Finite Group Databasebeta

← #14322443

Subgroups — #14322443

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×#6777C211yesmaximal, characteristic
2C2×#91761C211yesmaximal, characteristic, complemented
3C2×#91347C211yesmaximal, characteristic, complemented
4C5×#4939C211yesmaximal, characteristic, complemented
5C3×#65228C211yesmaximal, characteristic, complemented
6#11748940C214yesmaximal, complemented
7#11748916C214yesmaximal, complemented
8#11748797C211yesmaximal, characteristic, complemented
9#11748796C211yesmaximal, characteristic, complemented
10#10608159—31nomaximal, Hall
11C23×D3×D5C2212yes—
12C22×C4×D15C2211yescharacteristic
13C22×C5×D12C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×#1201C2212yes—
16C2×#6777—24no—
17C2×#6777—24no—
18C2×#6777C418yescomplemented
19C2×C3×C42×C5C2211yescharacteristic, complemented
20C2×#6714C2212yes—
21C2×#6712C2212yescomplemented
22C2×C4×Dic15C2211yescharacteristic, complemented
23#91761—24no—
24C2×C5×(C2×D3)⋊C4C2214yescomplemented
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C2×C3×#685C2214yescomplemented
27C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
28C2×#6667C2212yes—
29C2×(C2×D3)⋊Dic5C2214yescomplemented
30C2×#6665C2214yescomplemented
31C2×Dic3×Dic5C2212yescomplemented
32#91347—24no—
33#76428—51nomaximal, Hall
34C22×D4×D5—31no—
35C2×#4038—31no—
36C2×#4018—31no—
37C5×#390—31no—
38#65510—31no—
39#65277—31no—
40#65246—34no—
41#65244—34no—
42#65228D311yescharacteristic, complemented
43C23×D15C2311yescharacteristic
44C23×C5×D3C2312yes—
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—
54C22×Dic15C2311yescharacteristic
55C2×C4×D15C2×C414yes—
56C2×C4×D15D414yes—
57C2×C4×D15D414yes—
58C22×C5×Dic3C2312yes—
59C2×C5×D12—22no—
60C2×C5×D12—22no—
61C2×C5×D12C2×C414yes—
62C22×C3×Dic5C2312yes—
63C2×C3×D20—22no—
64C2×C3×D20—22no—
65C2×C3×D20C2×C414yes—
66C2×#1201—24no—
67C2×#1201—24no—
68C2×#1201C2×C418yes—
69#6777—232no—
70C3×C42×C5—22no—
71#6714—24no—
72#6712—24no—
73C4×Dic15—22no—
74C5×(C2×D3)⋊C4—44no—
75C5×C4⋊Dic3—22no—
76C3×#685—44no—
77C3×C4⋊Dic5—22no—
78#6667—24no—
79(C2×D3)⋊Dic5—44no—
80#6665—44no—
81Dic3×Dic5—24no—
82C22×D3×D4—51no—
83C2×#892—51no—
84C2×#872—51no—
85C3×#390—51no—
86#5221—51no—
87#4988—51no—
88#4957—54no—
89#4955—54no—
90#4939D511yescharacteristic, complemented
91C24×D5—32no—
92C22×C5×D4—31no—
93C22×C22⋊D5—32no—
94C2×D4×D5—38no—
95C2×D4×D5—64no—
96C2×D4×D5—64no—
97C22×D20C2×D311yescharacteristic
98C22×C4×D5—31no—
99C2×C5×C4⋊C4—31no—
100C2×C5×C22⋊C4—34no—
101C2×C42×C5C2×D311yescharacteristic, complemented
102C2×C22⋊Dic5—34no—
103C2×#685—32no—
104C2×#685—32no—
105C2×#685—34no—
106C2×#685C2×D314yescomplemented
107C2×C4⋊Dic5C2×D311yescharacteristic, complemented
108C2×#683—32no—
109C2×C4×Dic5—31no—
110C2×C4×Dic5—32no—
111#4038—64no—
112#4018—64no—
113#2309—151noSylow
114C23×C3×C5C2411yescharacteristic
115C22×D15—22no—
116C22×D15—22no—
117C22×D15C22×C412yes—
118C22×D15C2×D412yes—
119C22×D15C2×D412yes—
