Finite Group Databasebeta

← #14479074

Subgroups — #14479074

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 580 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
4Q8×#1200C212yesmaximal, complemented
5#11755149C212yesmaximal, complemented
6#11754916C216yesmaximal, complemented
7D4×#1200C216yesmaximal, complemented
8#11754506C213yesmaximal, complemented
9#11754496C213yesmaximal, complemented
10#11754461C213yesmaximal, complemented
11C2×#91437C213yesmaximal, complemented
12D5×#520—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14#41×D15C4116yescomplemented
15C2×#6821C2211yescharacteristic
16C2×Q8×D15C2211yescharacteristic
17C2×#6819C2213yes—
18C2×D4×D15C2213yes—
19C2×#6817C2213yes—
20C22×C4×D15C2213yes—
21C22×#1200C2216yes—
22C5×Q8×Dic3C2212yescomplemented
23C5×D4×Dic3C2216yescomplemented
24C5×#926C2213yescomplemented
25C2×C5×C4⋊Dic3C2213yescomplemented
26C3×Q8×Dic5C2212yescomplemented
27C3×D4×Dic5C2216yescomplemented
28C3×#4072C2213yescomplemented
29C2×C3×C4⋊Dic5C2213yescomplemented
30#91561C2216yes—
31#91556C22112yescomplemented
32#91552C22112yescomplemented
33C2×#6669C2216yescomplemented
34#91532C2216yescomplemented
35#91437C2216yes—
36#91437C2213yes—
37#91437C2211yescharacteristic
38#91437C2216yescomplemented
39#91437C2216yescomplemented
40#91428C2216yescomplemented
41#91418C2216yescomplemented
42C4×#1200C2216yes—
43#91386C2216yescomplemented
44#91347C2213yescomplemented
45#91347C2213yescomplemented
46#91340C2216yescomplemented
47#91333C2216yescomplemented
48D3×#520—51nomaximal, Hall
49C2×D5×#41—31no—
50C5×#520—31no—
51#66161D311yescharacteristic, complemented
52#65908—32no—
53C4×Q8×D5—32no—
54#65880—36no—
55C4×D4×D5—36no—
56#65857—33no—
57D5×#117—33no—
58#65838—33no—
59C2×D5×C4⋊C4—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×D15C2311yescharacteristic
76C2×C4×D15C2313yes—
77C2×C4×D15C2313yes—
78C2×Dic30C2313yes—
79C22×C5×Dic3C2316yes—
80C22×C3×Dic5C2316yes—
81C2×#1200—412no—
82C2×#1200C2312yes—
83C2×#1200C2316yes—
84C2×#1200C23112yes—
85C5×#217C2316yes—
86C5×C4⋊Dic3C2316yes—
87C5×C4⋊Dic3C2313yes—
88C5×C4⋊Dic3C2311yescharacteristic
89C4×C5×Dic3C2316yes—
90C3×C22⋊Dic5C2316yes—
91C3×C4⋊Dic5C2316yes—
92C3×C4⋊Dic5C2313yes—
93C3×C4⋊Dic5C2311yescharacteristic
94C3×C4×Dic5C2316yes—
95#6669C2316yes—
96#6669C23112yes—
97#6669C2312yes—
98#6667C2316yes—
99#6667C2316yes—
100Dic3×Dic5C2316yes—
101Dic3×Dic5C2316yes—
102C2×D3×#41—51no—
103C3×#520—51no—
104#5827D511yescharacteristic, complemented
105#5574—52no—
106C4×D3×Q8—52no—
107#5546—56no—
108C4×D3×D4—56no—
109#5523—53no—
110D3×#117—53no—
111#5504—53no—
112C2×D3×C4⋊C4—53no—
113C2×C5×#41C2×D311yescharacteristic
114D5×#41—316no—
115C2×#713—31no—
116C2×Q8×D5—31no—
117C2×#711—33no—
118C2×D4×D5—33no—
119C2×#709—33no—
120C22×C4×D5—33no—
