Finite Group Databasebeta

← #14323053

Subgroups — #14323053

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2#11751037C211yesmaximal, characteristic, complemented
3C5×#4937C211yesmaximal, characteristic, complemented
4#11748900C212yesmaximal, complemented
5#11748896C212yesmaximal
6D5×C3⋊#95C211yesmaximal, characteristic, complemented
7#11748772C212yesmaximal, complemented
8#11748738C211yesmaximal, characteristic, complemented
9#11748737C211yesmaximal, characteristic, complemented
10#11748702C211yesmaximal, characteristic, complemented
11#11748698C212yesmaximal, complemented
12#10606026—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×D5×Dic3C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4⋊Dic15C2212yes—
19C2×C3×#685C2211yescharacteristic
20C2×C3×#685C2211yescharacteristic
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C3×C4×D20C418yescomplemented
23C2×#6668C2212yes—
24C2×#6665C2212yes—
25C2×#6665C2212yes—
26C2×#6665C2212yes—
27C2×Dic3×Dic5C2212yes—
28#91115C2211yescharacteristic
29#91115C2212yes—
30#91115C2211yescharacteristic
31C5×C3⋊#95C2211yescharacteristic
32C5×C3⋊#95C2212yes—
33C5×C3⋊#95C2212yes—
34C5×C3⋊#95C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#82324—51nomaximal, Hall
38C2×C4×D20D311yescharacteristic
39C5×#383—31no—
40#65225—31no—
41#64959—32no—
42#64957—32no—
43#64956—31no—
44#64955—31no—
45#64954—32no—
46#64953—31no—
47D5×#95—31no—
48#64943—32no—
49C23×C3×D5C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2312yes—
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×D20—24no—
61C2×C3×D20C2×C414yes—
62C2×C3×C4×D5—42no—
63C2×C3×C4×D5—42no—
64C2×C3×C4×D5C2×C414yes—
65C2×C3×C4×D5C2×C414yescomplemented
66C2×D5×Dic3—24no—
67C2×D5×Dic3—42no—
68C2×D5×Dic3—42no—
69C3×C42×C5C2×C414yescomplemented
70C4⋊Dic15—42no—
71C3×#685C2×C414yes—
72C3×#685C2×C414yescomplemented
73C3×C4⋊Dic5C2×C414yescomplemented
74#6668—42no—
75#6665—24no—
76#6665—42no—
77#6665—42no—
78Dic3×Dic5—42no—
79C2×C3×C4×D4—51no—
80#5220—52no—
81#5212—51no—
82#5211—51no—
83C4×#217—51no—
84C2×C3⋊#95—51no—
85#4980—52no—
86#4951—52no—
87#4950—52no—
88#4937D511yescharacteristic, complemented
89#4936—51no—
90C22×D20C2×D311yescharacteristic
91C22×C4×D5—32no—
92C22×C4×D5C2×D311yescharacteristic
93C22×C4×D5C2×D311yescharacteristic
94C2×C42×C5C2×D311yescharacteristic
95C2×#685—32no—
96C2×#685—32no—
97C2×#685—32no—
98C2×#685C2×D311yescharacteristic
99C2×#685C2×D311yescharacteristic
100C2×C4⋊Dic5—32no—
101C2×C4⋊Dic5C2×D311yescharacteristic
102C2×#683—32no—
103C2×C4×Dic5—32no—
104C4×D20Dic318yescomplemented
105C5×#95—32no—
106C5×#95—31no—
107C5×#95—31no—
108C5×#95—32no—
109#3963—32no—
110#3963—31no—
111#3963—31no—
112#3963—32no—
113#3963—32no—
114#2318—151noSylow
115C23×C3×C5C2411yescharacteristic
116C22×C3×D5—21no—
117C22×C3×D5—22no—
118C22×C3×D5—21no—
119C22×C3×D5—22no—
120C22×C3×D5—21no—
121C22×C3×D5—22no—
122C22×C3×D5—21no—
123C22×C3×D5C22×C412yes—
