Finite Group Databasebeta

← #14302877

Subgroups — #14302877

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756589C211yesmaximal, characteristic
2#11756280C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic, complemented
4#11751337C211yesmaximal, characteristic, complemented
5C2×#91107C211yesmaximal, characteristic, complemented
6#11746378C211yesmaximal, characteristic, complemented
7#11746352C211yesmaximal, characteristic, complemented
8#10601201—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13#91836C412yescomplemented
14#91829C412yescomplemented
15#91826—22no—
16#91819—22no—
17#91815C2211yescharacteristic
18#91815C2211yescharacteristic
19C2×#6710C2211yescharacteristic
20#91782—22no—
21C22⋊C4×D15—22no—
22C4×D60—22no—
23C3×C5×#104—22no—
24#91121—22no—
25#91107—22no—
26#70408—51nomaximal, Hall
27#66164—31no—
28#65855—31no—
29C5×#421D311yescharacteristic, complemented
30#65525—31no—
31C2×#3955—31no—
32#64777—31no—
33#64751—31no—
34C23×D15D412yes—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C2×C3×C5×Q8C2×C411yescharacteristic, complemented
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C411yescharacteristic, complemented
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C2×#1220—24no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—21no—
48C2×D60—21no—
49C2×D60C2×C412yes—
50C2×D60D412yes—
51C2×C4×D15—24no—
52C3×C5×M16—21no—
53C3×C5×M16—21no—
54C2×C3×C5×C8—21no—
55C3×C5×C4⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C42×C5D412yescomplemented
58#6719—21no—
59#6719—21no—
60#6714—24no—
61#6714—24no—
62C4⋊Dic15—21no—
63C4⋊Dic15—21no—
64C4×Dic15C2×C412yescomplemented
65C4×Dic15D412yescomplemented
66#6710—21no—
67#6710—21no—
68C2×C3⋊#168—21no—
69#5830—51no—
70#5521—51no—
71C3×#421D511yescharacteristic, complemented
72#5236—51no—
73C2×#823—51no—
74#4557—51no—
75#4531—51no—
76C2×C5×#41C2×D311yescharacteristic
77C22×D20—31no—
78C2×C5×M16C2×D311yescharacteristic
79C5×#117C2×D311yescharacteristic
80#4093—32no—
81#4086—32no—
82#4083—62no—
83#4076—62no—
84#4072—31no—
85#4072—31no—
86C2×#681—31no—
87#4039—62no—
88D5×C22⋊C4—62no—
89C4×D20—62no—
90C5×#104—22no—
91#3969—62no—
92#3955—62no—
93#1911—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—22no—
97C22×D15—22no—
98C22×D15—82no—
99C22×D15C22⋊C414yes—
100C3×C5×Q8—21no—
101C3×C5×Q8—21no—
102C3×C5×D4—21no—
103C3×C5×D4—21no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116#1220—84no—
117C2×Dic15—22no—
118C2×Dic15—22no—
119D60—22no—
120D60—22no—
121D60—22no—
122D60—22no—
123C4×D15—84no—
124C3×C5×C8—41no—
125C3⋊#168—41no—
126C2×C3×#41C2×D511yescharacteristic
127C22×D12—51no—
128C2×C3×M16C2×D511yescharacteristic
129C3×#117C2×D511yescharacteristic
130#947—52no—
131#940—52no—
132#937—102no—
133#930—102no—
134#926—51no—
135#926—51no—
136C2×#208—51no—
137#893—102no—
138D3×C22⋊C4—102no—
139C4×D12—102no—
140C3×#104—22no—
141#837—102no—
142#823—102no—
143C23×D5—32no—
144C5×#41—21no—
145C5×#41—21no—
146C5×#41—21no—
147C5×#41—21no—
148C2×C5×Q8C4×D311yescharacteristic, complemented
149C2×C5×D4—21no—
150C2×C5×D4C4×D311yescharacteristic, complemented
151C22×C4×C5—21no—
152C22×C4×C5C22×D311yescharacteristic
153C2×C22⋊D5—64no—
154C2×D20—32no—
155C2×D20—32no—
156C2×D20—61no—
157C2×D20—61no—
158C2×D20—61no—
159C2×D20—61no—
160C2×C4×D5—64no—
161C5×M16—21no—
162C5×M16—21no—
163C2×C5×C8—21no—
164C5×C4⋊C4—21no—
165C5×C22⋊C4—21no—
166C42×C5#6712yescomplemented
167C22⋊Dic5—61no—
168C22⋊Dic5—61no—
169#685—64no—
170#685—64no—
171C4⋊Dic5—61no—
