Finite Group Databasebeta

← #14322449

Subgroups — #14322449

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×D4×D15C211yesmaximal, characteristic
2C2×#91386C211yesmaximal, characteristic, complemented
3C2×#91347C211yesmaximal, characteristic, complemented
4C5×#5221C211yesmaximal, characteristic, complemented
5C3×#65510C211yesmaximal, characteristic, complemented
6#11749502C214yesmaximal, complemented
7#11749483C214yesmaximal, complemented
8#11748789C211yesmaximal, characteristic, complemented
9#11748768C211yesmaximal, characteristic, complemented
10#10608159—31nomaximal, Hall
11C24×D15C2212yes—
12C22×C3×C5×D4C2211yescharacteristic
13C22×#1220C2212yes—
14C2×D4×D15—24no—
15C2×D4×D15—24no—
16C2×D4×D15C418yescomplemented
17C22×D60C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C2×C5×#217C2214yescomplemented
20C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
21C2×C4×C5×Dic3C2211yescharacteristic, complemented
22C2×C3×C22⋊Dic5C2214yescomplemented
23C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
24C2×C3×C4×Dic5C2211yescharacteristic, complemented
25C2×#6669C2212yescomplemented
26C2×#6667C2212yes—
27C2×#6667C2212yes—
28C2×#6667C2214yescomplemented
29C2×#6667C2214yescomplemented
30C2×Dic3×Dic5C2212yescomplemented
31#91386—24no—
32#91347—24no—
33#76428—51nomaximal, Hall
34C22×D4×D5—31no—
35C2×#4038—31no—
36C2×#4018—31no—
37C5×#390—31no—
38#65510D311yescharacteristic, complemented
39#65277—31no—
40#65246—34no—
41#65244—34no—
42#65228—31no—
43C24×C3×C5C2312yes—
44C23×D15—24no—
45C23×D15—24no—
46C23×D15—44no—
47C23×D15—44no—
48C23×D15C2×C418yes—
49C23×D15C2312yes—
50C23×D15C2311yescharacteristic
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4C2×C414yes—
54C22×C3×C4×C5C2311yescharacteristic
55C2×#1220—24no—
56C2×#1220—24no—
57C2×#1220C2×C418yes—
58C22×Dic15C2311yescharacteristic
59D4×D15—232no—
60C2×D60—22no—
61C2×D60—22no—
62C2×D60C2×C414yes—
63C2×C4×D15C2×C414yes—
64C2×C4×D15D414yes—
65C2×C4×D15D414yes—
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2312yes—
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2312yes—
70C5×#217—44no—
71C5×C4⋊Dic3—22no—
72C4×C5×Dic3—22no—
73C3×C22⋊Dic5—44no—
74C3×C4⋊Dic5—22no—
75C3×C4×Dic5—22no—
76#6669—24no—
77#6667—24no—
78#6667—24no—
79#6667—44no—
80#6667—44no—
81Dic3×Dic5—24no—
82C22×D3×D4—51no—
83C2×#892—51no—
84C2×#872—51no—
85C3×#390—51no—
86#5221D511yescharacteristic, complemented
87#4988—51no—
88#4957—54no—
89#4955—54no—
90#4939—51no—
91C24×D5—32no—
92C22×C5×D4C2×D311yescharacteristic
93C22×C22⋊D5—32no—
94C2×D4×D5—38no—
95C2×D4×D5—64no—
96C2×D4×D5—64no—
97C22×D20—31no—
98C22×C4×D5—31no—
99C2×C5×C4⋊C4—31no—
100C2×C5×C22⋊C4—34no—
101C2×C42×C5—31no—
102C2×C22⋊Dic5C2×D314yescomplemented
103C2×#685—32no—
104C2×#685—32no—
105C2×#685—34no—
106C2×#685—34no—
107C2×C4⋊Dic5C2×D311yescharacteristic, complemented
108C2×#683—32no—
109C2×C4×Dic5—32no—
110C2×C4×Dic5C2×D311yescharacteristic, complemented
111#4038—64no—
112#4018—64no—
113#2309—151noSylow
114C23×C3×C5—22no—
115C23×C3×C5—22no—
116C23×C3×C5—24no—
117C23×C3×C5—24no—
118C23×C3×C5C22×C414yes—
119C23×C3×C5C2411yescharacteristic
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—22no—
124C22×D15—24no—
125C22×D15—24no—
126C22×D15—216no—
127C22×D15—416no—
128C22×D15—48no—
129C22×D15—416no—
130C22×D15—48no—
