Finite Group Databasebeta

← #14297133

Subgroups — #14297133

Order 1920.

1340 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92095C211yesmaximal, characteristic
2C3×C5×#386C211yesmaximal, characteristic, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4#11751314C212yesmaximal, complemented
5C2×#91090C212yesmaximal, complemented
6#10600391—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×C3×C4×C5C2211yescharacteristic, complemented
9C22×#1220—21no—
10C22×#1220C2212yes—
11#92095—22no—
12#92095—24no—
13#92095C414yescomplemented
14C2×#6819—22no—
15C2×D4×D15—22no—
16C2×#6817—21no—
17C2×C3×C5×C22⋊C4—21no—
18C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
19C2×#6719C2212yescomplemented
20C2×#6714—22no—
21C3×C5×#95—21no—
22#91118—22no—
23#91115—22no—
24#91090—24no—
25#69598—51nomaximal, Hall
26C2×#4144—31no—
27C5×#386D311yescharacteristic, complemented
28C2×#3966—31no—
29#65502—32no—
30C2×#3938—32no—
31C24×C3×C5D411yescharacteristic
32C24×C3×C5C2311yescharacteristic
33C23×D15—21no—
34C23×D15D412yes—
35C2×C3×C5×D4—22no—
36C2×C3×C5×D4—22no—
37C2×C3×C5×D4C2×C412yes—
38C2×C3×C5×D4D412yes—
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—42no—
43C22×C3×C4×C5D411yescharacteristic
44C2×#1220—22no—
45C2×#1220—24no—
46C2×#1220—24no—
47C2×#1220—22no—
48C2×#1220—22no—
49C2×#1220—22no—
50C2×#1220—22no—
51C2×#1220C2×C414yes—
52C2×#1220D414yes—
53C22×Dic15—21no—
54C22×Dic15—22no—
55C22×Dic15D412yes—
56#6819—28no—
57#6819—28no—
58D4×D15—28no—
59D4×D15—28no—
60#6817—24no—
61#6817—24no—
62C2×D60—21no—
63C2×C4×D15—22no—
64C2×Dic30—21no—
65C3×C5×C22⋊C4—22no—
66C3×C5×C22⋊C4—42no—
67#6719—22no—
68#6719—22no—
69#6714—44no—
70C2×#1004—51no—
71C3×#386D511yescharacteristic, complemented
72C2×#834—51no—
73#5213—52no—
74C2×#806—52no—
75C22×C5×D4C2×D311yescharacteristic
76C23×C4×C5C2×D311yescharacteristic, complemented
77C22×C22⋊D5—32no—
78C22×C22⋊D5—61no—
79#4144—34no—
80#4144—64no—
81#4144—62no—
82C2×#711—62no—
83C2×D4×D5—62no—
84C2×#709—61no—
85C2×C5×C22⋊C4—21no—
86C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
87C2×C22⋊Dic5—32no—
88C2×#685—62no—
89C5×#95—21no—
90#3966—62no—
91#3963—62no—
92#3938—64no—
93#1790—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5—21no—
96C23×C3×C5—41no—
97C23×C3×C5—41no—
98C23×C3×C5—41no—
99C23×C3×C5—41no—
100C23×C3×C5C22⋊C412yescomplemented
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D412yes—
103C23×C3×C5C2×D411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D412yes—
106C22×D15—22no—
107C22×D15—24no—
108C22×D15—22no—
109C22×D15—42no—
110C22×D15—42no—
111C22×D15—81no—
112C22×D15—81no—
113C22×D15C22⋊C414yescomplemented
114C3×C5×D4—24no—
115C3×C5×D4—24no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—24no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—42no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5C22⋊C412yescomplemented
127#1220—28no—
128#1220—24no—
129#1220—24no—
130#1220—24no—
131#1220—24no—
132C2×Dic15—24no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—42no—
136C2×Dic15—42no—
137C2×Dic15—42no—
138C2×Dic15C22⋊C414yescomplemented
139D60—24no—
140C4×D15—28no—
141Dic30—24no—
142C22×C3×D4C2×D511yescharacteristic
143C23×C3×C4C2×D511yescharacteristic, complemented
