Finite Group Databasebeta

← #14323064

Subgroups — #14323064

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×C4×#1202C211yesmaximal, characteristic
2D15×#95C211yesmaximal, characteristic, complemented
3C5×#4651C211yesmaximal, characteristic, complemented
4C3×#64956C211yesmaximal, characteristic, complemented
5#11748917C212yesmaximal
6#11748737C211yesmaximal, characteristic, complemented
7#11748729C212yesmaximal, complemented
8#11748712C212yesmaximal, complemented
9#11748670C211yesmaximal, characteristic, complemented
10#11748665C212yesmaximal, complemented
11#11748600C211yesmaximal, characteristic, complemented
12#10606026—31nomaximal, Hall
13C22×C4×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1202C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C2×C3×#685C2212yes—
19C2×C3×#683C2212yes—
20C2×Dic3⋊Dic5C2212yes—
21C2×Dic3⋊Dic5C2211yescharacteristic
22C2×#6667C2212yes—
23C2×#6667C2211yescharacteristic
24C2×#6665C2212yes—
25C2×#6665C2211yescharacteristic
26C2×Dic3×Dic5C2212yes—
27C4×#1202C418yescomplemented
28C3×C5×#95C2211yescharacteristic
29#91115C2212yes—
30#91115C2211yescharacteristic
31C5×C3⋊#95C2212yes—
32C5×C3⋊#95C2211yescharacteristic
33C5×C3⋊#95C2212yes—
34C3×#3963C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#74006—51nomaximal, Hall
38C2×C4×D20—31no—
39C5×#383—31no—
40#65225—31no—
41#64959—32no—
42#64957—32no—
43#64956D311yescharacteristic, complemented
44#64955—31no—
45#64954—32no—
46#64953—31no—
47D5×#95—31no—
48#64943—32no—
49C23×D15C2311yescharacteristic
50C23×C3×D5C2311yescharacteristic
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C2×C4×D15—24no—
56C2×C4×D15—42no—
57C2×C4×D15—42no—
58C2×C4×D15—42no—
59C2×C4×D15C2×C414yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—42no—
66C2×C3×C4×D5C2×C414yescomplemented
67C2×#1202—24no—
68C2×#1202C2×C414yes—
69C4×C5×Dic3C2×C414yescomplemented
70C3×#685—42no—
71C3×#683—42no—
72Dic3⋊Dic5—42no—
73Dic3⋊Dic5C2×C414yescomplemented
74#6667—24no—
75#6667C2×C414yes—
76#6665—42no—
77#6665C2×C414yescomplemented
78Dic3×Dic5—42no—
79C2×C4×#67—51no—
80C3×#380—51no—
81#5211—51no—
82#4989—52no—
83#4978—52no—
84#4956—52no—
85#4945—52no—
86#4666—51no—
87D3×#95—51no—
88#4651D511yescharacteristic, complemented
89#4650—51no—
90C22×D20—31no—
91C22×C4×D5—31no—
92C22×C4×D5—32no—
93C22×C4×D5C2×D311yescharacteristic
94C2×C42×C5—31no—
95C2×#685—31no—
96C2×#685—31no—
97C2×#685—32no—
98C2×#685—32no—
99C2×#685C2×D312yes—
100C2×C4⋊Dic5—31no—
101C2×C4⋊Dic5—32no—
102C2×#683C2×D312yes—
103C2×C4×Dic5—32no—
104C4×D20—38no—
105C5×#95—32no—
106C5×#95—31no—
107C5×#95—32no—
108C5×#95C2×D311yescharacteristic
109#3963—32no—
110#3963—31no—
111#3963—32no—
112#3963—32no—
113#3963C2×D311yescharacteristic
114#2318—151noSylow
115C23×C3×C5C2411yescharacteristic
116C22×D15—22no—
