Finite Group Databasebeta

← #14319735

Subgroups — #14319735

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic
2C2×#91552C212yesmaximal
3C4×C5×#217C211yesmaximal, characteristic, complemented
4C2×C3×#3963C211yesmaximal, characteristic, complemented
5Dic5×#217C212yesmaximal, complemented
6#11748888C211yesmaximal, characteristic, complemented
7#11748881C212yesmaximal, complemented
8#11748670C211yesmaximal, characteristic, complemented
9#11748663C211yesmaximal, characteristic, complemented
10#11748653C211yesmaximal, characteristic, complemented
11#11748645C212yesmaximal, complemented
12#10605167—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C22×#1200C2212yes—
18C2×#6719C2211yescharacteristic
19C4×#1220C418yescomplemented
20C2×#6714C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×#217C2212yes—
24C2×C4×C5×Dic3C2212yes—
25#91552C4116yescomplemented
26C2×#6669C2212yes—
27C2×#6667C2212yes—
28C2×Dic3×Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31C5×C3⋊#95C2211yescharacteristic
32C5×C3⋊#95C2211yescharacteristic
33C3×#3963C2212yes—
34C3×#3963C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#73322—51nomaximal, Hall
39C2×C4×C22⋊D5—31no—
40C2×#4027—32no—
41C4×C5×C22⋊C4—31no—
42C2×#3963D311yescharacteristic, complemented
43C22⋊C4×Dic5—32no—
44C4×#685—32no—
45C4×#683—32no—
46#64955—31no—
47D5×#95—31no—
48#64938—31no—
49#64937—31no—
50C24×C3×C5C2311yescharacteristic
51C23×D15C2311yescharacteristic
52C22×C3×C4×C5—42no—
53C22×C3×C4×C5C2×C414yescomplemented
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220C2×C418yes—
57C2×#1220C2×C414yes—
58C22×Dic15C2311yescharacteristic
59C22×Dic15C2311yescharacteristic
60C22×Dic15C2311yescharacteristic
61C2×C4×D15—42no—
62C2×C4×D15C2×C414yescomplemented
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C3×Dic5—42no—
66C22×C3×Dic5—42no—
67C22×C3×Dic5C2×C418yescomplemented
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2312yes—
70C2×#1200—42no—
71C2×#1200—42no—
72C2×#1200C2×C418yescomplemented
73#6719C2×C414yescomplemented
74#6714C2×C414yescomplemented
75#6712C2×C414yescomplemented
76C4×Dic15C2×C414yescomplemented
77C5×#217C2×C418yescomplemented
78C4×C5×Dic3—42no—
79#6669C2×C418yescomplemented
80#6667C2×C418yescomplemented
81Dic3×Dic5—42no—
82Dic3×Dic5—42no—
83Dic3×Dic5C2×C418yescomplemented
84C2×C4×#67—51no—
85C2×C4×#67—52no—
86C2×C3×#95—51no—
87C4×#217—52no—
88C4×#217D511yescharacteristic, complemented
89#4666—52no—
90#4666—51no—
91D3×#95—51no—
92#4649—52no—
93#4649—51no—
94#4648—51no—
95C23×C4×C5C2×D311yescharacteristic
96C22×C22⋊D5—31no—
97C23×Dic5C2×D312yes—
98C22×C4×D5—31no—
99C22×C4×D5—32no—
100C2×C5×C22⋊C4—32no—
101C2×C42×C5—32no—
102C2×C22⋊Dic5—31no—
103C4×C22⋊D5—38no—
104C2×#685—31no—
105C2×#685—32no—
106C2×#683—31no—
107C2×#683—32no—
108C2×C4×Dic5—31no—
109C2×C4×Dic5—32no—
110C2×C4×Dic5—32no—
111C2×C4×Dic5—32no—
112#4027—316no—
113C5×#95—31no—
114C5×#95—31no—
115#3963—32no—
116#3963—32no—
117#3963C2×D311yescharacteristic
118#3963C2×D311yescharacteristic
119#3963C2×D312yes—
120#2275—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5—22no—
123C23×C3×C5—21no—
124C23×C3×C5C22×C414yes—
125C23×C3×C5C22×C412yes—
126C23×C3×C5C2411yescharacteristic
127C22×D15—21no—
128C22×D15—22no—
129C22×D15—21no—