144C22×#67—52no—
145C22×#67—101no—
146#1004—54no—
147#1004—104no—
148#1004—102no—
149C2×#237—102no—
150C2×D3×D4—102no—
151C2×#235—101no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
154C2×#217—52no—
155C2×(C2×D3)⋊C4—102no—
156C3×#95—21no—
157#834—102no—
158C3⋊#95—102no—
159#806—104no—
160C24×C5#6711yescharacteristic
161C24×C5C22×D311yescharacteristic
162C23×D5—32no—
163C23×D5—61no—
164C2×C5×D4—22no—
165C2×C5×D4—22no—
166C2×C5×D4C4×D312yes—
167C2×C5×D4D1212yes—
168C22×C4×C5—22no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—42no—
172C22×C4×C5#6711yescharacteristic
173C2×C22⋊D5—34no—
174C2×C22⋊D5—34no—
175C2×C22⋊D5—62no—
176C2×C22⋊D5—64no—
177C2×C22⋊D5—64no—
178C2×C22⋊D5—62no—
179C2×C22⋊D5—62no—
180C2×C22⋊D5—62no—
181C2×C22⋊D5—62no—
182C22×Dic5—32no—
183C22×Dic5—61no—
184C22×Dic5—62no—
185#711—68no—
186#711—68no—
187D4×D5—68no—
188D4×D5—68no—
189#709—64no—
190#709—64no—
191C2×D20—61no—
192C2×C4×D5—62no—
193C2×Dic10—61no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—42no—
196C22⋊Dic5—62no—
197C22⋊Dic5—62no—
198#685—124no—
199C2×H(5,𝔽2)—151no—
200C2×#99—151no—
201C2×#99—152no—
202#386—152no—
203#386D1511yescharacteristic, complemented
204C22×C3×C5—22no—
205C22×C3×C5—21no—
206C22×C3×C5—22no—
207C22×C3×C5—21no—
208C22×C3×C5—22no—
209C22×C3×C5—41no—
210C22×C3×C5—41no—
211C22×C3×C5—42no—
212C22×C3×C5—42no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—81no—
216C22×C3×C5C2×C22⋊C412yes—
217C22×C3×C5C2×C22⋊C411yescharacteristic
218C22×C3×C5#12012yes—
219C22×C3×C5#12011yescharacteristic
220C22×C3×C5#12011yescharacteristic
221C2×D15—24no—
222C2×D15—42no—
223C2×D15—42no—
224C2×D15—44no—
225C2×D15—82no—
226C2×D15—84no—
227C3×C4×C5—22no—
228C3×C4×C5—42no—
229C3×C4×C5—81no—
230Dic15—24no—
231Dic15—82no—
232C24×C3C22⋊D511yescharacteristic
233C24×C3C22×D511yescharacteristic
234C23×D3—52no—
235C23×D3—101no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4C4×D512yes—
239C2×C3×D4D2012yes—
240C22×C3×C4—22no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—42no—
244C22×C3×C4C22⋊D511yescharacteristic
245C2×#67—54no—
246C2×#67—54no—
247C2×#67—102no—
248C2×#67—104no—
249C2×#67—104no—
250C2×#67—102no—
251C2×#67—102no—
252C2×#67—102no—
253C2×#67—102no—
254C22×Dic3—52no—
255C22×Dic3—101no—
256C22×Dic3—102no—
257#237—108no—
258#237—108no—
259D3×D4—108no—
260D3×D4—108no—
261#235—104no—
262#235—104no—
263C2×D12—101no—
264C2×C4×D3—102no—
265C2×Dic6—101no—
266C3×C22⋊C4—22no—
267C3×C22⋊C4—42no—
268#217—102no—
269#217—102no—
270(C2×D3)⋊C4—204no—
271C23×C5—21no—
272C23×C5—21no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5(C2×D3)⋊C412yescomplemented
278C23×C5C2×C4×D311yescharacteristic
279C23×C5C2×D1211yescharacteristic
280C23×C5D3×D412yes—
281C23×C5D3×D412yes—
282C23×C5C2×#6711yescharacteristic
283C22×D5—34no—
284C22×D5—62no—
285C22×D5—64no—
286C22×D5—62no—
287C22×D5—122no—
288C22×D5—122no—
289C22×D5—241no—
290C22×D5—241no—
291C5×D4—24no—
292C5×D4—24no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—24no—
296C2×C4×C5—22no—
297C2×C4×C5—42no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5—41no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5(C2×D3)⋊C412yescomplemented
