Finite Group Databasebeta

← #14481757

Subgroups — #14481757

Order 1920.

2160 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D15C211yesmaximal, characteristic
2C5×#5500C211yesmaximal, characteristic, complemented
3C3×#65834C211yesmaximal, characteristic, complemented
4#11754620C212yesmaximal, complemented
5#11754461C212yesmaximal
6#11754383C214yesmaximal
7#11754183C214yesmaximal, complemented
8#11753620C214yesmaximal, complemented
9#11753425C214yesmaximal, complemented
10#11753389C214yesmaximal, complemented
11#11753332C214yesmaximal, complemented
12D5×#544—31nomaximal, Hall
13C22×C4×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C2×D15⋊Q8C2214yes—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×#6712C2212yes—
19C4⋊C4×D15C2214yes—
20C4⋊C4×D15C2214yes—
21C5×#926C2212yes—
22C5×#924C2214yes—
23C5×#890C2214yescomplemented
24C5×#888C2214yescomplemented
25C3×#4072C2212yes—
26C3×#4070C2214yes—
27C3×#4036C2214yescomplemented
28C3×#4034C2214yescomplemented
29#91576C2218yes—
30#91561C2214yes—
31#91532C2214yes—
32#91469C2214yescomplemented
33#91468C2214yescomplemented
34#91437C2214yes—
35#91437C2212yes—
36#91437C2212yes—
37#91404C2218yes—
38C4×#1200C2214yes—
39#91390C2214yes—
40#91388C2214yescomplemented
41#91386C2214yes—
42#91383C2214yes—
43#91381C2214yescomplemented
44#91377C2218yes—
45#91347C2212yes—
46#91347C2212yes—
47#91339C2218yescomplemented
48#91336C2218yescomplemented
49#91329C2218yescomplemented
50#91327C2218yescomplemented
51D3×#544—51nomaximal, Hall
52C5×#544—31no—
53#66063—34no—
54D5×C4⋊Q8—34no—
55#66023—34no—
56D5×#125—34no—
57D5×C22⋊Q8—34no—
58#65957—34no—
59D5×#117—32no—
60#65853—32no—
61C2×D5×C4⋊C4—31no—
62#65834D311yescharacteristic, complemented
63C23×D15C2311yescharacteristic
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C2×C4×D15—44no—
69C2×C4×D15Q818yescomplemented
70C2×C4×D15C2314yes—
71C2×C4×D15C2314yes—
72C2×C4×D15C2312yes—
73C2×C4×D15C2312yes—
74C2×C5×Dic6C2314yes—
75C2×C3×Dic10C2314yes—
76C2×#1204C2318yes—
77C2×#1200C2314yes—
78C2×#1200C2314yes—
79D15⋊Q8—48no—
80C3×C5×C4⋊C4C2314yes—
81C4⋊Dic15C2314yes—
82#6712C2318yes—
83C5×#217C2314yes—
84C5×C4⋊Dic3C2312yes—
85C5×C4⋊Dic3C2314yes—
86C5×C4⋊Dic3C2312yes—
87C5×Dic3⋊C4C2318yes—
88C4×C5×Dic3C2314yes—
89C3×C22⋊Dic5C2314yes—
90C3×C4⋊Dic5C2312yes—
91C3×C4⋊Dic5C2314yes—
92C3×C4⋊Dic5C2312yes—
93C3×#683C2318yes—
94C3×C4×Dic5C2314yes—
95Dic3⋊Dic5C2318yes—
96#6669C2314yes—
97#6669C2314yes—
98#6669C2318yes—
99#6668C2318yes—
100#6667C2314yes—
101#6667C2314yes—
102Dic3×Dic5C2314yes—
103Dic3×Dic5C2314yes—
