Finite Group Databasebeta

← #14479228

Subgroups — #14479228

Order 1920.

3320 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4149C211yesmaximal, characteristic
2#41×Dic15C211yesmaximal, characteristic, complemented
3C5×#5827C211yesmaximal, characteristic, complemented
4#11755217C212yesmaximal, complemented
5Dic3×#713C212yesmaximal, complemented
6#11754910C216yesmaximal, complemented
7D4×D5×Dic3C216yesmaximal, complemented
8#11754499C213yesmaximal, complemented
9#11754488C213yesmaximal, complemented
10#11754444C213yesmaximal, complemented
11C2×#91434C213yesmaximal, complemented
12#10617787—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C3×#4149C4116yescomplemented
15C2×C3×#713C2212yes—
16C2×C3×D4×D5C2216yes—
17C2×C3×#709C2213yes—
18C22×C3×D20C2213yes—
19C22×D5×Dic3C2216yescomplemented
20Q8×Dic15C2211yescharacteristic, complemented
21Q8×Dic15C2211yescharacteristic, complemented
22D4×Dic15C2213yescomplemented
23D4×Dic15C2213yescomplemented
24#91815C2213yescomplemented
25C2×C4×Dic15C2213yescomplemented
26C5×Q8×Dic3C2212yescomplemented
27C5×D4×Dic3C2216yescomplemented
28C5×#926C2213yescomplemented
29C2×C5×C4⋊Dic3C2213yescomplemented
30#91559C2216yescomplemented
31#91559C2216yescomplemented
32Dic3×C22⋊D5C22112yescomplemented
33D5×#217C22112yescomplemented
34C2×#6665C2216yescomplemented
35#91434C2216yescomplemented
36#91434C2216yescomplemented
37#91434C2213yescomplemented
38#91434C2216yescomplemented
39#91434C2213yescomplemented
40Dic3×D20C2216yescomplemented
41Dic3×D20C2216yescomplemented
42D5×C4⋊Dic3C2216yescomplemented
43C4×D5×Dic3C2216yescomplemented
44#91358C2216yescomplemented
45#91357C2216yescomplemented
46#91331C2213yescomplemented
47#91331C2211yescharacteristic, complemented
48Dic3×H(5,𝔽2)—51nomaximal, Hall
49C2×#4149D311yescharacteristic
50C5×#520—31no—
51#41×Dic5—31no—
52#65908—32no—
53C4×#713—32no—
54#65879—36no—
55C4×D4×D5—36no—
56#65856—33no—
57#65855—33no—
58#65838—33no—
59C2×#4039—33no—
60C23×C3×D5C2316yes—
61C3×C5×#41C2×C418yescomplemented
62C2×C3×C5×Q8C2311yescharacteristic
63C2×C3×C5×D4C2313yes—
64C22×C3×C4×C5C2313yes—
65C22×Dic15C2313yes—
66C22×Dic15C2313yes—
67C22×C5×Dic3C2316yes—
68C2×C3×C22⋊D5C2316yes—
69C3×#713C2×C4116yescomplemented
70C3×D4×D5C2×C4148yescomplemented
71C3×#709C2×C4124yescomplemented
72C2×C3×D20C2×C4124yescomplemented
73C2×C3×D20C2316yes—
74C2×C3×D20C2313yes—
75C2×C3×C4×D5C2316yes—
76C2×C3×Dic10C2311yescharacteristic
77C2×D5×Dic3—412no—
78C2×D5×Dic3C2316yes—
79C2×D5×Dic3C23112yes—