117C22×D15—21no—
118C22×D15—21no—
119C22×D15C22×C412yes—
120C22×D15#4114yes—
121C22×C3×D5—22no—
122C22×C3×D5—22no—
123C22×C3×D5—21no—
124C22×C3×D5—21no—
125C22×C3×D5C22×C412yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5C22×C412yes—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15C22×C412yes—
136C4×D15—44no—
137C4×D15—48no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3C22×C412yes—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5C22×C412yes—
151C3×C4×D5—44no—
152#1202—28no—
153C23×C3×C4—51no—
154C22×#67—51no—
155C22×C4×D3—51no—
156C22×C4×D3—52no—
157C2×C3×C4⋊C4—52no—
158C2×C3×C22⋊C4—52no—
159C2×#217—51no—
160C2×#217—52no—
161C4×#67—58no—
162C2×(C2×D3)⋊C4—51no—
163C2×(C2×D3)⋊C4—52no—
164C2×Dic3⋊C4—51no—
165C2×Dic3⋊C4—52no—
166C2×C4×Dic3—52no—
167C2×C4×Dic3C2×D511yescharacteristic
168C3×#95—51no—
169C3×#95C2×D511yescharacteristic
170C3⋊#95—51no—
171C3⋊#95—52no—
172C3⋊#95—52no—
173C3⋊#95—52no—
174C3⋊#95C2×D511yescharacteristic
175C3⋊#95C2×D512yes—
176C3⋊#95C2×D512yes—
177C23×D5—31no—
178C23×D5C22×D311yescharacteristic
179C22×C4×C5—31no—
180C22×C4×C5—31no—
181C22×C4×C5—32no—
182C22×C4×C5C22×D312yes—
183C22×C4×C5C22×D311yescharacteristic
184C22×Dic5—31no—
185C22×Dic5—32no—
186C22×Dic5C22×D312yes—
187C22×Dic5C22×D311yescharacteristic
188C2×D20—34no—
189C2×D20—64no—
190C2×C4×D5—34no—
191C2×C4×D5—42no—
192C2×C4×D5—64no—
193C2×C4×D5—122no—
194C2×C4×D5—122no—
195C2×C4×D5—122no—
196C2×C4×D5C4×D314yescomplemented
197C42×C5—34no—
198#685—34no—
199#685—34no—
200#685—42no—
201#685—64no—
202#685—122no—
203C4⋊Dic5—34no—
204C4⋊Dic5—122no—
205#683—42no—
206C4×Dic5—122no—
207C2×C4×D4—151no—
208#388—152no—
209#387—152no—
210#386—152no—
211#385—152no—
212#383—31no—
213#382—151no—
214#381—151no—
215#380—51no—
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×D15—22no—
224C2×D15—22no—
225C2×D15—24no—
226C2×D15—24no—
227C2×D15#11714yes—
228C2×C3×D5—22no—
229C2×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5—42no—
232C2×C3×D5—42no—
233C3×C4×C5—22no—
234C3×C4×C5—42no—
235Dic15—22no—
236Dic15—42no—
237C3×Dic5—22no—
238C3×Dic5—42no—
239C5×Dic3—22no—
240C5×Dic3—22no—
241C5×Dic3—42no—
242C24×C3—51no—
243C23×D3—51no—
244C22×C3×C4—51no—
245C22×C3×C4—54no—
246C22×C3×C4—52no—
247C22×C3×C4—202no—
248C22×C3×C4C22×D512yes—
249C22×C3×C4C22×D511yescharacteristic
250C2×#67—54no—
251C2×#67—104no—
252C22×Dic3—51no—
253C22×Dic3—52no—
254C22×Dic3C22×D512yes—
255C22×Dic3C22×D511yescharacteristic
256C22×Dic3C22×D511yescharacteristic
257C2×C4×D3—54no—
258C2×C4×D3—104no—
259C2×C4×D3—202no—
260C2×C4×D3—202no—
261C2×C4×D3—202no—
262C3×C4⋊C4—202no—
263C3×C22⋊C4—202no—
264#217—54no—
265#217—202no—
266(C2×D3)⋊C4—54no—
267(C2×D3)⋊C4—104no—
268Dic3⋊C4—54no—
269Dic3⋊C4—202no—
270C4×Dic3—202no—
271C4×Dic3C4×D514yescomplemented
