Finite Group Databasebeta

← #14303016

Subgroups — #14303016

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
1C5×#5804C211yesmaximal, characteristic
2#11755410C211yesmaximal, characteristic, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4C2×C3×#3966C211yesmaximal, characteristic, complemented
5C2×#90996C211yesmaximal, characteristic, complemented
6#11746020C211yesmaximal, characteristic, complemented
7#11746019C211yesmaximal, characteristic, complemented
8#10602641—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×#67C2211yescharacteristic
11C2×#6719C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C5×#953C412yescomplemented
14C2×C5×#217C2211yescharacteristic
15C5×#939—22no—
16C5×#937—21no—
17C5×#935—21no—
18C5×#929C412yescomplemented
19C2×C3×C22⋊Dic5C2211yescharacteristic
20C2×C3×C22⋊Dic5C2211yescharacteristic
21#67⋊Dic5—22no—
22D3×C22⋊Dic5—21no—
23Dic5×#67—22no—
24#91529—21no—
25#91118—22no—
26C3×#3966—22no—
27#90996—22no—
28#70034—51nomaximal, Hall
29C5×#534—31no—
30#66132—31no—
31C2×#3966—31no—
32C2×#3966—31no—
33C2×#3966D311yescharacteristic, complemented
34#64747—31no—
35#64747—31no—
36C24×C3×C5C2×C411yescharacteristic, complemented
37C24×C3×C5C2311yescharacteristic
38C23×C5×D3D411yescharacteristic
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C22×C3×C4×C5C2×C411yescharacteristic, complemented
46C22×Dic15—21no—
47C22×Dic15—21no—
48C2×C5×#67—21no—
49C2×C5×#67—21no—
50C2×C5×#67—21no—
51C2×C5×#67—21no—
52C2×C5×#67—22no—
53C2×C5×#67C2×C412yes—
54C2×C5×#67D412yes—
55C22×C5×Dic3—21no—
56C22×C5×Dic3D411yescharacteristic
57C22×C3×Dic5—21no—
58C22×C3×Dic5—21no—
59C2×D3×Dic5—22no—
60#6719—21no—
61#6719—21no—
62#6719—21no—
63#6719D412yescomplemented
64C5×#217—21no—
65C5×#217—22no—
66C5×#217C2×C412yescomplemented
67C5×(C2×D3)⋊C4—22no—
68C5×Dic3⋊C4—22no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×C22⋊Dic5—21no—
72C3×C22⋊Dic5D412yescomplemented
73Dic3⋊Dic5—22no—
74(C2×D3)⋊Dic5—22no—
75Dic3×Dic5—22no—
76#5804D511yescharacteristic
77#5486—51no—
78C2×C3×#99—51no—
79C2×#834—51no—
80C2×#806—51no—
81#4527—51no—
82#4526—51no—
83C22×C5×D4—31no—
84C22×C5×D4C2×D311yescharacteristic
85C5×#123—32no—
86C5×#123—61no—
87C5×#121—62no—
88C5×#120—32no—
89C5×#120—61no—
90C2×C5×C22⋊C4—31no—
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5—31no—
93C2×C22⋊Dic5—61no—
94C2×C22⋊Dic5C2×D311yescharacteristic
95C2×C22⋊Dic5C2×D311yescharacteristic
96D4×Dic5—62no—
97D4×Dic5—62no—
98#4072—61no—
99#3966—22no—
100#3966—62no—
101#3966—62no—
102#1913—151noSylow
103C23×C3×C5—21no—
104C23×C3×C5—21no—
105C23×C3×C5—21no—
106C23×C3×C5—81no—
107C23×C3×C5—81no—
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C2×D411yescharacteristic
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×D411yescharacteristic
113C23×C3×C5#4111yescharacteristic
114C23×C3×C5#4111yescharacteristic
115C22×C5×D3—21no—
116C22×C5×D3—21no—
117C22×C5×D3—81no—
118C22×C5×D3C22⋊C412yes—
119C3×C5×D4—41no—
120C3×C5×D4—41no—
121C3×C5×D4—41no—
122C3×C5×D4—41no—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—21no—
126C2×Dic15—22no—
127C2×Dic15—41no—
128C2×Dic15—81no—