172C4⋊Dic5—61no—
173C4×Dic5—32no—
174C4×Dic5—32no—
175#681—61no—
176#681—61no—
177C2×#168—61no—
178#535—151no—
179#518—151no—
180#421—151no—
181#421D1511yescharacteristic, complemented
182C2×#100—151no—
183H(3,ℤ/4)—151no—
184H(3,ℤ/4)—151no—
185C22×C3×C5—41no—
186C22×C3×C5—42no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5#12011yescharacteristic
190C22×C3×C5#12311yescharacteristic
191C2×D15—24no—
192C2×D15—44no—
193C2×D15—44no—
194C2×D15—82no—
195C3×C4×C5—42no—
196C3×C4×C5—41no—
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5C4×D411yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12111yescharacteristic
201Dic15—42no—
202Dic15—42no—
203C23×D3—52no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C3×#41—21no—
208C2×C3×Q8C4×D511yescharacteristic, complemented
209C2×C3×D4—21no—
210C2×C3×D4C4×D511yescharacteristic, complemented
211C22×C3×C4—21no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—104no—
214C2×D12—52no—
215C2×D12—52no—
216C2×D12—101no—
217C2×D12—101no—
218C2×D12—101no—
219C2×D12—101no—
220C2×C4×D3—104no—
221C3×M16—21no—
222C3×M16—21no—
223C2×C3×C8—21no—
224C3×C4⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C42C22⋊D512yescomplemented
227#217—101no—
228#217—101no—
229(C2×D3)⋊C4—104no—
230(C2×D3)⋊C4—104no—
231C4⋊Dic3—101no—
232C4⋊Dic3—101no—
233C4×Dic3—52no—
234C4×Dic3—52no—
235#208—101no—
236#208—101no—
237C2×C3⋊C8—101no—
238C23×C5—21no—
239C23×C5D3×D411yescharacteristic
240C22×D5—34no—
241C22×D5—62no—
242C22×D5—62no—
243C22×D5—242no—
244C5×Q8—21no—
245C5×Q8—21no—
246C5×D4—21no—
247C5×D4—21no—
248C5×D4—41no—
249C5×D4—41no—
250C2×C4×C5—21no—
251C2×C4×C5—22no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5C2×C4×D311yescharacteristic
255C2×C4×C5#23511yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5D3×D411yescharacteristic
258C2×C4×C5#23711yescharacteristic
259C2×C4×C5C2×#6711yescharacteristic
260C22⋊D5—244no—
261C2×Dic5—62no—
262C2×Dic5—62no—
263D20—62no—
264D20—62no—
265D20—62no—
266D20—62no—
267C4×D5—244no—
268C5×C8—41no—
269#168—121no—
270C2×#41C2×D1511yescharacteristic
271C22×D4—151no—
272C2×M16—151no—
273C2×M16C2×D1511yescharacteristic
274#127—152no—
275#124—152no—
276#121—302no—
277#120—302no—
278C4×D4—302no—
279C4×D4—302no—
280#117—151no—
281#117—151no—
282#117C2×D1511yescharacteristic
283C2×C22⋊C4—302no—
284#104—22no—
285#104—302no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5—81no—
291C2×C3×C5#38611yescharacteristic
292D15—44no—
293C23×C3—21no—
294C23×C3D4×D511yescharacteristic
295C22×D3—54no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—402no—
299C3×Q8—21no—
300C3×Q8—21no—
301C3×D4—21no—
302C3×D4—21no—
303C3×D4—41no—
304C3×D4—41no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4C2×C4×D511yescharacteristic
310C2×C3×C4#70911yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4#71111yescharacteristic
314C2×C3×C4C2×C22⋊D511yescharacteristic
315#67—404no—
316C2×Dic3—102no—
317C2×Dic3—102no—
318D12—102no—
319D12—102no—
320D12—102no—
321D12—102no—
322C4×D3—404no—
323C3×C8—41no—
324C3⋊C8—201no—
325C22×C5—41no—
326C22×C5—42no—
327C22×C5—41no—
328C22×C5D3×C22⋊C411yescharacteristic
329C22×C5#88311yescharacteristic
330C22×C5#93711yescharacteristic
331C2×D5—64no—
332C2×D5—124no—
333C2×D5—124no—
334C2×D5—242no—
335C4×C5—42no—
336C4×C5—41no—
337C4×C5#67⋊C411yescharacteristic
338C4×C5#88411yescharacteristic
339C4×C5C4×#6711yescharacteristic
340C4×C5#93811yescharacteristic
341Dic5—122no—
342Dic5—122no—
343C24—152no—
344#41—21no—
345#41—21no—
346#41—21no—
