Finite Group Databasebeta

← #14303007

Subgroups — #14303007

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
1C3×#65820C211yesmaximal, characteristic, complemented
2#11755427C211yesmaximal, characteristic
3C2×#91090C211yesmaximal, characteristic, complemented
4C2×#90997C211yesmaximal, characteristic, complemented
5C2×#90995C211yesmaximal, characteristic, complemented
6C5×#4527C211yesmaximal, characteristic, complemented
7#11746020C211yesmaximal, characteristic, complemented
8#10599757—31nomaximal, Hall
9C22×#1220C2211yescharacteristic
10C22×C3×C22⋊D5C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×C5×#217C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C2×C3×C22⋊Dic5C2211yescharacteristic
16C3×C4×C22⋊D5—22no—
17C3×#4027—22no—
18C3×D5×C22⋊C4—21no—
19C3×#4023—21no—
20#91572C412yescomplemented
21#91569—22no—
22#91564—21no—
23#91546—21no—
24#91537C412yescomplemented
25#91090—22no—
26#90997—22no—
27#90995—22no—
28#71656—51nomaximal, Hall
29#65827—31no—
30#65820D311yescharacteristic, complemented
31C2×#3938—31no—
32C2×#3938—31no—
33C2×#3938—31no—
34C5×#342—31no—
35#64747—31no—
36C24×C3×C5C2311yescharacteristic
37C23×D15C2×C411yescharacteristic, complemented
38C23×C3×D5D411yescharacteristic
39C22×C3×C4×C5—21no—
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220—21no—
45C2×#1220—21no—
46C22×Dic15—21no—
47C22×Dic15C2×C411yescharacteristic, complemented
48C22×C5×Dic3—21no—
49C22×C5×Dic3—21no—
50C2×C3×C22⋊D5—21no—
51C2×C3×C22⋊D5—21no—
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5—21no—
54C2×C3×C22⋊D5C2×C412yes—
55C2×C3×C22⋊D5D412yes—
56C22×C3×Dic5—21no—
57C22×C3×Dic5D411yescharacteristic
58C2×C3×C4×D5—22no—
59C2×#1202—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4D412yescomplemented
62#6719—21no—
63#6719—21no—
64C5×#217—21no—
65C5×#217—21no—
66C5×#217—21no—
67C5×#217C2×C412yescomplemented
68C3×C22⋊Dic5—21no—
69C3×C22⋊Dic5D412yescomplemented
70C3×#685—22no—
71C3×#683—22no—
72C3×C4×Dic5—22no—
73Dic3⋊Dic5—22no—
74#6667—22no—
75#6665—22no—
76C3×#518—51no—
77#5804—51no—
78C2×#834—51no—
79C2×#806—51no—
80C2×#806—51no—
81#4527—51no—
82#4527D511yescharacteristic, complemented
83C22×C22⋊D5—31no—
84C22×C22⋊D5C2×D311yescharacteristic
85C2×C5×C22⋊C4—31no—
86C2×C5×C22⋊C4—31no—
87C2×C5×C22⋊C4C2×D311yescharacteristic
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5C2×D311yescharacteristic
90#4076—62no—
91C4×C22⋊D5—22no—
92#4032—32no—
93#4032—61no—
94#4028—32no—
95#4028—61no—
96#4027—22no—
97D5×C22⋊C4—21no—
98#4023—21no—
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—81no—
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—81no—
118C22×C3×D5C22⋊C412yes—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—81no—
121#1220—41no—
122#1220—41no—
123#1220—41no—
124#1220—41no—
125C2×Dic15—21no—
126C2×Dic15—21no—
127C2×Dic15—21no—
128C2×Dic15—41no—
129C2×Dic15—81no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—41no—
132C2×C5×Dic3—81no—
133C2×C5×Dic3—81no—
134C3×C22⋊D5—22no—
