Finite Group Databasebeta

← #14327567

Subgroups — #14327567

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1202C211yesmaximal, characteristic
2#11750768C211yesmaximal, characteristic, complemented
3C5×#4648C211yesmaximal, characteristic, complemented
4C3×#64953C211yesmaximal, characteristic, complemented
5#11748888C211yesmaximal, characteristic, complemented
6#11748881C212yesmaximal, complemented
7#11748706C212yesmaximal, complemented
8#11748702C211yesmaximal, characteristic, complemented
9#11748700C212yesmaximal
10#11748660C212yesmaximal, complemented
11#11748618C211yesmaximal, characteristic, complemented
12#10605148—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1202C2211yescharacteristic
16C22×#1200C2212yes—
17C2×#6714C2212yes—
18C2×#6712C2212yes—
19C2×C4×C5×Dic3C2212yes—
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C3×#685C2212yes—
22C2×Dic3⋊Dic5C2211yescharacteristic
23C2×#6667C2211yescharacteristic
24C2×#6665C2212yes—
25C2×#6665C2211yescharacteristic
26C2×Dic3×Dic5C2212yes—
27C4×#1202C418yescomplemented
28C3×C5×#95C2211yescharacteristic
29#91115C2211yescharacteristic
30C5×C3⋊#95C2211yescharacteristic
31C5×C3⋊#95C2212yes—
32C3×#3963C2211yescharacteristic
33C3×#3963C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#74123—51nomaximal, Hall
38C2×C4×D20—31no—
39C5×#376—31no—
40#65229—32no—
41C4×#685—32no—
42#65226—31no—
43#64956—31no—
44#64955—31no—
45#64954—32no—
46#64953D311yescharacteristic, complemented
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—42no—
56C2×C4×D15C2×C414yes—
57C22×C5×Dic3C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2312yes—
60C22×C3×Dic5C2312yes—
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×C4×D5—42no—
63C2×C3×C4×D5C2×C414yescomplemented
64C2×#1202—22no—
65C2×#1202—22no—
66C2×#1202C2×C414yes—
67C2×#1200—24no—
68C2×#1200—24no—
69C2×#1200—42no—
70#6714—24no—
71#6712—42no—
72C4×C5×Dic3—24no—
73C4×C5×Dic3C2×C414yescomplemented
74C3×#685—42no—
75Dic3⋊Dic5C2×C414yescomplemented
76#6667C2×C414yes—
77#6665—24no—
78#6665C2×C414yescomplemented
79Dic3×Dic5—42no—
80C2×C4×#67—51no—
81C3×#381—51no—
82C4×#217—51no—
83#4956—52no—
84#4945—52no—
85#4667—51no—
86#4666—52no—
87D3×#95—51no—
88#4652—52no—
89#4651—51no—
90#4648D511yescharacteristic, complemented
91C22×D20—31no—
92C22×C4×D5—31no—
93C22×C4×D5—32no—
94C22×C4×D5C2×D311yescharacteristic
95C2×C42×C5—31no—
96C2×C42×C5—32no—
97C2×#685—31no—
98C2×#685—31no—
99C2×#685—32no—
100C2×#685—32no—
101C2×#685C2×D312yes—
102C2×C4⋊Dic5—31no—
103C2×#683—32no—
104C2×C4×Dic5—32no—
105C4×D20—38no—
106C5×#95—32no—
107C5×#95—31no—
108C5×#95C2×D311yescharacteristic
109#3963—31no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963C2×D312yes—
114#3963C2×D311yescharacteristic
115#2353—151noSylow
116C23×C3×C5C2411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15C22×C412yes—
120C22×D15#4112yes—
121C22×D15#4112yes—
122C22×C3×D5—22no—
123C22×C3×D5—21no—
124C22×C3×D5—21no—
125C22×C3×D5—22no—
126C22×C3×D5C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C22×C412yes—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15C22×C412yes—
137C4×D15—44no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3C22×C412yes—
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3#4114yes—
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—
153#1200—48no—
154C23×C3×C4—51no—
155C22×#67—51no—
156C22×C4×D3—51no—
157C22×C4×D3—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×D512yes—
168C2×C4×Dic3C2×D511yescharacteristic
169C3×#95—51no—
170C3×#95—52no—
171C3×#95C2×D511yescharacteristic
172C3⋊#95—51no—
173C3⋊#95—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95C2×D512yes—
177C3⋊#95C2×D511yescharacteristic
178C23×D5—31no—
179C23×D5C22×D311yescharacteristic
180C22×C4×C5—31no—