104C3×#544—51no—
105#5729—54no—
106D3×C4⋊Q8—54no—
107#5689—54no—
108D3×#125—54no—
109D3×C22⋊Q8—54no—
110#5623—54no—
111D3×#117—52no—
112#5519—52no—
113C2×D3×C4⋊C4—51no—
114#5500D511yescharacteristic, complemented
115C2×Q8×D5—34no—
116C22×C4×D5—31no—
117C22×C4×D5—32no—
118C5×C4⋊Q8—34no—
119C5×#125—34no—
120C5×C22⋊Q8—34no—
121C5×#117—32no—
122C2×C5×C4⋊C4C2×D311yescharacteristic
123#4092—34no—
124#4090—38no—
125#4072C2×D312yes—
126C2×C4⋊Dic5—31no—
127#4070C2×D314yes—
128C2×#683—32no—
129#4043—34no—
130#4042—38no—
131#4038—32no—
132#4038—32no—
133D5×C4⋊C4—34no—
134D5×C4⋊C4—34no—
135D5×C4⋊C4—32no—
136D5×C4⋊C4—32no—
137D5×C4⋊C4—34no—
138D5×C4⋊C4—38no—
139#4036—34no—
140#4036C2×D314yescomplemented
141#4035—38no—
142#4035—38no—
143#4034—38no—
144#4034—34no—
145#4034C2×D314yescomplemented
146D5×C22⋊C4—34no—
147#4024—38no—
148#4023—34no—
149#4018—34no—
150C42×D5—34no—
151#4016—34no—
152#4015—34no—
153C2×#544—151noSylow
154C23×C3×C5C2411yescharacteristic
155C22×D15—22no—
156C22×D15—22no—
157C22×D15C2×Q814yes—
158C22×D15C2411yescharacteristic
159C22×D15C2411yescharacteristic
160C2×C3×C4×C5—42no—
161C2×C3×C4×C5C2×Q814yescomplemented
162C2×C3×C4×C5C2414yes—
163C2×C3×C4×C5C2412yes—
164C2×Dic15—42no—
165C2×Dic15C2×Q814yescomplemented
166C2×Dic15C2414yes—
167C2×Dic15C2412yes—
168C4×D15—28no—
169C4×D15—44no—
170C4×D15C2×Q818yes—
171C4×D15C2×Q818yescomplemented
172C2×C5×Dic3C2414yes—
173C2×C5×Dic3C2414yes—
174C5×Dic6—44no—
175C2×C3×Dic5C2414yes—
176C2×C3×Dic5C2414yes—
177C3×Dic10—44no—
178#1204—48no—
179#1200—28no—
180#1200—28no—
181C2×D3×Q8—54no—
182C22×C4×D3—51no—
183C22×C4×D3—52no—
184C3×C4⋊Q8—54no—
185C3×#125—54no—
186C3×C22⋊Q8—54no—
187C3×#117—52no—
188C2×C3×C4⋊C4C2×D511yescharacteristic
189#946—54no—
190#944—58no—
191#926C2×D512yes—
192C2×C4⋊Dic3—51no—
193#924C2×D514yes—
194C2×Dic3⋊C4—52no—
195#897—54no—
196#896—58no—
197#892—52no—
198#892—52no—
199D3×C4⋊C4—54no—
200D3×C4⋊C4—54no—
201D3×C4⋊C4—52no—
202D3×C4⋊C4—54no—
203D3×C4⋊C4—52no—
204D3×C4⋊C4—58no—
205#890—54no—
206#890C2×D514yescomplemented
207#889—58no—
208#889—58no—
209#888—58no—
210#888—54no—
211#888C2×D514yescomplemented
212D3×C22⋊C4—54no—
213#878—58no—
214#877—54no—
215#872—54no—
216C42×D3—54no—
217#870—54no—
218#869—54no—
219C23×D5—31no—
220C2×C5×Q8—34no—
221C22×C4×C5C22×D312yes—
222C22×C4×C5C22×D311yescharacteristic
223C22×Dic5—31no—
224C22×Dic5—32no—
225Q8×D5—128no—
226C2×C4×D5—38no—
227C2×C4×D5—32no—
228C2×C4×D5—32no—
229C2×C4×D5—34no—
230C2×C4×D5—34no—
231C2×C4×D5—34no—
232C2×C4×D5—34no—
233C2×C4×D5—124no—
234C2×Dic10—38no—