131C22×D15C22×C414yes—
132C22×D15C22×C412yes—
133C22×D15C2×D412yes—
134C22×D15C2×D412yes—
135C3×C5×D4—28no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2×D412yes—
139#1220—216no—
140C2×Dic15C22×C412yes—
141C2×Dic15C2×D412yes—
142C2×Dic15C2×D412yes—
143D60—28no—
144C4×D15C22⋊C4116yescomplemented
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—24no—
149C2×C5×Dic3—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—24no—
154C2×C3×Dic5—22no—
155C24×D3—52no—
156C22×C3×D4C2×D511yescharacteristic
157C22×#67—52no—
158C2×D3×D4—58no—
159C2×D3×D4—104no—
160C2×D3×D4—104no—
161C22×D12—51no—
162C22×C4×D3—51no—
163C2×C3×C4⋊C4—51no—
164C2×C3×C22⋊C4—54no—
165C2×C3×C42—51no—
166C2×#217C2×D514yescomplemented
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—54no—
170C2×(C2×D3)⋊C4—54no—
171C2×C4⋊Dic3C2×D511yescharacteristic, complemented
172C2×Dic3⋊C4—52no—
173C2×C4×Dic3—52no—
174C2×C4×Dic3C2×D511yescharacteristic, complemented
175#892—104no—
176#872—104no—
177C24×C5C22×D312yes—
178C23×D5—31no—
179C23×D5—32no—
180C23×D5—38no—
181C23×D5—64no—
182C23×D5—64no—
183C23×D5—124no—
184C23×D5—124no—
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4C4×D314yes—
188C22×C4×C5—32no—
189C22×C4×C5—32no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—38no—
192C2×C22⋊D5—64no—
193C2×C22⋊D5—64no—
194C22×Dic5—31no—
195C22×Dic5C22×D312yes—
196C22×Dic5C22×D312yes—
197D4×D5—632no—
198C2×D20—34no—
199C2×D20—62no—
200C2×D20—62no—
201C2×C4×D5—34no—
202C2×C4×D5—34no—
203C2×C4×D5—34no—
204C5×C4⋊C4—62no—
205C5×C22⋊C4—124no—
206C42×C5—62no—
207C22⋊Dic5—44no—
208#685—64no—
209#685—64no—
210#685—124no—
211#685—124no—
212C4⋊Dic5—22no—
213#683—64no—
214C4×Dic5—22no—
215C4×Dic5—64no—
216C23×D4—151no—
217C2×#117—151no—
218C2×#117—151no—
219#390—31no—
220#390—51no—
221#390—151no—
222#390—151no—
223#390—154no—
224#379—154no—
225C22×C3×C5—24no—
226C22×C3×C5—28no—
227C22×C3×C5—42no—
228C22×C3×C5—44no—
229C22×C3×C5—42no—
230C22×C3×C5C23×C411yescharacteristic
231C22×C3×C5C22×D411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5H(5,𝔽2)12yes—
234C22×C3×C5H(5,𝔽2)12yes—
235C2×D15—24no—
236C2×D15—22no—
237C2×D15—24no—
238C2×D15—22no—
239C2×D15—24no—
240C2×D15—28no—
241C2×D15—432no—
242C2×D15—42no—
243C2×D15—44no—
244C2×D15—42no—
245C2×D15C2×C22⋊C414yes—
246C3×C4×C5C2×C22⋊C414yes—
247Dic15C2×C22⋊C414yes—
248C3×Dic5—42no—
249C3×Dic5—42no—
250C5×Dic3—42no—
251C5×Dic3—42no—
252C24×C3C22×D512yes—
253C23×D3—51no—
254C23×D3—52no—
255C23×D3—58no—
256C23×D3—104no—
257C23×D3—104no—
258C23×D3—204no—
259C23×D3—204no—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4C4×D514yes—
263C22×C3×C4—52no—
264C22×C3×C4—52no—
265C22×C3×C4C22×D511yescharacteristic
266C2×#67—58no—
267C2×#67—104no—
268C2×#67—104no—
269C22×Dic3—51no—
270C22×Dic3C22×D512yes—
271C22×Dic3C22×D512yes—
272D3×D4—1032no—
273C2×D12—54no—
274C2×D12—102no—
275C2×D12—102no—
276C2×C4×D3—54no—
277C2×C4×D3—54no—
278C2×C4×D3—54no—
279C3×C4⋊C4—102no—
280C3×C22⋊C4—204no—
281C3×C42—102no—
282#217—44no—
283(C2×D3)⋊C4—104no—
284(C2×D3)⋊C4—104no—
285(C2×D3)⋊C4—204no—
286(C2×D3)⋊C4—204no—
287C4⋊Dic3—22no—
288Dic3⋊C4—104no—
289C4×Dic3—22no—
290C4×Dic3—104no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—24no—
294C23×C5—24no—
295C23×C5C2×C4×D314yes—
296C23×C5C23×D311yescharacteristic
297C22×D5—32no—
298C22×D5—32no—