120C22×C5×D3—22no—
121C22×C5×D3—22no—
122C22×C5×D3—24no—
123C22×C5×D3—24no—
124C22×C5×D3C22×C414yes—
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—416no—
134C2×D3×D5—48no—
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—22no—
143C2×Dic15—22no—
144C2×Dic15C22×C412yes—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×D412yes—
147C4×D15C22⋊C4116yescomplemented
148C2×C5×Dic3—22no—
149C2×C5×Dic3—24no—
150C5×D12—28no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—24no—
153C3×D20—28no—
154#1201—216no—
155C24×D3—52no—
156C22×C3×D4—51no—
157C22×#67—52no—
158C2×D3×D4—58no—
159C2×D3×D4—104no—
160C2×D3×D4—104no—
161C22×D12C2×D511yescharacteristic
162C22×C4×D3—51no—
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—52no—
169C2×(C2×D3)⋊C4—54no—
170C2×(C2×D3)⋊C4C2×D514yescomplemented
171C2×C4⋊Dic3C2×D511yescharacteristic, complemented
172C2×Dic3⋊C4—52no—
173C2×C4×Dic3—51no—
174C2×C4×Dic3—52no—
175#892—104no—
176#872—104no—
177C24×C5—32no—
178C23×D5—31no—
179C23×D5—38no—
180C23×D5—64no—
181C23×D5—64no—
182C23×D5—124no—
183C23×D5—124no—
184C23×D5C22×D312yes—
185C2×C5×D4—34no—
186C2×C5×D4—62no—
187C2×C5×D4—62no—
188C22×C4×C5—32no—
189C22×C4×C5C22×D312yes—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—38no—
192C2×C22⋊D5—64no—
193C2×C22⋊D5—64no—
194C22×Dic5—31no—
195C22×Dic5—32no—
196C22×Dic5C22×D312yes—
197D4×D5—632no—
198C2×D20—22no—
199C2×D20—22no—
200C2×D20C4×D314yes—
201C2×C4×D5—34no—
202C2×C4×D5—34no—
203C2×C4×D5—34no—
204C5×C4⋊C4—62no—
205C5×C22⋊C4—124no—
206C42×C5—22no—
207C22⋊Dic5—124no—
208#685—44no—
209#685—64no—
210#685—64no—
211#685—124no—
212C4⋊Dic5—22no—
213#683—64no—
214C4×Dic5—64no—
215C4×Dic5—62no—
216C23×D4—151no—
217C2×#117—151no—
218C2×#117—151no—
219#390—31no—
220#390—51no—
221#390—154no—
222#390—151no—
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—22no—
232C2×D15—24no—
233C2×D15—22no—
234C2×D15C2×C22⋊C414yes—
235C2×C5×D3—24no—
236C2×C5×D3—28no—
237C2×C5×D3—42no—
238C2×C5×D3—44no—
239C2×C5×D3—42no—
240C2×C3×D5—24no—
241C2×C3×D5—28no—
242C2×C3×D5—42no—
243C2×C3×D5—44no—
244C2×C3×D5—42no—
245D3×D5—432no—
246C3×C4×C5—42no—
247C3×C4×C5C2×C22⋊C414yes—
248Dic15—42no—
249Dic15C2×C22⋊C414yes—
250C3×Dic5—42no—
251C5×Dic3—42no—
252C24×C3—52no—
253C23×D3—51no—
254C23×D3—58no—
255C23×D3—104no—
256C23×D3—104no—
257C23×D3—204no—
258C23×D3—204no—
259C23×D3C22×D512yes—
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—51no—
270C22×Dic3—52no—
271C22×Dic3C22×D512yes—
272D3×D4—1032no—
273C2×D12—22no—
274C2×D12—22no—
275C2×D12C4×D514yes—
276C2×C4×D3—54no—
277C2×C4×D3—54no—
278C2×C4×D3—54no—
279C3×C4⋊C4—102no—
280C3×C22⋊C4—204no—
281C3×C42—22no—
282#217—204no—
283(C2×D3)⋊C4—44no—
284(C2×D3)⋊C4—104no—
285(C2×D3)⋊C4—104no—
286(C2×D3)⋊C4—204no—
287C4⋊Dic3—22no—
288Dic3⋊C4—104no—
289C4×Dic3—104no—
290C4×Dic3—102no—
291C23×C5—34no—
292C23×C5—62no—
293C23×C5—62no—
294C23×C5—64no—
295C23×C5—64no—
296C23×C5C23×D311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—24no—
