Finite Group Databasebeta

← #14322448

Subgroups — #14322448

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×C3×D4×D5C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic, complemented
3C2×#91357C211yesmaximal, characteristic, complemented
4#11751322C211yesmaximal, characteristic, complemented
5C5×#5221C211yesmaximal, characteristic, complemented
6#11749489C214yesmaximal, complemented
7#11749488C214yesmaximal, complemented
8#11748796C211yesmaximal, characteristic, complemented
9#11748785C211yesmaximal, characteristic, complemented
10#10608159—31nomaximal, Hall
11C24×C3×D5C2212yes—
12C22×C3×C5×D4C2211yescharacteristic
13C22×C3×C22⋊D5C2212yes—
14C2×C3×D4×D5—24no—
15C2×C3×D4×D5—24no—
16C2×C3×D4×D5C418yescomplemented
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C2×#6719C2214yescomplemented
20C2×C4⋊Dic15C2211yescharacteristic, complemented
21C2×C4×Dic15C2211yescharacteristic, complemented
22C2×C5×#217C2214yescomplemented
23C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
24C2×C4×C5×Dic3C2211yescharacteristic, complemented
25C2×#6668C2212yescomplemented
26C2×#6665C2212yes—
27C2×#6665C2212yes—
28C2×#6665C2214yescomplemented
29C2×#6665C2214yescomplemented
30C2×Dic3×Dic5C2212yescomplemented
31#91358—24no—
32#91357—24no—
33#84044—51nomaximal, Hall
34C22×D4×D5D311yescharacteristic
35C2×#4038—31no—
36C2×#4018—31no—
37C5×#390—31no—
38#65510—31no—
39#65277—31no—
40#65246—34no—
41#65244—34no—
42#65228—31no—
43C24×C3×C5C2312yes—
44C23×C3×D5—24no—
45C23×C3×D5—24no—
46C23×C3×D5—44no—
47C23×C3×D5—44no—
48C23×C3×D5C2×C418yes—
49C23×C3×D5C2312yes—
50C23×C3×D5C2311yescharacteristic
51C2×C3×C5×D4—22no—
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4C2×C414yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2312yes—
59C2×C3×C22⋊D5—24no—
60C2×C3×C22⋊D5—24no—
61C2×C3×C22⋊D5C2×C418yes—
62C22×C3×Dic5C2311yescharacteristic
63C3×D4×D5—232no—
64C2×C3×D20—22no—
65C2×C3×D20—22no—
66C2×C3×D20C2×C414yes—
67C2×C3×C4×D5C2×C414yes—
68C2×C3×C4×D5D414yes—
69C2×C3×C4×D5D414yes—
70#6719—44no—
71C4⋊Dic15—22no—
72C4×Dic15—22no—
73C5×#217—44no—
74C5×C4⋊Dic3—22no—
75C4×C5×Dic3—22no—
76#6668—24no—
77#6665—24no—
78#6665—24no—
79#6665—44no—
80#6665—44no—
81Dic3×Dic5—24no—
82C23×C3×D4—51no—
83C2×#926—51no—
84C2×#926—51no—
85#5247—54no—
86#5221—51no—
87#5221—54no—
88#5221—51no—
89#5221—51no—
90#5221D511yescharacteristic, complemented
91C24×D5C2×D312yes—
92C22×C5×D4C2×D311yescharacteristic
93C22×C22⋊D5C2×D312yes—
94C2×D4×D5—24no—
95C2×D4×D5—24no—
96C2×D4×D5Dic318yescomplemented
97C22×D20C2×D311yescharacteristic
98C22×C4×D5C2×D311yescharacteristic
99C2×C5×C4⋊C4—31no—
100C2×C5×C22⋊C4—34no—
101C2×C42×C5—31no—
102C2×C22⋊Dic5—34no—
103C2×#685—32no—
104C2×#685—32no—
105C2×#685—34no—
106C2×#685—34no—
107C2×C4⋊Dic5—31no—
108C2×#683—32no—
109C2×C4×Dic5—31no—
110C2×C4×Dic5—32no—
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×C3×D5—22no—
121C22×C3×D5—22no—
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—24no—
125C22×C3×D5—24no—
126C22×C3×D5—216no—
127C22×C3×D5—416no—
128C22×C3×D5—48no—
129C22×C3×D5—416no—
130C22×C3×D5—48no—
131C22×C3×D5C22×C414yes—
132C22×C3×D5C22×C412yes—
133C22×C3×D5C2×D412yes—
