Finite Group Databasebeta

← #14322444

Subgroups — #14322444

Order 1920.

2208 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D20C211yesmaximal, characteristic
2C2×C5×#872C211yesmaximal, characteristic, complemented
3C2×#91338C211yesmaximal, characteristic, complemented
4#11751040C211yesmaximal, characteristic, complemented
5C3×#65228C211yesmaximal, characteristic, complemented
6#11748940C214yesmaximal, complemented
7#11748913C214yesmaximal, complemented
8#11748789C211yesmaximal, characteristic, complemented
9#11748785C211yesmaximal, characteristic, complemented
10#10614000—31nomaximal, Hall
11C23×D3×D5C2212yes—
12C22×D60C2211yescharacteristic
13C22×C4×C5×D3C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×#1202C2212yes—
16C2×D3×D20—24no—
17C2×D3×D20—24no—
18C2×D3×D20C418yescomplemented
19C2×C3×C42×C5C2211yescharacteristic, complemented
20C2×#6714C2214yescomplemented
21C2×C4⋊Dic15C2211yescharacteristic, complemented
22C2×C5×(C2×D3)⋊C4C2212yes—
23C2×C5×Dic3⋊C4C2212yescomplemented
24C2×C4×C5×Dic3C2211yescharacteristic, complemented
25C5×#872—24no—
26C2×C3×#685C2214yescomplemented
27C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
28C2×#6667C2214yescomplemented
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×#6665C2214yescomplemented
31C2×Dic3×Dic5C2212yescomplemented
32#91338—24no—
33#76428—51nomaximal, Hall
34C23×D20—31no—
35C2×C5×#117—31no—
36C2×#4072—31no—
37#65277—34no—
38#65244—34no—
39#65228—31no—
40#65228—31no—
41#65228—31no—
42#65228D311yescharacteristic, complemented
43C23×D15C2312yes—
44C23×C5×D3C2311yescharacteristic
45C23×C3×D5C2312yes—
46C22×D3×D5—24no—
47C22×D3×D5—24no—
48C22×D3×D5—44no—
49C22×D3×D5—44no—
50C22×D3×D5C2×C418yes—
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C2×D60—22no—
55C2×D60—22no—
56C2×D60C2×C414yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2311yescharacteristic
59C2×C4×C5×D3C2×C414yes—
60C2×C4×C5×D3D414yes—
61C2×C4×C5×D3D414yes—
62C22×C3×Dic5C2312yes—
63C2×C3×D20—22no—
64C2×C3×D20—22no—
65C2×C3×D20C2×C414yes—
66C2×#1202—24no—
67C2×#1202—24no—
68C2×#1202C2×C418yes—
69D3×D20—232no—
70C3×C42×C5—22no—
71#6714—44no—
72C4⋊Dic15—22no—
73C5×(C2×D3)⋊C4—24no—
74C5×Dic3⋊C4—24no—
75C4×C5×Dic3—22no—
76C3×#685—44no—
77C3×C4⋊Dic5—22no—
78#6667—44no—
79(C2×D3)⋊Dic5—24no—
80#6665—44no—
81Dic3×Dic5—24no—
82C22×D3×D4—51no—
83C2×#892—51no—
84C2×#872D511yescharacteristic, complemented
85C3×#390—51no—
86#5221—51no—
87#4988—51no—
88#4957—54no—
89#4955—54no—
90#4939—51no—
91C24×D5—32no—
92C23×C4×C5—31no—
93C22×D20—32no—
94C22×D20—31no—
95C22×D20—38no—
96C22×D20—64no—
97C22×D20—64no—
98C22×D20C2×D311yescharacteristic
99C5×#117—64no—
100C2×C5×C4⋊C4—32no—