181C22×C4×C5—32no—
182C22×C4×C5—31no—
183C22×C4×C5C22×D312yes—
184C22×C4×C5C22×D311yescharacteristic
185C22×Dic5—31no—
186C22×Dic5—32no—
187C22×Dic5C22×D312yes—
188C22×Dic5C22×D311yescharacteristic
189C2×D20—34no—
190C2×D20—62no—
191C2×D20—62no—
192C2×C4×D5—34no—
193C2×C4×D5—42no—
194C2×C4×D5—64no—
195C2×C4×D5—64no—
196C2×C4×D5—122no—
197C2×C4×D5—122no—
198C2×C4×D5C4×D314yescomplemented
199C42×C5—34no—
200C42×C5—64no—
201#685—34no—
202#685—34no—
203#685—42no—
204#685—64no—
205#685—64no—
206C4⋊Dic5—34no—
207#683—122no—
208C4×Dic5—122no—
209C2×C4×D4—151no—
210#388—152no—
211#387—152no—
212#386—152no—
213#383—151no—
214#381—51no—
215#380—151no—
216C4×C22⋊C4—151no—
217C4×C22⋊C4—152no—
218#376—31no—
219C2×#95—151no—
220C22×C3×C5C23×C411yescharacteristic
221C22×C3×C5C2×#4112yes—
222C22×C3×C5C2×#4111yescharacteristic
223C22×C3×C5C2×#4111yescharacteristic
224C22×C3×C5H(5,𝔽2)12yes—
225C2×D15—22no—
226C2×D15—22no—
227C2×D15—24no—
228C2×D15—24no—
229C2×D15#11714yes—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—22no—
233C2×C3×D5—42no—
234C2×C3×D5—42no—
235C3×C4×C5—22no—
236C3×C4×C5—42no—
237Dic15—22no—
238Dic15—42no—
239C3×Dic5—22no—
240C3×Dic5—42no—
241C5×Dic3—22no—
242C5×Dic3—22no—
243C5×Dic3—24no—
244C24×C3—51no—
245C23×D3—51no—
246C22×C3×C4—51no—
247C22×C3×C4—54no—
248C22×C3×C4—52no—
249C22×C3×C4—202no—
250C22×C3×C4C22×D512yes—
251C22×C3×C4C22×D511yescharacteristic
252C2×#67—54no—
253C2×#67—102no—
254C2×#67—102no—
255C22×Dic3—51no—
256C22×Dic3—52no—
257C22×Dic3C22×D511yescharacteristic
258C22×Dic3C22×D511yescharacteristic
259C22×Dic3C22×D512yes—
260C2×C4×D3—54no—
261C2×C4×D3—104no—
262C2×C4×D3—104no—
263C2×C4×D3—202no—
264C2×C4×D3—202no—
265C3×C22⋊C4—202no—
266#217—54no—
267#217—104no—
268(C2×D3)⋊C4—54no—
269(C2×D3)⋊C4—104no—
270Dic3⋊C4—54no—
271Dic3⋊C4—202no—
272C4×Dic3—24no—
273C4×Dic3—202no—
274C4×Dic3C4×D514yescomplemented
275C23×C5C23×D311yescharacteristic
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—21no—
279C22×D5—21no—
280C22×D5—32no—
281C22×D5—32no—
282C22×D5—32no—
283C22×D5—62no—
284C22×D5—62no—
285C22×D5C2×C4×D312yes—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—22no—
290C2×C4×C5—32no—
291C2×C4×C5—32no—
292C2×C4×C5—34no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5—62no—
296C2×C4×C5—61no—
297C2×C4×C5—61no—
298C2×C4×C5C2×C4×D312yes—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—32no—
304C2×Dic5—62no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C2×Dic5C2×C4×D312yes—
309D20—68no—
310C4×D5—44no—
311C4×D5—128no—
312C4×D5—124no—
313C22×D4—151no—
314C23×C4—51no—
315C23×C4—152no—
316C23×C4—151no—
317C4×D4—158no—
318C2×C4⋊C4—151no—
319C2×C4⋊C4—152no—
320C2×C22⋊C4—52no—
321C2×C22⋊C4—151no—
322C2×C22⋊C4—151no—
323C2×C22⋊C4—152no—
324C2×C22⋊C4—152no—
325C2×C42—31no—
326C2×C42—32no—
327C2×C42—152no—
328#95—31no—
329#95—32no—
330#95—51no—
331#95—52no—
332#95—152no—
333#95—152no—
334#95—152no—
335#95—151no—
336#95D3×D511yescharacteristic
337C2×C3×C5C2×#11711yescharacteristic
338C2×C3×C5C4×#4111yescharacteristic
339C2×C3×C5#51811yescharacteristic
340C2×C3×C5#55112yes—
341C2×C3×C5#55312yes—
342D15—24no—
343C3×D5—42no—
344C23×C3—52no—
345C23×C3—102no—
346C23×C3—101no—
347C23×C3—101no—
348C23×C3—102no—
349C23×C3C23×D511yescharacteristic
350C22×D3—52no—
351C22×D3—52no—
352C22×D3—52no—
353C22×D3—102no—
354C22×D3—102no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—52no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—204no—
365C2×C3×C4C2×C4×D512yes—
366#67—108no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—52no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C2×Dic3C2×C4×D512yes—
378C2×Dic3C2×C4×D512yes—
379C2×Dic3#70914yes—
380C4×D3—208no—
381C4×D3—204no—
382C22×C5C22×C4×D311yescharacteristic
383C22×C5#100412yes—
384C22×C5D3×#4112yes—