300C22×D5—24no—
301C22×D5—32no—
302C22×D5—32no—
303C22×D5—32no—
304C22×D5—616no—
305C22×D5—62no—
306C22×D5—62no—
307C22×D5—1216no—
308C22×D5—128no—
309C22×D5—128no—
310C22×D5—1216no—
311C22×D5C2×C4×D314yes—
312C5×D4—68no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—62no—
317C2×C4×C5—64no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5D3×D412yes—
320C2×C4×C5D3×D412yes—
321C22⋊D5—616no—
322C2×Dic5—22no—
323C2×Dic5—24no—
324C2×Dic5—32no—
325C2×Dic5—32no—
326C2×Dic5—32no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330D20—28no—
331C4×D5—316no—
332C25—152no—
333C22×D4—31no—
334C22×D4—51no—
335C22×D4—158no—
336C22×D4—152no—
337C22×D4—304no—
338C22×D4—304no—
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—152no—
352C2×C42—151no—
353C2×C42D3×D511yescharacteristic, complemented
354C2×C3×C5C22×C22⋊C411yescharacteristic
355C2×C3×C5#51812yes—
356C2×C3×C5#53511yescharacteristic
357C2×C3×C5#53512yes—
358C2×C3×C5#53511yescharacteristic
359D15—24no—
360C3×D5—44no—
361C5×D3—44no—
362C23×C3—54no—
363C23×C3—102no—
364C23×C3—102no—
365C23×C3—104no—
366C23×C3—104no—
367C23×C3C23×D511yescharacteristic
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—52no—
373C22×D3—52no—
374C22×D3—52no—
375C22×D3—1016no—
376C22×D3—102no—
377C22×D3—102no—
378C22×D3—2016no—
379C22×D3—208no—
380C22×D3—2016no—
381C22×D3—208no—
382C22×D3C2×C4×D514yes—
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×C4D4×D512yes—
391C2×C3×C4D4×D512yes—
392#67—1016no—
393C2×Dic3—22no—
394C2×Dic3—24no—
395C2×Dic3—52no—
396C2×Dic3—52no—
397C2×Dic3—52no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401D12—28no—
402C4×D3—516no—
403C22×C5—64no—
404C22×C5—68no—
405C22×C5—122no—
406C22×C5—122no—
407C22×C5—124no—
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—34no—
416C2×D5—42no—
417C2×D5—42no—
418C2×D5—44no—
419C2×D5—62no—
420C2×D5—62no—
421C2×D5—64no—
422C2×D5—64no—
423C2×D5—1232no—
424C4×C5—42no—
425C4×C5—122no—
426C4×C5D3×C22⋊C414yes—
427Dic5—34no—
428Dic5—42no—
429Dic5—122no—
430C24—32no—
431C24—52no—
432C24—158no—
433C24—151no—
434C24—304no—
435C24—304no—
436C24—604no—
437C24—604no—
438C2×D4—34no—
439C2×D4—54no—
440C2×D4—62no—
441C2×D4—62no—
442C2×D4—102no—
443C2×D4—102no—
444C2×D4—158no—
445C2×D4—3032no—
446C2×D4—304no—
447C2×D4—304no—
448C22×C4—32no—
449C22×C4—52no—
450C22×C4—151no—
451C22×C4—154no—
452C22×C4—154no—
453C22×C4—154no—
454C22×C4—152no—
455C22×C4C2×D3×D512yes—
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—22no—
467C42—304no—
468C42—302no—
469C3×C5#230911yescharacteristic, complemented, Hall
470C22×C3—104no—
471C22×C3—108no—
472C22×C3—202no—
473C22×C3—204no—
474C22×C3—202no—
475C22×C3C22×C4×D511yescharacteristic
476C22×C3C2×D4×D511yescharacteristic
477C22×C3C2×D4×D511yescharacteristic
478C22×C3#414412yes—
479C22×C3#414912yes—
480C2×D3—24no—
481C2×D3—28no—
482C2×D3—42no—
483C2×D3—44no—
484C2×D3—42no—
485C2×D3—54no—
486C2×D3—102no—
487C2×D3—104no—
488C2×D3—104no—
489C2×D3—102no—
