Dic3×Dic5C2216yescomplemented
35#91435C2216yescomplemented
36D3×C4⋊Dic5C2213yescomplemented
37D3×C4⋊Dic5C2213yescomplemented
38Dic5×D12C2216yescomplemented
39C4×D3×Dic5C2216yescomplemented
40#91371C2216yes—
41#91344C2216yescomplemented
42#91338C2216yes—
43#91338C2211yescharacteristic
44#91338C2213yes—
45#91338C2216yescomplemented
46#91338C2216yescomplemented
47Dic5×Dic6C2216yescomplemented
48#85885—51nomaximal, Hall
49C22×C5×#41—31no—
50#66161—33no—
51#66161—33no—
52#66161—31no—
53#66161D311yescharacteristic, complemented
54#41×Dic5—32no—
55#41×Dic5—36no—
56#66146—32no—
57#66132—36no—
58C2×#4072—33no—
59C2×#4072—33no—
60C23×C5×D3C2313yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C22×Dic15C2316yes—
66C2×C5×#67C2316yes—
67C22×C5×Dic3C2313yes—
68C5×#239C2×C418yescomplemented
69C5×D3×Q8C2×C418yescomplemented
70C5×#237C2×C4124yescomplemented
71C5×D3×D4C2×C4124yescomplemented
72C5×#235C2×C4124yescomplemented
73C2×C5×D12C2313yes—
74C2×C4×C5×D3C2×C4124yescomplemented
75C2×C4×C5×D3C2313yes—
76C2×C4×C5×D3C2313yes—
77C2×C4×C5×D3C2311yescharacteristic
78C2×C4×C5×D3C2313yes—
79C2×C5×Dic6C2313yes—
80C22×C3×Dic5C2316yes—
81C2×D3×Dic5C2316yes—
82C2×D3×Dic5C2316yes—
83#6719C2316yes—
84C4⋊Dic15C2316yes—
85C4⋊Dic15C2311yescharacteristic
86C4⋊Dic15C2313yes—
87C4×Dic15C2316yes—
88C3×C22⋊Dic5C2316yes—
89C3×C4⋊Dic5C2316yes—
90C3×C4⋊Dic5C2311yescharacteristic
91C3×C4⋊Dic5C2313yes—
92C3×C4×Dic5C2316yes—
93Dic3⋊Dic5C2316yes—
94Dic3⋊Dic5C2316yes—
95(C2×D3)⋊Dic5C23112yes—
96(C2×D3)⋊Dic5C2316yes—
97(C2×D3)⋊Dic5C2312yes—
98Dic3×Dic5C2312yes—
99Dic3×Dic5C2316yes—
100Dic3×Dic5C23112yes—
101C2×D3×#41D511yescharacteristic
102C3×#520—51no—
103#5827—51no—
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×#41—316no—
113C2×C5×#41—31no—
114C2×C5×#41—33no—
115C2×C5×#41—33no—
116C2×C5×#41C2×D311yescharacteristic
117C22×C5×Q8—31no—
118C22×C5×D4—33no—
119C23×C4×C5—33no—
120C2×C22⋊Dic5—36no—
121C2×C22⋊Dic5—36no—
122Q8×Dic5—32no—
123Q8×Dic5—36no—
124Q8×Dic5—36no—
125Q8×Dic5C2×D312yescomplemented
126D4×Dic5—36no—
127D4×Dic5—312no—
128D4×Dic5—312no—
129D4×Dic5—36no—
130D4×Dic5—36no—
131D4×Dic5C2×D316yescomplemented
132#4072—33no—
133#4072—36no—
134#4072—31no—
135#4072—33no—
136#4072—36no—
137#4072—36no—
138#4072—36no—
139#4072—36no—
140#4072C2×D313yescomplemented
141C2×C4⋊Dic5—33no—
142C2×C4⋊Dic5—33no—
143C2×C4⋊Dic5—33no—
144C2×C4⋊Dic5C2×D313yescomplemented