130C22×D15C22×C414yes—
131C22×D15C22×C412yes—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—44no—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C22×C412yes—
137#1220C42116yescomplemented
138C2×Dic15—21no—
139C2×Dic15—22no—
140C2×Dic15—21no—
141C2×Dic15C22×C412yes—
142C2×Dic15C22×C412yes—
143C2×Dic15C22×C414yes—
144C2×Dic15C22×C412yes—
145C4×D15—44no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3C22×C414yes—
151C2×C5×Dic3C22×C414yes—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—48no—
157C2×C3×Dic5C22×C414yes—
158C2×C3×Dic5C22×C414yes—
159#1200—48no—
160C23×C3×C4—52no—
161C23×C3×C4C2×D511yescharacteristic
162C22×#67—51no—
163C22×C4×D3—51no—
164C22×C4×D3—52no—
165C2×#217—51no—
166C2×#217C2×D512yes—
167C4×#67—58no—
168C4×#67—516no—
169C2×(C2×D3)⋊C4—51no—
170C2×(C2×D3)⋊C4—52no—
171C2×Dic3⋊C4—51no—
172C2×Dic3⋊C4—52no—
173C2×C4×Dic3—51no—
174C2×C4×Dic3—52no—
175C2×C4×Dic3—52no—
176C2×C4×Dic3—52no—
177C2×C4×Dic3C2×D512yes—
178C3×#95—51no—
179C3×#95—52no—
180C3×#95—51no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95C2×D511yescharacteristic
184C3⋊#95C2×D511yescharacteristic
185C24×C5C22×D311yescharacteristic
186C23×D5—31no—
187C22×C4×C5—32no—
188C22×C4×C5—32no—
189C22×C4×C5—42no—
190C22×C4×C5C4×D314yescomplemented
191C22×C4×C5C22×D311yescharacteristic
192C22×C4×C5C22×D311yescharacteristic
193C2×C22⋊D5—38no—
194C2×C22⋊D5—34no—
195C22×Dic5—31no—
196C22×Dic5—31no—
197C22×Dic5—31no—
198C22×Dic5—42no—
199C22×Dic5—42no—
200C22×Dic5C4×D318yescomplemented
201C22×Dic5C22×D312yes—
202C22×Dic5C22×D312yes—
203C2×C4×D5—34no—
204C2×C4×D5—38no—
205C2×C4×D5—122no—
206C2×C4×D5—122no—
207C2×C4×D5—122no—
208C5×C22⋊C4—38no—
209C42×C5—122no—
210C22⋊Dic5—34no—
211#685—34no—
212#685—38no—
213#683—34no—
214#683—38no—
215C4×Dic5—34no—
216C4×Dic5—38no—
217C4×Dic5—122no—
218C4×Dic5—122no—
219C2×C4×D4—152no—
220C2×C4×D4—151no—
221C4×C4⋊C4—151no—
222C4×C4⋊C4—152no—
223C4×C22⋊C4—31no—
224C4×C22⋊C4—151no—
225C4×C22⋊C4—152no—
226C4×C22⋊C4—152no—
227#376—151no—
228C2×#95—51no—
229C2×#95—151no—
230C22×C3×C5—24no—
231C22×C3×C5—22no—
232C22×C3×C5—22no—
233C22×C3×C5—24no—
234C22×C3×C5C2×C4214yes—
235C22×C3×C5C23×C412yes—
236C22×C3×C5C23×C411yescharacteristic
237C22×C3×C5H(5,𝔽2)12yes—
238C22×C3×C5H(5,𝔽2)11yescharacteristic
239C22×C3×C52−1+411yescharacteristic
240C2×D15—24no—
241C2×D15—22no—
242C2×D15—22no—
243C2×D15—24no—
244C2×D15C2×C4214yes—
245C3×C4×C5—22no—
246C3×C4×C5—22no—
247Dic15—22no—
248Dic15—22no—
249Dic15C2×C4214yes—
250C3×Dic5—24no—
251C3×Dic5—24no—
252C5×Dic3—24no—
253C5×Dic3—24no—
254C24×C3C22×D511yescharacteristic
255C23×D3—51no—
256C22×C3×C4—42no—
257C22×C3×C4—52no—
258C22×C3×C4—52no—
259C22×C3×C4—58no—
260C22×C3×C4—202no—
261C22×C3×C4—202no—
262C22×C3×C4C4×D514yescomplemented
263C22×C3×C4C22×D511yescharacteristic
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—58no—
266C2×#67—54no—
267C22×Dic3—51no—
268C22×Dic3—51no—
269C22×Dic3—51no—
270C22×Dic3C22×D512yes—
271C22×Dic3C22×D512yes—
272C2×C4×D3—54no—
273C2×C4×D3—58no—
274C2×C4×D3—202no—
275C2×C4×D3—202no—
276C2×C4×D3—202no—
277#217—54no—
278#217C4×D518yescomplemented
279(C2×D3)⋊C4—54no—
280(C2×D3)⋊C4—58no—
281Dic3⋊C4—54no—
282Dic3⋊C4—58no—
283C4×Dic3—42no—
284C4×Dic3—54no—
285C4×Dic3—58no—
286C4×Dic3—202no—
287C4×Dic3—202no—