80C2×D5×Dic3C2316yes—
81#6719C2316yes—
82C4⋊Dic15C2313yes—
83C4⋊Dic15C2313yes—
84C4×Dic15C2311yescharacteristic
85C4×Dic15C2313yes—
86C4×Dic15C2313yes—
87C4×Dic15C2313yes—
88C5×#217C2316yes—
89C5×C4⋊Dic3C2316yes—
90C5×C4⋊Dic3C2313yes—
91C5×C4⋊Dic3C2311yescharacteristic
92C4×C5×Dic3C2316yes—
93#6668C2316yes—
94#6668C2312yes—
95#6665C2316yes—
96#6665C23112yes—
97#6665C2316yes—
98Dic3×Dic5C2316yes—
99Dic3×Dic5C2312yes—
100C2×C3×H(5,𝔽2)—51no—
101#5827—52no—
102#5827—53no—
103#5827D511yescharacteristic, complemented
104Dic3×#41—51no—
105Dic3×#41—52no—
106Dic3×#41—53no—
107#5798—56no—
108#5798—53no—
109C2×D4×Dic3—56no—
110C2×D4×Dic3—53no—
111C2×C5×#41C2×D311yescharacteristic
112#4149Dic3116yescomplemented
113C2×#713C2×D312yes—
114C2×D4×D5C2×D316yes—
115C2×#709C2×D313yes—
116C22×D20C2×D313yes—
117C22×C4×D5—36no—
118C4×C5×Q8—32no—
119C4×C5×D4—36no—
120C5×#117—33no—
121C2×C5×C4⋊C4—33no—
122Q8×Dic5—31no—
123Q8×Dic5—31no—
124D4×Dic5—33no—
125D4×Dic5—33no—
126C4×C22⋊D5—312no—
127C2×#685—36no—
128#4072—33no—
129C2×C4×Dic5—33no—
130#4039—33no—
131#4039—36no—
132#4039—36no—
133#4039—36no—
134#4039—33no—
135#4038—36no—
136D5×C4⋊C4—36no—
137#4033—33no—
138#4033—31no—
139#4027—36no—
140#4027—36no—
141D5×C22⋊C4—312no—
142C4×D20—36no—
143C4×D20—36no—
144#4018—36no—
145C42×D5—36no—
146C4×H(5,𝔽2)—151noSylow
147C23×C3×C5C2413yes—
148C22×C3×D5—46no—
149C22×C3×D5—46no—
150C22×C3×D5C22×C4124yescomplemented
151C22×C3×D5C2416yes—
152C3×C5×Q8C22×C414yescomplemented
153C3×C5×D4C22×C4112yescomplemented
154C2×C3×C4×C5C22×C4112yescomplemented
155C2×C3×C4×C5C2413yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—26no—
158C2×Dic15—43no—
159C2×Dic15C2413yes—
160C2×Dic15C2411yescharacteristic
161C2×Dic15C2413yes—
162C2×Dic15C2411yescharacteristic
163C2×C5×Dic3—46no—
164C2×C5×Dic3C2412yes—
165C2×C5×Dic3C2416yes—
166C3×C22⋊D5C22×C4124yescomplemented
167C2×C3×Dic5C2412yes—
168C3×D20C22×C4112yescomplemented
169C3×D20C22×C4124yescomplemented
170C3×C4×D5C22×C4124yescomplemented
171C3×Dic10C22×C414yescomplemented
172D5×Dic3—212no—
173D5×Dic3—412no—
174D5×Dic3—46no—
175C3×H(5,𝔽2)—516no—
176C2×C3×#41—52no—
177C2×C3×#41—53no—
178C2×C3×#41C2×D511yescharacteristic
179C22×C3×D4—56no—
180C22×C3×D4—53no—
181C23×Dic3—56no—
182C2×#217—56no—
183C2×#217—512no—
184Q8×Dic3—51no—
185Q8×Dic3—51no—
186Q8×Dic3—51no—
187Q8×Dic3—53no—
188Q8×Dic3C2×D512yescomplemented
189D4×Dic3—53no—
190D4×Dic3—53no—
191D4×Dic3—512no—
192D4×Dic3—56no—
193D4×Dic3—56no—
194D4×Dic3—56no—
195D4×Dic3—53no—