121C22×C4×D5—36no—
122C4×C5×Q8—32no—
123C4×C5×D4—36no—
124C5×#117—33no—
125C2×C5×C4⋊C4—33no—
126Q8×Dic5C2×D312yescomplemented
127D4×Dic5C2×D316yescomplemented
128C4×C22⋊D5—312no—
129#4072C2×D313yescomplemented
130C2×C4⋊Dic5C2×D313yescomplemented
131C2×#683—36no—
132#4039—36no—
133#4038—33no—
134#4038—33no—
135D5×C4⋊C4—33no—
136D5×C4⋊C4—36no—
137D5×C4⋊C4—36no—
138D5×C4⋊C4—36no—
139D5×C4⋊C4—31no—
140#4033—36no—
141#4027—312no—
142D5×C22⋊C4—36no—
143#4023—36no—
144C4×D20—36no—
145#4018—36no—
146C42×D5—36no—
147C4×Dic10—36no—
148C2×#520—151noSylow
149C23×C3×C5C2413yes—
150C22×D15—26no—
151C22×D15—26no—
152C22×D15C22×C4112yes—
153C22×D15C2413yes—
154C22×D15C2411yescharacteristic
155C3×C5×Q8C22×C414yescomplemented
156C3×C5×D4C22×C4112yescomplemented
157C2×C3×C4×C5C22×C4112yescomplemented
158C2×C3×C4×C5C2413yes—
159C2×C3×C4×C5C2411yescharacteristic
160#1220C22×C4124yescomplemented
161C2×Dic15C22×C4112yescomplemented
162C2×Dic15C2413yes—
163C2×Dic15C2411yescharacteristic
164D60C22×C4112yescomplemented
165C4×D15C22×C414yes—
166C4×D15C22×C4112yes—
167C4×D15C22×C4112yescomplemented
168C4×D15C22×C4112yescomplemented
169Dic30C22×C4112yescomplemented
170C2×C5×Dic3—46no—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2416yes—
173C2×C3×Dic5—46no—
174C2×C3×Dic5C2412yes—
175C2×C3×Dic5C2416yes—
176#1200—212no—
177#1200—24no—
178#1200—412no—
179C2×C3×#41C2×D511yescharacteristic
180D3×#41—516no—
181C2×#239—51no—
182C2×D3×Q8—51no—
183C2×#237—53no—
184C2×D3×D4—53no—
185C2×#235—53no—
186C22×C4×D3—53no—
187C22×C4×D3—56no—
188C3×C4×Q8—52no—
189C3×C4×D4—56no—
190C3×#117—53no—
191C2×C3×C4⋊C4—53no—
192Q8×Dic3C2×D512yescomplemented
193D4×Dic3C2×D516yescomplemented
194C4×#67—512no—
195#926C2×D513yescomplemented
196C2×C4⋊Dic3C2×D513yescomplemented
197C2×Dic3⋊C4—56no—
198#893—56no—
199#892—53no—
200#892—53no—
201D3×C4⋊C4—53no—
202D3×C4⋊C4—56no—
203D3×C4⋊C4—51no—
204D3×C4⋊C4—56no—
205D3×C4⋊C4—56no—
206#887—56no—
207#67⋊C4—512no—
208D3×C22⋊C4—56no—
209#877—56no—
210C4×D12—56no—
211#872—56no—
212C42×D3—56no—
213C4×Dic6—56no—
214C23×D5—33no—
215C5×#41C4×D318yescomplemented
216C2×C5×Q8C22×D311yescharacteristic
217C2×C5×D4C22×D313yes—
218C22×C4×C5—36no—
219C22×C4×C5C22×D313yes—
220C2×C22⋊D5—36no—
221C22×Dic5—33no—
222C22×Dic5C22×D316yes—
223#713—38no—
224Q8×D5—38no—
225#711—324no—
226D4×D5—324no—
227#709—324no—
228C2×D20—33no—
229C2×C4×D5—324no—
230C2×C4×D5—31no—
231C2×C4×D5—33no—
232C2×C4×D5—33no—
233C2×C4×D5—33no—
234C2×C4×D5—36no—
235C2×C4×D5—32no—
236C2×C4×D5—312no—
237C2×C4×D5—1212no—
238C2×Dic10—33no—
239C5×C4⋊C4—33no—
240C5×C4⋊C4—36no—
241C5×C4⋊C4—31no—
242C5×C22⋊C4—36no—
243C42×C5—36no—
244C22⋊Dic5C22×D316yes—
245#685—36no—
246#685—36no—
247C4⋊Dic5C22×D316yes—
248C4⋊Dic5C22×D313yes—
249C4⋊Dic5C22×D311yescharacteristic
250#683—312no—