235C2×Dic10C22×D314yes—
236C5×C4⋊C4—32no—
237C5×C4⋊C4—32no—
238C5×C4⋊C4—34no—
239C5×C4⋊C4—38no—
240C5×C4⋊C4C22×D314yes—
241C5×C22⋊C4—34no—
242C42×C5—34no—
243C22⋊Dic5C22×D314yes—
244#685—34no—
245#685—34no—
246C4⋊Dic5—34no—
247C4⋊Dic5—38no—
248C4⋊Dic5C22×D312yes—
249C4⋊Dic5C22×D312yes—
250C4⋊Dic5C22×D314yes—
251#683—38no—
252#683—38no—
253#683—38no—
254#683—34no—
255#683—34no—
256#683C22×D318yes—
257C4×Dic5—34no—
258C4×Dic5—34no—
259C4×Dic5C22×D314yes—
260#544—31no—
261#544—51no—
262#544—152no—
263#544—154no—
264#544—154no—
265#544—154no—
266C2×C4⋊Q8—154no—
267C2×#125—154no—
268C2×C22⋊Q8—154no—
269C2×#117—152no—
270C22×C4⋊C4—151no—
271C22×C3×C5—21no—
272C22×C3×C5—21no—
273C22×C3×C5C22×Q812yes—
274C22×C3×C5C2511yescharacteristic
275C2×D15—21no—
276C2×D15—21no—
277C2×D15—28no—
278C2×D15C22×Q812yes—
279C2×D15C22×Q812yes—
280C2×D15H(5,𝔽2)12yes—
281C2×D152−1+412yes—
282C3×C4×C5—24no—
283C3×C4×C5C22×Q814yes—
284Dic15—24no—
285Dic15C22×Q814yes—
286C3×Dic5—24no—
287C3×Dic5—24no—
288C5×Dic3—24no—
289C5×Dic3—24no—
290C23×D3—51no—
291C2×C3×Q8—54no—
292C22×C3×C4C22×D512yes—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—51no—
295C22×Dic3—52no—
296D3×Q8—208no—
297C2×C4×D3—58no—
298C2×C4×D3—52no—
299C2×C4×D3—52no—
300C2×C4×D3—54no—
301C2×C4×D3—54no—
302C2×C4×D3—54no—
303C2×C4×D3—54no—
304C2×C4×D3—204no—
305C2×Dic6—58no—
306C2×Dic6C22×D514yes—
307C3×C4⋊C4—58no—
308C3×C4⋊C4—52no—
309C3×C4⋊C4—54no—
310C3×C4⋊C4—52no—
311C3×C4⋊C4C22×D514yes—
312C3×C22⋊C4—54no—
313C3×C42—54no—
314#217C22×D514yes—
315(C2×D3)⋊C4—54no—
316(C2×D3)⋊C4—54no—
317C4⋊Dic3—54no—
318C4⋊Dic3—58no—
319C4⋊Dic3C22×D512yes—
320C4⋊Dic3C22×D512yes—
321C4⋊Dic3C22×D514yes—
322Dic3⋊C4—58no—
323Dic3⋊C4—58no—
324Dic3⋊C4—54no—
325Dic3⋊C4—54no—
326Dic3⋊C4—58no—
327Dic3⋊C4C22×D518yes—
328C4×Dic3—54no—
329C4×Dic3—54no—
330C4×Dic3C22×D514yes—
331C23×C5C23×D311yescharacteristic
332C22×D5—31no—
333C22×D5—34no—
334C22×D5—31no—
335C22×D5—62no—
336C22×D5—62no—
337C5×Q8—124no—
338C2×C4×C5—34no—
339C2×C4×C5—34no—
340C2×C4×C5—42no—
341C2×C4×C5D3×Q814yescomplemented
342C2×C4×C5C23×D314yes—
343C2×C4×C5C23×D312yes—
344C2×Dic5—34no—
345C2×Dic5—32no—
346C2×Dic5—34no—
347C2×Dic5—122no—
348C2×Dic5C23×D314yes—
349C2×Dic5C23×D314yes—
350C4×D5—38no—
351C4×D5—38no—
352C4×D5—68no—
353C4×D5—68no—
354C4×D5—68no—
355C4×D5—124no—
356Dic10—44no—
357Dic10—128no—
358C22×Q8—154no—
359C23×C4—151no—
360C23×C4—152no—
361C4⋊Q8—34no—
362C4⋊Q8—54no—
363C4⋊Q8—154no—
364C4⋊Q8—154no—
365C4⋊Q8—158no—
366C4⋊Q8—158no—
367#125—34no—
368#125—54no—
369#125—154no—
