Finite Group Databasebeta

← #14303000

Subgroups — #14303000

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#11755427C211yesmaximal, characteristic
2#11755413C211yesmaximal, characteristic, complemented
3C2×#91090C211yesmaximal, characteristic, complemented
4C2×C3×#3938C211yesmaximal, characteristic, complemented
5C2×#90995C211yesmaximal, characteristic, complemented
6C5×#4526C211yesmaximal, 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
16#91572—21no—
17#91569—22no—
18#91564C412yescomplemented
19#91561—21no—
20#91556—22no—
21#91552—22no—
22#91546C412yescomplemented
23#91537—21no—
24#91532—21no—
25#91090—22no—
26C3×#3938—22no—
27#90995—22no—
28#70034—51nomaximal, Hall
29#65827—31no—
30#65820—31no—
31C2×#3938—31no—
32C2×#3938—31no—
33C2×#3938D311yescharacteristic, complemented
34C5×#342—31no—
35#64747—31no—
36C24×C3×C5C2311yescharacteristic
37C23×D15D411yescharacteristic
38C23×C3×D5C2×C411yescharacteristic, complemented
39C22×C3×C4×C5—21no—
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220C2×C412yes—
45C2×#1220D412yes—
46C22×Dic15—21no—
47C22×Dic15D411yescharacteristic
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⋊D5—21no—
55C2×C3×C22⋊D5—21no—
56C22×C3×Dic5—21no—
57C22×C3×Dic5C2×C411yescharacteristic, complemented
58C2×#1202—22no—
59C2×#1200—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62#6719—21no—
63#6719—21no—
64C5×#217—21no—
65C5×#217—21no—
66C5×#217C2×C412yescomplemented
67C5×#217D412yescomplemented
68C3×C22⋊Dic5—21no—
69C3×C22⋊Dic5D412yescomplemented
70Dic3⋊Dic5—22no—
71#6669—22no—
72#6667—22no—
73#6667—22no—
74#6665—22no—
75Dic3×Dic5—22no—
76#5804—51no—
77#5486—51no—
78C2×C3×#99—51no—
79C2×#834—51no—
80C2×#806—51no—
81#4527—51no—
82#4526D511yescharacteristic, 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—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—22no—
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—81no—
114C22×D15C22⋊C412yes—
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—21no—
118C22×C3×D5—81no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5—81no—
121#1220—22no—
122#1220—22no—
123#1220—22no—
124#1220—22no—
125C2×Dic15—21no—
126C2×Dic15—21no—
127C2×Dic15—41no—
128C2×Dic15—81no—
129C2×Dic15C22⋊C412yes—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—81no—
133C2×C5×Dic3—81no—
134C3×C22⋊D5—41no—
135C3×C22⋊D5—41no—
136C3×C22⋊D5—41no—
137C3×C22⋊D5—41no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—81no—
143#1202—82no—
144#1200—82no—
145C22×C3×D4—51no—
146C22×#67—51no—
147C2×C3×C22⋊C4—51no—
148C2×C3×C22⋊C4C2×D511yescharacteristic
149#953—52no—
150C2×#217—51no—
151C2×#217C2×D511yescharacteristic
152C2×#217C2×D511yescharacteristic
153#939—102no—
154#937—101no—
155#935—101no—
156#929—52no—
157C4×#67—102no—
158#67⋊C4—102no—
159D3×C22⋊C4—101no—
160#877—101no—
161C3×#99—102no—
162#834—102no—
163#806—102no—
164C24×C5C22×D311yescharacteristic
165C23×D5—31no—
166C23×D5C4×D311yescharacteristic, complemented
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—21no—
175C2×C22⋊D5—21no—
176C2×C22⋊D5—32no—
177C2×C22⋊D5—32no—
178C2×C22⋊D5—61no—
179C2×C22⋊D5—61no—
180C2×C22⋊D5—61no—
181C2×C22⋊D5—61no—
182C22×Dic5—21no—
183C22×Dic5—31no—
184C22×Dic5—61no—
185C22×Dic5C4×D311yescharacteristic, complemented
186C2×D20—62no—
187C2×C4×D5—62no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—21no—
190C5×C22⋊C4—32no—
