Finite Group Databasebeta

← #14302914

Subgroups — #14302914

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
1C5×#5830C211yesmaximal, characteristic
2#11754503C211yesmaximal, characteristic, complemented
3#11751337C211yesmaximal, characteristic, complemented
4C3×#65525C211yesmaximal, characteristic, complemented
5C2×#90959C211yesmaximal, characteristic, complemented
6#11745971C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10602646—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#947C412yescomplemented
14C5×#940C412yescomplemented
15C5×#937—22no—
16C5×#930—22no—
17C5×#926C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20D3×C22⋊Dic5—22no—
21#91435—22no—
22Dic5×D12—22no—
23#91121—22no—
24C3×#3969—22no—
25#90959—22no—
26#70408—51nomaximal, Hall
27C5×#535—31no—
28#66132—31no—
29#65525—31no—
30#65525D311yescharacteristic, complemented
31C2×#3965—31no—
32#64751—31no—
33#64751—31no—
34C23×C5×D3D412yes—
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×C5×#67—24no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12C2×C412yes—
50C2×C5×D12D412yes—
51C2×D3×Dic5—24no—
52#6719—21no—
53C4⋊Dic15—21no—
54C4×Dic15D412yescomplemented
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×#217—21no—
59C5×(C2×D3)⋊C4—24no—
60C5×C4⋊Dic3—21no—
61C4×C5×Dic3C2×C412yescomplemented
62C3×C22⋊Dic5—21no—
63C3×C4⋊Dic5—21no—
64C3×C4×Dic5D412yescomplemented
65C3×#681—21no—
66C3×#681—21no—
67C2×C3×#168—21no—
68(C2×D3)⋊Dic5—24no—
69#5830D511yescharacteristic
70#5521—51no—
71C3×#421—51no—
72#5236—51no—
73C2×#823—51no—
74#4557—51no—
75#4531—51no—
76C2×C5×#41C2×D311yescharacteristic
77C22×C5×D4—31no—
78C5×#127—32no—
79C5×#124—32no—
80C5×#121—62no—
81C5×#120—62no—
82C5×#117—31no—
83C2×C22⋊Dic5—62no—
84D4×Dic5—62no—
85D4×Dic5—62no—
86#4072—31no—
87#4072C2×D311yescharacteristic
88C2×#681—31no—
89C2×#681C2×D311yescharacteristic
90#3969—22no—
91#3969—62no—
92#3965—62no—
93#1911—151noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—22no—
97C22×C5×D3—22no—
98C22×C5×D3—82no—
99C22×C5×D3C22⋊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—41no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×Dic15—22no—
116C5×#67—84no—
117C2×C5×Dic3—22no—
118C5×D12—22no—
119C5×D12—22no—
120C5×D12—22no—
121C5×D12—22no—
122C2×C3×Dic5—22no—
123D3×Dic5—84no—
124C3⋊#168—41no—
125C3×#168—41no—
126C2×C3×#41C2×D511yescharacteristic
127C22×D12C2×D511yescharacteristic
128C2×C3×M16—51no—
129C3×#117—51no—
130#947Dic512yescomplemented
131#940Dic512yescomplemented
132#937—22no—
133#930—22no—
134#926—51no—
135#926C2×D511yescharacteristic
136C2×#208—51no—
137#893—102no—
138D3×C22⋊C4—102no—
139C4×D12—102no—
140C3×#104—102no—
141#837—102no—
142#823—102no—
143C24×C5—32no—
144C5×#41—21no—
145C5×#41—21no—
146C5×#41—21no—
147C5×#41—21no—
148C2×C5×Q8C4×D311yescharacteristic, complemented
149C2×C5×D4—21no—
150C2×C5×D4—32no—
151C2×C5×D4—32no—
152C2×C5×D4—64no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C2×C5×D4—61no—
157C2×C5×D4C4×D311yescharacteristic, complemented
158C22×C4×C5—21no—
159C22×C4×C5C22×D311yescharacteristic
160C22×Dic5—64no—
161C5×C4⋊C4—61no—
162C5×C22⋊C4—64no—
163C5×C22⋊C4—61no—
164C42×C5—32no—
165C22⋊Dic5—21no—
166C22⋊Dic5—64no—
167C22⋊Dic5—61no—
168C4⋊Dic5—21no—
169C4⋊Dic5—61no—
170C4×Dic5—32no—
171C4×Dic5#6712yescomplemented