101C2×C5×C22⋊C4—32no—
102C2×C42×C5—31no—
103C2×C42×C5C2×D311yescharacteristic, complemented
104C2×C22⋊Dic5—32no—
105C2×#685—34no—
106C2×#685—34no—
107C2×#685—34no—
108C2×#685C2×D314yescomplemented
109#4072—64no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5C2×D311yescharacteristic, complemented
112C2×C4×Dic5—32no—
113#2309—151noSylow
114C23×C3×C5C2411yescharacteristic
115C22×D15—22no—
116C22×D15—22no—
117C22×D15—24no—
118C22×D15—24no—
119C22×D15C22×C414yes—
120C22×C5×D3—22no—
121C22×C5×D3—22no—
122C22×C5×D3C22×C412yes—
123C22×C5×D3C2×D412yes—
124C22×C5×D3C2×D412yes—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—24no—
128C22×C3×D5—24no—
129C22×C3×D5C22×C414yes—
130C2×D3×D5—216no—
131C2×D3×D5—416no—
132C2×D3×D5—48no—
133C2×D3×D5—48no—
134C2×D3×D5—416no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×Dic15—22no—
142C2×Dic15—24no—
143D60—28no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3C2×D412yes—
149C2×C5×Dic3C2×D412yes—
150C4×C5×D3C22⋊C4116yescomplemented
151C2×C3×Dic5—22no—
152C2×C3×Dic5—24no—
153C3×D20—28no—
154#1202—216no—
155C24×D3—52no—
156C22×C3×D4—51no—
157C22×#67—52no—
158C2×D3×D4—58no—
159C2×D3×D4—104no—
160C2×D3×D4—104no—
161C22×D12—51no—
162C22×C4×D3C2×D511yescharacteristic
163C2×C3×C4⋊C4—51no—
164C2×C3×C22⋊C4—54no—
165C2×C3×C42C2×D511yescharacteristic, complemented
166C2×#217—54no—
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—54no—
169C2×(C2×D3)⋊C4—54no—
170C2×(C2×D3)⋊C4C2×D512yes—
171C2×C4⋊Dic3—51no—
172C2×Dic3⋊C4C2×D512yescomplemented
173C2×C4×Dic3—52no—
174C2×C4×Dic3C2×D511yescharacteristic, complemented
175#892—104no—
176#872—24no—
177C24×C5—31no—
178C23×D5—32no—
179C23×D5—38no—
180C23×D5—64no—
181C23×D5—64no—
182C23×D5—124no—
183C23×D5—124no—
184C23×D5C22×D312yes—
185C22×C4×C5—31no—
186C22×C4×C5—34no—
187C22×C4×C5—34no—
188C22×C4×C5—34no—
189C22×C4×C5—32no—
190C22×C4×C5C22×D312yes—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—32no—
193C22×Dic5C22×D312yes—
194C2×D20—22no—
195C2×D20—22no—
196C2×D20—38no—
197C2×D20—34no—
198C2×D20—632no—
199C2×D20—64no—
200C2×D20—64no—
201C2×D20—62no—
202C2×D20—62no—
203C2×D20C4×D314yes—
204C5×C4⋊C4—64no—
205C5×C22⋊C4—64no—
206C42×C5—22no—
207C42×C5—62no—
208C22⋊Dic5—64no—
209#685—44no—
210#685—124no—
211#685—124no—
212#685—124no—
213C4⋊Dic5—22no—
214C4⋊Dic5—62no—
215C4×Dic5—64no—
216C23×D4—151no—
217C2×#117—31no—
218C2×#117—151no—
219#390—51no—
220#390—151no—
221#390—151no—
222#390—154no—
223#390—151no—
224#379—154no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C22×D411yescharacteristic
227C22×C3×C5C22×D411yescharacteristic
228C22×C3×C5H(5,𝔽2)12yes—
229C22×C3×C5H(5,𝔽2)12yes—
230C2×D15—24no—
231C2×D15—28no—
232C2×D15—42no—