196D4×Dic3—56no—
197D4×Dic3—56no—
198D4×Dic3—53no—
199D4×Dic3—56no—
200D4×Dic3—56no—
201D4×Dic3C2×D516yescomplemented
202#926—53no—
203#926—56no—
204#926—56no—
205#926C2×D513yescomplemented
206C2×C4⋊Dic3—56no—
207C2×C4⋊Dic3C2×D513yescomplemented
208C2×C4×Dic3—53no—
209C2×C4×Dic3—56no—
210C23×D5C22×D316yes—
211C5×#41C2×Dic318yescomplemented
212C2×C5×Q8C22×D311yescharacteristic
213C2×C5×D4C22×D313yes—
214C22×C4×C5—36no—
215C22×C4×C5C22×D313yes—
216C2×C22⋊D5C22×D316yes—
217C22×Dic5—33no—
218C22×Dic5—33no—
219#713C2×Dic3116yescomplemented
220D4×D5C2×Dic3148yescomplemented
221#709C2×Dic3124yescomplemented
222C2×D20C2×Dic3124yescomplemented
223C2×D20C22×D313yes—
224C2×D20C22×D316yes—
225C2×C4×D5—36no—
226C2×C4×D5—312no—
227C2×C4×D5—36no—
228C2×C4×D5—1212no—
229C2×C4×D5C22×D316yes—
230C2×Dic10C22×D311yescharacteristic
231C5×C4⋊C4—33no—
232C5×C4⋊C4—36no—
233C5×C4⋊C4—31no—
234C5×C22⋊C4—36no—
235C42×C5—36no—
236C22⋊Dic5—36no—
237#685—36no—
238#685—36no—
239#685—312no—
240C4⋊Dic5—33no—
241C4⋊Dic5—33no—
242#683—32no—
243#683—36no—
244C4×Dic5—33no—
245C4×Dic5—33no—
246C4×Dic5—31no—
247C4×Dic5—33no—
248C4×Dic5—32no—
249C4×Dic5—36no—
250C2×H(5,𝔽2)—51no—
251#520—31no—
252#520—153no—
253#520—152no—
254#518—153no—
255#518—156no—
256C4×#41—153no—
257C4×#41—152no—
258C4×#41—151no—
259C2×C4×D4—153no—
260C2×C4×D4—156no—
261C22×C3×C5—23no—
262C22×C3×C5—23no—
263C22×C3×C5C23×C416yes—
264C22×C3×C5C2511yescharacteristic
265C2×C3×D5—26no—
266C2×C3×D5—26no—
267C2×C3×D5—424no—
268C2×C3×D5C23×C4112yes—
269C3×C4×C5C23×C412yes—
270C3×C4×C5C23×C416yes—
271Dic15—23no—
272Dic15—23no—
273Dic15—21no—
274Dic15H(5,𝔽2)12yescomplemented
275C3×Dic5C23×C414yes—
276C5×Dic3—26no—
277C5×Dic3—22no—
278C24×C3—56no—
279C3×#41—516no—
280C3×#41—524no—
281C3×#41C4×D518yescomplemented
282C2×C3×Q8—51no—
283C2×C3×Q8C22×D511yescharacteristic
284C2×C3×D4—56no—
285C2×C3×D4—548no—
286C2×C3×D4—524no—
287C2×C3×D4—53no—
288C2×C3×D4—56no—
289C2×C3×D4C22×D513yes—
290C22×C3×C4—56no—
291C22×C3×C4C22×D513yes—
292C22×Dic3—53no—
293C22×Dic3—53no—
294C22×Dic3—56no—
295C22×Dic3—56no—
296C22×Dic3—512no—
297C22×Dic3—2012no—
298C22×Dic3C22×D516yes—
299#217—56no—
300#217—512no—
301#217—56no—
302#217—56no—
303#217C22×D516yes—
304C4⋊Dic3—53no—
305C4⋊Dic3—53no—
306C4⋊Dic3—56no—
307C4⋊Dic3—52no—
308C4⋊Dic3C22×D516yes—
309C4⋊Dic3C22×D513yes—
310C4⋊Dic3C22×D511yescharacteristic
311C4×Dic3—51no—
312C4×Dic3—53no—
313C4×Dic3—53no—
314C4×Dic3—53no—
315C4×Dic3—52no—
316C4×Dic3—56no—
317C4×Dic3C22×D516yes—
318C23×C5C23×D313yes—