172#681—21no—
173#681—21no—
174#681—61no—
175#681—61no—
176C2×#168—21no—
177C2×#168—61no—
178#535—31no—
179#518—151no—
180#421—51no—
181#421—151no—
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×C5×D3—24no—
192C2×C5×D3—44no—
193C2×C5×D3—44no—
194C2×C5×D3—82no—
195C3×C4×C5—41no—
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200Dic15—42no—
201C3×Dic5—42no—
202C5×Dic3—42no—
203C23×D3C22⋊D512yes—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C3×#41—21no—
208C2×C3×Q8C2×Dic511yescharacteristic, complemented
209C2×C3×D4—21no—
210C2×C3×D4C2×Dic511yescharacteristic, complemented
211C22×C3×C4—21no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—24no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12C2×Dic512yes—
219C2×D12C22⋊D512yes—
220C2×C4×D3—104no—
221C3×M16—101no—
222C3×M16—101no—
223C2×C3×C8—101no—
224C3×C4⋊C4—101no—
225C3×C22⋊C4—101no—
226C3×C42—52no—
227#217—21no—
228#217—101no—
229(C2×D3)⋊C4—24no—
230(C2×D3)⋊C4—104no—
231C4⋊Dic3—21no—
232C4⋊Dic3—101no—
233C4×Dic3—52no—
234C4×Dic3C2×Dic512yescomplemented
235#208—101no—
236#208—101no—
237C2×C3⋊C8—101no—
238C23×C5—21no—
239C23×C5—34no—
240C23×C5—62no—
241C23×C5—62no—
242C23×C5—242no—
243C23×C5D3×D411yescharacteristic
244C5×Q8—21no—
245C5×Q8—21no—
246C5×D4—21no—
247C5×D4—21no—
248C5×D4—41no—
249C5×D4—41no—
250C5×D4—62no—
251C5×D4—62no—
252C5×D4—62no—
253C5×D4—62no—
254C5×D4—244no—
255C2×C4×C5—21no—
256C2×C4×C5—41no—
257C2×C4×C5—41no—
258C2×C4×C5—62no—
259C2×C4×C5C2×C4×D311yescharacteristic
260C2×C4×C5#23511yescharacteristic
261C2×C4×C5D3×D411yescharacteristic
262C2×C4×C5D3×D411yescharacteristic
263C2×C4×C5#23711yescharacteristic
264C2×C4×C5C2×#6711yescharacteristic
265C2×Dic5—22no—
266C2×Dic5—62no—
267C2×Dic5—244no—
268#168—41no—
269#168—121no—
270C2×#41D3×D511yescharacteristic
271C22×D4—31no—
272C2×M16—51no—
273C2×M16—151no—
274#127—32no—
275#124—32no—
276#121—62no—
277#120—62no—
278C4×D4—302no—
279C4×D4—302no—
280#117—31no—
281#117—51no—
282#117—151no—
283C2×C22⋊C4—302no—
284#104—102no—
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
292C5×D3—44no—
293C23×C3—21no—
294C23×C3C2×C22⋊D511yescharacteristic
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—82no—
298C22×D3C22⋊Dic514yes—
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—41no—
307C2×C3×C4—41no—
308C2×C3×C4—102no—
309C2×C3×C4D4×D511yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4#71111yescharacteristic
312C2×C3×C4#71111yescharacteristic
313C2×C3×C4C22×Dic511yescharacteristic
314C2×C3×C4C2×C22⋊D511yescharacteristic
315#67—84no—
316C2×Dic3—22no—
317C2×Dic3—102no—
318D12—22no—
319D12—22no—
320D12—22no—
321D12—22no—
322C4×D3—404no—
323C3×C8—201no—
324C3⋊C8—201no—
325C22×C5—41no—
326C22×C5—42no—
327C22×C5—41no—
328C22×C5—64no—
329C22×C5—124no—
330C22×C5—124no—
331C22×C5—242no—
332C22×C5D3×C22⋊C411yescharacteristic
333C22×C5#88311yescharacteristic
334C22×C5#93711yescharacteristic
335C4×C5—41no—
336C4×C5—122no—
337C4×C5#67⋊C411yescharacteristic
338C4×C5#88411yescharacteristic
339C4×C5C4×#6711yescharacteristic
340C4×C5#93811yescharacteristic
341Dic5—42no—
342Dic5—122no—
343C24—32no—
344#41—21no—
345#41—21no—
346#41—21no—
347#41—21no—
348C2×Q8D3×Dic511yescharacteristic, complemented
349C2×D4—21no—
350C2×D4—32no—
351C2×D4—32no—
