Finite Group Databasebeta

← #14302985

Subgroups — #14302985

Order 1920.

760 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
1#11756252C211yesmaximal, characteristic
2#11756245C211yesmaximal, characteristic, complemented
3C2×#91090C211yesmaximal, characteristic, complemented
4C2×#91090C211yesmaximal, characteristic, complemented
5C2×#91090C211yesmaximal, characteristic, complemented
6C3×C5×#342C211yesmaximal, characteristic, complemented
7#11746348C211yesmaximal, characteristic, complemented
8#10599757—31nomaximal, Hall
9C22×#1220C2211yescharacteristic
10C22×#1220C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×#6719C2211yescharacteristic
16#91819—22no—
17C4×#1220—22no—
18#91775—21no—
19#91775C412yescomplemented
20#91771—21no—
21#91771C412yescomplemented
22#91770—22no—
23C22⋊C4×D15—21no—
24#91766—21no—
25#91090—22no—
26#91090—22no—
27#91090—22no—
28#68964—51nomaximal, Hall
29#65827—31no—
30#65820—31no—
31C2×#3938—31no—
32C2×#3938—31no—
33C2×#3938—31no—
34C5×#342D311yescharacteristic, complemented
35#64747—31no—
36C24×C3×C5C2311yescharacteristic
37C23×D15C2×C411yescharacteristic, complemented
38C23×D15D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220—21no—
45C2×#1220—21no—
46C2×#1220—21no—
47C2×#1220—21no—
48C2×#1220—21no—
49C2×#1220—21no—
50C2×#1220—21no—
51C2×#1220—21no—
52C2×#1220C2×C412yes—
53C2×#1220D412yes—
54C22×Dic15—21no—
55C22×Dic15—21no—
56C22×Dic15C2×C411yescharacteristic, complemented
57C22×Dic15D411yescharacteristic
58C2×D60—22no—
59C2×C4×D15—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4—21no—
63C3×C5×C22⋊C4—21no—
64C3×C5×C22⋊C4C2×C412yescomplemented
65C3×C5×C22⋊C4D412yescomplemented
66#6719—21no—
67#6719—21no—
68#6719—21no—
69#6719D412yescomplemented
70#6714—22no—
71#6714—22no—
72#6714—22no—
73C4⋊Dic15—22no—
74#6712—22no—
75C4×Dic15—22no—
76#5493—51no—
77#5486—51no—
78C2×#806—51no—
79C2×#806—51no—
80C2×#806—51no—
81C3×#342D511yescharacteristic, complemented
82#4527—51no—
83C22×C22⋊D5—31no—
84C22×C22⋊D5—31no—
85C2×C5×C22⋊C4C2×D311yescharacteristic
86C2×C5×C22⋊C4C2×D311yescharacteristic
87C2×C5×C22⋊C4C2×D311yescharacteristic
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5—31no—
90#4076—62no—
91C4×C22⋊D5—62no—
92#4032—32no—
93#4032—61no—
94#4028—32no—
95#4028—61no—
96#4027—62no—
97D5×C22⋊C4—61no—
98#4023—61no—
99#3938—62no—
100#3938—62no—
101#3938—62no—
102#1913—151noSylow
103C23×C3×C5—81no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5C2×D411yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C22×D15—21no—
112C22×D15—21no—
113C22×D15—21no—
114C22×D15—21no—
115C22×D15—21no—
116C22×D15—81no—
117C22×D15—81no—
118C22×D15C22⋊C412yes—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—81no—
123C2×C3×C4×C5—81no—
124C2×C3×C4×C5—81no—
125#1220—22no—
126#1220—22no—
127#1220—22no—
128#1220—22no—
129#1220—41no—
130#1220—41no—
131#1220—41no—
132#1220—41no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—21no—
137C2×Dic15—21no—
138C2×Dic15—22no—
139C2×Dic15—41no—
140C2×Dic15—81no—
141C2×Dic15—81no—
142C2×Dic15C22⋊C412yes—
143D60—82no—
144C4×D15—82no—