299C22×D5—32no—
300C22×D5—34no—
301C22×D5—616no—
302C22×D5—62no—
303C22×D5—62no—
304C22×D5—62no—
305C22×D5—62no—
306C22×D5—64no—
307C22×D5—64no—
308C22×D5—1216no—
309C22×D5—128no—
310C22×D5—128no—
311C22×D5—1216no—
312C5×D4—28no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—64no—
317C2×C4×C5—62no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5D3×D412yes—
320C2×C4×C5D3×D412yes—
321C22⋊D5—616no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—24no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—32no—
328C2×Dic5—32no—
329C2×Dic5—32no—
330D20—68no—
331C4×D5—316no—
332C25—152no—
333C22×D4—152no—
334C22×D4—158no—
335C22×D4—151no—
336C22×D4—304no—
337C22×D4—304no—
338C22×D4D3×D511yescharacteristic
339C23×C4—151no—
340#117—304no—
341#117—304no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—152no—
345C2×C22⋊C4—34no—
346C2×C22⋊C4—54no—
347C2×C22⋊C4—152no—
348C2×C22⋊C4—152no—
349C2×C22⋊C4—154no—
350C2×C22⋊C4—154no—
351C2×C42—31no—
352C2×C42—51no—
353C2×C42—152no—
354C2×C3×C5—44no—
355C2×C3×C5C22×C22⋊C411yescharacteristic
356C2×C3×C5#51812yes—
357C2×C3×C5#53511yescharacteristic
358C2×C3×C5#53512yes—
359C2×C3×C5#53511yescharacteristic
360D15—24no—
361D15—44no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3C2×C4×D514yes—
367C23×C3C23×D511yescharacteristic
368C22×D3—52no—
369C22×D3—52no—
370C22×D3—52no—
371C22×D3—54no—
372C22×D3—1016no—
373C22×D3—102no—
374C22×D3—102no—
375C22×D3—102no—
376C22×D3—102no—
377C22×D3—104no—
378C22×D3—104no—
379C22×D3—2016no—
380C22×D3—208no—
381C22×D3—2016no—
382C22×D3—208no—
383C3×D4—28no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—104no—
388C2×C3×C4—102no—
389C2×C3×C4C2×C4×D512yes—
390C2×C3×C4D4×D512yes—
391C2×C3×C4D4×D512yes—
392#67—1016no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—24no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—52no—
399C2×Dic3—52no—
400C2×Dic3—52no—
401D12—108no—
402C4×D3—516no—
403C22×C5—24no—
404C22×C5—28no—
405C22×C5—42no—
406C22×C5—42no—
407C22×C5—44no—
408C22×C5C22×C4×D311yescharacteristic
409C22×C5C2×D3×D411yescharacteristic
410C22×C5C2×D3×D411yescharacteristic
411C22×C5#100412yes—
412C22×C5#100912yes—
413C2×D5—34no—
414C2×D5—62no—
415C2×D5—62no—
416C2×D5—64no—
417C2×D5—64no—
418C2×D5—64no—
419C2×D5—68no—
420C2×D5—1232no—
421C2×D5—122no—
422C2×D5—122no—
423C2×D5—124no—
424C4×C5—122no—
425C4×C5—122no—
426C4×C5D3×C22⋊C414yes—
427Dic5—34no—
428Dic5—42no—
429Dic5—42no—
430C24—151no—
431C24—152no—
432C24—158no—
433C24—304no—
434C24—304no—
435C24—604no—
436C24—604no—
437C24C2×D3×D512yes—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—158no—
441C2×D4—154no—
442C2×D4—3032no—
443C2×D4—304no—
444C2×D4—304no—
445C2×D4—302no—
446C2×D4—302no—
447C2×D4#120014yes—
448C22×C4—32no—
449C22×C4—32no—
450C22×C4—52no—
451C22×C4—52no—
452C22×C4—151no—
453C22×C4—154no—
454C22×C4—154no—
455C22×C4—154no—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—62no—
458C4⋊C4—102no—
459C4⋊C4—304no—
460C22⋊C4—124no—
461C22⋊C4—204no—
462C22⋊C4—304no—
463C22⋊C4—304no—
464C22⋊C4—604no—
465C22⋊C4—604no—
466C42—62no—
467C42—102no—
468C42—304no—
469C3×C5#230911yescharacteristic, complemented, Hall
470C22×C3—24no—
471C22×C3—28no—
472C22×C3—42no—
473C22×C3—44no—
474C22×C3—42no—
475C22×C3C22×C4×D511yescharacteristic
476C22×C3C2×D4×D511yescharacteristic