370#125—154no—
371#125—158no—
372#125—158no—
373C22⋊Q8—34no—
374C22⋊Q8—54no—
375C22⋊Q8—158no—
376C22⋊Q8—158no—
377C22⋊Q8—154no—
378C22⋊Q8—154no—
379#117—32no—
380#117—52no—
381#117—154no—
382#117—154no—
383#117—152no—
384#117—152no—
385C2×C4⋊C4—152no—
386C2×C4⋊C4—152no—
387C2×C4⋊C4—154no—
388C2×C4⋊C4—158no—
389C2×C4⋊C4—152no—
390C2×C4⋊C4—151no—
391C2×C4⋊C4—154no—
392C2×C4⋊C4—154no—
393C2×C4⋊C4D3×D511yescharacteristic
394C2×C22⋊C4—154no—
395C2×C42—154no—
396C2×C3×C5—22no—
397C2×C3×C5C23×Q811yescharacteristic
398C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
399C2×C3×C5C2×2−1+411yescharacteristic
400D15—22no—
401D15#54414yescomplemented
402C23×C3C23×D511yescharacteristic
403C22×D3—51no—
404C22×D3—54no—
405C22×D3—51no—
406C22×D3—102no—
407C22×D3—102no—
408C3×Q8—204no—
409C2×C3×C4—42no—
410C2×C3×C4—54no—
411C2×C3×C4—54no—
412C2×C3×C4Q8×D514yescomplemented
413C2×C3×C4C23×D514yes—
414C2×C3×C4C23×D512yes—
415C2×Dic3—54no—
416C2×Dic3—52no—
417C2×Dic3—54no—
418C2×Dic3—202no—
419C2×Dic3C23×D514yes—
420C2×Dic3C23×D514yes—
421C4×D3—58no—
422C4×D3—58no—
423C4×D3—108no—
424C4×D3—108no—
425C4×D3—108no—
426C4×D3—204no—
427Dic6—44no—
428Dic6—208no—
429C22×C5—21no—
430C22×C5—21no—
431C22×C5C2×D3×Q812yes—
432C22×C5C24×D311yescharacteristic
433C2×D5—32no—
434C2×D5—32no—
435C2×D5—32no—
436C2×D5—32no—
437C2×D5—68no—
438C2×D5—61no—
439C2×D5—61no—
440C4×C5—24no—
441C4×C5—64no—
442C4×C5—64no—
443C4×C5C2×D3×Q814yes—
444Dic5—24no—
445Dic5—24no—
446Dic5—34no—
447Dic5—64no—
448C24—151no—
449C2×Q8—34no—
450C2×Q8—54no—
451C2×Q8—158no—
452C2×Q8—608no—
453C22×C4—154no—
454C22×C4—154no—
455C22×C4—151no—
456C22×C4—158no—
457C22×C4—152no—
458C22×C4—152no—
459C22×C4—152no—
460C22×C4—154no—
461C22×C4—154no—
462C22×C4—604no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—32no—
466C4⋊C4—32no—
467C4⋊C4—34no—
468C4⋊C4—38no—
469C4⋊C4—52no—
470C4⋊C4—52no—
471C4⋊C4—54no—
472C4⋊C4—58no—
473C4⋊C4—154no—
474C4⋊C4—154no—
475C4⋊C4—158no—
476C4⋊C4—158no—
477C4⋊C4—158no—
478C4⋊C4—158no—
479C4⋊C4—154no—
480C4⋊C4C2×D3×D514yes—
481C22⋊C4—34no—
482C22⋊C4—54no—
483C22⋊C4—154no—
484C22⋊C4—154no—
485C42—34no—
486C42—54no—
487C42—154no—
488C42—154no—
489C3×C5C2×#54411yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3C2×Q8×D512yes—
493C22×C3C24×D511yescharacteristic
494C2×D3—52no—
495C2×D3—52no—
496C2×D3—52no—
497C2×D3—52no—
498C2×D3—108no—
499C2×D3—101no—
500C2×D3—101no—
501C3×C4—24no—
502C3×C4—104no—
503C3×C4—104no—
504C3×C4C2×Q8×D514yes—
505Dic3—24no—
506Dic3—24no—
507Dic3—54no—
508Dic3—104no—
509C2×C5—22no—