129C2×Dic15—81no—
130C5×#67—22no—
131C5×#67—22no—
132C5×#67—22no—
133C5×#67—22no—
134C5×#67—82no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—81no—
139C2×C5×Dic3C22⋊C412yes—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—41no—
142C2×C3×Dic5—81no—
143C2×C3×Dic5—81no—
144D3×Dic5—82no—
145C22×C3×D4C2×D511yescharacteristic
146C22×#67C2×D511yescharacteristic
147C2×C3×C22⋊C4—51no—
148C2×C3×C22⋊C4—51no—
149#953Dic512yescomplemented
150C2×#217—51no—
151C2×#217—51no—
152C2×#217C2×D511yescharacteristic
153#939—22no—
154#937—21no—
155#935—21no—
156#929Dic512yescomplemented
157C4×#67—102no—
158#67⋊C4—102no—
159D3×C22⋊C4—101no—
160#877—101no—
161C3×#99—102no—
162#834—102no—
163#806—102no—
164C24×C5—31no—
165C24×C5C4×D311yescharacteristic, complemented
166C24×C5C22×D311yescharacteristic
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4—21no—
172C2×C5×D4—21no—
173C2×C5×D4—32no—
174C2×C5×D4—32no—
175C2×C5×D4—61no—
176C2×C5×D4—61no—
177C2×C5×D4—61no—
178C2×C5×D4—61no—
179C2×C5×D4—62no—
180C22×C4×C5—31no—
181C22×C4×C5—61no—
182C22×C4×C5C4×D311yescharacteristic, complemented
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—62no—
186C22×Dic5—61no—
187C22×Dic5—61no—
188C5×C4⋊C4—62no—
189C5×C22⋊C4—32no—
190C5×C22⋊C4—62no—
191C5×C22⋊C4—62no—
192C5×C22⋊C4—61no—
193C22⋊Dic5—21no—
194C22⋊Dic5—21no—
195C22⋊Dic5—21no—
196C22⋊Dic5—32no—
197C22⋊Dic5—62no—
198C22⋊Dic5—61no—
199C22⋊Dic5—61no—
200C22⋊Dic5—61no—
201C22⋊Dic5#6712yescomplemented
202C4⋊Dic5—62no—
203C4×Dic5—62no—
204#534—31no—
205#518—151no—
206C2×#99—51no—
207C2×#99—151no—
208C2×#99—151no—
209#342—151no—
210#342—151no—
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×C5—42no—
219C22×C3×C5—41no—
220C22×C3×C5—81no—
221C22×C3×C5—81no—
222C22×C3×C5C2×C22⋊C411yescharacteristic
223C22×C3×C5C4×D411yescharacteristic
224C22×C3×C5C4×D411yescharacteristic
225C22×C3×C5#12011yescharacteristic
226C22×C3×C5#12111yescharacteristic
227C22×C3×C5#12111yescharacteristic
228C22×C3×C5#12311yescharacteristic
229C2×C5×D3—22no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3—81no—
233C3×C4×C5—41no—
234Dic15—42no—
235Dic15—81no—
236C3×Dic5—42no—
237C3×Dic5—81no—
238C5×Dic3—22no—
239C5×Dic3—42no—
240C24×C3C2×Dic511yescharacteristic, complemented
241C24×C3C22×D511yescharacteristic
242C23×D3C22⋊D511yescharacteristic
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C22×C3×C4—101no—
250C22×C3×C4—101no—
251C22×C3×C4C2×Dic511yescharacteristic, complemented
252C2×#67—21no—
253C2×#67—21no—
254C2×#67—21no—
255C2×#67—21no—
256C2×#67—22no—
257C2×#67C2×Dic512yes—
258C2×#67C22⋊D512yes—
259C22×Dic3—21no—
260C22×Dic3—101no—
261C22×Dic3—101no—
262C22×Dic3C22⋊D511yescharacteristic
263C2×C4×D3—102no—
264C3×C22⋊C4—52no—
265C3×C22⋊C4—101no—
266C3×C22⋊C4—101no—
267C3×C22⋊C4—101no—
268#217—21no—
269#217—22no—
270#217—52no—
271#217—101no—
272#217—101no—
273#217—101no—
274#217C2×Dic512yescomplemented
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—102no—
277Dic3⋊C4—22no—
278Dic3⋊C4—102no—
279C4×Dic3—102no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—32no—
284C23×C5—61no—
285C23×C5—61no—