134C22×C3×D5C2×D412yes—
135C3×C5×D4—28no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C2×D412yes—
138C2×C3×C4×C5C2×D412yes—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—24no—
143C2×Dic15—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—24no—
148C2×C5×Dic3—22no—
149C3×C22⋊D5—216no—
150C2×C3×Dic5C22×C412yes—
151C2×C3×Dic5C2×D412yes—
152C2×C3×Dic5C2×D412yes—
153C3×D20—28no—
154C3×C4×D5C22⋊C4116yescomplemented
155C25×C3—52no—
156C22×C3×D4—52no—
157C22×C3×D4—58no—
158C22×C3×D4—51no—
159C22×C3×D4—104no—
160C22×C3×D4—104no—
161C22×C3×D4C2×D511yescharacteristic
162C23×C3×C4—51no—
163C2×#217—52no—
164C2×#217—52no—
165C2×#217—54no—
166C2×#217—54no—
167C2×#217—54no—
168C2×#217C2×D514yescomplemented
169#926—104no—
170#926—104no—
171C2×C4⋊Dic3—51no—
172C2×C4⋊Dic3—52no—
173C2×C4⋊Dic3C2×D511yescharacteristic, complemented
174C2×C4×Dic3—51no—
175C2×C4×Dic3—52no—
176C2×C4×Dic3C2×D511yescharacteristic, complemented
177C24×C5C22×D312yes—
178C23×D5—24no—
179C23×D5—24no—
180C23×D5—44no—
181C23×D5—44no—
182C23×D5C2×Dic318yes—
183C23×D5C22×D312yes—
184C23×D5C22×D311yescharacteristic
185C2×C5×D4—22no—
186C2×C5×D4—22no—
187C2×C5×D4C2×Dic314yes—
188C22×C4×C5—32no—
189C22×C4×C5—32no—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—24no—
192C2×C22⋊D5—24no—
193C2×C22⋊D5C2×Dic318yes—
194C22×Dic5—32no—
195C22×Dic5—32no—
196C22×Dic5C22×D311yescharacteristic
197D4×D5—232no—
198C2×D20—22no—
199C2×D20—22no—
200C2×D20C2×Dic314yes—
201C2×C4×D5C2×Dic314yes—
202C2×C4×D5#6714yes—
203C2×C4×D5#6714yes—
204C5×C4⋊C4—62no—
205C5×C22⋊C4—124no—
206C42×C5—62no—
207C22⋊Dic5—124no—
208#685—64no—
209#685—64no—
210#685—124no—
211#685—124no—
212C4⋊Dic5—62no—
213#683—64no—
214C4×Dic5—62no—
215C4×Dic5—64no—
216C23×D4—51no—
217C2×#117—151no—
218C2×#117—151no—
219#390—31no—
220#390—151no—
221#390—154no—
222#390—151no—
223#390—151no—
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×C3×D5—24no—
236C2×C3×D5—22no—
237C2×C3×D5—24no—
238C2×C3×D5—22no—
239C2×C3×D5—24no—
240C2×C3×D5—28no—
241C2×C3×D5—432no—
242C2×C3×D5—42no—
243C2×C3×D5—44no—
244C2×C3×D5—42no—
245C2×C3×D5C2×C22⋊C414yes—
246C3×C4×C5C2×C22⋊C414yes—
247Dic15—42no—
248Dic15—42no—
249C3×Dic5C2×C22⋊C414yes—
250C5×Dic3—42no—
251C5×Dic3—42no—
252C24×C3—51no—
253C24×C3—52no—
254C24×C3—58no—
255C24×C3—104no—
256C24×C3—104no—
257C24×C3—204no—
258C24×C3—204no—
259C24×C3C22×D512yes—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4—58no—
263C2×C3×D4—54no—
264C2×C3×D4—1032no—
265C2×C3×D4—104no—
266C2×C3×D4—104no—
267C2×C3×D4—102no—
268C2×C3×D4—102no—
269C2×C3×D4C4×D514yes—
270C22×C3×C4—51no—
271C22×C3×C4—54no—
272C22×C3×C4—54no—
273C22×C3×C4—54no—
274C22×C3×C4C22×D511yescharacteristic
275C22×Dic3—52no—
276C22×Dic3—52no—
277C22×Dic3C22×D512yes—
278C22×Dic3C22×D512yes—
279#217—44no—
280#217—104no—
281#217—104no—
282#217—204no—
283#217—204no—
284#217—204no—
285C4⋊Dic3—22no—
286C4⋊Dic3—104no—
287C4⋊Dic3—102no—
288C4×Dic3—22no—
289C4×Dic3—104no—
290C4×Dic3—102no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5C22×Dic314yes—
296C23×C5C23×D311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—24no—
300C22×D5—24no—
301C22×D5—22no—
302C22×D5—22no—