251#683—32no—
252#683—36no—
253C4×Dic5—36no—
254C4×Dic5—36no—
255C4×Dic5C22×D316yes—
256C22×#41—151no—
257#520—31no—
258#520—51no—
259#520—153no—
260#520—153no—
261#520—156no—
262#520—152no—
263C2×C4×Q8—152no—
264C2×C4×D4—156no—
265C2×#117—153no—
266C22×C4⋊C4—153no—
267C22×C3×C5—23no—
268C22×C3×C5—23no—
269C22×C3×C5C23×C416yes—
270C22×C3×C5C2511yescharacteristic
271C2×D15—23no—
272C2×D15—23no—
273C2×D15—224no—
274C2×D15C23×C416yes—
275C2×D15C23×C412yes—
276C2×D15H(5,𝔽2)12yes—
277C2×D152−1+412yes—
278C3×C4×C5C23×C416yes—
279C3×C4×C5C23×C412yes—
280Dic15C23×C416yes—
281Dic15C23×C412yes—
282C3×Dic5—26no—
283C3×Dic5—22no—
284C5×Dic3—26no—
285C5×Dic3—22no—
286C23×D3—53no—
287C3×#41C4×D518yescomplemented
288C2×C3×Q8C22×D511yescharacteristic
289C2×C3×D4C22×D513yes—
290C22×C3×C4—56no—
291C22×C3×C4C22×D513yes—
292C2×#67—56no—
293C22×Dic3—53no—
294C22×Dic3C22×D516yes—
295#239—58no—
296D3×Q8—58no—
297#237—524no—
298D3×D4—524no—
299#235—524no—
300C2×D12—53no—
301C2×C4×D3—524no—
302C2×C4×D3—53no—
303C2×C4×D3—53no—
304C2×C4×D3—51no—
305C2×C4×D3—53no—
306C2×C4×D3—52no—
307C2×C4×D3—56no—
308C2×C4×D3—512no—
309C2×C4×D3—2012no—
310C2×Dic6—53no—
311C3×C4⋊C4—56no—
312C3×C4⋊C4—53no—
313C3×C4⋊C4—51no—
314C3×C22⋊C4—56no—
315C3×C42—56no—
316#217C22×D516yes—
317(C2×D3)⋊C4—56no—
318(C2×D3)⋊C4—56no—
319C4⋊Dic3C22×D516yes—
320C4⋊Dic3C22×D513yes—
321C4⋊Dic3C22×D511yescharacteristic
322Dic3⋊C4—512no—
323Dic3⋊C4—52no—
324Dic3⋊C4—56no—
325C4×Dic3—56no—
326C4×Dic3—56no—
327C4×Dic3C22×D516yes—
328C23×C5C23×D313yes—
329C22×D5—31no—
330C22×D5—312no—
331C22×D5—33no—
332C22×D5—66no—
333C22×D5—66no—
334C5×Q8C2×C4×D314yescomplemented
335C5×D4C2×C4×D3112yescomplemented
336C2×C4×C5—32no—
337C2×C4×C5—36no—
338C2×C4×C5—126no—
339C2×C4×C5C2×C4×D3112yescomplemented
340C2×C4×C5C23×D313yes—
341C2×C4×C5C23×D311yescharacteristic
342C22⋊D5—324no—
343C2×Dic5—312no—
344C2×Dic5—33no—
345C2×Dic5—31no—
346C2×Dic5—46no—
347C2×Dic5C23×D312yes—
348C2×Dic5C23×D316yes—
349D20—312no—
350C4×D5—34no—
351C4×D5—312no—
352C4×D5—312no—
353C4×D5—312no—
354C4×D5—64no—
355C4×D5—612no—
356C4×D5—1212no—
357Dic10—312no—
358C2×#41—1516no—
359C2×#41—151no—
360C2×#41—153no—
361C2×#41—153no—
362C2×#41D3×D511yescharacteristic
363C22×Q8—151no—
364C22×D4—153no—
365C23×C4—156no—
366C23×C4—153no—
367C4×Q8—32no—
368C4×Q8—52no—
369C4×Q8—156no—
370C4×Q8—156no—
371C4×D4—36no—
372C4×D4—56no—
373C4×D4—156no—
374C4×D4—156no—
375C4×D4—1512no—
376C4×D4—1512no—
377#117—33no—
378#117—53no—
379#117—156no—
380#117—156no—
381#117—153no—
382#117—153no—
383C2×C4⋊C4—33no—
384C2×C4⋊C4—53no—
385C2×C4⋊C4—153no—
386C2×C4⋊C4—156no—
387C2×C4⋊C4—156no—
388C2×C4⋊C4—156no—
389C2×C4⋊C4—151no—
390C2×C4⋊C4—156no—
391C2×C22⋊C4—156no—
392C2×C42—156no—
393C2×C3×C5—26no—
394C2×C3×C5C24×C411yescharacteristic