145C2×C4×Dic5—36no—
146C2×C4×Dic5—36no—
147#3428—151noSylow
148C23×C3×C5C2413yes—
149C22×C5×D3—43no—
150C22×C5×D3—43no—
151C22×C5×D3C22×C4112yes—
152C22×C5×D3C2411yescharacteristic
153C22×C5×D3C2413yes—
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—
162C5×#67C22×C4124yes—
163C2×C5×Dic3C22×C4112yes—
164C2×C5×Dic3C2411yescharacteristic
165C2×C5×Dic3C2413yes—
166C5×D12C22×C4112yes—
167C4×C5×D3C22×C414yes—
168C4×C5×D3C22×C4112yes—
169C4×C5×D3C22×C4112yes—
170C4×C5×D3C22×C4112yes—
171C5×Dic6C22×C4112yes—
172C2×C3×Dic5—46no—
173C2×C3×Dic5C2416yes—
174C2×C3×Dic5C2412yes—
175D3×Dic5—46no—
176D3×Dic5—46no—
177C2×C3×#41C2×D511yescharacteristic
178D3×#41Dic5116yescomplemented
179C2×#239C2×D511yescharacteristic
180C2×D3×Q8C2×D511yescharacteristic
181C2×#237C2×D513yes—
182C2×D3×D4C2×D513yes—
183C2×#235C2×D513yes—
184C22×C4×D3C2×D513yes—
185C3×C4×Q8—52no—
186C3×C4×D4—56no—
187C3×#117—53no—
188C2×C3×C4⋊C4—53no—
189Q8×Dic3—52no—
190D4×Dic3—56no—
191C4×#67—512no—
192C2×(C2×D3)⋊C4—56no—
193#926—53no—
194C2×C4⋊Dic3—53no—
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—
212C24×C5—33no—
213C5×#41—38no—
214C5×#41—324no—
215C5×#41—324no—
216C5×#41C4×D318yescomplemented
217C2×C5×Q8—38no—
218C2×C5×Q8—33no—
219C2×C5×Q8C22×D311yescharacteristic
220C2×C5×D4—36no—
221C2×C5×D4—324no—
222C2×C5×D4—33no—
223C2×C5×D4C22×D313yes—
224C22×C4×C5—33no—
225C22×C4×C5—324no—
226C22×C4×C5—31no—
227C22×C4×C5—33no—
228C22×C4×C5—33no—
229C22×C4×C5—33no—
230C22×C4×C5C22×D313yes—
231C22×Dic5—36no—
232C22×Dic5—36no—
233C22×Dic5—36no—
234C22×Dic5C22×D316yes—
235C22⋊Dic5—36no—
236C22⋊Dic5—36no—
237C22⋊Dic5—32no—
238C22⋊Dic5—312no—
239C22⋊Dic5C22×D316yes—
240C4⋊Dic5—31no—
241C4⋊Dic5—33no—
242C4⋊Dic5—36no—
243C4⋊Dic5—36no—
244C4⋊Dic5—36no—
245C4⋊Dic5C22×D311yescharacteristic
246C4⋊Dic5C22×D313yes—
247C4⋊Dic5C22×D316yes—
248C4×Dic5—36no—
249C4×Dic5—36no—
250C4×Dic5—32no—
251C4×Dic5—312no—
252C4×Dic5C22×D316yes—
253C22×#41—31no—
254#520—51no—
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×C5×D3—23no—
269C2×C5×D3—23no—
270C2×C5×D3—21no—
271C2×C5×D3—21no—
272C2×C5×D3—412no—
273C2×C5×D3C23×C412yes—
274C2×C5×D3C23×C416yes—
275C3×C4×C5C23×C416yes—
276C3×C4×C5C23×C412yes—
277Dic15—22no—
278Dic15—26no—
279C3×Dic5—22no—
280C3×Dic5—26no—
281C5×Dic3C23×C416yes—
282C5×Dic3C23×C412yes—
283C23×D3C22×D513yes—
284C3×#41C2×Dic518yescomplemented
285C2×C3×Q8C22×D511yescharacteristic