286C23×C5—81no—
287C23×C5—81no—
288C23×C5—241no—
289C23×C5C2×C4×D311yescharacteristic
290C23×C5#23511yescharacteristic
291C23×C5D3×D411yescharacteristic
292C23×C5D3×D411yescharacteristic
293C23×C5D3×D411yescharacteristic
294C23×C5#23711yescharacteristic
295C23×C5C2×#6711yescharacteristic
296C5×D4—41no—
297C5×D4—41no—
298C5×D4—41no—
299C5×D4—41no—
300C5×D4—62no—
301C5×D4—62no—
302C5×D4—62no—
303C5×D4—62no—
304C5×D4—242no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—32no—
309C2×C4×C5—61no—
310C2×C4×C5—61no—
311C2×C4×C5—62no—
312C2×C4×C5—241no—
313C2×Dic5—22no—
314C2×Dic5—41no—
315C2×Dic5—62no—
316C2×Dic5—81no—
317C2×Dic5—81no—
318C2×Dic5—121no—
319C2×Dic5—242no—
320C2×Dic5—241no—
321C2×Dic5—241no—
322C22×D4—31no—
323C22×D4D3×D511yescharacteristic
324#123—32no—
325#123—61no—
326#121—62no—
327#120—32no—
328#120—61no—
329C4×D4—302no—
330C4×D4—302no—
331#117—301no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—51no—
334C2×C22⋊C4—51no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—151no—
337C2×C22⋊C4—301no—
338#99—102no—
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—81no—
349C2×C3×C5#38611yescharacteristic
350C5×D3—42no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—81no—
355C23×C3—81no—
356C23×C3D4×D511yescharacteristic
357C23×C3D4×D511yescharacteristic
358C23×C3#71111yescharacteristic
359C23×C3#71111yescharacteristic
360C23×C3C22×Dic511yescharacteristic
361C23×C3C2×C22⋊D511yescharacteristic
362C23×C3C2×C22⋊D511yescharacteristic
363C22×D3—21no—
364C22×D3—21no—
365C22×D3—81no—
366C22×D3C22⋊Dic512yes—
367C3×D4—41no—
368C3×D4—41no—
369C3×D4—41no—
370C3×D4—41no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—102no—
375C2×C3×C4—201no—
376C2×C3×C4—401no—
377C2×C3×C4—401no—
378#67—22no—
379#67—22no—
380#67—22no—
381#67—22no—
382#67—82no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—81no—
387C2×Dic3—102no—
388C2×Dic3—201no—
389C2×Dic3—401no—
390C2×Dic3—401no—
391C2×Dic3C22⋊Dic512yes—
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×C5—42no—
401C22×C5—41no—
402C22×C5—62no—
403C22×C5—81no—
404C22×C5—81no—
405C22×C5—122no—
406C22×C5—122no—
407C22×C5—241no—
408C22×C5D3×C22⋊C411yescharacteristic
409C22×C5#67⋊C411yescharacteristic
410C22×C5#88311yescharacteristic
411C22×C5#88411yescharacteristic
412C22×C5C4×#6711yescharacteristic
413C22×C5#93711yescharacteristic
414C22×C5#93811yescharacteristic
415C4×C5—41no—
416C4×C5—62no—
417C4×C5—122no—
418Dic5—42no—
419Dic5—81no—
420Dic5—122no—
421Dic5—241no—
422C24—31no—
423C24D3×Dic511yescharacteristic, complemented
424C24C2×D3×D511yescharacteristic
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—32no—
432C2×D4—32no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—62no—
438C22×C4—31no—
439C22×C4—61no—
440C22×C4—101no—
441C22×C4—101no—
442C22×C4—302no—
443C22×C4—301no—
444C22×C4—301no—
445C22×C4D3×Dic511yescharacteristic, complemented
446C4⋊C4—62no—
447C4⋊C4—302no—
448C22⋊C4—32no—
449C22⋊C4—52no—
450C22⋊C4—62no—
451C22⋊C4—62no—
452C22⋊C4—61no—
453C22⋊C4—101no—
454C22⋊C4—101no—
455C22⋊C4—101no—
456C22⋊C4—152no—
457C22⋊C4—302no—
458C22⋊C4—301no—
459C22⋊C4—301no—