124C22×C3×D5C22×C412yes—
125C22×C3×D5#4114yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C412yes—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5C22×C412yes—
148C2×C3×Dic5C22×C412yes—
149C3×D20—28no—
150C3×C4×D5—44no—
151C3×C4×D5—44no—
152D5×Dic3—48no—
153C22×C3×D4—51no—
154C23×C3×C4—51no—
155C23×C3×C4—51no—
156C23×Dic3—52no—
157C3×C4×D4—58no—
158C2×C3×C4⋊C4—51no—
159C2×C3×C22⋊C4—51no—
160C2×C3×C22⋊C4—51no—
161C2×C3×C42C2×D511yescharacteristic
162C2×#217—52no—
163C2×#217—52no—
164C2×#217—52no—
165C2×C4⋊Dic3—52no—
166C2×C4⋊Dic3—52no—
167C2×C4×Dic3—52no—
168C3⋊#95—51no—
169C3⋊#95—51no—
170C3⋊#95—52no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95C2×D512yes—
174C3⋊#95C2×D511yescharacteristic
175C3⋊#95C2×D511yescharacteristic
176C3⋊#95C2×D512yes—
177C23×D5C22×D311yescharacteristic
178C23×D5C22×D311yescharacteristic
179C22×C4×C5—32no—
180C22×C4×C5—32no—
181C22×C4×C5C22×D311yescharacteristic
182C22×C4×C5C22×D311yescharacteristic
183C22×C4×C5C22×D311yescharacteristic
184C22×Dic5—32no—
185C22×Dic5—32no—
186C22×Dic5C22×D311yescharacteristic
187C22×Dic5C22×D311yescharacteristic
188C2×D20—24no—
189C2×D20C2×Dic314yes—
190C2×C4×D5—42no—
191C2×C4×D5—42no—
192C2×C4×D5—64no—
193C2×C4×D5—122no—
194C2×C4×D5—122no—
195C2×C4×D5C2×Dic314yes—
196C2×C4×D5C2×Dic314yescomplemented
197C42×C5C2×Dic314yescomplemented
198#685—64no—
199#685—122no—
200#685—122no—
201#685C2×Dic314yes—
202#685C2×Dic314yescomplemented
203C4⋊Dic5—122no—
204C4⋊Dic5C2×Dic314yescomplemented
205#683—122no—
206C4×Dic5—122no—
207C2×C4×D4—51no—
208#388—152no—
209#387—152no—
210#386—152no—
211#385—152no—
212#383—31no—
213#382—151no—
214#381—151no—
215#380—151no—
216C4×C22⋊C4—151no—
217C2×#95—151no—
218C22×C3×C5C23×C411yescharacteristic
219C22×C3×C5C2×#4112yes—
220C22×C3×C5H(5,𝔽2)12yes—
221C22×C3×C5H(5,𝔽2)11yescharacteristic
222C22×C3×C52−1+411yescharacteristic
223C2×C3×D5—22no—
224C2×C3×D5—22no—
225C2×C3×D5—24no—
226C2×C3×D5—24no—
227C2×C3×D5—22no—
228C2×C3×D5—22no—
229C2×C3×D5—22no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5#11714yes—
233C3×C4×C5—22no—
234C3×C4×C5—22no—
235C3×C4×C5—22no—
236Dic15—42no—
237Dic15—42no—
238C3×Dic5—22no—
239C3×Dic5—22no—
240C5×Dic3—42no—
241C5×Dic3—42no—
242C24×C3—51no—
243C24×C3—51no—
244C2×C3×D4—54no—
245C2×C3×D4—104no—
246C22×C3×C4—51no—
247C22×C3×C4—51no—
248C22×C3×C4—54no—
249C22×C3×C4—54no—
250C22×C3×C4—202no—
251C22×C3×C4—202no—
252C22×C3×C4C22×D511yescharacteristic
253C22×C3×C4C22×D511yescharacteristic
254C22×C3×C4C22×D511yescharacteristic
255C22×Dic3—52no—
256C22×Dic3—52no—
257C22×Dic3—104no—
258C22×Dic3—202no—
259C22×Dic3—202no—
260C22×Dic3C22×D512yes—
261C22×Dic3C22×D512yes—
262C3×C4⋊C4—54no—
263C3×C22⋊C4—54no—
264C3×C22⋊C4—54no—
265C3×C42C4×D514yescomplemented
266#217—104no—
267#217—202no—
268#217—202no—
269C4⋊Dic3—202no—
270C4⋊Dic3—202no—
271C4×Dic3—202no—
272C23×C5C23×D311yescharacteristic
273C22×D5—22no—
274C22×D5—21no—
275C22×D5—21no—