286C2×C3×D4C22×D513yes—
287C22×C3×C4—56no—
288C22×C3×C4C22×D513yes—
289C2×#67C22×D516yes—
290C22×Dic3—56no—
291C22×Dic3C22×D513yes—
292#239C2×Dic518yescomplemented
293D3×Q8C2×Dic518yescomplemented
294#237C2×Dic5124yescomplemented
295D3×D4C2×Dic5124yescomplemented
296#235C2×Dic5124yescomplemented
297C2×D12C22×D513yes—
298C2×C4×D3—56no—
299C2×C4×D3—56no—
300C2×C4×D3C2×Dic5124yescomplemented
301C2×C4×D3C22×D513yes—
302C2×C4×D3C22×D513yes—
303C2×C4×D3C22×D513yes—
304C2×C4×D3C22×D511yescharacteristic
305C2×Dic6C22×D513yes—
306C3×C4⋊C4—56no—
307C3×C4⋊C4—51no—
308C3×C4⋊C4—53no—
309C3×C22⋊C4—56no—
310C3×C42—56no—
311#217—56no—
312(C2×D3)⋊C4—52no—
313(C2×D3)⋊C4—56no—
314(C2×D3)⋊C4—512no—
315C4⋊Dic3—56no—
316C4⋊Dic3—51no—
317C4⋊Dic3—53no—
318Dic3⋊C4—56no—
319Dic3⋊C4—56no—
320C4×Dic3—56no—
321C4×Dic3—512no—
322C4×Dic3—52no—
323C4×Dic3—56no—
324C23×C5—31no—
325C23×C5—33no—
326C23×C5—312no—
327C23×C5—123no—
328C23×C5—123no—
329C23×C5C23×D313yes—
330C5×Q8—312no—
331C5×Q8C2×C4×D314yes—
332C5×D4—324no—
333C5×D4—312no—
334C5×D4C2×C4×D3112yes—
335C2×C4×C5—312no—
336C2×C4×C5—31no—
337C2×C4×C5—33no—
338C2×C4×C5—34no—
339C2×C4×C5—312no—
340C2×C4×C5—312no—
341C2×C4×C5—312no—
342C2×C4×C5C2×C4×D3112yes—
343C2×C4×C5C23×D313yes—
344C2×C4×C5C23×D311yescharacteristic
345C2×Dic5—32no—
346C2×Dic5—36no—
347C2×Dic5—46no—
348C2×Dic5—126no—
349C2×Dic5—126no—
350C2×Dic5—126no—
351C2×Dic5C23×D316yes—
352C2×Dic5C23×D312yes—
353C2×#41—316no—
354C2×#41—31no—
355C2×#41—33no—
356C2×#41—33no—
357C2×#41D3×D511yescharacteristic
358C22×Q8—31no—
359C22×D4—33no—
360C23×C4—33no—
361C4×Q8—52no—
362C4×Q8—156no—
363C4×Q8—156no—
364C4×Q8—152no—
365C4×D4—56no—
366C4×D4—156no—
367C4×D4—1512no—
368C4×D4—156no—
369C4×D4—1512no—
370C4×D4—156no—
371#117—53no—
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—53no—
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
392C5×D3—22no—
393C5×D3—26no—
394C23×C3C23×D513yes—
395C22×D3—43no—
396C22×D3—43no—
397C22×D3C22×Dic5112yes—
398C22×D3C23×D511yescharacteristic
399C22×D3C23×D513yes—
400C3×Q8C22×Dic514yes—
401C3×D4C22×Dic5112yes—
402C2×C3×C4—56no—
403C2×C3×C4—52no—
404C2×C3×C4—206no—
405C2×C3×C4C22×Dic5112yes—
406C2×C3×C4C23×D513yes—
407C2×C3×C4C23×D511yescharacteristic
408#67C22×Dic5124yes—
409C2×Dic3—52no—
410C2×Dic3—56no—
411C2×Dic3—206no—
412C2×Dic3C22×Dic5112yes—
413C2×Dic3C23×D511yescharacteristic
414C2×Dic3C23×D513yes—