145C22×#67—51no—
146C22×#67—51no—
147C2×C3×C22⋊C4C2×D511yescharacteristic
148C2×C3×C22⋊C4C2×D511yescharacteristic
149C2×C3×C22⋊C4C2×D511yescharacteristic
150C2×#217—51no—
151C2×#217—51no—
152#930—102no—
153C4×#67—102no—
154#886—52no—
155#886—101no—
156#882—52no—
157#882—101no—
158#67⋊C4—102no—
159D3×C22⋊C4—101no—
160#877—101no—
161#806—102no—
162#806—102no—
163#806—102no—
164C24×C5C22×D311yescharacteristic
165C23×D5—31no—
166C23×D5—31no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C2×C22⋊D5—32no—
171C2×C22⋊D5—32no—
172C2×C22⋊D5—61no—
173C2×C22⋊D5—61no—
174C2×C22⋊D5—61no—
175C2×C22⋊D5—61no—
176C2×C22⋊D5—61no—
177C2×C22⋊D5—61no—
178C2×C22⋊D5—61no—
179C2×C22⋊D5—61no—
180C2×C22⋊D5—61no—
181C2×C22⋊D5—61no—
182C22×Dic5—31no—
183C22×Dic5—31no—
184C22×Dic5—61no—
185C22×Dic5—61no—
186C2×D20—62no—
187C2×C4×D5—62no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—21no—
190C5×C22⋊C4—21no—
191C5×C22⋊C4—21no—
192C5×C22⋊C4C4×D312yescomplemented
193C5×C22⋊C4D1212yescomplemented
194C22⋊Dic5—32no—
195C22⋊Dic5—61no—
196C22⋊Dic5—61no—
197C22⋊Dic5—61no—
198#685—62no—
199#685—62no—
200#685—62no—
201C4⋊Dic5—62no—
202#683—62no—
203C4×Dic5—62no—
204#534—151no—
205#518—151no—
206C2×#99—151no—
207C2×#99—151no—
208C2×#99—151no—
209#342—151no—
210#342D1511yescharacteristic, complemented
211C22×C3×C5—41no—
212C22×C3×C5—41no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×D411yescharacteristic
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5#12011yescharacteristic
222C22×C3×C5#12111yescharacteristic
223C22×C3×C5#12111yescharacteristic
224C22×C3×C5#12311yescharacteristic
225C2×D15—22no—
226C2×D15—42no—
227C2×D15—42no—
228C2×D15—42no—
229C2×D15—41no—
230C2×D15—81no—
231C2×D15—81no—
232C2×D15—81no—
233C3×C4×C5—42no—
234C3×C4×C5—42no—
235C3×C4×C5—81no—
236Dic15—22no—
237Dic15—42no—
238Dic15—41no—
239Dic15—81no—
240C24×C3C22×D511yescharacteristic
241C23×D3—51no—
242C23×D3—51no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C2×#67—52no—
247C2×#67—52no—
248C2×#67—101no—
249C2×#67—101no—
250C2×#67—101no—
251C2×#67—101no—
252C2×#67—101no—
253C2×#67—101no—
254C2×#67—101no—
255C2×#67—101no—
256C2×#67—101no—
257C2×#67—101no—
258C22×Dic3—51no—
259C22×Dic3—51no—
260C22×Dic3—101no—
261C22×Dic3—101no—
262C2×D12—102no—
263C2×C4×D3—102no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4C4×D512yescomplemented
269C3×C22⋊C4D2012yescomplemented
270#217—52no—
271#217—101no—
272#217—101no—
273#217—101no—
274(C2×D3)⋊C4—102no—
275(C2×D3)⋊C4—102no—
276(C2×D3)⋊C4—102no—
277C4⋊Dic3—102no—
278Dic3⋊C4—102no—
279C4×Dic3—102no—
280C23×C5—81no—
281C23×C5C2×C4×D311yescharacteristic
282C23×C5C2×D1211yescharacteristic
283C23×C5#23511yescharacteristic
284C23×C5D3×D411yescharacteristic
285C23×C5D3×D411yescharacteristic
286C23×C5D3×D411yescharacteristic
287C23×C5#23911yescharacteristic
288C22×D5—32no—
289C22×D5—61no—
290C22×D5—61no—
291C22×D5—61no—
292C22×D5—61no—
293C22×D5—61no—
294C22×D5—241no—
295C22×D5—241no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—41no—
299C2×C4×C5—81no—
300C2×C4×C5—81no—
301C2×C4×C5—81no—