233C2×D15—42no—
234C2×D15—44no—
235C2×C5×D3—24no—
236C2×C5×D3—22no—
237C2×C5×D3—22no—
238C2×C5×D3—24no—
239C2×C5×D3C2×C22⋊C414yes—
240C2×C3×D5—24no—
241C2×C3×D5—28no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—44no—
245D3×D5—432no—
246C3×C4×C5—42no—
247C3×C4×C5C2×C22⋊C414yes—
248Dic15—42no—
249C3×Dic5—42no—
250C5×Dic3—42no—
251C5×Dic3C2×C22⋊C414yes—
252C24×C3—52no—
253C23×D3—52no—
254C23×D3—58no—
255C23×D3—104no—
256C23×D3—104no—
257C23×D3—204no—
258C23×D3—204no—
259C23×D3C22×D511yescharacteristic
260C2×C3×D4—54no—
261C2×C3×D4—102no—
262C2×C3×D4—102no—
263C22×C3×C4—52no—
264C22×C3×C4C22×D512yes—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—58no—
267C2×#67—104no—
268C2×#67—104no—
269C22×Dic3—52no—
270C22×Dic3C22×D512yes—
271C22×Dic3C22×D511yescharacteristic
272D3×D4—1032no—
273C2×D12—54no—
274C2×D12—102no—
275C2×D12—102no—
276C2×C4×D3C4×D514yes—
277C2×C4×D3D2014yes—
278C2×C4×D3C22⋊D514yes—
279C3×C4⋊C4—102no—
280C3×C22⋊C4—204no—
281C3×C42—22no—
282#217—204no—
283(C2×D3)⋊C4—24no—
284(C2×D3)⋊C4—104no—
285(C2×D3)⋊C4—204no—
286(C2×D3)⋊C4—204no—
287C4⋊Dic3—102no—
288Dic3⋊C4—24no—
289C4×Dic3—22no—
290C4×Dic3—104no—
291C23×C5—32no—
292C23×C5—32no—
293C23×C5—32no—
294C23×C5—62no—
295C23×C5—62no—
296C23×C5C23×D311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—24no—
300C22×D5—24no—
301C22×D5—34no—
302C22×D5—616no—
303C22×D5—62no—
304C22×D5—62no—
305C22×D5—64no—
306C22×D5—64no—
307C22×D5—1216no—
308C22×D5—128no—
309C22×D5—128no—
310C22×D5—1216no—
311C22×D5C2×C4×D314yes—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—32no—
316C2×C4×C5—32no—
317C2×C4×C5—32no—
318C2×C4×C5—316no—
319C2×C4×C5—62no—
320C2×C4×C5—62no—
321C2×C4×C5—62no—
322C2×C4×C5C2×C4×D312yes—
323C2×C4×C5D3×D412yes—
324C2×C4×C5D3×D412yes—
325C2×Dic5—22no—
326C2×Dic5—24no—
327C2×Dic5—62no—
328C2×Dic5—64no—
329D20—28no—
330D20—616no—
331D20—68no—
332C25—152no—
333C22×D4—51no—
334C22×D4—158no—
335C22×D4—152no—
336C22×D4—151no—
337C22×D4—304no—
338C22×D4—304no—
339C23×C4—31no—
340#117—64no—
341#117—304no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—151no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—54no—
347C2×C22⋊C4—152no—
348C2×C22⋊C4—154no—
349C2×C22⋊C4—154no—
350C2×C22⋊C4—154no—
351C2×C42—31no—
352C2×C42—152no—
353C2×C42D3×D511yescharacteristic, complemented
354C2×C3×C5C22×C22⋊C411yescharacteristic
355C2×C3×C5#51812yes—
356C2×C3×C5#53511yescharacteristic
357C2×C3×C5#53511yescharacteristic
358C2×C3×C5#53512yes—
359D15—44no—
360C3×D5—44no—
361C5×D3—24no—
362C23×C3—54no—
363C23×C3—102no—
364C23×C3—104no—
365C23×C3—104no—
366C23×C3—102no—
367C23×C3C23×D511yescharacteristic
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—54no—