272C23×C5C23×D311yescharacteristic
273C22×D5—21no—
274C22×D5—22no—
275C22×D5—21no—
276C22×D5—22no—
277C22×D5—32no—
278C22×D5—34no—
279C22×D5—62no—
280C22×D5—61no—
281C22×D5—61no—
282C22×D5C2×C4×D312yes—
283C2×C4×C5—22no—
284C2×C4×C5—22no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—32no—
288C2×C4×C5—32no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5C2×C4×D312yes—
296C2×Dic5—22no—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—32no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5C2×C4×D312yes—
306D20—68no—
307C4×D5—44no—
308C4×D5—124no—
309C4×D5—128no—
310C22×D4—151no—
311C23×C4—51no—
312C23×C4—151no—
313C23×C4—152no—
314C4×D4—158no—
315C2×C4⋊C4—52no—
316C2×C4⋊C4—151no—
317C2×C4⋊C4—152no—
318C2×C22⋊C4—52no—
319C2×C22⋊C4—151no—
320C2×C22⋊C4—151no—
321C2×C22⋊C4—152no—
322C2×C22⋊C4—152no—
323C2×C42—31no—
324C2×C42—152no—
325#95—31no—
326#95—32no—
327#95—32no—
328#95—51no—
329#95—152no—
330#95—152no—
331#95—151no—
332#95—152no—
333#95D3×D511yescharacteristic
334C2×C3×C5C2×#11711yescharacteristic
335C2×C3×C5#51811yescharacteristic
336C2×C3×C5#52011yescharacteristic
337C2×C3×C5#53812yes—
338C2×C3×C5#53912yes—
339D15—24no—
340C3×D5—42no—
341C23×C3—52no—
342C23×C3—102no—
343C23×C3—102no—
344C23×C3—101no—
345C23×C3—101no—
346C23×C3C23×D511yescharacteristic
347C22×D3—52no—
348C22×D3—54no—
349C22×D3—102no—
350C22×D3—101no—
351C22×D3—101no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—52no—
357C2×C3×C4—102no—
358C2×C3×C4—102no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—204no—
362C2×C3×C4C2×C4×D512yes—
363#67—108no—
364C2×Dic3—22no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—52no—
371C2×Dic3—102no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3C2×C4×D512yes—
376C2×Dic3C2×C4×D512yes—
377C4×D3—204no—
378C4×D3—208no—
379C22×C5C22×C4×D311yescharacteristic
380C22×C5#100412yes—
381C22×C5#100411yescharacteristic
382C22×C5#100711yescharacteristic
383C22×C5D3×#4112yes—
384C2×D5—22no—
385C2×D5—22no—
386C2×D5—22no—
387C2×D5—34no—
388C2×D5—42no—
389C2×D5—42no—
390C2×D5—64no—
391C2×D5—62no—
392C2×D5—62no—
393C2×D5—64no—
394C4×C5—22no—
395C4×C5—42no—
396C4×C5—62no—
397C4×C5—62no—
398C4×C5—122no—
399Dic5—22no—
400Dic5—42no—
401Dic5—62no—
402Dic5—122no—
403C24—51no—
404C24—151no—
405C2×D4—154no—
406C2×D4—304no—
407C22×C4—31no—
408C22×C4—31no—
409C22×C4—32no—
410C22×C4—51no—
411C22×C4—54no—
412C22×C4—52no—
413C22×C4—151no—
414C22×C4—154no—
415C22×C4—152no—
416C22×C4—202no—
417C22×C4—304no—
418C22×C4—602no—
419C22×C4—602no—
420C22×C4—602no—
421C22×C4C2×D3×D512yes—
422C22×C4C2×D3×D511yescharacteristic
423C4⋊C4—154no—
424C4⋊C4—202no—
425C4⋊C4—602no—
426C22⋊C4—154no—
427C22⋊C4—154no—
428C22⋊C4—202no—
429C22⋊C4—304no—
430C22⋊C4—602no—
431C42—34no—
432C42—602no—
433C3×C5#231811yescharacteristic, complemented, Hall