510C2×C5C22×D3×Q811yescharacteristic
511C2×C5D3×H(5,𝔽2)11yescharacteristic
512C2×C5D3×2−1+411yescharacteristic
513D5—34no—
514D5—62no—
515C23—151no—
516C23—154no—
517C23—151no—
518C23—302no—
519C23—302no—
520C23C22×D3×D511yescharacteristic
521Q8—124no—
522Q8—204no—
523Q8—608no—
524C2×C4—34no—
525C2×C4—34no—
526C2×C4—42no—
527C2×C4—54no—
528C2×C4—54no—
529C2×C4—154no—
530C2×C4—152no—
531C2×C4—158no—
532C2×C4—158no—
533C2×C4—154no—
534C2×C4—308no—
535C2×C4—308no—
536C2×C4—308no—
537C2×C4—604no—
538C2×C4—602no—
539C2×C4D15⋊Q814yescomplemented
540C2×C4C22×D3×D514yes—
541C2×C4C22×D3×D512yes—
542C2×C3—22no—
543C2×C3C22×Q8×D511yescharacteristic
544C2×C3D5×H(5,𝔽2)11yescharacteristic
545C2×C3D5×2−1+411yescharacteristic
546D3—54no—
547D3—102no—
548C5D3×#54411yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—152no—
552C22—152no—
553C22—152no—
554C22—152no—
555C22—308no—
556C22—301no—
557C22—301no—
558C22C2×D15⋊Q812yes—
559C22C23×D3×D511yescharacteristic
560C4—24no—
561C4—64no—
562C4—64no—
563C4—104no—
564C4—104no—
565C4—154no—
566C4—304no—
567C4C2×D15⋊Q814yes—
568C3D5×#54411yescharacteristic, complemented, Sylow
569C2—22no—
570C2—154no—
571C2—302no—
572C2C22×D15⋊Q811yescharacteristic
573C2#1175703011yescharacteristic
574C2#1175704711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×C4⋊C4C22
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#544
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C5×#5500C2semidirect
3. C3×#65834C2semidirect
4. #11754620C2semidirect
7. #11754183C2semidirect
8. #11753620C2semidirect
9. #11753425C2semidirect
10. #11753389C2semidirect
11. #11753332C2semidirect
23. C5×#890C22semidirect
24. C5×#888C22semidirect
27. C3×#4036C22semidirect
28. C3×#4034C22semidirect
32. #91469C22semidirect
33. #91468C22semidirect
40. #91388C22semidirect
43. #91381C22semidirect
47. #91339C22semidirect
48. #91336C22semidirect
49. #91329C22semidirect
50. #91327C22semidirect
62. #65834D3semidirect
69. C2×C4×D15Q8semidirect
114. #5500D5semidirect
140. #4036C2×D3semidirect
145. #4034C2×D3semidirect
161. C2×C3×C4×C5C2×Q8semidirect
165. C2×Dic15C2×Q8semidirect
171. C4×D15C2×Q8semidirect
206. #890C2×D5semidirect
211. #888C2×D5semidirect
341. C2×C4×C5D3×Q8semidirect
401. D15#544semidirect
412. C2×C3×C4Q8×D5semidirect
489. C3×C5C2×#544semidirect
539. C2×C4D15⋊Q8semidirect
548. C5D3×#544semidirect
568. C3D5×#544semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C5×#55002
C3×#658342
#117546202
#117544612
#117543832
#117541832
#117536202
#117534252
#117533892
#117533322
D5×#5443
D3×#5445