371C22×D3—102no—
372C22×D3—104no—
373C22×D3—104no—
374C22×D3—102no—
375C22×D3—1016no—
376C22×D3—2016no—
377C22×D3—208no—
378C22×D3—208no—
379C22×D3—2016no—
380C22×D3C2×C4×D512yes—
381C22×D3C2×D2012yes—
382C22×D3C2×C22⋊D512yes—
383C3×D4—108no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—102no—
388C2×C3×C4—104no—
389C2×C3×C4C2×C4×D512yes—
390C2×C3×C4C2×D2012yes—
391C2×C3×C4C2×C22⋊D512yes—
392#67—1016no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—102no—
397C2×Dic3—104no—
398C2×Dic3C2×C4×D512yes—
399C2×Dic3C2×D2012yes—
400C2×Dic3C2×C22⋊D512yes—
401D12—108no—
402C4×D3#685116yescomplemented
403C22×C5—34no—
404C22×C5—62no—
405C22×C5—62no—
406C22×C5—64no—
407C22×C5—64no—
408C22×C5C22×C4×D311yescharacteristic
409C22×C5C2×D3×D411yescharacteristic
410C22×C5C2×D3×D411yescharacteristic
411C22×C5#100412yes—
412C22×C5#100912yes—
413C2×D5—24no—
414C2×D5—28no—
415C2×D5—42no—
416C2×D5—42no—
417C2×D5—44no—
418C2×D5—64no—
419C2×D5—68no—
420C2×D5—1232no—
421C2×D5—122no—
422C2×D5—122no—
423C2×D5—124no—
424C4×C5—34no—
425C4×C5—42no—
426C4×C5—122no—
427C4×C5D3×C22⋊C414yes—
428Dic5—42no—
429Dic5—122no—
430C24—31no—
431C24—52no—
432C24—158no—
433C24—152no—
434C24—304no—
435C24—304no—
436C24—604no—
437C24—604no—
438C2×D4—54no—
439C2×D4—102no—
440C2×D4—102no—
441C2×D4—158no—
442C2×D4—154no—
443C2×D4—3032no—
444C2×D4—304no—
445C2×D4—304no—
446C2×D4—302no—
447C2×D4—302no—
448C22×C4—31no—
449C22×C4—34no—
450C22×C4—34no—
451C22×C4—34no—
452C22×C4—32no—
453C22×C4—52no—
454C22×C4—152no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—64no—
458C4⋊C4—102no—
459C4⋊C4—302no—
460C22⋊C4—64no—
461C22⋊C4—204no—
462C22⋊C4—304no—
463C22⋊C4—604no—
464C22⋊C4—604no—
465C22⋊C4—604no—
466C42—22no—
467C42—62no—
468C42—304no—
469C3×C5#230911yescharacteristic, complemented, Hall
470C22×C3—108no—
471C22×C3—104no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—204no—
475C22×C3C22×C4×D511yescharacteristic
476C22×C3C22×D2011yescharacteristic
477C22×C3#414912yes—
478C22×C3#414912yes—
479C22×C3C22×C22⋊D511yescharacteristic
480C2×D3—24no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—24no—
484C2×D3—108no—
485C2×D3—104no—
486C2×D3—2032no—
487C2×D3—202no—
488C2×D3—202no—
489C2×D3—204no—
490C2×D3C2×#68514yes—
491C3×C4—42no—
492C3×C4—202no—
493C3×C4C2×#68514yes—
494Dic3—42no—
495Dic3—202no—
496Dic3C2×#68514yes—
497C2×C5—64no—
498C2×C5C2×D3×C22⋊C411yescharacteristic
499C2×C5#554512yes—
500C2×C5#560712yes—
501C2×C5#567411yescharacteristic
502C2×C5#571511yescharacteristic
503D5—44no—
504D5—124no—
505C23—32no—
506C23—32no—
507C23—32no—
508C23—54no—
509C23—62no—
510C23—62no—
511C23—102no—
512C23—104no—
513C23—104no—