415D12C22×Dic5112yes—
416C4×D3—206no—
417C4×D3—206no—
418C4×D3C22×Dic514yes—
419C4×D3C22×Dic5112yes—
420C4×D3C22×Dic5112yes—
421C4×D3C22×Dic5112yes—
422Dic6C22×Dic5112yes—
423C22×C5—23no—
424C22×C5—23no—
425C22×C5—32no—
426C22×C5—36no—
427C22×C5—63no—
428C22×C5—61no—
429C22×C5—63no—
430C22×C5—61no—
431C22×C5—1212no—
432C22×C5C22×C4×D316yes—
433C22×C5C24×D311yescharacteristic
434C4×C5—32no—
435C4×C5—36no—
436C4×C5C22×C4×D312yes—
437C4×C5C22×C4×D316yes—
438Dic5—26no—
439Dic5—22no—
440Dic5—62no—
441Dic5—66no—
442C24—33no—
443#41—38no—
444#41—324no—
445#41—324no—
446#41D3×Dic518yescomplemented
447C2×Q8—38no—
448C2×Q8—33no—
449C2×Q8C2×D3×D511yescharacteristic
450C2×D4—36no—
451C2×D4—324no—
452C2×D4—33no—
453C2×D4C2×D3×D513yes—
454C22×C4—33no—
455C22×C4—324no—
456C22×C4—33no—
457C22×C4—33no—
458C22×C4—31no—
459C22×C4—33no—
460C22×C4—56no—
461C22×C4—156no—
462C22×C4—156no—
463C22×C4—156no—
464C22×C4C2×D3×D513yes—
465C4⋊C4—53no—
466C4⋊C4—56no—
467C4⋊C4—51no—
468C4⋊C4—156no—
469C4⋊C4—156no—
470C4⋊C4—151no—
471C4⋊C4—153no—
472C4⋊C4—156no—
473C22⋊C4—56no—
474C22⋊C4—152no—
475C22⋊C4—156no—
476C22⋊C4—1512no—
477C22⋊C4—156no—
478C42—56no—
479C42—152no—
480C42—156no—
481C42—1512no—
482C42—156no—
483C3×C5#342811yescharacteristic, complemented, Hall
484C22×C3—23no—
485C22×C3—23no—
486C22×C3C23×Dic516yes—
487C22×C3C24×D511yescharacteristic
488C2×D3—23no—
489C2×D3—23no—
490C2×D3—21no—
491C2×D3—21no—
492C2×D3—412no—
493C2×D3C23×Dic512yes—
494C2×D3C23×Dic516yes—
495C3×C4—102no—
496C3×C4—106no—
497C3×C4C23×Dic516yes—
498C3×C4C23×Dic512yes—
499Dic3—102no—
500Dic3—106no—
501Dic3C23×Dic516yes—
502Dic3C23×Dic512yes—
503C2×C5—26no—
504C2×C5—62no—
505C2×C5—66no—
506C2×C5C23×C4×D311yescharacteristic
507C2×C5#596611yescharacteristic
508C2×C5#596811yescharacteristic
509C23—31no—
510C23—33no—
511C23—312no—
512C23—123no—
513C23—123no—
514C23C22×D3×D513yes—
515Q8—312no—
516Q8C2×D3×Dic514yes—
517D4—324no—
518D4—312no—
519D4C2×D3×Dic5112yes—
520C2×C4—312no—
521C2×C4—31no—
522C2×C4—33no—
523C2×C4—34no—
524C2×C4—312no—
525C2×C4—312no—
526C2×C4—312no—
527C2×C4—52no—
528C2×C4—56no—
529C2×C4—152no—
530C2×C4—156no—
531C2×C4—206no—
532C2×C4—606no—
533C2×C4—606no—
534C2×C4—606no—
535C2×C4C2×D3×Dic5112yes—
536C2×C4C22×D3×D513yes—
537C2×C4C22×D3×D511yescharacteristic
538C2×C3—26no—
539C2×C3#6628311yescharacteristic
540C2×C3#6628311yescharacteristic