434C22×C3—102no—
435C22×C3—102no—
436C22×C3—102no—
437C22×C3—202no—
438C22×C3—202no—
439C22×C3C22×C4×D511yescharacteristic
440C22×C3D5×#4112yes—
441C22×C3#414912yes—
442C22×C3#414911yescharacteristic
443C22×C3#415011yescharacteristic
444C2×D3—54no—
445C2×D3—102no—
446C2×D3—102no—
447C2×D3—104no—
448C2×D3—104no—
449C3×C4—22no—
450C3×C4—42no—
451C3×C4—102no—
452C3×C4—202no—
453Dic3—22no—
454Dic3—22no—
455Dic3—42no—
456Dic3—102no—
457Dic3—202no—
458C2×C5#548611yescharacteristic
459C2×C5#550411yescharacteristic
460C2×C5D3×#11711yescharacteristic
461C2×C5#561312yes—
462C2×C5#563812yes—
463D5—42no—
464D5—64no—
465C23—52no—
466C23—102no—
467C23—101no—
468C23—102no—
469C23—101no—
470C23—152no—
471C23—154no—
472C23—302no—
473C23—301no—
474C23—301no—
475C23C22×D3×D511yescharacteristic
476D4—308no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—52no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—152no—
495C2×C4—204no—
496C2×C4—302no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4—302no—
500C2×C4—604no—
501C2×C4—608no—
502C2×C4C4×D3×D512yes—
503C2×C3—202no—
504C2×C3D5×#11711yescharacteristic
505C2×C3#6585511yescharacteristic
506C2×C3#6585711yescharacteristic
507C2×C3#6603812yes—
508C2×C3#6604112yes—
509D3—104no—
510C5#7400611yescharacteristic, complemented, Sylow
511C22—102no—
512C22—102no—
513C22—102no—
514C22—154no—
515C22—202no—
516C22—202no—
517C22—304no—
518C22—302no—
519C22—304no—
520C22—302no—
521C22C2×C4×D3×D511yescharacteristic
522C22#9201612yes—
523C22#9202612yes—
524C22#9202611yescharacteristic
525C22#9203011yescharacteristic
526C4—22no—
527C4—42no—
528C4—62no—
529C4—62no—
530C4—102no—
531C4—122no—
532C4—202no—
533C4—302no—
534C4—602no—
535C3#1060602611yescharacteristic, complemented, Sylow
536C2—202no—
537C2—304no—
538C2#1175272311yescharacteristic
539C2#1175306611yescharacteristic
540C2#1175315012yes—
541C2#1175366811yescharacteristic
542C2#1175379312yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenter#95D3×D5
hypocenterC3×C5#2318
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. D15×#95C2semidirect
3. C5×#4651C2semidirect
4. C3×#64956C2semidirect
6. #11748737C2semidirect
7. #11748729C2semidirect
8. #11748712C2semidirect
9. #11748670C2semidirect
10. #11748665C2semidirect
11. #11748600C2semidirect
27. C4×#1202C4semidirect
43. #64956D3semidirect
66. C2×C3×C4×D5C2×C4semidirect
69. C4×C5×Dic3C2×C4semidirect
73. Dic3⋊Dic5C2×C4semidirect
77. #6665C2×C4semidirect
88. #4651D5semidirect
196. C2×C4×D5C4×D3semidirect
271. C4×Dic3C4×D5semidirect
433. C3×C5#2318semidirect
510. C5#74006semidirect
535. C3#10606026semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12022
D15×#952
C5×#46512
C3×#649562
#117489172
#117487372
#117487292
#117487122
#117486702
#117486652
#117486002
#106060263
#740065