514C23—102no—
515C23—154no—
516C23—3016no—
517C23—302no—
518C23—304no—
519C23—304no—
520C23—302no—
521C23—6016no—
522C23—608no—
523C23—608no—
524C23—6016no—
525C23C22×D3×D511yescharacteristic
526D4—108no—
527D4—3016no—
528D4—308no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—32no—
533C2×C4—32no—
534C2×C4—32no—
535C2×C4—316no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—102no—
540C2×C4—104no—
541C2×C4—302no—
542C2×C4—304no—
543C2×C4C4×D3×D512yes—
544C2×C4D3×D2012yes—
545C2×C4D3×C22⋊D512yes—
546C2×C3—204no—
547C2×C3#6585512yes—
548C2×C3#6585911yescharacteristic
549C2×C3#6585911yescharacteristic
550C2×C3C22×#68511yescharacteristic
551C2×C3#6616412yes—
552D3—24no—
553D3—204no—
554C5#7642811yescharacteristic, complemented, Sylow
555C22—34no—
556C22—64no—
557C22—62no—
558C22—62no—
559C22—64no—
560C22—108no—
561C22—104no—
562C22—202no—
563C22—202no—
564C22—204no—
565C22—308no—
566C22—304no—
567C22—6032no—
568C22—602no—
569C22—602no—
570C22—604no—
571C22C2×C4×D3×D511yescharacteristic
572C22C2×D3×D2011yescharacteristic
573C22#9201712yes—
574C22#9201912yes—
575C22C2×D3×C22⋊D511yescharacteristic
576C4—34no—
577C4—42no—
578C4—122no—
579C4—202no—
580C4—602no—
581C4D3×#68514yes—
582C3#1061400011yescharacteristic, complemented, Sylow
583C2—64no—
584C2—204no—
585C2—604no—
586C2#1175272712yes—
587C2#1175274311yescharacteristic
588C2#1175274411yescharacteristic
589C2C2×D3×#68511yescharacteristic
590C2#1175465512yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D3×D20C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#2309
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C5×#872C2semidirect
3. C2×#91338C2semidirect
4. #11751040C2semidirect
5. C3×#65228C2semidirect
6. #11748940C2semidirect
7. #11748913C2semidirect
8. #11748789C2semidirect
9. #11748785C2semidirect
18. C2×D3×D20C4semidirect
19. C2×C3×C42×C5C22semidirect
20. C2×#6714C22semidirect
21. C2×C4⋊Dic15C22semidirect
23. C2×C5×Dic3⋊C4C22semidirect
24. C2×C4×C5×Dic3C22semidirect
26. C2×C3×#685C22semidirect
27. C2×C3×C4⋊Dic5C22semidirect
28. C2×#6667C22semidirect
30. C2×#6665C22semidirect
31. C2×Dic3×Dic5C22semidirect
42. #65228D3semidirect
84. C2×#872D5semidirect
103. C2×C42×C5C2×D3semidirect
108. C2×#685C2×D3semidirect
111. C2×C4⋊Dic5C2×D3semidirect
150. C4×C5×D3C22⋊C4semidirect
165. C2×C3×C42C2×D5semidirect
172. C2×Dic3⋊C4C2×D5semidirect
174. C2×C4×Dic3C2×D5semidirect
353. C2×C42D3×D5semidirect
402. C4×D3#685semidirect
469. C3×C5#2309semidirect
554. C5#76428semidirect
582. C3#10614000semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D202
C2×C5×#8722
C2×#913382
#117510402
C3×#652282
#117489402
#117489132
#117487892
#117487852
#106140003
#764285