303C22×D5—216no—
304C22×D5—416no—
305C22×D5—416no—
306C22×D5—48no—
307C22×D5—48no—
308C22×D5C22×Dic314yes—
309C22×D5C22×Dic312yes—
310C22×D5C2×#6712yes—
311C22×D5C2×#6712yes—
312C5×D4—28no—
313C2×C4×C5—62no—
314C2×C4×C5—64no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5C22×Dic312yes—
319C2×C4×C5C2×#6712yes—
320C2×C4×C5C2×#6712yes—
321C22⋊D5—216no—
322C2×Dic5—62no—
323C2×Dic5—64no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5C22×Dic312yes—
328C2×Dic5C2×#6712yes—
329C2×Dic5C2×#6712yes—
330D20—28no—
331C4×D5#217116yescomplemented
332C25—52no—
333C22×D4—52no—
334C22×D4—58no—
335C22×D4—51no—
336C22×D4—104no—
337C22×D4—104no—
338C22×D4D3×D511yescharacteristic
339C23×C4—51no—
340#117—304no—
341#117—304no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—152no—
344C2×C4⋊C4—151no—
345C2×C22⋊C4—34no—
346C2×C22⋊C4—152no—
347C2×C22⋊C4—152no—
348C2×C22⋊C4—154no—
349C2×C22⋊C4—154no—
350C2×C22⋊C4—154no—
351C2×C42—31no—
352C2×C42—152no—
353C2×C42—151no—
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
360C3×D5—24no—
361C3×D5—44no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—52no—
367C23×C3—52no—
368C23×C3—52no—
369C23×C3—54no—
370C23×C3—1016no—
371C23×C3—102no—
372C23×C3—102no—
373C23×C3—102no—
374C23×C3—102no—
375C23×C3—104no—
376C23×C3—104no—
377C23×C3—2016no—
378C23×C3—208no—
379C23×C3—2016no—
380C23×C3—208no—
381C23×C3C2×C4×D514yes—
382C23×C3C23×D511yescharacteristic
383C3×D4—28no—
384C3×D4—1016no—
385C3×D4—108no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—52no—
389C2×C3×C4—516no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4D4×D512yes—
392C2×C3×C4D4×D512yes—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—24no—
397C2×Dic3—22no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—104no—
403C22×C5—28no—
404C22×C5—24no—
405C22×C5—44no—
406C22×C5—42no—
407C22×C5—42no—
408C22×C5#100412yes—
409C22×C5#100412yes—
410C22×C5C23×Dic311yescharacteristic
411C22×C5C22×#6711yescharacteristic
412C22×C5C22×#6711yescharacteristic
413C2×D5—24no—
414C2×D5—24no—
415C2×D5—22no—
416C2×D5—22no—
417C2×D5—28no—
418C2×D5—24no—
419C2×D5—432no—
420C2×D5—44no—
421C2×D5—42no—
422C2×D5—42no—
423C2×D5C2×#21714yes—
424C4×C5—122no—
425C4×C5—122no—
426C4×C5C2×#21714yes—
427Dic5—122no—
428Dic5—122no—
429Dic5C2×#21714yes—
430C24—51no—
431C24—52no—
432C24—58no—
433C24—104no—
434C24—104no—
435C24—204no—
436C24—204no—
437C24C2×D3×D512yes—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—58no—
441C2×D4—54no—
442C2×D4—1032no—
443C2×D4—104no—
444C2×D4—104no—
445C2×D4—102no—
446C2×D4—102no—
447C2×D4D5×Dic314yes—
448C22×C4—32no—
449C22×C4—32no—
450C22×C4—51no—
451C22×C4—54no—
452C22×C4—54no—
453C22×C4—54no—
454C22×C4—152no—
455C22×C4—152no—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—62no—
458C4⋊C4—304no—
459C4⋊C4—302no—
460C22⋊C4—124no—
461C22⋊C4—304no—
462C22⋊C4—304no—
463C22⋊C4—604no—
464C22⋊C4—604no—
465C22⋊C4—604no—
466C42—62no—
467C42—304no—
468C42—302no—
469C3×C5#230911yescharacteristic, complemented, Hall
470C22×C3—24no—
471C22×C3—28no—
472C22×C3—42no—
473C22×C3—44no—
474C22×C3—42no—
475C22×C3—54no—
476C22×C3—102no—
477C22×C3—104no—
478C22×C3—104no—
479C22×C3—102no—