395C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
396C2×C3×C5C2×2−1+411yescharacteristic
397D15—26no—
398D15#52014yescomplemented
399C23×C3C23×D513yes—
400C22×D3—51no—
401C22×D3—512no—
402C22×D3—53no—
403C22×D3—106no—
404C22×D3—106no—
405C3×Q8C2×C4×D514yescomplemented
406C3×D4C2×C4×D5112yescomplemented
407C2×C3×C4—52no—
408C2×C3×C4—56no—
409C2×C3×C4—206no—
410C2×C3×C4C2×C4×D5112yescomplemented
411C2×C3×C4C23×D513yes—
412C2×C3×C4C23×D511yescharacteristic
413#67—524no—
414C2×Dic3—46no—
415C2×Dic3—512no—
416C2×Dic3—53no—
417C2×Dic3—51no—
418C2×Dic3C23×D512yes—
419C2×Dic3C23×D516yes—
420D12—512no—
421C4×D3—54no—
422C4×D3—512no—
423C4×D3—512no—
424C4×D3—512no—
425C4×D3—104no—
426C4×D3—1012no—
427C4×D3—2012no—
428Dic6—512no—
429C22×C5—23no—
430C22×C5—23no—
431C22×C5C22×C4×D316yes—
432C22×C5C24×D311yescharacteristic
433C2×D5—32no—
434C2×D5—32no—
435C2×D5—32no—
436C2×D5—36no—
437C2×D5—624no—
438C2×D5—63no—
439C2×D5—63no—
440C4×C5—66no—
441C4×C5—62no—
442C4×C5C22×C4×D316yes—
443C4×C5C22×C4×D312yes—
444Dic5—26no—
445Dic5—22no—
446Dic5—36no—
447Dic5—32no—
448C24—153no—
449#41—158no—
450#41—1524no—
451#41—1524no—
452#41#120018yescomplemented
453C2×Q8—158no—
454C2×Q8—153no—
455C2×Q8C2×D3×D511yescharacteristic
456C2×D4—156no—
457C2×D4—1524no—
458C2×D4—153no—
459C2×D4C2×D3×D513yes—
460C22×C4—36no—
461C22×C4—56no—
462C22×C4—152no—
463C22×C4—156no—
464C22×C4—1512no—
465C22×C4—153no—
466C22×C4—1524no—
467C22×C4—153no—
468C22×C4—151no—
469C22×C4—153no—
470C22×C4—153no—
471C22×C4—6012no—
472C22×C4C2×D3×D513yes—
473C4⋊C4—33no—
474C4⋊C4—36no—
475C4⋊C4—31no—
476C4⋊C4—53no—
477C4⋊C4—56no—
478C4⋊C4—51no—
479C4⋊C4—156no—
480C4⋊C4—1512no—
481C4⋊C4—152no—
482C22⋊C4—36no—
483C22⋊C4—56no—
484C22⋊C4—156no—
485C22⋊C4—156no—
486C42—36no—
487C42—56no—
488C42—156no—
489C42—156no—
490C3×C5C2×#52011yescharacteristic, complemented, Hall
491C22×C3—23no—
492C22×C3—23no—
493C22×C3C22×C4×D516yes—
494C22×C3C24×D511yescharacteristic
495C2×D3—52no—
496C2×D3—52no—
497C2×D3—52no—
498C2×D3—56no—
499C2×D3—1024no—
500C2×D3—103no—
501C2×D3—103no—
502C3×C4—106no—
503C3×C4—102no—
504C3×C4C22×C4×D516yes—
505C3×C4C22×C4×D512yes—
506Dic3—26no—
507Dic3—22no—
508Dic3—56no—
509Dic3—52no—
510C2×C5—26no—
511C2×C5C23×C4×D311yescharacteristic
512C2×C5D3×H(5,𝔽2)11yescharacteristic
513C2×C5D3×2−1+411yescharacteristic
514D5—34no—
515D5—66no—
516C23—151no—
517C23—1512no—
518C23—153no—
519C23—306no—
520C23—306no—
521C23C22×D3×D513yes—
522Q8—1512no—
523Q8C2×#120014yescomplemented
524D4—1524no—
525D4—1512no—
526D4C2×#1200112yescomplemented
527C2×C4—32no—
528C2×C4—36no—
529C2×C4—52no—
530C2×C4—56no—
531C2×C4—126no—
532C2×C4—1512no—
533C2×C4—153no—
534C2×C4—151no—
535C2×C4—154no—
536C2×C4—1512no—
537C2×C4—1512no—
538C2×C4—1512no—
539C2×C4—206no—
540C2×C4—3012no—