191C5×C22⋊C4—32no—
192C5×C22⋊C4—61no—
193C5×C22⋊C4—61no—
194C22⋊Dic5—21no—
195C22⋊Dic5—61no—
196C22⋊Dic5—61no—
197C22⋊Dic5#6712yescomplemented
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—51no—
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—22no—
226C2×D15—42no—
227C2×D15—42no—
228C2×D15—81no—
229C2×C3×D5—42no—
230C2×C3×D5—41no—
231C2×C3×D5—81no—
232C2×C3×D5—81no—
233C3×C4×C5—81no—
234Dic15—22no—
235Dic15—81no—
236C3×Dic5—42no—
237C3×Dic5—41no—
238C5×Dic3—42no—
239C5×Dic3—42no—
240C24×C3—51no—
241C24×C3C22×D511yescharacteristic
242C23×D3—51no—
243C2×C3×D4—101no—
244C2×C3×D4—101no—
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—101no—
252C2×#67—52no—
253C2×#67—52no—
254C2×#67—102no—
255C2×#67—101no—
256C2×#67—101no—
257C2×#67—101no—
258C2×#67—101no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—51no—
262C22×Dic3—101no—
263C2×C4×D3—102no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—52no—
267C3×C22⋊C4—101no—
268#217—21no—
269#217—21no—
270#217—102no—
271#217—101no—
272#217—101no—
273#217C4×D512yescomplemented
274#217D2012yescomplemented
275(C2×D3)⋊C4—102no—
276(C2×D3)⋊C4—102no—
277Dic3⋊C4—102no—
278Dic3⋊C4—102no—
279C4×Dic3—102no—
280C23×C5—81no—
281C23×C5C2×C4×D311yescharacteristic
282C23×C5#23511yescharacteristic
283C23×C5D3×D411yescharacteristic
284C23×C5D3×D411yescharacteristic
285C23×C5D3×D411yescharacteristic
286C23×C5#23711yescharacteristic
287C23×C5C2×#6711yescharacteristic
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—21no—
291C22×D5—32no—
292C22×D5—61no—
293C22×D5—61no—
294C22×D5—81no—
295C22×D5—241no—
296C2×C4×C5—41no—
297C2×C4×C5—62no—
298C2×C4×C5—62no—
299C2×C4×C5—81no—
300C2×C4×C5—241no—
301C2×C4×C5—241no—
302C22⋊D5—41no—
303C22⋊D5—41no—
304C22⋊D5—41no—
305C22⋊D5—41no—
306C22⋊D5—62no—
307C22⋊D5—62no—
308C22⋊D5—62no—
309C22⋊D5—62no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—22no—
314C2×Dic5—32no—
315C2×Dic5—61no—
316C2×Dic5—61no—
317C2×Dic5—81no—
318C2×Dic5—121no—
319C2×Dic5—241no—
320D20—242no—
321C4×D5—242no—
322C22×D4—51no—
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—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—51no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—301no—
337C2×C22⋊C4D3×D511yescharacteristic
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#38611yescharacteristic
349D15—42no—
350C3×D5—81no—
351C23×C3—81no—
352C23×C3—101no—
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—52no—
364C22×D3—101no—
365C22×D3—101no—
366C22×D3—401no—
367C3×D4—201no—
368C3×D4—201no—
369C3×D4—201no—
370C3×D4—201no—
371C2×C3×C4—41no—
372C2×C3×C4—81no—
373C2×C3×C4—101no—
374C2×C3×C4—101no—
375C2×C3×C4—102no—
376C2×C3×C4—101no—
377C2×C3×C4—401no—
378#67—102no—
379#67—102no—
380#67—102no—
381#67—102no—
382#67—402no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—52no—
386C2×Dic3—81no—
387C2×Dic3—81no—
388C2×Dic3—101no—
389C2×Dic3—101no—
390C2×Dic3—201no—
391C2×Dic3—401no—
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×C5D3×C22⋊C411yescharacteristic
401C22×C5#67⋊C411yescharacteristic
402C22×C5#88311yescharacteristic
403C22×C5#88411yescharacteristic
404C22×C5C4×#6711yescharacteristic
405C22×C5#93711yescharacteristic
406C22×C5#93811yescharacteristic
407C2×D5—42no—
408C2×D5—41no—
409C2×D5—62no—
410C2×D5—81no—
411C2×D5—81no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—241no—
415C4×C5—81no—
416C4×C5—122no—