460C22⋊C4—301no—
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×C3—42no—
471C22×C3—41no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3D4×Dic511yescharacteristic
475C22×C3D4×Dic511yescharacteristic
476C22×C3#408111yescharacteristic
477C22×C3#408311yescharacteristic
478C22×C3#408511yescharacteristic
479C22×C3#408511yescharacteristic
480C22×C3C2×C22⋊Dic511yescharacteristic
481C2×D3—22no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3—81no—
485C3×C4—41no—
486C3×C4—202no—
487C3×C4—401no—
488Dic3—22no—
489Dic3—42no—
490Dic3—202no—
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—81no—
500C2×C5—122no—
501C2×C5#495611yescharacteristic
502C23—21no—
503C23—21no—
504C23—21no—
505C23—32no—
506C23—61no—
507C23—61no—
508C23—81no—
509C23—81no—
510C23—241no—
511C23#678011yescharacteristic
512C23C2×D3×Dic511yescharacteristic
513C23#678211yescharacteristic
514C23D5×#6711yescharacteristic
515C23D3×C22⋊D511yescharacteristic
516C23D3×C22⋊D511yescharacteristic
517C23#679011yescharacteristic
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—62no—
523D4—62no—
524D4—62no—
525D4—62no—
526D4—242no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—32no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—62no—
534C2×C4—102no—
535C2×C4—201no—
536C2×C4—241no—
537C2×C4—302no—
538C2×C4—401no—
539C2×C4—401no—
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—81no—
552C2×C3#6550911yescharacteristic
553D3—42no—
554C5#7003411yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—62no—
565C22—81no—
566C22—81no—
567C22—122no—
568C22—122no—
569C22—241no—
570C22Dic5×#6711yescharacteristic
571C22D3×C22⋊Dic511yescharacteristic
572C22#9155511yescharacteristic
573C22#9155811yescharacteristic
574C22#67⋊Dic511yescharacteristic
575C22#9156511yescharacteristic
576C22#9157711yescharacteristic
577C4—41no—
578C4—62no—
579C4—122no—
580C4—202no—
581C4—401no—
582C4—602no—
583C4—1201no—
584C3#1060264111yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—81no—
593C2—122no—
594C2#1174951911yescharacteristic
subgroupG/H
centerC2#11749519
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#386
prime radicalC5×#5804C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11755410C2semidirect
3. C2×#91118C2semidirect
4. C2×C3×#3966C2semidirect
5. C2×#90996C2semidirect
6. #11746020C2semidirect
7. #11746019C2semidirect
13. C5×#953C4semidirect
18. C5×#929C4semidirect
33. C2×#3966D3semidirect
36. C24×C3×C5C2×C4semidirect
45. C22×C3×C4×C5C2×C4semidirect
63. #6719D4semidirect
66. C5×#217C2×C4semidirect
72. C3×C22⋊Dic5D4semidirect
149. #953Dic5semidirect
156. #929Dic5semidirect
165. C24×C5C4×D3semidirect
182. C22×C4×C5C4×D3semidirect
201. C22⋊Dic5#67semidirect
240. C24×C3C2×Dic5semidirect
251. C22×C3×C4C2×Dic5semidirect
274. #217C2×Dic5semidirect
423. C24D3×Dic5semidirect
445. C22×C4D3×Dic5semidirect
462. C3×C5#1913semidirect
554. C5#70034semidirect
584. C3#10602641semidirect

Maximal subgroups

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

subgroupindex
C5×#58042
#117554102
C2×#911182
C2×C3×#39662
C2×#909962
#117460202
#117460192
#106026413
#700345