Finite Group Databasebeta

← #14313205

Subgroups — #14313205

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756563C211yesmaximal, characteristic
2C2×C3×C5×#100C211yesmaximal, characteristic, complemented
3C2×#91118C211yesmaximal, characteristic, complemented
4#11746297C212yesmaximal, complemented
5#11746296C212yesmaximal, complemented
6#10600887—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×#1220C411yescharacteristic, complemented
9C2×C3×C5×M16—21no—
10#91842—21no—
11C2×#6719—21no—
12C2×#6719C411yescharacteristic, complemented
13#91828—21no—
14#91828—21no—
15#91826C411yescharacteristic, complemented
16#91826C2211yescharacteristic
17#91824C411yescharacteristic, complemented
18#91824C2211yescharacteristic
19#91818—21no—
20C3×C5×#100—21no—
21C3×C5×#100C2212yes—
22#91118—21no—
23#91118C2212yes—
24#70094—51nomaximal, Hall
25#66138—31no—
26C2×C5×#100D311yescharacteristic, complemented
27C2×#3966—31no—
28#64696—32no—
29#64695—32no—
30C24×C3×C5C2×C411yescharacteristic
31C24×C3×C5D411yescharacteristic
32C23×D15C2×C411yescharacteristic, complemented
33C2×C3×C5×D4—41no—
34C2×C3×C5×D4—41no—
35C2×C3×C5×D4C2×C411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C2×C3×C5×D4C2311yescharacteristic
39C22×C3×C4×C5D411yescharacteristic
40C2×#1220—21no—
41C2×#1220—21no—
42C2×#1220—21no—
43C2×#1220—21no—
44C2×#1220—41no—
45C2×#1220—41no—
46C22×Dic15—21no—
47C22×Dic15—41no—
48C22×Dic15C2×C411yescharacteristic, complemented
49C3×C5×M16—22no—
50C3×C5×M16—41no—
51C2×C3×C5×C8—41no—
52#6719—21no—
53#6719—21no—
54#6719—21no—
55#6719—22no—
56#6719—41no—
57#6719C2×C411yescharacteristic, complemented
58#6719C2×C411yescharacteristic, complemented
59#6714—21no—
60#6714—21no—
61#6712—21no—
62#6712—21no—
63#5804—51no—
64C2×C3×#100D511yescharacteristic, complemented
65C2×#834—51no—
66#4476—52no—
67#4475—52no—
68C22×C5×D4C2×D311yescharacteristic
69C22×C22⋊D5—31no—
70C2×C5×M16—21no—
71#4099—61no—
72C2×C22⋊Dic5—31no—
73C2×C22⋊Dic5—61no—
74#4085—61no—
75#4085—61no—
76#4083—31no—
77#4083—31no—
78#4081—31no—
79#4081—31no—
80#4075—61no—
81C5×#100—21no—
82C5×#100C2×D312yes—
83#3966—32no—
84#3966—61no—
85#2121—151noSylow
86C23×C3×C5—21no—
87C23×C3×C5—21no—
88C23×C3×C5—21no—
89C23×C3×C5—21no—
90C23×C3×C5—81no—
91C23×C3×C5—81no—
92C23×C3×C5C22⋊C411yescharacteristic
93C23×C3×C5C22⋊C411yescharacteristic
94C23×C3×C5C22⋊C411yescharacteristic
95C23×C3×C5C22×C411yescharacteristic
96C23×C3×C5C2×D411yescharacteristic
97C22×D15—21no—
98C22×D15—41no—
99C22×D15—81no—
100C3×C5×D4—41no—
101C3×C5×D4—41no—
102C3×C5×D4—41no—
103C3×C5×D4—41no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5C22⋊C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108#1220—42no—
109#1220—41no—
110#1220—41no—
111#1220—81no—
112#1220—81no—
113C2×Dic15—21no—
114C2×Dic15—21no—
115C2×Dic15—21no—
116C2×Dic15—41no—
117C2×Dic15—42no—
118C2×Dic15—81no—
119C2×Dic15—82no—
120C3×C5×C8—42no—
121C22×C3×D4C2×D511yescharacteristic
122C22×#67—51no—
123C2×C3×M16—21no—
124#953—101no—
125C2×#217—51no—
126C2×#217—101no—
127#939—101no—
128#939—101no—
129#937—51no—
130#937—51no—
131#935—51no—
132#935—51no—
133#929—101no—
134C3×#100—21no—
135C3×#100C2×D512yes—
136#834—52no—
137#834—101no—
138C24×C5C4×D311yescharacteristic
139C24×C5D1211yescharacteristic
140C23×D5—31no—
141C2×C5×D4—41no—
142C2×C5×D4—41no—
143C2×C5×D4C4×D311yescharacteristic
144C2×C5×D4D1211yescharacteristic
145C2×C5×D4#6711yescharacteristic
146C2×C5×D4C22×D311yescharacteristic
147C22×C4×C5#6711yescharacteristic
148C2×C22⋊D5—61no—
149C2×C22⋊D5—61no—
150C2×C22⋊D5—61no—
151C2×C22⋊D5—61no—
152C2×C22⋊D5—121no—
153C2×C22⋊D5—121no—
154C22×Dic5—31no—
155C22×Dic5—61no—
156C22×Dic5—121no—
157C5×M16—22no—
158C5×M16—41no—