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—21no—
279C22×D5—21no—
280C22×D5#23514yes—
281C22×D5C22×Dic312yes—
282C22×D5C22×Dic312yes—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—62no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5—62no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5C22×Dic312yes—
294C2×C4×C5C22×Dic312yes—
295C2×C4×C5C22×Dic312yes—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—62no—
299C2×Dic5—62no—
300C2×Dic5—62no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5C22×Dic312yes—
305C2×Dic5C22×Dic312yes—
306D20—28no—
307C4×D5—44no—
308C4×D5—44no—
309C4×D5—128no—
310C22×D4—51no—
311C23×C4—51no—
312C23×C4—51no—
313C23×C4—152no—
314C4×D4—58no—
315C2×C4⋊C4—51no—
316C2×C4⋊C4—152no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—51no—
319C2×C22⋊C4—51no—
320C2×C22⋊C4—152no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4—152no—
323C2×C42—152no—
324C2×C42D3×D511yescharacteristic
325#95—31no—
326#95—31no—
327#95—32no—
328#95—32no—
329#95—152no—
330#95—152no—
331#95—151no—
332#95—151no—
333#95—152no—
334C2×C3×C5C2×#11711yescharacteristic
335C2×C3×C5#51811yescharacteristic
336C2×C3×C5#52011yescharacteristic
337C2×C3×C5#53812yes—
338C2×C3×C5#53912yes—
339C3×D5—24no—
340C3×D5—42no—
341C23×C3—52no—
342C23×C3—54no—
343C23×C3—52no—
344C23×C3—101no—
345C23×C3—102no—
346C23×C3—101no—
347C23×C3—102no—
348C23×C3—101no—
349C23×C3—102no—
350C23×C3—101no—
351C23×C3C23×D511yescharacteristic
352C3×D4—108no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—52no—
358C2×C3×C4—52no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—204no—
362C2×C3×C4—204no—
363C2×C3×C4C2×C4×D512yes—
364C2×C3×C4C2×C4×D512yes—
365C2×C3×C4C2×C4×D512yes—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C2×Dic3—102no—
378C2×Dic3—208no—
379C22×C5C2×#23512yes—
380C22×C5#100412yes—
381C22×C5#100911yescharacteristic
382C22×C5#101011yescharacteristic
383C22×C5C23×Dic311yescharacteristic
384C2×D5—22no—
385C2×D5—24no—
386C2×D5—24no—
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—22no—
390C2×D5—22no—
391C2×D5—42no—
392C2×D5—42no—
393C2×D5#92614yes—
394C4×C5—22no—
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—122no—
398C4×C5—122no—
399Dic5—22no—
400Dic5—22no—
401Dic5—122no—
402Dic5—122no—
403C24—51no—
404C24—51no—
405C2×D4—54no—
406C2×D4—104no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—51no—
410C22×C4—51no—
411C22×C4—54no—
412C22×C4—54no—
413C22×C4—152no—
414C22×C4—152no—
415C22×C4—202no—
416C22×C4—202no—
417C22×C4—304no—
418C22×C4—602no—
419C22×C4—602no—
420C22×C4C2×D3×D511yescharacteristic
421C22×C4C2×D3×D511yescharacteristic
422C22×C4C2×D3×D511yescharacteristic
423C4⋊C4—54no—
424C4⋊C4—602no—
425C4⋊C4—602no—
426C22⋊C4—54no—
427C22⋊C4—54no—
428C22⋊C4—304no—
429C22⋊C4—602no—
430C22⋊C4—602no—
431C42—602no—
432C42D5×Dic314yescomplemented
433C3×C5#231811yescharacteristic, complemented, Hall
434C22×C3—54no—