352C2×D4—64no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4D3×Dic511yescharacteristic, complemented
358C22×C4—21no—
359C22×C4—304no—
360C22×C4C2×D3×D511yescharacteristic
361M16—101no—
362M16—101no—
363M16—301no—
364M16—301no—
365C2×C8—101no—
366C2×C8—301no—
367C4⋊C4—61no—
368C4⋊C4—101no—
369C4⋊C4—301no—
370C22⋊C4—64no—
371C22⋊C4—61no—
372C22⋊C4—101no—
373C22⋊C4—304no—
374C22⋊C4—301no—
375C42—32no—
376C42—52no—
377C42—152no—
378C3×C5#191111yescharacteristic, complemented, Hall
379C22×C3—41no—
380C22×C3—42no—
381C22×C3—41no—
382C22×C3#408111yescharacteristic
383C22×C3#408311yescharacteristic
384C22×C3C2×C22⋊Dic511yescharacteristic
385C2×D3—24no—
386C2×D3—44no—
387C2×D3—44no—
388C2×D3—82no—
389C3×C4—41no—
390C3×C4—202no—
391C3×C4D4×Dic511yescharacteristic
392C3×C4D4×Dic511yescharacteristic
393C3×C4#408511yescharacteristic
394C3×C4#408511yescharacteristic
395Dic3—42no—
396Dic3—202no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5—81no—
401C2×C5—124no—
402C2×C5#495611yescharacteristic
403C23—21no—
404C23—34no—
405C23—62no—
406C23—62no—
407C23—242no—
408C23D3×C22⋊D511yescharacteristic
409Q8—21no—
410Q8—21no—
411D4—21no—
412D4—21no—
413D4—41no—
414D4—41no—
415D4—62no—
416D4—62no—
417D4—62no—
418D4—62no—
419D4—244no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—62no—
424C2×C4—102no—
425C2×C4—302no—
426C2×C4—1204no—
427C2×C4#678011yescharacteristic
428C2×C4C2×D3×Dic511yescharacteristic
429C2×C4#678211yescharacteristic
430C2×C4D5×#6711yescharacteristic
431C2×C4D3×C22⋊D511yescharacteristic
432C2×C4#679011yescharacteristic
433C8—201no—
434C8—601no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—81no—
439C2×C3#6550911yescharacteristic
440D3—44no—
441C5#7040811yescharacteristic, complemented, Sylow
442C22—41no—
443C22—42no—
444C22—41no—
445C22—64no—
446C22—124no—
447C22—124no—
448C22—242no—
449C22D3×C22⋊Dic511yescharacteristic
450C22#9155511yescharacteristic
451C22#9157711yescharacteristic
452C4—41no—
453C4—122no—
454C4—202no—
455C4—602no—
456C4Dic5×#6711yescharacteristic
457C4#9155811yescharacteristic
458C4#67⋊Dic511yescharacteristic
459C4#9156511yescharacteristic
460C3#1060264611yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—81no—
465C2—124no—
466C2#1174951911yescharacteristic
subgroupG/H
centerC2#11749519
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radicalC5×#5830C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754503C2semidirect
3. #11751337C2semidirect
4. C3×#65525C2semidirect
5. C2×#90959C2semidirect
6. #11745971C2semidirect
7. #11745969C2semidirect
13. C5×#947C4semidirect
14. C5×#940C4semidirect
30. #65525D3semidirect
39. C2×C3×C5×Q8C2×C4semidirect
41. C2×C3×C5×D4C2×C4semidirect
54. C4×Dic15D4semidirect
61. C4×C5×Dic3C2×C4semidirect
64. C3×C4×Dic5D4semidirect
130. #947Dic5semidirect
131. #940Dic5semidirect
148. C2×C5×Q8C4×D3semidirect
157. C2×C5×D4C4×D3semidirect
171. C4×Dic5#67semidirect
208. C2×C3×Q8C2×Dic5semidirect
210. C2×C3×D4C2×Dic5semidirect
234. C4×Dic3C2×Dic5semidirect
348. C2×Q8D3×Dic5semidirect
357. C2×D4D3×Dic5semidirect
378. C3×C5#1911semidirect
441. C5#70408semidirect
460. C3#10602646semidirect

Maximal subgroups

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

subgroupindex
C5×#58302
#117545032
#117513372
C3×#655252
C2×#909592
#117459712
#117459692
#106026463
#704085