304C22⋊D5—68no—
305C22⋊D5—64no—
306C22⋊D5—64no—
307C22⋊D5—64no—
308C22⋊D5—64no—
309C2×Dic5—34no—
310C2×Dic5—64no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C2×Dic5—122no—
314C2×Dic5—122no—
315C2×Dic5—122no—
316D20—64no—
317C4×D5—68no—
318Dic10—64no—
319H(5,𝔽2)—154no—
320H(5,𝔽2)—304no—
321H(5,𝔽2)—302no—
322C2×#41—302no—
323C2×#41—301no—
324C22×D4—152no—
325C22×D4—302no—
326C22×D4—301no—
327C22×D4C2×D1511yescharacteristic
328C23×C4C2×D1511yescharacteristic, complemented
329C2×C22⋊C4—21no—
330C2×C22⋊C4—152no—
331C2×C22⋊C4—302no—
332C2×C22⋊C4C2×D1511yescharacteristic, complemented
333#99—304no—
334#99—302no—
335#95—21no—
336#95—302no—
337C2×C3×C5—22no—
338C2×C3×C5—21no—
339C2×C3×C5—22no—
340C2×C3×C5—21no—
341C2×C3×C5—42no—
342C2×C3×C5#37911yescharacteristic
343C2×C3×C5B(4,𝔽2)11yescharacteristic
344C2×C3×C5#45811yescharacteristic
345D15—44no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3#68512yescomplemented
353C23×C3C2×C4×D511yescharacteristic
354C23×C3C2×D2011yescharacteristic
355C23×C3D4×D512yes—
356C23×C3D4×D512yes—
357C23×C3C2×C22⋊D511yescharacteristic
358C22×D3—54no—
359C22×D3—102no—
360C22×D3—104no—
361C22×D3—102no—
362C22×D3—202no—
363C22×D3—202no—
364C22×D3—401no—
365C22×D3—401no—
366C3×D4—24no—
367C3×D4—24no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—24no—
371C2×C3×C4—22no—
372C2×C3×C4—42no—
373C2×C3×C4—41no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4#68512yescomplemented
379#67—108no—
380#67—104no—
381#67—104no—
382#67—104no—
383#67—104no—
384C2×Dic3—54no—
385C2×Dic3—104no—
386C2×Dic3—102no—
387C2×Dic3—102no—
388C2×Dic3—202no—
389C2×Dic3—202no—
390C2×Dic3—202no—
391D12—104no—
392C4×D3—108no—
393Dic6—104no—
394C22×C5—22no—
395C22×C5—21no—
396C22×C5—22no—
397C22×C5—21no—
398C22×C5—22no—
399C22×C5—41no—
400C22×C5—41no—
401C22×C5—42no—
402C22×C5—42no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—81no—
406C22×C5D3×C22⋊C412yes—
407C22×C5#88212yes—
408C22×C5C2×(C2×D3)⋊C411yescharacteristic
409C22×C5#93711yescharacteristic
410C22×C5#93711yescharacteristic
411C2×D5—64no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—124no—
415C2×D5—242no—
416C2×D5—244no—
417C4×C5—22no—
418C4×C5—42no—
419C4×C5—81no—
420Dic5—64no—
421Dic5—242no—
422C24—152no—
423C24—301no—
424C24#122011yescharacteristic
425C24C22×D1511yescharacteristic
426#41—304no—
427#41—308no—
428#41—308no—
429#41—304no—
430C2×Q8—301no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—154no—
434C2×D4—154no—
435C2×D4—301no—
436C2×D4—308no—
437C2×D4—308no—
438C2×D4—302no—
439C2×D4—304no—
440C2×D4—304no—
441C2×D4—302no—
442C2×D4—302no—
443C2×D4—302no—
444C2×D4—302no—
445C2×D4C4×D1512yes—
446C2×D4D6012yes—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—152no—
452C22×C4—302no—
453C22×C4—301no—
454C22×C4—302no—
455C22×C4#122011yescharacteristic
456C22⋊C4—22no—
457C22⋊C4—42no—
458C22⋊C4—302no—
459C22⋊C4—302no—
460C22⋊C4—604no—
461C3×C5#179011yescharacteristic, complemented, Hall
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—22no—
465C22×C3—21no—
466C22×C3—22no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—81no—
474C22×C3D5×C22⋊C412yes—
475C22×C3#402812yes—
476C22×C3C2×#68511yescharacteristic
477C22×C3#408311yescharacteristic