435C22×C3—102no—
436C22×C3—102no—
437C22×C3—104no—
438C22×C3—104no—
439C22×C3—102no—
440C22×C3—102no—
441C22×C3—102no—
442C22×C3—202no—
443C22×C3—202no—
444C22×C3C22×C4×D511yescharacteristic
445C22×C3D5×#4112yes—
446C22×C3#414912yes—
447C22×C3#414911yescharacteristic
448C22×C3#415011yescharacteristic
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—22no—
452C3×C4—102no—
453C3×C4—102no—
454Dic3—42no—
455Dic3—42no—
456Dic3—202no—
457Dic3—202no—
458C2×C5#556012yes—
459C2×C5#556412yes—
460C2×C5C2×#92611yescharacteristic
461C2×C5#579811yescharacteristic
462C2×C5#582711yescharacteristic
463D5—24no—
464D5—42no—
465C23—54no—
466C23—52no—
467C23—52no—
468C23—101no—
469C23—102no—
470C23—101no—
471C23—101no—
472C23—102no—
473C23—102no—
474C23—101no—
475C23C22×D3×D511yescharacteristic
476D4—108no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—52no—
482C2×C4—52no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—204no—
492C2×C4—204no—
493C2×C4—302no—
494C2×C4—302no—
495C2×C4—302no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—608no—
500C2×C4C2×D5×Dic312yes—
501C2×C4C2×D5×Dic312yes—
502C2×C4C2×D5×Dic312yes—
503C2×C3—104no—
504C2×C3—202no—
505C2×C3D5×#11711yescharacteristic
506C2×C3#6585511yescharacteristic
507C2×C3#6585711yescharacteristic
508C2×C3#6603812yes—
509C2×C3#6604112yes—
510C5#8232411yescharacteristic, complemented, Sylow
511C22—54no—
512C22—102no—
513C22—104no—
514C22—104no—
515C22—102no—
516C22—102no—
517C22—102no—
518C22—102no—
519C22—202no—
520C22—202no—
521C22#9200111yescharacteristic
522C22D5×#23512yes—
523C22#9201712yes—
524C22#9201911yescharacteristic
525C22C22×D5×Dic311yescharacteristic
526C4—22no—
527C4—22no—
528C4—22no—
529C4—102no—
530C4—102no—
531C4—122no—
532C4—122no—
533C4—602no—
534C4—602no—
535C3#1060602611yescharacteristic, complemented, Sylow
536C2—104no—
537C2—202no—
538C2#1175256712yes—
539C2#1175275612yes—
540C2D5×#92611yescharacteristic
541C2#1175448811yescharacteristic
542C2#1175450911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2318
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. #11751037C2semidirect
3. C5×#4937C2semidirect
4. #11748900C2semidirect
6. D5×C3⋊#95C2semidirect
7. #11748772C2semidirect
8. #11748738C2semidirect
9. #11748737C2semidirect
10. #11748702C2semidirect
11. #11748698C2semidirect
22. C3×C4×D20C4semidirect
65. C2×C3×C4×D5C2×C4semidirect
69. C3×C42×C5C2×C4semidirect
72. C3×#685C2×C4semidirect
73. C3×C4⋊Dic5C2×C4semidirect
88. #4937D5semidirect
104. C4×D20Dic3semidirect
196. C2×C4×D5C2×Dic3semidirect
197. C42×C5C2×Dic3semidirect
202. #685C2×Dic3semidirect
204. C4⋊Dic5C2×Dic3semidirect
265. C3×C42C4×D5semidirect
432. C42D5×Dic3semidirect
433. C3×C5#2318semidirect
510. C5#82324semidirect
535. C3#10606026semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
#117510372
C5×#49372
#117489002
#117488962
D5×C3⋊#952
#117487722
#117487382
#117487372
#117487022
#117486982
#106060263
#823245