385C22×C5D3×#4111yescharacteristic
386C22×C5D3×#4111yescharacteristic
387C2×D5—22no—
388C2×D5—22no—
389C2×D5—22no—
390C2×D5—34no—
391C2×D5—42no—
392C2×D5—42no—
393C2×D5—64no—
394C2×D5—64no—
395C2×D5—62no—
396C2×D5—62no—
397C4×C5—22no—
398C4×C5—42no—
399C4×C5—64no—
400C4×C5—62no—
401C4×C5—62no—
402Dic5—22no—
403Dic5—42no—
404Dic5—62no—
405Dic5—122no—
406C24—51no—
407C24—151no—
408C2×D4—154no—
409C2×D4—302no—
410C2×D4—302no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—31no—
414C22×C4—51no—
415C22×C4—54no—
416C22×C4—52no—
417C22×C4—151no—
418C22×C4—154no—
419C22×C4—152no—
420C22×C4—202no—
421C22×C4—304no—
422C22×C4—304no—
423C22×C4—602no—
424C22×C4—602no—
425C22×C4C2×D3×D512yes—
426C22×C4C2×D3×D511yescharacteristic
427C4⋊C4—154no—
428C4⋊C4—602no—
429C22⋊C4—154no—
430C22⋊C4—154no—
431C22⋊C4—202no—
432C22⋊C4—304no—
433C22⋊C4—304no—
434C42—34no—
435C42—64no—
436C42—602no—
437C3×C5#235311yescharacteristic, complemented, Hall
438C22×C3—102no—
439C22×C3—102no—
440C22×C3—102no—
441C22×C3—202no—
442C22×C3—202no—
443C22×C3C22×C4×D511yescharacteristic
444C22×C3C2×#70912yes—
445C22×C3D5×#4111yescharacteristic
446C22×C3D5×#4111yescharacteristic
447C22×C3#414912yes—
448C2×D3—54no—
449C2×D3—102no—
450C2×D3—102no—
451C2×D3—104no—
452C2×D3—104no—
453C3×C4—22no—
454C3×C4—42no—
455C3×C4—102no—
456C3×C4—202no—
457Dic3—22no—
458Dic3—22no—
459Dic3—24no—
460Dic3—102no—
461Dic3—202no—
462C2×C5#548611yescharacteristic
463C2×C5D3×#11711yescharacteristic
464C2×C5#552211yescharacteristic
465C2×C5#565912yes—
466C2×C5#566112yes—
467D5—42no—
468D5—64no—
469C23—52no—
470C23—102no—
471C23—101no—
472C23—102no—
473C23—101no—
474C23—152no—
475C23—152no—
476C23—152no—
477C23—302no—
478C23—302no—
479C23C22×D3×D511yescharacteristic
480D4—308no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—34no—
488C2×C4—52no—
489C2×C4—62no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—61no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—152no—
499C2×C4—204no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—604no—
505C2×C4—608no—
506C2×C4C4×D3×D512yes—
507C2×C3—202no—
508C2×C3C4×#70911yescharacteristic
509C2×C3D5×#11711yescharacteristic
510C2×C3#6585511yescharacteristic
511C2×C3#6586112yes—
512C2×C3#6586412yes—
513D3—104no—
514C5#7412311yescharacteristic, complemented, Sylow
515C22—102no—
516C22—102no—
517C22—102no—
518C22—154no—
519C22—202no—
520C22—202no—
521C22—302no—
522C22—304no—
523C22—304no—
524C22—302no—
525C22C2×C4×D3×D511yescharacteristic
526C22D3×#70912yes—
527C22#9202411yescharacteristic
528C22#9202612yes—
529C22#9203411yescharacteristic
530C4—22no—
531C4—42no—
532C4—62no—
533C4—64no—
534C4—62no—
535C4—102no—
536C4—202no—
537C4—302no—
538C4—602no—
539C3#1060514811yescharacteristic, complemented, Sylow
540C2—202no—
541C2—304no—
542C2#1175266611yescharacteristic
543C2#1175306611yescharacteristic
544C2#1175312512yes—
545C2#1175383511yescharacteristic
546C2#1175392112yes—
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#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #11750768C2semidirect
3. C5×#4648C2semidirect
4. C3×#64953C2semidirect
5. #11748888C2semidirect
6. #11748881C2semidirect
7. #11748706C2semidirect
8. #11748702C2semidirect
10. #11748660C2semidirect
11. #11748618C2semidirect
27. C4×#1202C4semidirect
46. #64953D3semidirect
63. C2×C3×C4×D5C2×C4semidirect
73. C4×C5×Dic3C2×C4semidirect
75. Dic3⋊Dic5C2×C4semidirect
78. #6665C2×C4semidirect
90. #4648D5semidirect
198. C2×C4×D5C4×D3semidirect
274. C4×Dic3C4×D5semidirect
437. C3×C5#2353semidirect
514. C5#74123semidirect
539. C3#10605148semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12022
#117507682
C5×#46482
C3×#649532
#117488882
#117488812
#117487062
#117487022
#117487002
#117486602
#117486182
#106051483
#741235