541C2×C3C24×Dic511yescharacteristic
542D3—22no—
543D3—26no—
544C5#8588511yescharacteristic, complemented, Sylow
545C22—23no—
546C22—23no—
547C22—32no—
548C22—36no—
549C22—63no—
550C22—61no—
551C22—63no—
552C22—61no—
553C22—1212no—
554C22C22×D3×Dic516yes—
555C22C23×D3×D511yescharacteristic
556C4—32no—
557C4—36no—
558C4—106no—
559C4—102no—
560C4—302no—
561C4—306no—
562C4C22×D3×Dic512yes—
563C4C22×D3×Dic516yes—
564C3#1061916111yescharacteristic, complemented, Sylow
565C2—26no—
566C2—62no—
567C2—66no—
568C2#1175706111yescharacteristic
569C2#1175706311yescharacteristic
570C2C23×D3×Dic511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×C5×D3×#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. C3×#66161C2semidirect
4. Dic5×#239C2semidirect
5. #11755144C2semidirect
6. #11754914C2semidirect
7. Dic5×#237C2semidirect
8. #11754513C2semidirect
9. #11754492C2semidirect
10. D3×#4072C2semidirect
11. C2×#91338C2semidirect
14. C5×D3×#41C4semidirect
21. Q8×Dic15C22semidirect
22. D4×Dic15C22semidirect
23. #91815C22semidirect
24. C2×C4⋊Dic15C22semidirect
25. C3×Q8×Dic5C22semidirect
26. C3×D4×Dic5C22semidirect
27. C3×#4072C22semidirect
28. C2×C3×C4⋊Dic5C22semidirect
29. #67⋊Dic5C22semidirect
31. Dic5×#67C22semidirect
33. #91529C22semidirect
34. C2×Dic3×Dic5C22semidirect
35. #91435C22semidirect
36. D3×C4⋊Dic5C22semidirect
37. D3×C4⋊Dic5C22semidirect
38. Dic5×D12C22semidirect
39. C4×D3×Dic5C22semidirect
41. #91344C22semidirect
45. #91338C22semidirect
46. #91338C22semidirect
47. Dic5×Dic6C22semidirect
53. #66161D3semidirect
61. C3×C5×#41C2×C4semidirect
68. C5×#239C2×C4semidirect
69. C5×D3×Q8C2×C4semidirect
70. C5×#237C2×C4semidirect
71. C5×D3×D4C2×C4semidirect
72. C5×#235C2×C4semidirect
74. C2×C4×C5×D3C2×C4semidirect
125. Q8×Dic5C2×D3semidirect
131. D4×Dic5C2×D3semidirect
140. #4072C2×D3semidirect
144. C2×C4⋊Dic5C2×D3semidirect
178. D3×#41Dic5semidirect
216. C5×#41C4×D3semidirect
284. C3×#41C2×Dic5semidirect
292. #239C2×Dic5semidirect
293. D3×Q8C2×Dic5semidirect
294. #237C2×Dic5semidirect
295. D3×D4C2×Dic5semidirect
296. #235C2×Dic5semidirect
300. C2×C4×D3C2×Dic5semidirect
446. #41D3×Dic5semidirect
483. C3×C5#3428semidirect
544. C5#85885semidirect
564. C3#10619161semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
#117565862
C3×#661612
Dic5×#2392
#117551442
#117549142
Dic5×#2372
#117545132
#117544922
D3×#40722
C2×#913382
#106191613
#858855