135C3×C22⋊D5—22no—
136C3×C22⋊D5—22no—
137C3×C22⋊D5—22no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—81no—
142C2×C3×Dic5C22⋊C412yes—
143C3×C4×D5—82no—
144#1202—82no—
145C22×C3×D4—51no—
146C22×#67—51no—
147C3×C4×D4—102no—
148C3×C4×D4—102no—
149C3×#117—101no—
150C2×C3×C22⋊C4—51no—
151C2×C3×C22⋊C4—101no—
152C2×C3×C22⋊C4C2×D511yescharacteristic
153#953—101no—
154C2×#217—51no—
155C2×#217C2×D511yescharacteristic
156C2×#217C2×D511yescharacteristic
157#939—102no—
158#937—52no—
159#935—52no—
160#929—101no—
161#834—102no—
162#806—102no—
163#806—102no—
164C24×C5C22×D311yescharacteristic
165C23×D5—31no—
166C23×D5#6711yescharacteristic
167C22×C4×C5—21no—
168C22×C4×C5—61no—
169C22×C4×C5—61no—
170C2×C22⋊D5—21no—
171C2×C22⋊D5—21no—
172C2×C22⋊D5—21no—
173C2×C22⋊D5—21no—
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⋊D5C4×D312yes—
181C2×C22⋊D5D1212yes—
182C22×Dic5—21no—
183C22×Dic5—31no—
184C22×Dic5—61no—
185C22×Dic5#6711yescharacteristic
186C2×D20—62no—
187C2×C4×D5—22no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—32no—
190C5×C22⋊C4—61no—
191C5×C22⋊C4—61no—
192C5×C22⋊C4—61no—
193C5×C22⋊C4#6712yescomplemented
194C22⋊Dic5—21no—
195C22⋊Dic5—61no—
196C22⋊Dic5—61no—
197C22⋊Dic5#6712yescomplemented
198#685—22no—
199#685—62no—
200#685—62no—
201C4⋊Dic5—62no—
202#683—22no—
203C4×Dic5—22no—
204#534—151no—
205#518—51no—
206C2×#99—151no—
207C2×#99—151no—
208C2×#99—151no—
209#342—31no—
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×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—42no—
226C2×D15—41no—
227C2×D15—81no—
228C2×D15—81no—
229C2×C3×D5—22no—
230C2×C3×D5—42no—
231C2×C3×D5—42no—
232C2×C3×D5—81no—
233C3×C4×C5—42no—
234Dic15—41no—
235Dic15—81no—
236C3×Dic5—22no—
237C3×Dic5—42no—
238C5×Dic3—42no—
239C5×Dic3—81no—
240C24×C3—51no—
241C24×C3C22×D511yescharacteristic
242C23×D3—51no—
243C2×C3×D4—52no—
244C2×C3×D4—52no—
245C2×C3×D4—101no—
246C2×C3×D4—101no—
247C2×C3×D4—101no—
248C2×C3×D4—101no—
249C22×C3×C4—21no—
250C22×C3×C4—51no—
251C22×C3×C4—102no—
252C22×C3×C4—101no—
253C2×#67—102no—
254C2×#67—101no—
255C2×#67—101no—
256C2×#67—101no—
257C2×#67—101no—
258C2×#67—101no—
259C2×#67—101no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262C22×Dic3—51no—
263C22×Dic3—101no—
264C3×C4⋊C4—102no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—52no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4—101no—
269C3×C22⋊C4D2012yescomplemented
270C3×C42—102no—
271#217—21no—
272#217—21no—
273#217—21no—
274#217—102no—
275#217—101no—
276#217—101no—
277#217C4×D512yescomplemented
278(C2×D3)⋊C4—102no—
279Dic3⋊C4—102no—
280C23×C5—81no—
281C23×C5C2×C4×D311yescharacteristic
282C23×C5C2×D1211yescharacteristic
283C23×C5#23511yescharacteristic
284C23×C5#23511yescharacteristic
285C23×C5C2×#6711yescharacteristic
286C23×C5C2×#6711yescharacteristic
287C23×C5C2×#6711yescharacteristic
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—61no—
291C22×D5—61no—
292C22×D5—61no—
293C22×D5—81no—
294C22×D5—241no—