347#41—21no—
348C2×Q8C4×D1511yescharacteristic, complemented
349C2×D4—21no—
350C2×D4—152no—
351C2×D4—152no—
352C2×D4—304no—
353C2×D4—301no—
354C2×D4—301no—
355C2×D4—301no—
356C2×D4—301no—
357C2×D4C4×D1511yescharacteristic, complemented
358C22×C4—21no—
359C22×C4—304no—
360C22×C4C22×D1511yescharacteristic
361M16—21no—
362M16—21no—
363M16—301no—
364M16—301no—
365C2×C8—21no—
366C2×C8—301no—
367C4⋊C4—21no—
368C4⋊C4—301no—
369C4⋊C4—301no—
370C22⋊C4—21no—
371C22⋊C4—304no—
372C22⋊C4—304no—
373C22⋊C4—301no—
374C22⋊C4—301no—
375C42—152no—
376C42—152no—
377C42#122012yescomplemented
378C3×C5#191111yescharacteristic, complemented, Hall
379C22×C3—41no—
380C22×C3—42no—
381C22×C3—41no—
382C22×C3D5×C22⋊C411yescharacteristic
383C22×C3#402911yescharacteristic
384C22×C3#408311yescharacteristic
385C2×D3—104no—
386C2×D3—204no—
387C2×D3—204no—
388C2×D3—402no—
389C3×C4—42no—
390C3×C4—41no—
391C3×C4#402711yescharacteristic
392C3×C4#403011yescharacteristic
393C3×C4C4×C22⋊D511yescharacteristic
394C3×C4#408411yescharacteristic
395Dic3—202no—
396Dic3—202no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5—81no—
401C2×C5#495611yescharacteristic
402D5—124no—
403C23—21no—
404C23—154no—
405C23—302no—
406C23—302no—
407C23—1202no—
408C23D4×D1511yescharacteristic
409Q8—21no—
410Q8—21no—
411D4—21no—
412D4—21no—
413D4—41no—
414D4—41no—
415D4—302no—
416D4—302no—
417D4—302no—
418D4—302no—
419D4—1204no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—302no—
425C2×C4—302no—
426C2×C4—1204no—
427C2×C4C2×C4×D1511yescharacteristic
428C2×C4#681711yescharacteristic
429C2×C4D4×D1511yescharacteristic
430C2×C4D4×D1511yescharacteristic
431C2×C4#681911yescharacteristic
432C2×C4C2×#122011yescharacteristic
433C8—41no—
434C8—601no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—81no—
439C2×C3#6524511yescharacteristic
440D3—204no—
441C5#7040811yescharacteristic, complemented, Sylow
442C22—41no—
443C22—42no—
444C22—41no—
445C22—304no—
446C22—604no—
447C22—604no—
448C22—1202no—
449C22C22⋊C4×D1511yescharacteristic
450C22#9177211yescharacteristic
451C22#9182611yescharacteristic
452C4—42no—
453C4—41no—
454C4—602no—
455C4—602no—
456C4#9177011yescharacteristic
457C4#9177311yescharacteristic
458C4C4×#122011yescharacteristic
459C4#9182711yescharacteristic
460C3#1060120111yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—81no—
465C2—604no—
466C2#1175105711yescharacteristic
subgroupG/H
centerC2#11751057
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radical#11756589C2
cosocleC22×C3×C4×C5C23
hypercenter#421D15
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #11756280C2semidirect
3. C3×C5×#421C2semidirect
4. #11751337C2semidirect
5. C2×#91107C2semidirect
6. #11746378C2semidirect
7. #11746352C2semidirect
13. #91836C4semidirect
14. #91829C4semidirect
29. C5×#421D3semidirect
39. C2×C3×C5×Q8C2×C4semidirect
41. C2×C3×C5×D4C2×C4semidirect
57. C3×C42×C5D4semidirect
64. C4×Dic15C2×C4semidirect
65. C4×Dic15D4semidirect
71. C3×#421D5semidirect
148. C2×C5×Q8C4×D3semidirect
150. C2×C5×D4C4×D3semidirect
166. C42×C5#67semidirect
181. #421D15semidirect
208. C2×C3×Q8C4×D5semidirect
210. C2×C3×D4C4×D5semidirect
226. C3×C42C22⋊D5semidirect
348. C2×Q8C4×D15semidirect
357. C2×D4C4×D15semidirect
377. C42#1220semidirect
378. C3×C5#1911semidirect
441. C5#70408semidirect
460. C3#10601201semidirect

Maximal subgroups

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

subgroupindex
#117565892
#117562802
C3×C5×#4212
#117513372
C2×#911072
#117463782
#117463522
#106012013
#704085