541C2×C4—304no—
542C2×C4—6012no—
543C2×C4C2×#1200112yescomplemented
544C2×C4C22×D3×D513yes—
545C2×C4C22×D3×D511yescharacteristic
546C2×C3—26no—
547C2×C3C23×C4×D511yescharacteristic
548C2×C3D5×H(5,𝔽2)11yescharacteristic
549C2×C3D5×2−1+411yescharacteristic
550D3—54no—
551D3—106no—
552C5D3×#52011yescharacteristic, complemented, Sylow
553C22—23no—
554C22—23no—
555C22—152no—
556C22—152no—
557C22—152no—
558C22—156no—
559C22—3024no—
560C22—303no—
561C22—303no—
562C22C22×#120016yes—
563C22C23×D3×D511yescharacteristic
564C4—62no—
565C4—66no—
566C4—102no—
567C4—106no—
568C4—152no—
569C4—156no—
570C4C22×#120012yes—
571C4C22×#120016yes—
572C3D5×#52011yescharacteristic, complemented, Sylow
573C2—26no—
574C2—154no—
575C2—306no—
576C2#1175705411yescharacteristic
577C2#1175705711yescharacteristic
578C2C23×#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×C5C2×#520
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. Q8×#1200C2semidirect
5. #11755149C2semidirect
6. #11754916C2semidirect
7. D4×#1200C2semidirect
8. #11754506C2semidirect
9. #11754496C2semidirect
10. #11754461C2semidirect
11. C2×#91437C2semidirect
14. #41×D15C4semidirect
22. C5×Q8×Dic3C22semidirect
23. C5×D4×Dic3C22semidirect
24. C5×#926C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
26. C3×Q8×Dic5C22semidirect
27. C3×D4×Dic5C22semidirect
28. C3×#4072C22semidirect
29. C2×C3×C4⋊Dic5C22semidirect
31. #91556C22semidirect
32. #91552C22semidirect
33. C2×#6669C22semidirect
34. #91532C22semidirect
38. #91437C22semidirect
39. #91437C22semidirect
40. #91428C22semidirect
41. #91418C22semidirect
43. #91386C22semidirect
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
104. #5827D5semidirect
126. Q8×Dic5C2×D3semidirect
127. D4×Dic5C2×D3semidirect
129. #4072C2×D3semidirect
130. C2×C4⋊Dic5C2×D3semidirect
155. C3×C5×Q8C22×C4semidirect
156. C3×C5×D4C22×C4semidirect
157. C2×C3×C4×C5C22×C4semidirect
160. #1220C22×C4semidirect
161. C2×Dic15C22×C4semidirect
164. D60C22×C4semidirect
167. C4×D15C22×C4semidirect
168. C4×D15C22×C4semidirect
169. Dic30C22×C4semidirect
192. Q8×Dic3C2×D5semidirect
193. D4×Dic3C2×D5semidirect
195. #926C2×D5semidirect
196. C2×C4⋊Dic3C2×D5semidirect
215. C5×#41C4×D3semidirect
287. C3×#41C4×D5semidirect
334. C5×Q8C2×C4×D3semidirect
335. C5×D4C2×C4×D3semidirect
339. C2×C4×C5C2×C4×D3semidirect
398. D15#520semidirect
405. C3×Q8C2×C4×D5semidirect
406. C3×D4C2×C4×D5semidirect
410. C2×C3×C4C2×C4×D5semidirect
452. #41#1200semidirect
490. C3×C5C2×#520semidirect
523. Q8C2×#1200semidirect
526. D4C2×#1200semidirect
543. C2×C4C2×#1200semidirect
552. C5D3×#520semidirect
572. C3D5×#520semidirect

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
Q8×#12002
#117551492
#117549162
D4×#12002
#117545062
#117544962
#117544612
C2×#914372
D5×#5203
D3×#5205