477C22×C3C2×D4×D511yescharacteristic
478C22×C3#414412yes—
479C22×C3#414912yes—
480C2×D3—54no—
481C2×D3—102no—
482C2×D3—104no—
483C2×D3—104no—
484C2×D3—102no—
485C2×D3—104no—
486C2×D3—108no—
487C2×D3—2032no—
488C2×D3—202no—
489C2×D3—204no—
490C2×D3—202no—
491C3×C4—202no—
492C3×C4—202no—
493C3×C4D5×C22⋊C414yes—
494Dic3—42no—
495Dic3—42no—
496Dic3—54no—
497C2×C5—44no—
498C2×C5C2×D3×C22⋊C411yescharacteristic
499C2×C5#554512yes—
500C2×C5#560712yes—
501C2×C5#567411yescharacteristic
502C2×C5#571511yescharacteristic
503D5—64no—
504D5—124no—
505C23—24no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—152no—
510C23—152no—
511C23—152no—
512C23—154no—
513C23—3016no—
514C23—302no—
515C23—302no—
516C23—304no—
517C23—304no—
518C23—302no—
519C23—302no—
520C23—6016no—
521C23—608no—
522C23—608no—
523C23—6016no—
524C23C2×#120014yes—
525C23C22×D3×D511yescharacteristic
526D4—28no—
527D4—3016no—
528D4—308no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—64no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—102no—
535C2×C4—104no—
536C2×C4—102no—
537C2×C4—102no—
538C2×C4—102no—
539C2×C4—152no—
540C2×C4—152no—
541C2×C4—152no—
542C2×C4—1516no—
543C2×C4C2×#120012yes—
544C2×C4#679012yes—
545C2×C4#679012yes—
546C2×C3—44no—
547C2×C3C2×D5×C22⋊C411yescharacteristic
548C2×C3#6587912yes—
549C2×C3#6594112yes—
550C2×C3#6600811yescharacteristic
551C2×C3#6604911yescharacteristic
552D3—104no—
553D3—204no—
554C5#7642811yescharacteristic, complemented, Sylow
555C22—24no—
556C22—28no—
557C22—42no—
558C22—42no—
559C22—44no—
560C22—154no—
561C22—302no—
562C22—302no—
563C22—304no—
564C22—304no—
565C22—304no—
566C22—308no—
567C22—6032no—
568C22—602no—
569C22—602no—
570C22—604no—
571C22#9202612yes—
572C22#9202712yes—
573C22C22×#120011yescharacteristic
574C22C2×#679011yescharacteristic
575C22C2×#679011yescharacteristic
576C4—122no—
577C4—122no—
578C4—154no—
579C4—202no—
580C4—202no—
581C4#9156114yes—
582C3#1060815911yescharacteristic, complemented, Sylow
583C2—44no—
584C2—304no—
585C2—604no—
586C2#1175482311yescharacteristic
587C2#1175482911yescharacteristic
588C2#1175492212yes—
589C2#1175495512yes—
590C2C2×#9156111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D4×D15C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2309
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91386C2semidirect
3. C2×#91347C2semidirect
4. C5×#5221C2semidirect
5. C3×#65510C2semidirect
6. #11749502C2semidirect
7. #11749483C2semidirect
8. #11748789C2semidirect
9. #11748768C2semidirect
16. C2×D4×D15C4semidirect
19. C2×C5×#217C22semidirect
20. C2×C5×C4⋊Dic3C22semidirect
21. C2×C4×C5×Dic3C22semidirect
22. C2×C3×C22⋊Dic5C22semidirect
23. C2×C3×C4⋊Dic5C22semidirect
24. C2×C3×C4×Dic5C22semidirect
25. C2×#6669C22semidirect
28. C2×#6667C22semidirect
29. C2×#6667C22semidirect
30. C2×Dic3×Dic5C22semidirect
38. #65510D3semidirect
86. #5221D5semidirect
102. C2×C22⋊Dic5C2×D3semidirect
107. C2×C4⋊Dic5C2×D3semidirect
110. C2×C4×Dic5C2×D3semidirect
144. C4×D15C22⋊C4semidirect
166. C2×#217C2×D5semidirect
171. C2×C4⋊Dic3C2×D5semidirect
174. C2×C4×Dic3C2×D5semidirect
469. C3×C5#2309semidirect
554. C5#76428semidirect
582. C3#10608159semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D152
C2×#913862
C2×#913472
C5×#52212
C3×#655102
#117495022
#117494832
#117487892
#117487682
#106081593
#764285