319C22×D5—46no—
320C22×D5—46no—
321C22×D5C22×Dic3124yescomplemented
322C22×D5C23×D316yes—
323C5×Q8C22×Dic314yescomplemented
324C5×D4C22×Dic3112yescomplemented
325C2×C4×C5—32no—
326C2×C4×C5—36no—
327C2×C4×C5—126no—
328C2×C4×C5C22×Dic3112yescomplemented
329C2×C4×C5C23×D311yescharacteristic
330C2×C4×C5C23×D313yes—
331C22⋊D5C22×Dic3124yescomplemented
332C2×Dic5—31no—
333C2×Dic5—31no—
334C2×Dic5—33no—
335C2×Dic5—33no—
336C2×Dic5—66no—
337C2×Dic5—123no—
338C2×Dic5C23×D312yes—
339D20C22×Dic3112yescomplemented
340D20C22×Dic3124yescomplemented
341C4×D5—612no—
342C4×D5—126no—
343C4×D5—1212no—
344C4×D5C22×Dic3124yescomplemented
345Dic10C22×Dic314yescomplemented
346H(5,𝔽2)—516no—
347C2×#41—52no—
348C2×#41—53no—
349C2×#41D3×D511yescharacteristic
350C22×D4—56no—
351C22×D4—53no—
352C23×C4—156no—
353C4×Q8—32no—
354C4×Q8—151no—
355C4×Q8—153no—
356C4×Q8—151no—
357C4×Q8—151no—
358C4×D4—36no—
359C4×D4—156no—
360C4×D4—156no—
361C4×D4—156no—
362C4×D4—156no—
363C4×D4—153no—
364C4×D4—156no—
365C4×D4—156no—
366C4×D4—156no—
367C4×D4—153no—
368C4×D4—1512no—
369C4×D4—153no—
370C4×D4—153no—
371#117—33no—
372#117—156no—
373#117—156no—
374#117—153no—
375C2×C4⋊C4—33no—
376C2×C4⋊C4—156no—
377C2×C22⋊C4—1512no—
378C2×C22⋊C4—156no—
379C2×C42—156no—
380C2×C42—153no—
381C2×C3×C5—26no—
382C2×C3×C5C24×C411yescharacteristic
383C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
384C2×C3×C5#58511yescharacteristic
385C3×D5—212no—
386C23×C3—56no—
387C23×C3—524no—
388C23×C3—206no—
389C23×C3—206no—
390C23×C3C23×D513yes—
391C3×Q8—54no—
392C3×Q8C2×C4×D514yescomplemented
393C3×D4—524no—
394C3×D4—524no—
395C3×D4—512no—
396C3×D4C2×C4×D5112yescomplemented
397C2×C3×C4—52no—
398C2×C3×C4—524no—
399C2×C3×C4C2×C4×D5112yescomplemented
400C2×C3×C4C23×D511yescharacteristic
401C2×C3×C4C23×D513yes—
402C2×Dic3—46no—
403C2×Dic3—51no—
404C2×Dic3—53no—
405C2×Dic3—51no—
406C2×Dic3—53no—
407C2×Dic3—1012no—
408C2×Dic3—106no—
409C2×Dic3—206no—
410C2×Dic3—2012no—
411C2×Dic3—203no—
412C2×Dic3C23×D512yes—
413C2×Dic3C23×D516yes—
414C22×C5—23no—
415C22×C5—23no—
416C22×C5C23×Dic316yes—
417C22×C5C24×D311yescharacteristic
418C2×D5—26no—
419C2×D5—26no—
420C2×D5—424no—
421C2×D5C23×Dic3112yes—
422C4×C5—66no—
423C4×C5—62no—
424C4×C5C23×Dic312yes—
425C4×C5C23×Dic316yes—
426Dic5—32no—
427Dic5—63no—
428Dic5—63no—
429Dic5—61no—
430Dic5C23×Dic314yes—
431C24—56no—
432#41—516no—
433#41—524no—
434#41D5×Dic318yescomplemented
435C2×Q8—51no—
436C2×Q8C2×D3×D511yescharacteristic
437C2×D4—56no—
438C2×D4—548no—
439C2×D4—524no—