295C22×D5(C2×D3)⋊C412yes—
296C2×C4×C5—22no—
297C2×C4×C5—62no—
298C2×C4×C5—81no—
299C2×C4×C5—121no—
300C2×C4×C5—241no—
301C2×C4×C5—241no—
302C22⋊D5—22no—
303C22⋊D5—22no—
304C22⋊D5—22no—
305C22⋊D5—22no—
306C22⋊D5—121no—
307C22⋊D5—121no—
308C22⋊D5—121no—
309C22⋊D5—121no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—22no—
313C2×Dic5—61no—
314C2×Dic5—61no—
315C2×Dic5—61no—
316C2×Dic5—81no—
317C2×Dic5—121no—
318C2×Dic5—241no—
319C2×Dic5(C2×D3)⋊C412yes—
320D20—242no—
321C4×D5—82no—
322C22×D4—51no—
323C22×D4—151no—
324#123—152no—
325#123—301no—
326#121—302no—
327#120—152no—
328#120—301no—
329C4×D4—102no—
330C4×D4—102no—
331#117—101no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—51no—
335C2×C22⋊C4—101no—
336C2×C22⋊C4—151no—
337C2×C22⋊C4D3×D511yescharacteristic
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—81no—
350C3×D5—42no—
351C23×C3—52no—
352C23×C3—81no—
353C23×C3—101no—
354C23×C3—101no—
355C23×C3—401no—
356C23×C3C2×C4×D511yescharacteristic
357C23×C3C2×D2011yescharacteristic
358C23×C3#70911yescharacteristic
359C23×C3D4×D511yescharacteristic
360C23×C3D4×D511yescharacteristic
361C23×C3D4×D511yescharacteristic
362C23×C3#71311yescharacteristic
363C22×D3—101no—
364C22×D3—101no—
365C22×D3—101no—
366C22×D3—401no—
367C3×D4—102no—
368C3×D4—102no—
369C3×D4—102no—
370C3×D4—102no—
371C2×C3×C4—22no—
372C2×C3×C4—52no—
373C2×C3×C4—81no—
374C2×C3×C4—101no—
375C2×C3×C4—101no—
376C2×C3×C4—102no—
377C2×C3×C4—402no—
378C2×C3×C4—401no—
379#67—201no—
380#67—201no—
381#67—201no—
382#67—201no—
383#67—402no—
384C2×Dic3—22no—
385C2×Dic3—41no—
386C2×Dic3—81no—
387C2×Dic3—81no—
388C2×Dic3—101no—
389C2×Dic3—101no—
390C2×Dic3—101no—
391C2×Dic3—201no—
392C2×Dic3—401no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5C2×(C2×D3)⋊C411yescharacteristic
401C22×C5C4×#6711yescharacteristic
402C22×C5C4×#6711yescharacteristic
403C22×C5#92911yescharacteristic
404C22×C5#93011yescharacteristic
405C22×C5#93011yescharacteristic
406C22×C5#95311yescharacteristic
407C2×D5—22no—
408C2×D5—42no—
409C2×D5—42no—
410C2×D5—81no—
411C2×D5—122no—
412C2×D5—121no—
413C2×D5—241no—
414C2×D5—241no—
415C4×C5—42no—
416C4×C5—122no—
417C4×C5—241no—
418Dic5—22no—
419Dic5—42no—
420Dic5—121no—
421Dic5—241no—
422C24—51no—
423C24—151no—
424C24C2×D3×D511yescharacteristic
425C2×D4—52no—
426C2×D4—52no—
427C2×D4—101no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—101no—
431C2×D4—302no—
432C2×D4—301no—
433C2×D4—301no—
434C2×D4—301no—
435C2×D4—301no—
436C2×D4—301no—
437C2×D4—301no—
438C22×C4—21no—
439C22×C4—51no—
440C22×C4—61no—
441C22×C4—61no—
442C22×C4—102no—
443C22×C4—101no—
444C22×C4—151no—
445C22×C4—301no—
446C4⋊C4—102no—
447C4⋊C4—302no—
448C22⋊C4—21no—
449C22⋊C4—32no—
450C22⋊C4—52no—
451C22⋊C4—61no—
452C22⋊C4—61no—
453C22⋊C4—61no—
454C22⋊C4—102no—
455C22⋊C4—101no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—301no—
459C22⋊C4—301no—
460C22⋊C4#120212yescomplemented
461C42—102no—
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—102no—