302C22⋊D5—62no—
303C22⋊D5—62no—
304C22⋊D5—62no—
305C22⋊D5—62no—
306C22⋊D5—121no—
307C22⋊D5—121no—
308C22⋊D5—121no—
309C22⋊D5—121no—
310C2×Dic5—32no—
311C2×Dic5—61no—
312C2×Dic5—61no—
313C2×Dic5—61no—
314C2×Dic5—61no—
315C2×Dic5—62no—
316C2×Dic5—61no—
317C2×Dic5—121no—
318C2×Dic5—241no—
319C2×Dic5—241no—
320D20—242no—
321C4×D5—242no—
322C22×D4—151no—
323C22×D4—151no—
324#123—152no—
325#123—301no—
326#121—302no—
327#120—152no—
328#120—301no—
329C4×D4—302no—
330C4×D4—302no—
331#117—301no—
332C2×C22⋊C4—151no—
333C2×C22⋊C4—151no—
334C2×C22⋊C4—301no—
335C2×C22⋊C4C2×D1511yescharacteristic
336C2×C22⋊C4C2×D1511yescharacteristic
337C2×C22⋊C4C2×D1511yescharacteristic
338#99—302no—
339#99—302no—
340#99—302no—
341C2×C3×C5—21no—
342C2×C3×C5—21no—
343C2×C3×C5—21no—
344C2×C3×C5—21no—
345C2×C3×C5—21no—
346C2×C3×C5—21no—
347C2×C3×C5—21no—
348C2×C3×C5#38611yescharacteristic
349D15—42no—
350D15—81no—
351C23×C3—81no—
352C23×C3C2×C4×D511yescharacteristic
353C23×C3C2×D2011yescharacteristic
354C23×C3#70911yescharacteristic
355C23×C3D4×D511yescharacteristic
356C23×C3D4×D511yescharacteristic
357C23×C3D4×D511yescharacteristic
358C23×C3#71311yescharacteristic
359C22×D3—52no—
360C22×D3—101no—
361C22×D3—101no—
362C22×D3—101no—
363C22×D3—101no—
364C22×D3—101no—
365C22×D3—401no—
366C22×D3—401no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—41no—
370C2×C3×C4—81no—
371C2×C3×C4—81no—
372C2×C3×C4—81no—
373#67—102no—
374#67—102no—
375#67—102no—
376#67—102no—
377#67—201no—
378#67—201no—
379#67—201no—
380#67—201no—
381C2×Dic3—52no—
382C2×Dic3—101no—
383C2×Dic3—101no—
384C2×Dic3—101no—
385C2×Dic3—101no—
386C2×Dic3—102no—
387C2×Dic3—101no—
388C2×Dic3—201no—
389C2×Dic3—401no—
390C2×Dic3—401no—
391D12—402no—
392C4×D3—402no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C4×D1211yescharacteristic
401C22×C5D3×C22⋊C411yescharacteristic
402C22×C5#88211yescharacteristic
403C22×C5#88411yescharacteristic
404C22×C5#89311yescharacteristic
405C22×C5#89411yescharacteristic
406C22×C5#89511yescharacteristic
407C2×D5—62no—
408C2×D5—122no—
409C2×D5—122no—
410C2×D5—122no—
411C2×D5—121no—
412C2×D5—241no—
413C2×D5—241no—
414C2×D5—241no—
415C4×C5—42no—
416C4×C5—42no—
417C4×C5—81no—
418Dic5—62no—
419Dic5—122no—
420Dic5—121no—
421Dic5—241no—
422C24—151no—
423C24—151no—
424C24C22×D1511yescharacteristic
425C2×D4—152no—
426C2×D4—152no—
427C2×D4—302no—
428C2×D4—301no—
429C2×D4—301no—
430C2×D4—301no—
431C2×D4—301no—
432C2×D4—301no—
433C2×D4—301no—
434C2×D4—301no—
435C2×D4—301no—
436C2×D4—301no—
437C2×D4—301no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—151no—
442C22×C4—151no—
443C22×C4—302no—
444C22×C4—301no—
445C22×C4—301no—
446C4⋊C4—302no—
447C4⋊C4—302no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—152no—
453C22⋊C4—302no—
454C22⋊C4—302no—
455C22⋊C4—302no—
456C22⋊C4—301no—
457C22⋊C4—301no—
458C22⋊C4—301no—
459C22⋊C4C4×D1512yescomplemented
460C22⋊C4D6012yescomplemented
461C42—302no—
462C3×C5#191311yescharacteristic, complemented, Hall
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3C4×D2011yescharacteristic
471C22×C3D5×C22⋊C411yescharacteristic