288C23×C5—21no—
289C23×C5—22no—
290C23×C5—21no—
291C23×C5C2×C4×D314yes—
292C23×C5C2×C4×D312yes—
293C23×C5C23×D311yescharacteristic
294C22×D5—34no—
295C22×D5—32no—
296C22×D5—61no—
297C22×D5—62no—
298C22×D5—61no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—34no—
302C2×C4×C5—34no—
303C2×C4×C5—44no—
304C2×C4×C5—62no—
305C2×C4×C5—62no—
306C2×C4×C5—62no—
307C2×C4×C5—62no—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5C2×C4×D312yes—
310C22⋊D5—316no—
311C2×Dic5—22no—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—34no—
316C2×Dic5—32no—
317C2×Dic5—32no—
318C2×Dic5—32no—
319C2×Dic5—48no—
320C2×Dic5—61no—
321C2×Dic5—62no—
322C2×Dic5—61no—
323C2×Dic5C2×C4×D314yes—
324C2×Dic5C2×C4×D314yes—
325C4×D5—128no—
326C4×D5—124no—
327C22×D4—151no—
328C23×C4—52no—
329C23×C4—152no—
330C23×C4—151no—
331C23×C4D3×D511yescharacteristic
332C4×D4—1516no—
333C4×D4—158no—
334C2×C4⋊C4—152no—
335C2×C4⋊C4—151no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—152no—
338C2×C22⋊C4—151no—
339C2×C22⋊C4—151no—
340C2×C42—32no—
341C2×C42—152no—
342C2×C42—151no—
343C2×C42—152no—
344C2×C42—152no—
345#95—31no—
346#95—31no—
347#95—51no—
348#95—52no—
349#95—51no—
350#95—152no—
351#95—152no—
352C2×C3×C5—24no—
353C2×C3×C5C22×C4211yescharacteristic
354C2×C3×C5#51811yescharacteristic
355C2×C3×C5#51812yes—
356C2×C3×C5#52011yescharacteristic
357C2×C3×C5#52012yes—
358D15—24no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3C2×C4×D514yes—
363C23×C3C2×C4×D512yes—
364C23×C3C23×D511yescharacteristic
365C22×D3—54no—
366C22×D3—52no—
367C22×D3—102no—
368C22×D3—101no—
369C22×D3—101no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—44no—
373C2×C3×C4—54no—
374C2×C3×C4—54no—
375C2×C3×C4—102no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—102no—
379C2×C3×C4—208no—
380C2×C3×C4C2×C4×D512yes—
381C2×C3×C4C2×C4×D512yes—
382#67—516no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—54no—
388C2×Dic3—52no—
389C2×Dic3—52no—
390C2×Dic3—52no—
391C2×Dic3—102no—
392C2×Dic3—101no—
393C2×Dic3—101no—
394C2×Dic3C2×C4×D514yes—
395C2×Dic3C2×C4×D514yes—
396C4×D3—208no—
397C4×D3—204no—
398C22×C5—24no—
399C22×C5—22no—
400C22×C5—22no—
401C22×C5—24no—
402C22×C5C42×D314yes—
403C22×C5C22×C4×D312yes—
404C22×C5C22×C4×D311yescharacteristic
405C22×C5#100411yescharacteristic
406C22×C5#100412yes—
407C22×C5#100711yescharacteristic
408C2×D5—34no—
409C2×D5—64no—
410C2×D5—62no—
411C2×D5—62no—
412C2×D5—64no—
413C4×C5—22no—
414C4×C5—22no—
415C4×C5—64no—
416C4×C5—64no—
417Dic5—24no—
418Dic5—24no—
419Dic5—34no—
420Dic5—62no—
421Dic5—62no—
422C24—151no—
423C24C2×D3×D511yescharacteristic
424C2×D4—158no—
425C2×D4—154no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—42no—
429C22×C4—52no—
430C22×C4—52no—
431C22×C4—58no—
432C22×C4—158no—
433C22×C4—151no—
434C22×C4—151no—
435C22×C4—151no—
436C22×C4—154no—
437C22×C4—202no—
438C22×C4—202no—
439C22×C4—602no—
440C22×C4—602no—
441C22×C4—602no—
442C22×C4#120014yescomplemented
443C22×C4C2×D3×D511yescharacteristic
444C22×C4C2×D3×D511yescharacteristic
445C4⋊C4—158no—
446C4⋊C4—154no—
447C22⋊C4—38no—
448C22⋊C4—158no—
449C22⋊C4—154no—
450C22⋊C4—154no—
451C42—122no—
452C42—158no—
453C42—154no—
454C42—602no—
455C42—602no—
456C3×C5#227511yescharacteristic, complemented, Hall
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3C42×D514yes—