480C22×C3—104no—
481C22×C3—108no—
482C22×C3—2032no—
483C22×C3—202no—
484C22×C3—204no—
485C22×C3—202no—
486C22×C3C22×C4×D511yescharacteristic
487C22×C3C2×D4×D511yescharacteristic
488C22×C3C2×D4×D511yescharacteristic
489C22×C3#414412yes—
490C22×C3#414912yes—
491C3×C4—54no—
492C3×C4D5×C22⋊C414yes—
493Dic3—42no—
494Dic3—42no—
495Dic3—202no—
496Dic3—202no—
497C2×C5—44no—
498C2×C5#579812yes—
499C2×C5#580512yes—
500C2×C5#580511yescharacteristic
501C2×C5#580511yescharacteristic
502C2×C5C22×#21711yescharacteristic
503D5—24no—
504D5—44no—
505C23—24no—
506C23—24no—
507C23—22no—
508C23—22no—
509C23—52no—
510C23—52no—
511C23—52no—
512C23—54no—
513C23—1016no—
514C23—102no—
515C23—102no—
516C23—104no—
517C23—104no—
518C23—102no—
519C23—102no—
520C23—2016no—
521C23—2016no—
522C23—208no—
523C23—208no—
524C23C2×D5×Dic314yes—
525C23C22×D3×D511yescharacteristic
526D4—28no—
527D4—1016no—
528D4—108no—
529C2×C4—52no—
530C2×C4—52no—
531C2×C4—52no—
532C2×C4—516no—
533C2×C4—62no—
534C2×C4—64no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—302no—
539C2×C4—302no—
540C2×C4—304no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4C2×D5×Dic312yes—
544C2×C4D5×#6712yes—
545C2×C4D5×#6712yes—
546C2×C3—44no—
547C2×C3—104no—
548C2×C3—204no—
549C2×C3C2×D5×C22⋊C411yescharacteristic
550C2×C3#6587912yes—
551C2×C3#6594112yes—
552C2×C3#6600811yescharacteristic
553C2×C3#6604911yescharacteristic
554C5#8404411yescharacteristic, complemented, Sylow
555C22—24no—
556C22—28no—
557C22—44no—
558C22—42no—
559C22—42no—
560C22—54no—
561C22—104no—
562C22—104no—
563C22—102no—
564C22—102no—
565C22—104no—
566C22—108no—
567C22—2032no—
568C22—204no—
569C22—202no—
570C22—202no—
571C22#9202512yes—
572C22#9202612yes—
573C22C22×D5×Dic311yescharacteristic
574C22C2×D5×#6711yescharacteristic
575C22C2×D5×#6711yescharacteristic
576C4—54no—
577C4—122no—
578C4—122no—
579C4—602no—
580C4—602no—
581C4D5×#21714yes—
582C3#1060815911yescharacteristic, complemented, Sylow
583C2—44no—
584C2—104no—
585C2—204no—
586C2#1175491012yes—
587C2#1175493312yes—
588C2#1175493511yescharacteristic
589C2#1175493711yescharacteristic
590C2C2×D5×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D4×D5C2
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×#91358C2semidirect
3. C2×#91357C2semidirect
4. #11751322C2semidirect
5. C5×#5221C2semidirect
6. #11749489C2semidirect
7. #11749488C2semidirect
8. #11748796C2semidirect
9. #11748785C2semidirect
16. C2×C3×D4×D5C4semidirect
19. C2×#6719C22semidirect
20. C2×C4⋊Dic15C22semidirect
21. C2×C4×Dic15C22semidirect
22. C2×C5×#217C22semidirect
23. C2×C5×C4⋊Dic3C22semidirect
24. C2×C4×C5×Dic3C22semidirect
25. C2×#6668C22semidirect
28. C2×#6665C22semidirect
29. C2×#6665C22semidirect
30. C2×Dic3×Dic5C22semidirect
90. #5221D5semidirect
96. C2×D4×D5Dic3semidirect
154. C3×C4×D5C22⋊C4semidirect
168. C2×#217C2×D5semidirect
173. C2×C4⋊Dic3C2×D5semidirect
176. C2×C4×Dic3C2×D5semidirect
331. C4×D5#217semidirect
469. C3×C5#2309semidirect
554. C5#84044semidirect
582. C3#10608159semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C2×#913582
C2×#913572
#117513222
C5×#52212
#117494892
#117494882
#117487962
#117487852
#106081593
#840445