159C2×C5×C8—41no—
160C22⋊Dic5—31no—
161C22⋊Dic5—31no—
162C22⋊Dic5—61no—
163C22⋊Dic5—61no—
164C22⋊Dic5—61no—
165C22⋊Dic5—62no—
166C22⋊Dic5—121no—
167#685—61no—
168#685—61no—
169#683—61no—
170#683—61no—
171#534—151no—
172C2×#100D1511yescharacteristic, complemented
173C2×#99—151no—
174#352—152no—
175AΣL(1,𝔽16)—152no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5—21no—
180C22×C3×C5—41no—
181C22×C3×C5—41no—
182C22×C3×C5—41no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—42no—
186C22×C3×C5—81no—
187C22×C3×C5—81no—
188C22×C3×C5—81no—
189C22×C3×C5#9911yescharacteristic
190C22×C3×C5#9911yescharacteristic
191C22×C3×C5C2×C22⋊C411yescharacteristic
192C2×D15—41no—
193C2×D15—41no—
194C2×D15—41no—
195C2×D15—82no—
196C3×C4×C5—21no—
197C3×C4×C5—21no—
198Dic15—41no—
199Dic15—41no—
200Dic15—41no—
201Dic15—82no—
202C24×C3C4×D511yescharacteristic
203C24×C3D2011yescharacteristic
204C23×D3—51no—
205C2×C3×D4—41no—
206C2×C3×D4—41no—
207C2×C3×D4C4×D511yescharacteristic
208C2×C3×D4D2011yescharacteristic
209C2×C3×D4C22⋊D511yescharacteristic
210C2×C3×D4C22×D511yescharacteristic
211C22×C3×C4C22⋊D511yescharacteristic
212C2×#67—101no—
213C2×#67—101no—
214C2×#67—101no—
215C2×#67—101no—
216C2×#67—201no—
217C2×#67—201no—
218C22×Dic3—51no—
219C22×Dic3—101no—
220C22×Dic3—201no—
221C3×M16—22no—
222C3×M16—41no—
223C2×C3×C8—41no—
224#217—51no—
225#217—51no—
226#217—101no—
227#217—101no—
228#217—101no—
229#217—102no—
230#217—201no—
231(C2×D3)⋊C4—101no—
232(C2×D3)⋊C4—101no—
233Dic3⋊C4—101no—
234Dic3⋊C4—101no—
235C23×C5—21no—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—21no—
239C23×C5—81no—
240C23×C5—81no—
241C23×C5(C2×D3)⋊C411yescharacteristic
242C23×C5(C2×D3)⋊C411yescharacteristic
243C23×C5(C2×D3)⋊C411yescharacteristic
244C23×C5C2×C4×D311yescharacteristic
245C23×C5C2×D1211yescharacteristic
246C22×D5—61no—
247C22×D5—121no—
248C22×D5—241no—
249C5×D4—41no—
250C5×D4—41no—
251C5×D4—41no—
252C5×D4—41no—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5(C2×D3)⋊C411yescharacteristic
256C2×C4×C5C2×#6711yescharacteristic
257C22⋊D5—122no—
258C22⋊D5—121no—
259C22⋊D5—121no—
260C22⋊D5—241no—
261C22⋊D5—241no—
262C2×Dic5—61no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265C2×Dic5—121no—
266C2×Dic5—122no—
267C2×Dic5—241no—
268C2×Dic5—242no—
269C5×C8—42no—
270C22×D4—151no—
271C22×D4C2×D1511yescharacteristic
272C2×M16—21no—
273#123—151no—
274#123—151no—
275#123—301no—
276#121—301no—
277#121—301no—
278#120—151no—
279#120—151no—
280#120—301no—
281C2×C22⋊C4—151no—
282C2×C22⋊C4—301no—
283#100—21no—
284#100C2×D1512yes—
285#99—152no—
286#99—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5—41no—
291C2×C3×C5—41no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295D15—81no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—81no—
301C23×C3—81no—
302C23×C3#68511yescharacteristic
303C23×C3#68511yescharacteristic
304C23×C3#68511yescharacteristic
305C23×C3C2×C4×D511yescharacteristic
306C23×C3C2×D2011yescharacteristic
307C22×D3—101no—
308C22×D3—201no—
309C22×D3—401no—
310C3×D4—41no—
311C3×D4—41no—
312C3×D4—41no—
313C3×D4—41no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4#68511yescharacteristic
317C2×C3×C4C2×C22⋊D511yescharacteristic
318#67—202no—
319#67—201no—
320#67—201no—
321#67—401no—
322#67—401no—
323C2×Dic3—101no—
324C2×Dic3—101no—
325C2×Dic3—101no—
326C2×Dic3—201no—
327C2×Dic3—202no—
328C2×Dic3—401no—
329C2×Dic3—402no—
330C3×C8—42no—
331C22×C5—21no—
332C22×C5—21no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5—41no—
336C22×C5—41no—
337C22×C5—41no—
338C22×C5—41no—
339C22×C5—41no—
340C22×C5—42no—
341C22×C5—81no—
342C22×C5—81no—
343C22×C5—81no—
344C22×C5#80611yescharacteristic