417C4×C5—122no—
418Dic5—42no—
419Dic5—41no—
420Dic5—62no—
421Dic5—241no—
422C24—51no—
423C24—151no—
424C24C2×D3×D511yescharacteristic
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—101no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—101no—
431C2×D4—152no—
432C2×D4—152no—
433C2×D4—302no—
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—101no—
443C22×C4—151no—
444C22×C4—302no—
445C22×C4—301no—
446C4⋊C4—302no—
447C4⋊C4—302no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—32no—
451C22⋊C4—32no—
452C22⋊C4—52no—
453C22⋊C4—61no—
454C22⋊C4—61no—
455C22⋊C4—101no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—302no—
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—202no—
471C22×C3—201no—
472C22×C3—401no—
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—102no—
482C2×D3—202no—
483C2×D3—202no—
484C2×D3—401no—
485C3×C4—81no—
486C3×C4—202no—
487C3×C4—201no—
488Dic3—42no—
489Dic3—42no—
490Dic3—102no—
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#495611yescharacteristic
500D5—81no—
501D5—122no—
502C23—81no—
503C23—101no—
504C23—101no—
505C23—101no—
506C23—152no—
507C23—301no—
508C23—301no—
509C23—401no—
510C23—1201no—
511C23#677311yescharacteristic
512C23C4×D3×D511yescharacteristic
513C23D3×D2011yescharacteristic
514C23#677711yescharacteristic
515C23#677911yescharacteristic
516C23D5×#6711yescharacteristic
517C23#679011yescharacteristic
518D4—201no—
519D4—201no—
520D4—201no—
521D4—201no—
522D4—302no—
523D4—302no—
524D4—302no—
525D4—302no—
526D4—1202no—
527C2×C4—41no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—81no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—102no—
535C2×C4—152no—
536C2×C4—241no—
537C2×C4—241no—
538C2×C4—301no—
539C2×C4—301no—
540C2×C4—401no—
541C2×C4—601no—
542C2×C4—1202no—
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—401no—
552C2×C3#6495411yescharacteristic
553D3—202no—
554C5#7003411yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—202no—
563C22—201no—
564C22—302no—
565C22—401no—
566C22—401no—
567C22—602no—
568C22—602no—
569C22—1201no—
570C22#9135611yescharacteristic
571C22#9139511yescharacteristic
572C22#9144411yescharacteristic
573C22#9145911yescharacteristic
574C22#9147311yescharacteristic
575C22#9147411yescharacteristic
576C22#9153311yescharacteristic
577C4—81no—
578C4—122no—
579C4—122no—
580C4—202no—
581C4—201no—
582C4—302no—
583C4—1201no—
584C3#1059975711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—401no—
593C2—602no—
594C2#1174870011yescharacteristic
subgroupG/H
centerC2#11748700
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
2. #11755413C2semidirect
3. C2×#91090C2semidirect
4. C2×C3×#3938C2semidirect
5. C2×#90995C2semidirect
6. C5×#4526C2semidirect
7. #11746020C2semidirect
18. #91564C4semidirect
22. #91546C4semidirect
33. C2×#3938D3semidirect
38. C23×C3×D5C2×C4semidirect
57. C22×C3×Dic5C2×C4semidirect
66. C5×#217C2×C4semidirect
67. C5×#217D4semidirect
69. C3×C22⋊Dic5D4semidirect
82. #4526D5semidirect
166. C23×D5C4×D3semidirect
185. C22×Dic5C4×D3semidirect
197. C22⋊Dic5#67semidirect
273. #217C4×D5semidirect
274. #217D20semidirect
462. C3×C5#1913semidirect
554. C5#70034semidirect
584. C3#10599757semidirect

Maximal subgroups

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

subgroupindex
#117554272
#117554132
C2×#910902
C2×C3×#39382
C2×#909952
C5×#45262
#117460202
#105997573
#700345