471C22×C3—202no—
472C22×C3—202no—
473C22×C3—401no—
474C22×C3C4×D2011yescharacteristic
475C22×C3D5×C22⋊C411yescharacteristic
476C22×C3#402811yescharacteristic
477C22×C3#403011yescharacteristic
478C22×C3#403911yescharacteristic
479C22×C3#404011yescharacteristic
480C22×C3#404111yescharacteristic
481C2×D3—202no—
482C2×D3—201no—
483C2×D3—401no—
484C2×D3—401no—
485C3×C4—42no—
486C3×C4—102no—
487C3×C4—202no—
488Dic3—42no—
489Dic3—81no—
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#521311yescharacteristic
500D5—42no—
501D5—241no—
502C23—52no—
503C23—81no—
504C23—101no—
505C23—101no—
506C23—301no—
507C23—301no—
508C23—301no—
509C23—401no—
510C23—1201no—
511C23#677111yescharacteristic
512C23#677311yescharacteristic
513C23C4×D3×D511yescharacteristic
514C23D5×D1211yescharacteristic
515C23C2×#120211yescharacteristic
516C23D5×#6711yescharacteristic
517C23D5×#6711yescharacteristic
518D4—102no—
519D4—102no—
520D4—102no—
521D4—102no—
522D4—601no—
523D4—601no—
524D4—601no—
525D4—601no—
526D4—1202no—
527C2×C4—22no—
528C2×C4—52no—
529C2×C4—62no—
530C2×C4—81no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—102no—
534C2×C4—121no—
535C2×C4—241no—
536C2×C4—241no—
537C2×C4—301no—
538C2×C4—301no—
539C2×C4—301no—
540C2×C4—402no—
541C2×C4—401no—
542C2×C4—601no—
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—202no—
552C2×C3#6495411yescharacteristic
553D3—401no—
554C5#7165611yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—102no—
563C22—202no—
564C22—202no—
565C22—401no—
566C22—602no—
567C22—601no—
568C22—1201no—
569C22—1201no—
570C22#9134811yescharacteristic
571C22C4×#120211yescharacteristic
572C22#9144411yescharacteristic
573C22#9144811yescharacteristic
574C22#9145011yescharacteristic
575C22D5×(C2×D3)⋊C411yescharacteristic
576C22#9156411yescharacteristic
577C4—42no—
578C4—102no—
579C4—122no—
580C4—202no—
581C4—241no—
582C4—601no—
583C4—1201no—
584C3#1059975711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—202no—
593C2—1201no—
594C2#1174890711yescharacteristic
subgroupG/H
centerC2#11748907
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC2×C3×C5#386
prime radical#11755427C2
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65820C2semidirect
3. C2×#91090C2semidirect
4. C2×#90997C2semidirect
5. C2×#90995C2semidirect
6. C5×#4527C2semidirect
7. #11746020C2semidirect
20. #91572C4semidirect
24. #91537C4semidirect
30. #65820D3semidirect
37. C23×D15C2×C4semidirect
47. C22×Dic15C2×C4semidirect
61. C3×C5×C22⋊C4D4semidirect
67. C5×#217C2×C4semidirect
69. C3×C22⋊Dic5D4semidirect
82. #4527D5semidirect
193. C5×C22⋊C4#67semidirect
197. C22⋊Dic5#67semidirect
269. C3×C22⋊C4D20semidirect
277. #217C4×D5semidirect
460. C22⋊C4#1202semidirect
462. C3×C5#1913semidirect
554. C5#71656semidirect
584. C3#10599757semidirect

Maximal subgroups

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

subgroupindex
C3×#658202
#117554272
C2×#910902
C2×#909972
C2×#909952
C5×#45272
#117460202
#105997573
#716565