478C22×C3#408311yescharacteristic
479C2×D3—104no—
480C2×D3—202no—
481C2×D3—202no—
482C2×D3—204no—
483C2×D3—402no—
484C2×D3—404no—
485C3×C4—22no—
486C3×C4—42no—
487C3×C4—81no—
488Dic3—104no—
489Dic3—402no—
490C2×C5—22no—
491C2×C5—21no—
492C2×C5—22no—
493C2×C5—21no—
494C2×C5—42no—
495C2×C5#495511yescharacteristic
496C2×C5#503211yescharacteristic
497C2×C5#505311yescharacteristic
498D5—124no—
499C23—21no—
500C23—21no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—154no—
506C23—304no—
507C23—302no—
508C23—302no—
509C23—602no—
510C23—602no—
511C23—1201no—
512C23—1201no—
513C23#671412yescomplemented
514C23C2×C4×D1511yescharacteristic
515C23C2×D6011yescharacteristic
516C23D4×D1512yes—
517C23D4×D1512yes—
518C23C2×#122011yescharacteristic
519Q8—304no—
520D4—24no—
521D4—24no—
522D4—304no—
523D4—308no—
524D4—304no—
525D4—304no—
526D4—304no—
527D4—304no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—154no—
539C2×C4—308no—
540C2×C4—304no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4—602no—
544C2×C4—602no—
545C2×C4—602no—
546C2×C4#671412yescomplemented
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—42no—
552C2×C3#6524411yescharacteristic
553C2×C3#6532111yescharacteristic
554C2×C3#6534211yescharacteristic
555D3—204no—
556C5#6959811yescharacteristic, complemented, Sylow
557C22—21no—
558C22—22no—
559C22—21no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—304no—
570C22—604no—
571C22—602no—
572C22—602no—
573C22—1202no—
574C22—1204no—
575C22C22⋊C4×D1512yes—
576C22#9177112yes—
577C22C2×#671411yescharacteristic
578C22#9182611yescharacteristic
579C22#9182611yescharacteristic
580C4—22no—
581C4—42no—
582C4—81no—
583C4—304no—
584C4—1202no—
585C3#1060039111yescharacteristic, complemented, Sylow
586C2—21no—
587C2—22no—
588C2—21no—
589C2—22no—
590C2—42no—
591C2—604no—
592C2#1175105611yescharacteristic
593C2#1175113311yescharacteristic
594C2#1175115411yescharacteristic
subgroupG/H
centerC22#91826
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
FittingC3×C5×#386C2
socleC22×C3×C5#120
prime radicalC2×#92095C2
cosocleC24×C3×C5C23
hypercenter#386D15
hypocenterC3×C5#1790
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C3×C5×#386C2semidirect
3. C2×#91118C2semidirect
4. #11751314C2semidirect
5. C2×#91090C2semidirect
8. C23×C3×C4×C5C22semidirect
13. #92095C4semidirect
18. C2×C3×C5×C22⋊C4C22semidirect
19. C2×#6719C22semidirect
27. C5×#386D3semidirect
71. C3×#386D5semidirect
76. C23×C4×C5C2×D3semidirect
86. C2×C5×C22⋊C4C2×D3semidirect
100. C23×C3×C5C22⋊C4semidirect
113. C22×D15C22⋊C4semidirect
126. C2×C3×C4×C5C22⋊C4semidirect
138. C2×Dic15C22⋊C4semidirect
143. C23×C3×C4C2×D5semidirect
153. C2×C3×C22⋊C4C2×D5semidirect
203. #386D15semidirect
277. C23×C5(C2×D3)⋊C4semidirect
303. C2×C4×C5(C2×D3)⋊C4semidirect
328. C23×C4C2×D15semidirect
332. C2×C22⋊C4C2×D15semidirect
352. C23×C3#685semidirect
378. C2×C3×C4#685semidirect
461. C3×C5#1790semidirect
513. C23#6714semidirect
546. C2×C4#6714semidirect
556. C5#69598semidirect
585. C3#10600391semidirect

Maximal subgroups

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

subgroupindex
C2×#920952
C3×C5×#3862
C2×#911182
#117513142
C2×#910902
#106003913
#695985