440C2×D4—56no—
441C2×D4—53no—
442C2×D4C2×D3×D513yes—
443C22×C4—36no—
444C22×C4—56no—
445C22×C4—156no—
446C22×C4—156no—
447C22×C4—1512no—
448C22×C4—153no—
449C22×C4—153no—
450C22×C4—6012no—
451C22×C4C2×D3×D513yes—
452C4⋊C4—33no—
453C4⋊C4—36no—
454C4⋊C4—31no—
455C4⋊C4—156no—
456C4⋊C4—152no—
457C4⋊C4—153no—
458C4⋊C4—153no—
459C22⋊C4—36no—
460C22⋊C4—156no—
461C22⋊C4—1512no—
462C22⋊C4—156no—
463C22⋊C4—156no—
464C42—36no—
465C42—152no—
466C42—156no—
467C42—153no—
468C42—151no—
469C42—153no—
470C42—153no—
471C3×C5C4×H(5,𝔽2)11yescharacteristic, complemented, Hall
472C22×C3—23no—
473C22×C3—23no—
474C22×C3—512no—
475C22×C3—106no—
476C22×C3—106no—
477C22×C3—2024no—
478C22×C3C22×C4×D516yes—
479C22×C3C24×D511yescharacteristic
480C3×C4—54no—
481C3×C4C22×C4×D516yes—
482C3×C4C22×C4×D512yes—
483Dic3—26no—
484Dic3—22no—
485Dic3—52no—
486Dic3—103no—
487Dic3—103no—
488Dic3—101no—
489C2×C5—26no—
490C2×C5D3×H(5,𝔽2)11yescharacteristic
491C2×C5#596611yescharacteristic
492C2×C5C24×Dic311yescharacteristic
493D5—212no—
494C23—56no—
495C23—524no—
496C23—206no—
497C23—206no—
498C23C22×D3×D513yes—
499Q8—54no—
500Q8C2×D5×Dic314yescomplemented
501D4—524no—
502D4—524no—
503D4—512no—
504D4C2×D5×Dic3112yescomplemented
505C2×C4—32no—
506C2×C4—36no—
507C2×C4—52no—
508C2×C4—524no—
509C2×C4—126no—
510C2×C4—151no—
511C2×C4—153no—
512C2×C4—151no—
513C2×C4—153no—
514C2×C4—3012no—
515C2×C4—306no—
516C2×C4—6012no—
517C2×C4—606no—
518C2×C4—603no—
519C2×C4C2×D5×Dic3112yescomplemented
520C2×C4C22×D3×D513yes—
521C2×C4C22×D3×D511yescharacteristic
522C2×C3—26no—
523C2×C3—1012no—
524C2×C3C23×C4×D511yescharacteristic
525C2×C3D5×H(5,𝔽2)11yescharacteristic
526C2×C3#6628711yescharacteristic
527C5Dic3×H(5,𝔽2)11yescharacteristic, complemented, Sylow
528C22—23no—
529C22—23no—
530C22—512no—
531C22—106no—
532C22—106no—
533C22—2024no—
534C22C22×D5×Dic316yes—
535C22C23×D3×D511yescharacteristic
536C4—54no—
537C4—62no—
538C4—66no—
539C4—152no—
540C4—303no—
541C4—301no—
542C4—303no—
543C4C22×D5×Dic316yes—
544C4C22×D5×Dic312yes—
545C3#1061778711yescharacteristic, complemented, Sylow
546C2—26no—
547C2—1012no—
548C2#1175705411yescharacteristic
549C2#1175706211yescharacteristic
550C2C23×D5×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutatorC2×C3×C5C24×C4
FittingC2×C3×C5×#41C22
socle, cosocleC22×C3×C5C25
prime radicalC2×C3×#4149C2
hypercenterC2×#41D3×D5
hypocenterC3×C5C4×H(5,𝔽2)
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. #41×Dic15C2semidirect
3. C5×#5827C2semidirect