462C22×C3C22×C4×D512yes—
463C22×C3C22×C4×D511yescharacteristic
464C22×C3#414412yes—
465C22×C3#414911yescharacteristic
466C22×C3#415011yescharacteristic
467C2×D3—54no—
468C2×D3—102no—
469C2×D3—102no—
470C2×D3—104no—
471C2×D3—104no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—104no—
475C3×C4—104no—
476Dic3—24no—
477Dic3—24no—
478Dic3—54no—
479Dic3—102no—
480Dic3—102no—
481C2×C5—24no—
482C2×C5C2×C42×D311yescharacteristic
483C2×C5#548612yes—
484C2×C5#548611yescharacteristic
485C2×C5#550411yescharacteristic
486C2×C5#550412yes—
487D5—64no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—154no—
492C23—152no—
493C23—301no—
494C23—301no—
495C23—302no—
496C23C4×D3×D514yes—
497C23C2×#120012yes—
498C23C22×D3×D511yescharacteristic
499D4—1516no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—34no—
503C2×C4—34no—
504C2×C4—44no—
505C2×C4—54no—
506C2×C4—54no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—102no—
512C2×C4—102no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—154no—
516C2×C4—152no—
517C2×C4—152no—
518C2×C4—152no—
519C2×C4—208no—
520C2×C4—301no—
521C2×C4—301no—
522C2×C4—302no—
523C2×C4—604no—
524C2×C4—608no—
525C2×C4C2×#120012yes—
526C2×C4C2×#120012yes—
527C2×C3—24no—
528C2×C3C2×C42×D511yescharacteristic
529C2×C3#6582011yescharacteristic
530C2×C3#6585711yescharacteristic
531C2×C3#6587912yes—
532C2×C3#6588012yes—
533D3—104no—
534C5#7332211yescharacteristic, complemented, Sylow
535C22—22no—
536C22—24no—
537C22—24no—
538C22—22no—
539C22—154no—
540C22—302no—
541C22—304no—
542C22—304no—
543C22—302no—
544C22C4×#120014yes—
545C22#9200411yescharacteristic
546C22C2×C4×D3×D512yes—
547C22#9201711yescharacteristic
548C22C22×#120011yescharacteristic
549C22#9204912yes—
550C4—22no—
551C4—22no—
552C4—64no—
553C4—64no—
554C4—104no—
555C4—104no—
556C4—154no—
557C4—302no—
558C4—302no—
559C3#1060516711yescharacteristic, complemented, Sylow
560C2—24no—
561C2—304no—
562C2#1175429412yes—
563C2C2×C4×#120011yescharacteristic
564C2#1175449611yescharacteristic
565C2#1175462512yes—
566C2#1175541311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2275
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C4×C5×#217C2semidirect
4. C2×C3×#3963C2semidirect
5. Dic5×#217C2semidirect
6. #11748888C2semidirect
7. #11748881C2semidirect
8. #11748670C2semidirect
9. #11748663C2semidirect
10. #11748653C2semidirect
11. #11748645C2semidirect
19. C4×#1220C4semidirect
25. #91552C4semidirect
42. C2×#3963D3semidirect
53. C22×C3×C4×C5C2×C4semidirect
62. C2×C4×D15C2×C4semidirect
67. C22×C3×Dic5C2×C4semidirect
72. C2×#1200C2×C4semidirect
73. #6719C2×C4semidirect
74. #6714C2×C4semidirect
75. #6712C2×C4semidirect
76. C4×Dic15C2×C4semidirect
77. C5×#217C2×C4semidirect
79. #6669C2×C4semidirect
80. #6667C2×C4semidirect
83. Dic3×Dic5C2×C4semidirect
88. C4×#217D5semidirect
137. #1220C42semidirect
190. C22×C4×C5C4×D3semidirect
200. C22×Dic5C4×D3semidirect
262. C22×C3×C4C4×D5semidirect
278. #217C4×D5semidirect
442. C22×C4#1200semidirect
456. C3×C5#2275semidirect
534. C5#73322semidirect
559. C3#10605167semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×#915522
C4×C5×#2172
C2×C3×#39632
Dic5×#2172
#117488882
#117488812
#117486702
#117486632
#117486532
#117486452
#106051673
#733225