472C22×C3#402811yescharacteristic
473C22×C3#403011yescharacteristic
474C22×C3#403911yescharacteristic
475C22×C3#404011yescharacteristic
476C22×C3#404111yescharacteristic
477C2×D3—102no—
478C2×D3—202no—
479C2×D3—202no—
480C2×D3—202no—
481C2×D3—201no—
482C2×D3—401no—
483C2×D3—401no—
484C2×D3—401no—
485C3×C4—42no—
486C3×C4—42no—
487C3×C4—81no—
488Dic3—102no—
489Dic3—202no—
490Dic3—201no—
491Dic3—401no—
492C2×C5—21no—
493C2×C5—21no—
494C2×C5—21no—
495C2×C5—21no—
496C2×C5—21no—
497C2×C5—21no—
498C2×C5—21no—
499C2×C5#466511yescharacteristic
500D5—122no—
501D5—241no—
502C23—81no—
503C23—152no—
504C23—301no—
505C23—301no—
506C23—301no—
507C23—301no—
508C23—301no—
509C23—1201no—
510C23—1201no—
511C23C2×C4×D1511yescharacteristic
512C23C2×D6011yescharacteristic
513C23#681711yescharacteristic
514C23D4×D1511yescharacteristic
515C23D4×D1511yescharacteristic
516C23D4×D1511yescharacteristic
517C23#682111yescharacteristic
518D4—302no—
519D4—302no—
520D4—302no—
521D4—302no—
522D4—601no—
523D4—601no—
524D4—601no—
525D4—601no—
526D4—1202no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—152no—
534C2×C4—301no—
535C2×C4—301no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—302no—
539C2×C4—301no—
540C2×C4—601no—
541C2×C4—1202no—
542C2×C4—1201no—
543C2×C4—1201no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3#6495411yescharacteristic
552D3—202no—
553D3—401no—
554C5#6896411yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—302no—
563C22—602no—
564C22—602no—
565C22—602no—
566C22—601no—
567C22—1201no—
568C22—1201no—
569C22—1201no—
570C22C4×D6011yescharacteristic
571C22C22⋊C4×D1511yescharacteristic
572C22#9177111yescharacteristic
573C22#9177311yescharacteristic
574C22#9178211yescharacteristic
575C22#9178311yescharacteristic
576C22#9178411yescharacteristic
577C4—42no—
578C4—42no—
579C4—81no—
580C4—302no—
581C4—602no—
582C4—601no—
583C4—1201no—
584C3#1059975711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—602no—
593C2—1201no—
594C2#1175076611yescharacteristic
subgroupG/H
centerC2#11750766
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
FittingC3×C5×#342C2
socleC2×C3×C5#386
prime radical#11756252C2
cosocleC24×C3×C5C23
hypercenter#342D15
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. #11756245C2semidirect
3. C2×#91090C2semidirect
4. C2×#91090C2semidirect
5. C2×#91090C2semidirect
6. C3×C5×#342C2semidirect
7. #11746348C2semidirect
19. #91775C4semidirect
21. #91771C4semidirect
34. C5×#342D3semidirect
37. C23×D15C2×C4semidirect
56. C22×Dic15C2×C4semidirect
64. C3×C5×C22⋊C4C2×C4semidirect
65. C3×C5×C22⋊C4D4semidirect
69. #6719D4semidirect
81. C3×#342D5semidirect
192. C5×C22⋊C4C4×D3semidirect
193. C5×C22⋊C4D12semidirect
210. #342D15semidirect
268. C3×C22⋊C4C4×D5semidirect
269. C3×C22⋊C4D20semidirect
459. C22⋊C4C4×D15semidirect
460. C22⋊C4D60semidirect
462. C3×C5#1913semidirect
554. C5#68964semidirect
584. C3#10599757semidirect

Maximal subgroups

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

subgroupindex
#117562522
#117562452
C2×#910902
C3×C5×#3422
#117463482
#105997573
#689645