4. #11755217C2semidirect
5. Dic3×#713C2semidirect
6. #11754910C2semidirect
7. D4×D5×Dic3C2semidirect
8. #11754499C2semidirect
9. #11754488C2semidirect
10. #11754444C2semidirect
11. C2×#91434C2semidirect
14. C3×#4149C4semidirect
19. C22×D5×Dic3C22semidirect
20. Q8×Dic15C22semidirect
21. Q8×Dic15C22semidirect
22. D4×Dic15C22semidirect
23. D4×Dic15C22semidirect
24. #91815C22semidirect
25. C2×C4×Dic15C22semidirect
26. C5×Q8×Dic3C22semidirect
27. C5×D4×Dic3C22semidirect
28. C5×#926C22semidirect
29. C2×C5×C4⋊Dic3C22semidirect
30. #91559C22semidirect
31. #91559C22semidirect
32. Dic3×C22⋊D5C22semidirect
33. D5×#217C22semidirect
34. C2×#6665C22semidirect
35. #91434C22semidirect
36. #91434C22semidirect
37. #91434C22semidirect
38. #91434C22semidirect
39. #91434C22semidirect
40. Dic3×D20C22semidirect
41. Dic3×D20C22semidirect
42. D5×C4⋊Dic3C22semidirect
43. C4×D5×Dic3C22semidirect
44. #91358C22semidirect
45. #91357C22semidirect
46. #91331C22semidirect
47. #91331C22semidirect
61. C3×C5×#41C2×C4semidirect
69. C3×#713C2×C4semidirect
70. C3×D4×D5C2×C4semidirect
71. C3×#709C2×C4semidirect
72. C2×C3×D20C2×C4semidirect
103. #5827D5semidirect
112. #4149Dic3semidirect
150. C22×C3×D5C22×C4semidirect
152. C3×C5×Q8C22×C4semidirect
153. C3×C5×D4C22×C4semidirect
154. C2×C3×C4×C5C22×C4semidirect
166. C3×C22⋊D5C22×C4semidirect
168. C3×D20C22×C4semidirect
169. C3×D20C22×C4semidirect
170. C3×C4×D5C22×C4semidirect
171. C3×Dic10C22×C4semidirect
188. Q8×Dic3C2×D5semidirect
201. D4×Dic3C2×D5semidirect
205. #926C2×D5semidirect
207. C2×C4⋊Dic3C2×D5semidirect
211. C5×#41C2×Dic3semidirect
219. #713C2×Dic3semidirect
220. D4×D5C2×Dic3semidirect
221. #709C2×Dic3semidirect
222. C2×D20C2×Dic3semidirect
274. Dic15H(5,𝔽2)semidirect
281. C3×#41C4×D5semidirect
321. C22×D5C22×Dic3semidirect
323. C5×Q8C22×Dic3semidirect
324. C5×D4C22×Dic3semidirect
328. C2×C4×C5C22×Dic3semidirect
331. C22⋊D5C22×Dic3semidirect
339. D20C22×Dic3semidirect
340. D20C22×Dic3semidirect
344. C4×D5C22×Dic3semidirect
345. Dic10C22×Dic3semidirect
392. C3×Q8C2×C4×D5semidirect
396. C3×D4C2×C4×D5semidirect
399. C2×C3×C4C2×C4×D5semidirect
434. #41D5×Dic3semidirect
471. C3×C5C4×H(5,𝔽2)semidirect
500. Q8C2×D5×Dic3semidirect
504. D4C2×D5×Dic3semidirect
519. C2×C4C2×D5×Dic3semidirect
527. C5Dic3×H(5,𝔽2)semidirect
545. C3#10617787semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41492
#41×Dic152
C5×#58272
#117552172
Dic3×#7132
#117549102
D4×D5×Dic32
#117544992
#117544882
#117544442
C2×#914342
#106177873
Dic3×H(5,𝔽2)5