345C22×C5#80611yescharacteristic
346C22×C5C2×(C2×D3)⋊C411yescharacteristic
347C2×D5—121no—
348C2×D5—121no—
349C2×D5—121no—
350C2×D5—242no—
351C4×C5—21no—
352C4×C5—21no—
353Dic5—121no—
354Dic5—121no—
355Dic5—121no—
356Dic5—242no—
357C24—151no—
358C24C4×D1511yescharacteristic
359C24D6011yescharacteristic
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—301no—
363C2×D4—301no—
364C2×D4—301no—
365C2×D4—301no—
366C2×D4—601no—
367C2×D4—601no—
368C2×D4C4×D1511yescharacteristic
369C2×D4D6011yescharacteristic
370C2×D4#122011yescharacteristic
371C2×D4C22×D1511yescharacteristic
372C22×C4—151no—
373C22×C4—301no—
374C22×C4—601no—
375C22×C4#122011yescharacteristic
376M16—22no—
377M16—41no—
378C2×C8—41no—
379C4⋊C4—301no—
380C4⋊C4—301no—
381C22⋊C4—151no—
382C22⋊C4—151no—
383C22⋊C4—301no—
384C22⋊C4—301no—
385C22⋊C4—301no—
386C22⋊C4—301no—
387C22⋊C4—301no—
388C22⋊C4—302no—
389C22⋊C4—601no—
390C3×C5#212111yescharacteristic, complemented, Hall
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—42no—
401C22×C3—81no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3#393811yescharacteristic
405C22×C3#393811yescharacteristic
406C22×C3C2×#68511yescharacteristic
407C2×D3—201no—
408C2×D3—201no—
409C2×D3—201no—
410C2×D3—402no—
411C3×C4—21no—
412C3×C4—21no—
413Dic3—201no—
414Dic3—201no—
415Dic3—201no—
416Dic3—402no—
417C2×C5—21no—
418C2×C5—21no—
419C2×C5—21no—
420C2×C5—41no—
421C2×C5—41no—
422C2×C5—41no—
423C2×C5—41no—
424C2×C5C2×#80611yescharacteristic
425D5—241no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—81no—
431C23—81no—
432C23—301no—
433C23—601no—
434C23—1201no—
435C23#671411yescharacteristic
436C23#671411yescharacteristic
437C23#671411yescharacteristic
438C23C2×C4×D1511yescharacteristic
439C23C2×D6011yescharacteristic
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444D4—602no—
445D4—601no—
446D4—601no—
447D4—1201no—
448D4—1201no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—301no—
452C2×C4—301no—
453C2×C4—301no—
454C2×C4—601no—
455C2×C4—602no—
456C2×C4—1201no—
457C2×C4—1202no—
458C2×C4#671411yescharacteristic
459C2×C4C2×#122011yescharacteristic
460C8—42no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—41no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3C2×#393811yescharacteristic
469D3—401no—
470C5#7009411yescharacteristic, complemented, Sylow
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—601no—
485C22—601no—
486C22—601no—
487C22—1202no—
488C22#9109011yescharacteristic
489C22#9109011yescharacteristic
490C22C2×#671411yescharacteristic
491C4—21no—
492C4—21no—
493C4—601no—
494C4—601no—
495C4—601no—
496C4—1202no—
497C3#1060088711yescharacteristic, complemented, Sylow
498C2—21no—
499C2—21no—
500C2—21no—
501C2—41no—
502C2—41no—
503C2—41no—
504C2—41no—
505C2—1201no—
506C2C2×#9109011yescharacteristic
subgroupG/H
centerC2C2×#91090
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C22×D15
FittingC2×C3×C5×#100C2
socleC2×C3×C5C2×#99
prime radical#11756563C2
cosocleC2×C3×C5×D4C23
hypercenterC2×#100D15
hypocenterC3×C5#2121
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#100C2semidirect
3. C2×#91118C2semidirect
4. #11746297C2semidirect
5. #11746296C2semidirect
8. C22×#1220C4semidirect
12. C2×#6719C4semidirect
15. #91826C4semidirect
17. #91824C4semidirect
26. C2×C5×#100D3semidirect
32. C23×D15C2×C4semidirect
48. C22×Dic15C2×C4semidirect
57. #6719C2×C4semidirect
58. #6719C2×C4semidirect
64. C2×C3×#100D5semidirect
172. C2×#100D15semidirect
390. C3×C5#2121semidirect
470. C5#70094semidirect
497. C3#10600887semidirect

Maximal subgroups

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

subgroupindex
#117565632
C2×C3×C5×#1002
C2×#911182
#117462972
#117462962
#106008873
#700945