490C2×D3—2032no—
491C3×C4—42no—
492C3×C4—202no—
493C3×C4D5×C22⋊C414yes—
494Dic3—42no—
495Dic3—54no—
496Dic3—202no—
497C2×C5—124no—
498C2×C5C2×D3×C22⋊C411yescharacteristic
499C2×C5#554512yes—
500C2×C5#560712yes—
501C2×C5#567411yescharacteristic
502C2×C5#571511yescharacteristic
503D5—44no—
504D5—64no—
505C23—34no—
506C23—54no—
507C23—62no—
508C23—64no—
509C23—64no—
510C23—62no—
511C23—102no—
512C23—104no—
513C23—104no—
514C23—102no—
515C23—152no—
516C23—152no—
517C23—152no—
518C23—3016no—
519C23—302no—
520C23—302no—
521C23—6016no—
522C23—608no—
523C23—608no—
524C23—6016no—
525C23C22×D3×D511yescharacteristic
526D4—68no—
527D4—108no—
528D4—3016no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—62no—
533C2×C4—64no—
534C2×C4—102no—
535C2×C4—104no—
536C2×C4—152no—
537C2×C4—152no—
538C2×C4—152no—
539C2×C4—1516no—
540C2×C4—302no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4C4×D3×D512yes—
544C2×C4#677712yes—
545C2×C4#679012yes—
546C2×C3—204no—
547C2×C3C2×D5×C22⋊C411yescharacteristic
548C2×C3#6587912yes—
549C2×C3#6594112yes—
550C2×C3#6600811yescharacteristic
551C2×C3#6604911yescharacteristic
552D3—44no—
553D3—104no—
554C5#7642811yescharacteristic, complemented, Sylow
555C22—68no—
556C22—64no—
557C22—108no—
558C22—104no—
559C22—122no—
560C22—122no—
561C22—124no—
562C22—154no—
563C22—202no—
564C22—202no—
565C22—204no—
566C22—304no—
567C22—302no—
568C22—302no—
569C22—304no—
570C22—6032no—
571C22C2×C4×D3×D511yescharacteristic
572C22C2×#677711yescharacteristic
573C22#9201712yes—
574C22#9201812yes—
575C22C2×#679011yescharacteristic
576C4—42no—
577C4—122no—
578C4—154no—
579C4—202no—
580C4—602no—
581C4#9147314yes—
582C3#1060815911yescharacteristic, complemented, Sylow
583C2—124no—
584C2—204no—
585C2—304no—
586C2#1175272912yes—
587C2#1175275211yescharacteristic
588C2#1175275311yescharacteristic
589C2C2×#9147311yescharacteristic
590C2#1175467112yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#6777C2
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×#91761C2semidirect
3. C2×#91347C2semidirect
4. C5×#4939C2semidirect
5. C3×#65228C2semidirect
6. #11748940C2semidirect
7. #11748916C2semidirect
8. #11748797C2semidirect
9. #11748796C2semidirect
18. C2×#6777C4semidirect
19. C2×C3×C42×C5C22semidirect
21. C2×#6712C22semidirect
22. C2×C4×Dic15C22semidirect
24. C2×C5×(C2×D3)⋊C4C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
26. C2×C3×#685C22semidirect
27. C2×C3×C4⋊Dic5C22semidirect
29. C2×(C2×D3)⋊Dic5C22semidirect
30. C2×#6665C22semidirect
31. C2×Dic3×Dic5C22semidirect
42. #65228D3semidirect
90. #4939D5semidirect
101. C2×C42×C5C2×D3semidirect
106. C2×#685C2×D3semidirect
107. C2×C4⋊Dic5C2×D3semidirect
147. C4×D15C22⋊C4semidirect
165. C2×C3×C42C2×D5semidirect
170. C2×(C2×D3)⋊C4C2×D5semidirect
171. C2×C4⋊Dic3C2×D5semidirect
353. C2×C42D3×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×#67772
C2×#917612
C2×#913472
C5×#49392
C3×#652282
#117489402
#117489162
#117487972
#117487962
#106081593
#764285